materials science research: volume 16 sintering and heterogeneous catalysis

MATERIALS SCIENCE RESEARCH Volume 16

SINTERING AND HETEROGENEOUS

CATALYSIS

MATERIALS SCIENCE RESEARCH

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CERAMIC ENGINEERING AND SCIENCE: Emerging Priorities Edited by V. D. Frechette, L. D. Pye, and J. S. Reed

MASS TRANSPORT PHENOMENA IN CERAMICS Edited by A. R. Cooper and A. H. Heuer

SINTERING AND CATALYSIS Edited by G. C. Kuczynski

PROCESSING OF CRYSTALLINE CERAMICS Edited by Hayne Palmour III, R. F. Davis, T. M. Hare

BORATE GLASSES: Structure, Properties, Applications Edited by L. D. Pye, V. D. Frechette and N. J. Kreidl

SINTERING PROCESSES Edited by G. C. Kuczynski

SURFACES AND INTERFACES IN CERAMIC AND CERAMIC-METAL SYSTEMS Edited by Joseph Pask and Anthony Evans

ADVANCES IN MATERIALS CHARACTERIZATION Edited by David R. Rossington, Robert A. Condrate, and Robert L. Snyder

SINTERING AND HETEROGENEOUS CATALYSIS Edited by G. C. Kuczynski, Albert E. Miller, and Gordon A. Sargent

EMERGENT PROCESS METHODS FOR HIGH-TECHNOLOGY CERAMICS Edited by Robert F. Davis, Hayne Palmour III, and Richard L. Porter

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MATERIALS SCIENCE RESEARCH • Volume 16

SINTERING AND HETEROGENEOUS

CATALYSIS

Edited by

G. C. Kuczynski Albert E. Miller

and

Gordon A. Sargent University of Notre Dame

Notre Dame, Indiana

PLENUM PRESS • NEW YORK AND LONDON

Library of Congress Cataloging in Publication Data

International Conference on Sintering and Related Phenomena (6th: 1983: University of Notre Dame) Sintering and heterogeneous catalysis.

(Materials science research; v. 16) Includes bibliographical references and index. 1. Sintering-Congresses. 2. Catalysis-Congresses. I. Kuczynski, G. C. (George

Czeslaw), 1914- II. Miller, Albert E. III. Sargent, Gordon A. IV. Title. V. Series. TN695.156 1983

ISBN-I3: 978-1-4612-9707-9 DOl: 10.1007/978-1-4613-2761-5

671.3'7 84-3278

e-ISBN-13: 978-1-4613-2761-5

Proceedings of the Sixth International Conference on Sintering and Related Phenomena, held June 6-8, 1983, at the University of Notre Dame,

Notre Dame, Indiana

© 1984 Plenum Press, New York

Softcover reprint of the hardcover I st edition 1984

A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013

All rights reserved

No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,

recording, or otherwise, without written permission from the Publisher

This volume is dedicated to the memory of Dr. Andreus Leopoldus Stuijts,

friend, scientist and engineer

PREFACE

The Sixth International Conference on Sintering and Related Phenomena took place at the University of Notre Dame, Notre Dame, Indiana June 6-8, 1983. This conference was also the twentieth Conference on Ceramic Sciences organized yearly by a "confederation" of four institutions: North Carolina University at Raleigh, N.C., the University of California at Berkeley, CA, Alfred University at Alfred, NY and the University of Notre Dame, Notre Dame, IN.

The papers presented at the last Notre Dame conference collected in this volume, reflect the progress in our understanding of the process of sintering achieved in the past four years.

It seems that the analysis of the two particle models is finally extended to the analysis of the models of compacts. In these investigations strong emphasis is put on pore-grain boundaries interaction which appear to be central to this problem. It is to be hoped that in the near future an adequate model of the compact will be developed which may serve as a useful basis of powder technology. Also, the effects of atmosphere on the sintering of ceramics after a long period of neglect, seem to attract the attention of more workers in the field.

During the 1975 Conference at Notre Dame, chemical engineers and chemists working in the field of catalysis, joined our discussions for the first time. The volume of proceedings of that particular conference was aptly entitled "Sintering of Catalysis." This collaboration persists and in the recent converence we had a special session on Sintering of Catalysts, attended by the best scientists working in the field.

We wish at this point to express our gratitude to the National Science Foundation, Division of Materials Research for their support under grant DMR-83099l6 and to the Department of the Army, U. S. Army Research Office, Metallurgy and Materials Science Division for their support under grant DAAGZ9-83-M-OZ6Z.

vii

viii PREFACE

It should be noted that the views, op~n~ons, and/or findings contained in these conference proceedings are those of the authors and should not be construed as an official Department of the Army position, policy, or decision unless so designated by other documentation.

Due to the grants of these agencies, more students could take part in this conference than at any previous conferences.

Our gratitude is due to all participants and especially to those authors who have sent their manuscripts early enough so that they could be included in this volume.

It is our pleasant duty to thank all our students who helped in performing various tasks during the conference. Special thanks are due to Mrs. J. Peiffer and Miss Tina Widerquist for their help in editing the conference papers.

Notre Dame, Indiana October, 1983

G. G. A. D. J.

C. Kuczynski A. Sargent E. Miller Kolar J. Carberry

CONTENTS

MODELS AND MECHANISMS

1. The Sintering of Monodisperse Ti02 by E. A. Barringer, R. Brook, and H. K. Bowen

2. A Cell Model for Microstructural Evolution During Sintering

by R. T. DeHoff

3. Analysis of Initial Stage Sintering by Computer

1

23

Simulation 35 by K-S. Hwang and R. M. German

4. Channel Network Decay in Sintering 49 by F. N. Rhines and R. T. DeHoff

5. The Applicability of Herring's Scaling Law to the Sintering of Powders 63

by H. Song and R. L. Coble

6. On the Mechanism of Pore Coarsening 81 by D. Kolar, G. C. Kuczynski and S. K. Chiang

7. The Influence of Green Density Upon Sintering 89 by M. A. Occhionero and J. W. Halloran

8. An Overview of Enhanced Sintering Treatments for Iron 103 by R. M. German

EFFECT OF ATMOSPHERE AND PRESSURE

9. Vapor Transport and Sintering of Ceramics by D. W. Readey, J. Lee and T. Quadir

ix

115

x

10. Effects of Oxygen Pressure and Water Vapor on Sintering of ZnO

by o. J. Whittemore and S. L. Powell

11. Microstructure Development of Fe203 in HCL Vapor by J. Lee and D. W. Readey

12. Microstructure Evolution in Sn02 and CdO in Reducing Atmospheres

by T. Quadir and D. W. Readey

13. Reactive Sintering of Diamond-Titanium System Under High Pressure

by I. Kushtalova, I. Krstanovic, I. Stasyuk, S. M. Radic and M. M. Ristic

SINTERING OF CATALYSTS

14. Application of X-Ray Diffraction Techniques to Study

CONTENTS

137

145

159

171

the Sintering of Catalysts 181 by R. J. DeAngelis, A. G. Dhere, J. D. Lewis and Hai-Ku Kuo

15. The Effect of Interactions Among Metal, Support and Atmosphere on the Behaviour of Supported Metal Catalysts 199

by E. Ruckenstein

16. Sintering and Redispersion of Conventional Supported Metal Catalysts in Hydrogen and Oxygen Atmospheres 223

by Siehard E. Wanke

NON-ISOTHERMAL SINTERING AND CHEMICAL REACTIONS

17. Ultra-Rapid Sintering 243 by D. Lynn Johnson

18. Characterization and Initial Sintering of a Fine Alumina Powder 253

by S. V. Raman, R. H. Doremus and R. M. German

19. Sintering Behavior of Overcompacted Shock-Conditioned Alumina Powder 265

by T. H. Hare, K. L. More, A. D. Batchelor, and Hayne Palmour, III

CONTENTS

20. Sintering of LiF Fluxed SrTi03 by Harlan U. Anderson and Marie C. Proudian

21. Influence of Bismuth Oxide Additions on Cadmium Oxide Sintering

by B. V. Mikijelj and V. D. Mikijelj

xi

281

293

22. Sintering of Combustion-Synthesized Titanium Carbide 303 by B. Manley, J. B. Holt, and Z. A. Munir

23. Activated Sintering of Chromium and Manganese Powders with Nickel and Palladium Additions 317

by R. Watanabe, K. Taguchi and Y. Masuda

24. Reactive Phase Calsintering of Dolomite 329 by G. L. Messing, A. R. Selcuker and R. C. Bradt

25. A Contribution to the Study of Consolidation of Precipitation Strengthened Materials 341

by D. C. Stefanovic, I. P. Arsentjeva and M. M. Ristic

INDEX 347

THE SINTERING OF MONODISPERSE Ti0 2

ABSTRACT

E. A. Barringer, R. Brook, and H. K. Bowen

Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, Massachusetts

The emergence of new techniques to produce uniform-size, spherical particles offers opportunities to quantitatively study sintering kinetics. The ability to control the average particle size and to form uniformly packed green microstructures enhances the applicability of many conventional experimental studies, such as isothermal and constant heating rate dilatometry and surface area behavior.

Monodisperse, spherical Ti0 2 powders, synthesized by controlled hydrolysis of titanium alkoxides, were employed as a model experimental system. Densification kinetics were determined by isothermal and constant heating rate dilatometry using heat treated (crystallized) and amorphous powders. Microstructural evolution was followed by SEM observations for isothermal conditions of 1060, 1100 and l160°C and was correlated to the sintering process.

INTRODUCTION

In recent years, many attempts have been made to understand the sintering mechanisms through transformation of the fundamental atomic flux equations into sintering models. Models exist for the different stages of sintering, yet most sintering data cannot be adequately described by anyone model. As an example, Pejovnik, et al. 1 attempted to fit carefully selected U0 2 shrinkage data to the various models; no discrimination between the models was

2 E. A. BARRINGER ET AL.

observed (i.e., several gave equivalent fits to the data). This inability of the models to quantitatively describe sintering kinetics is due to the simple assumptions on which the models are based. 2

Most existing models are derived for regular arrays of particles (and/or pores) haying a uniform size and shape and assume that a single mechanism is rate controlling. However, in experimental systems multiple (coupled) mechanisms may control the dens ification kinetics; this alone invalidates most simple models. 3,4 In addition, particles having appreciable distributions of size and shape are usually nonuniformly packed; this leads to nonuniform local densification and porosity rearrangement during sintering which are not in the models. Therfore, mechanistic interpretations for densification based on a simple data set (e.g., shrinkage data only) must be treated with caution. 3

Investigations of sintering kinetics and microstructural development which utilize compacts having a uniform, dense packing of monodisperse, spherical particles avoid many of the limitations discussed previously. Thus, quantitative sintering studies which employ conventional measuring techniques and the existing models may be possible. Three aspects of monodisperse powders are important when considering the benefits for sintering research, namely the spherical particle shape, the narrow size distribution, and the uniform particle packing in the green microstructures.

In this paper, the potential for improvements in experimental sintering studies allowed. by the three factors is briefly reviewed. As an example, this potential is demonstrated in the sintering of monodisperse Ti0 2 and the application of an intermediate stage sintering model. S

MONODISPERSE POWDERS: BENEFITS FOR SINTERING RESEARCH

Spherical powders have been a feature of sintering studies for many years, notably in metallic and glass systems. Many early contributions to the sintering literature involved solutions for geometrical changes (neck growth, shrinkage) for spherical particles in contact, with the observed kinetics then being an indicator of the specific transport mechanism controlling the process. 6 Thus, a basic requirement of materials employed to test such models is a spherical (or at least equiaxed) particle shape.

The narrow particle size distribution of the monodi.sperse powders is a relatively new feature (and concept) for ceramic powders. When coupled with the ability to choose the actual mean size of a particular powder through controlled chemical synthesis techniques, the monodisperse powders represent unique experimental

SINTERING OF MONODISPERSE TiO, 3

systems. (Alum-derived a-Al 20 3 powders, one of the best commercially available powders, has received much attention because it offers a narrow size distribution centered at 0.3.~; however, these ~articles are neither spherical nor easy to obtain in other sizes. ) The benefit of the monodisperse powders is the excellent opportunity provided for mechanism studies based on the variation of mean particle size and using the scaling law approach 8 and the relatively strong suppression of the tendency for particle coarsening (e.g., by grain growth 20 ).

The scaling law approach considers the relative times for a given degree of microstructural change (e.g., density) in powder compacts that differ only in particle size, r. Then

A ~ = (~) t2 r2

(1)

where the index, A, takes on set integer values for different rate controlling mechanisms. The law only gives simple integer values when the same transport mechanism dominates in both powders throughout the span of the observed microstructural change. This condition is favored by a small difference in rl and r2 for the two powders. Accordingly, the very narrow size distributions available offer the possibility for careful and precise scaling law studies using a wide range of r values, but for each experiment using a value of rl close to that of r2' In this way the controlling mechanism may be estimated across a field of T and r with a degree of precision that has been difficult to obtain using conventional powders.

The coarsening processes arise from the tendency of a powder to reduce its surface free energy by growth of particles (a parallel process to sintering). The driving force for coarsening is related to

(2 )

where y is the interfacial energy and ra < r b; the flow of matter is from the smaller particles to the larger particles. Thus, the coarsening tendency is proportional to the size differences (i.e., distribution width) present in the powder. For the monodisperse powders the distribution width is small (width + 0) and hence the coarsening process and the associated interference in the sintering kinetics should be suppressed. A similar argument holds for grain growth, where the driving force is proportional to the grain boundary curvature. 20 Not only do these factors enhance the use of the powders in scalin~ law studies, it also allows wider use of those model equations , in which coarsening (or grain growth) cannot be readily included.


The most novel feature of monodisperse powders is the ease in forming dense, uniformly packed green compacts; in some cases well ordered particle arrays are formed. S Uniform packing, which is allowed by the equiaxed shape and uniform size, immediately removes one of the severe problems in the study of sintering kinetics in the treatment of particle rearrangement, thereby enhancing the ability to yield meaningful conclusions. A further advantage of uniform packing (no agglomerates present) is that the coordination number of each particle in terms of its neighbors is high (CN ~ 11) and constant throughout the volume of the compact. Thus, densification is uniform throughout the compact; kinetic data can then be analyzed using the sintering models which were derived for set packing geometries.

THE SINTERING OF MONODISPERSE Ti0 2

Experimental

The monodisperse, spherical Ti0 2 powder was formed by the hydrolysis of dilute ethanolic solutions of titanium tetraethoxide; the synthesis and washing procedures are described e1sewhere. S,lO The initial reagent concentrations for the reaction, conducted at 25°C in a dry box, were 0.15 M Ti(OC 2HS)4 and 0.5 M H20. The mean diameter of the amorphous particles was 0.34 ~ and the standard deviation was 0.13~. The powder had a high purity; inductively coupled plasma emission spectroscopy showed only 80 ppm Si and 40 ppm Ca.

The powder was dispersed in H20 at a pH = 8 using an ultrasonic probe, so that no agglomerates were present in the suspension. The dispersion was poured into polypropylene vials and the powder was allowed to settle to form concentrated sediments (particles not touching). The sediments were collapsed into rigid disk-shaped compacts by the addition of a 1 M (NH4)2C03 solution to the clear supernatant in the vials. The liquid was extracted and the sediments were slowly air dried for 24 hours, followed by vacuum drying at 100°C for 18 hours. The amorphous particles (p = 3.1 g/cm 3) in the compacts were converted to rutile (p = 4.25 g/cm 3) by prefiring the compacts at 780°C for 3 hours; X-ray diffraction confirmed the rutile structure. During crystallization the average particle size decreased to about 0.30~. Figure 1 shows the green microstructure of the crystallized powder compact.

Sintering kinetics were determined by isothermal and Constant heating rate (CHR) dilatometry using a Netzsch 402E Electronic Dilatometer (Netzsch, Inc., Exton, PA). Isothermal dilatometry was conducted in air in an A1 20 3-tube furnace at temperatures of 1020, 1060, 1100, and l160°C; a heating rate of 55°C/min was used to attain the desired firing temperature. Essentially no shrinkage

SINTERING OF MONODISPERSE Ti02

Fig. 1. Top surface of a crystallized-particle compact (rutile) showing the uniform particle packing: the green density was 55% of theoretical Bar = 1 ~.

5

occurred during heat-up to the lower temperatures; however, some shrinkage (~ 4% of the total) occurred prior to reaching 11000e and about 30% of the total occurred prior to l160 o e. The eRR experiments were conducted using heating rates of 5, 10, 21, and 55°e/min.

Microstructural development was investigated using scanning electron microscopy for the isothermal conditions of 1060, 1100, and l160 0 e and firing times ranging from 3 minutes to 8.4 hours. The samples, wrapped in platinum foil, were rapidly heated to the sintering temperature and then air-quenched after the prescribed time. Polished and fracture surfaces were viewed, and the approximate grain size for a specific time and temperature was obtained from micrographs of the fracture surface (30 to 50 grains were measured for each condition).

Results and Discussion

Isothermal Sintering. The isothermal shrinkage data are presented in Fig. 2 as a plot of relative shrinkage, ~~/~o, as a function of time, where ~o is the initial thickness and ~~ the shrinkage. The data show that as temperature is increased from 1020° to l160 0e the densification kinetics increase significantly. Although quantitative curve fitting procedures were not employed,


three linear regions are present in Fig. 2, which correspond to the initial, intermediate, and final stages of the sintering process. The parallel behavior of the four curves for the intermediate stage and the three curves for the final stage suggests that a single mechanism dominates the densification process, hence further analysis of the data in these regions is warranted. However, the uncertainty in the initial time for isothermal sintering, especially for the data obtained at 1100° and l160°C, causes quantitative analysis of the data in this form to be questionable.

An alternate, and more useful form of representation is the plot of relative density as a function of time, as shown in Fig. 3. The relative densities, P/Pth' were calculated from the shrinkage data in Fig. 2 using the relation

(3 )

where Po/Pth was the initial (green) density. The measured value for green density of 0.55 was also the value calculated, using

I I

o 1020° C

'" 1060° C

o 1100· C c 1160° C

-

-

- 5.0~----,-1_...J1L--_.L..-1--11 __ L--1 ----,-1_...J1_--,

o 234567 8 .In t (min)

Fig. 2. The relative linear shrinkage (bl/lo) as a function of time for the isothermal sintering temperatures of 1020, 1060, 1100, and l160°C.


Eq. 3, from the total relative shrinkage, ~~/~o = 0.18 (average value for 1060, 1100, and 1160°C experiments), assuming that the dilatometry curves flattened out as P/Pth approached 1.0. This assumption was valid based on the observed final microstructures. The densification rates observed in Fig. 3 decrease as temperature is decreased; densification is significantly slower at 1020°C than at 1060°C. Even after 5 hours at 1020°C the relative density is only 0.83. This value is much lower than the density of 0.98 achieved for the same sintering time at a 40°C higher temperature. However, this is consistent with the sintering model, due to the exponential temperature dependence of mass transport. This will be shown later.

Figure 4 shows the polished and fracture surfaces for samples sintered at 1060°C for 3, 25, and 50 minutes; the relative densities reported on the micrographs were extracted from Fig. 3. This series of micrographs, which represent the only polished surfaces successfully examined, illustrate the relationship between the polished surfaces and the fracture surfaces. The fracture surfaces for times ranging from 3 minutes to 8.4 hours are presented in Fig. 5. The transitions from the initial stage (3 min.) of sintering through the intermediate stage (25, 50, and 120 min.) and into the final stage (3.5 and 8.4 hours) are clearly illustrated in Figs. 4 and 5.

10[ c .0- .0 0-0 00 _---.-1---. 00 ~o-- ___ 6-l y c __ c

09 001° ./ fo ,,/

~ ,': __ 0

PIp' 08, " ___ 0-0

th ___ 0 TiO, 07 0......-

0

c 1060'C ",.')', 0' o 1020'C

Fig. 3. The relative density, P/Pth' as a function of time for the isothermal sintering conditions.

8

106QOC 3 min P/Plh = 0.61

E. A. BARRINGER ET AL.

Fig. 4. The polished and fracture surfaces for samples sintered at 1060°C for 3, 25, and 50 minutes. Bar = lum.

SINTERING OF MONODISPERSE TiO,

1060°C 50 min p/Pu. = 0.84 .............. -

I060°C 8.4 hours

r.-.1IiiIB!!!I!!IiI~. p. / = O. 99

Fig. 5. Micrographs of the fracture surfaces for firing times ranging from 3 minutes to 8.4 hours showing the microstructural development at l060°C. Bar = lum.

9

10

IlOooe 50 min p/Pu. = 0.91

E. A. BARRINGER ET AL.

_ .... -

11 aooe 3.5 hours P / P u. = o. 99+

Iloooe 25 min p/Pu. = 0.84

IlOaoe 2 hours P/PU. = a .98

Fig. 6. Micrographs of the fracture surfaces for firing times ranging from 3 minutes to 3.5 hours showing the microstructural development at IIOOoe. Bar = lum.

SINTERING OF MONODISPERSE TiO, 1 1

Similar sets of micrographs for the fracture surfaces are given for 1100°C and 1160°C in Figs. 6 and 7, respectively. These micrographs, in accordance with the data in Fig. 6.4, illustrate the more rapid densification process which occurs as temperature is increased. The final micrograph given in each of the three series (Figs. 5, 6 and 7) is for the dilatometer sample; these microstructures agree with the final densities calculated for Fig. 3.

At this point, several important microstructural features should be discussed. First, transgranular fracture was observed in many of these microstructures, especially for the higher relative densities. Although this mode of fracture is unusual for ~ 1 ~

1160°C 50 min p/Pu. = 0.98+

Fig. 7. Micrographs of the fracture surfaces for firing times ranging from 3 minutes to 50 minutes showing the microstructural development at 1160°C. Bar = 1 ~.


grain-size systems, this behavior may be a result of the high purity of the Ti0 2• 11 Second, coarsening, as well as exaggerated grain growth, was suppressed in this system; this is discussed in more detail later. Third, the pores remained at the grain boundaries and the triple-grain junctions; no intragranular porosity was observed! These three features, which are well illustrated in the micrographs, enhance the applicability of sintering models for analysis of the densification data.

3 12 1+ 13 Although Johnson,' and others,' have stressed the

necessity of using general, multiple-mechanism models to analyze sintering kinetics (e.g., simultaneous shrinkage and grain growth l2), the data in Fig. 2 suggested a single dominant mechanism, especially during the intermediate stage. This conclusion is supported by the parallel behavior observed in the plot (Fig. 8) of densification rate at a specific relative density as a function of inverse temperature. These rates were obtained by fitting the densification data for a given temperature in Fig. 3 (actually fitted P/Pth versus log t) with a fifth degree polynomial; slopes were then calculated for relative densities of 0.75, 0.80, 0.85, 0.90 and 0.95. An estimate of the activation energy for the sintering process was obtained from the slope of the five curves in Fig. 8; the average value was 72 kcal/mol. This value agrees well with activation energies reported in the literature. I 4-16

Quantitative analysis of the sintering kinetics requires grain growth data. 3,12 Fig. 9 gives the relative grain size, i.e. grain size divided by the initial particle size (GS/PSo), as a function of relative density, where the grain sizes were obtained from the micrographs. These data indicate that the grain size at a specific relative density is independent of the sintering temperature (for the measured range). This conclusion is in accord with the results reported by Coble and Gupta,17 and COble l8 , where grain size was found to be independent of temperature as long as the initial density was constant. For such c~ses, the boundaries are pinned by the pores and the coarsening rate does not change rapidly with temperature. 17, 19

An important feature observed in the microstructures and in Fig. 9 is that little grain growth occured until the relative density became greater than 0.93 (GS/PSo ~ 2); above this density grain growth was rapid. Yet the onset of rapid grain growth was at a much higher density (and lower GS/PSo) than for the Ti0 2 powder investigated by Yan 20 (P/Pth ~ 0.80, GS/PSo > 5) and the Al 20 3 powder by Wang 21 (P/Pth ~ 0.90, GS/PSo > 4). Since the initial average grain sizes and the initial densities were very similar for these cases, the more rapid grain growth behavior was probably caused by wider particle size distributions and less uniform packing.

SINTERING OF MONODISPERSE Ti02

-3

-4

..---....

'l1_-5 S" " -----~

-6

-7

-8

f-

I-

f-

I-

I I I

~:~, Ti 02

Q = 72 keal/mole

\~~\ 0.75

''\:;\ 0.80

,\6\ PiA 0.85 th

o 6 \\ 0.90

6 0.95 I \ I

7 8

13

-

-

-

-

Fig. 8. The natural logarithm of the densification rate as a function of liT for the relative densities of 0.75, 0.80, 0.85, 0.90 and 0.95. The average slope yields an activation energy, Q, of 72 kcal/mol.

The intermediate stage sintering models applicable to this study were introduced by Coble 9 and extended by Coble and Gupta. 17

The models for various geometries and controlling mechanisms have the general form I7

(4 )

where P is the porosity (= l-p/Pth)' K a constant defined by the geometry, y the solid-vapor surface free energy, Q the molecular volume, ks the Boltzmann constant, and D the diffusivity (actually wDb for boundary diffusion). The exponent, m, has a value of 3 for lattice diffusion controlled kinetics and a value of 4 for boundary diffusion control. 17


5 , Ti02 '" t 4 ",1060 0 e

o Iloooe 0 0 01160° e

L CJ)

a.. 3 "- PSo = 0.30 p'm CJ)

(.!)

/ 2

<!' -"'--'

0.5

Fig. 9. Relative grain size (grain size divided by the initial particle size) as a function of relative density; the grain size at a specific density is independent of firing temperature.

To determine which mechanism controlled intermediate stage sintering for the monodisperse TiO z powder. the grain size exponent was required. This value was obtained by extracting the grain size and densification rate for given values of p/pth and temperature from Figs. 9 and 8. respectively. and plotting the 1n(rate) versus In(GS). as shown in Fig. 10. The average exponent value given by the slopes was 2.96 (standard deviation = 0.18). This grain size dependence indicates that volume diffusion controls intermediate stage sintering.

To obtain the activation energy, Q. for the process represented in Fig. 3. the rate equation (Eq. 4) was written as

(GS)3 kBT d(P~~th) = KyQD; exp(-Q/RT) (5 )

where 0; was assumed to be constant. The activation energy was determined, using the data in Figs. 8 and 9, by plotting the natural logarithm of the LHS of Eq. 5 as a function of liT

SINTERING OF MONODISPERSE TiO,

(Fig 11). Rather than drawing lines through the five sets of points (corresponding to the relative densities, 0.75-0.95), the average of the five points for the three temperatures were fitted using a least squares procedure. The activation energy given by the slope (correlation coefficient = 0.9999) was 74.3 kcal/mol.

The preexponential term was obtained by multiplying Eq. 5 by T, and plotting the average value of the LHS as a function of T. The slope, given as

Slope = ~n(KyQD!) (5 )

15

was equal to -38.02 (corr. coef. = 0.9999). By using a molecular volume ~f 3.13 x 10-23cm 3, a value for the surface free energy22 of 600 erg/cm2 , and a value for K of 335,17 the value of D; was calculated to be 4.9. Therefore, application of the intermediate stage sintering model 17 to the densification and grain size data yielded the rate controlling diffusivity,

D = 4.9 exp(-74300/RT), (cm2/sec) (6)

which is in accord with the measured values for oxygen tracer diffusion in Ti0 223 and those determined from sintering data. 14- 16

Constant Heating Rate Sintering. The use of constant heating rate conditions to investigate densification kinetics has recently been emphasized because of the potential for a rapid review of sintering mechanisms and the avoidance of experimental errors associated with isothermal dilatometry (i.e. transient temperature changes and errors in the initial time).24-26 However, quantitative analysis and interpretation of experimental results is very difficult. This is due to the microstructural features in green compacts which also limit the applicability of isothermal sintering models (e.g., wide distribution widths, rearrangements) and the additional uncertainty of possible overlapping and changing mechanisms. Nevertheless, constant heating rate sintering was performed to examine the effects of heating rates on the densification kinetics and the final microstructures.

The CRR dilatometry data is given in Fig. 12 as a plot of ~n(~~/~o) versus 1fT for the heating rates, C, of 5°, 10°, 21°, and 55°C/min. The shrinkage, and thus density, for a given temperature is higher for the slower heating rates because the transient time for a given temperature range is longer than for the fast heating rates. That is, 20 minutes was required at SO/min to traverse the temperature range of 1100 to l200°C, whereas less than 2 minutes were required at 55°C/min.

-3 I -4~ "~

i>l

\~~~

-3

"0

'"

\

~

\ 0\

_ -6

" \

0, ,,

10

60

°C

"\ \

_ 7 f-

° 11

00

° C

"

<>

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SINTERING OF MONODISPERSE Ti02 17

The approximate activation energy for the CHR processess was obtained by extracting the temperature required to achieve a specific relative shrinkage from Fig. 12, and plotting these data as a function of heating rates, as shown in Fig. 13. The parallel behavior of the three curves for the intermediate stage (~i/io= 0.07, 0.10 and 0.15) suggests that a single mechanism is operative, thus this data may be suitable for application of CHR models (not done in this paper). The average activation energy obtained from the slopes of these curves was 64.9 kcal/mol

- 3.0

0 - 4 .0 .... ~ <l

-5.0

-6.0

° 5· C/min Q 10· C/min

o 21· C/min o 55°C/min

7.0 8.0 9.0 I 4

-:f(0K) x 10

Fig. 12. Relative shrinkage as a function of inverse temperature for the constant heating rates of 5, 10, 21 and 55°C/min.


(0 = 5 kcal/mol); this activation energy is slightly lower than that obtained from the isothermal sintering data, but is still in agreement with the reported values for diffusion processes in Ti02·14-16,23

The microstructures of the CRR dilatometry samples were all similar; as an example, Fig. 14 shows the fracture surface for 5°C/min to l350°C. Although this sample was exposed to higher temperatures than the maximum isothermal condition employed (1160°C) for over 100 min, the approximate average grain size is only 3 ~ (GS/PSo ~ 10) and all pores have remained at the grain boundaries. Hence grain growth, and especially exaggerted grain growth, are suppressed for the monodisperse powders, in agreement with expectations.

5 I I

4 -\ \\ \ 61110 00.02

\\\ \ "'0.07 00.10

00.15

o 0 '" 0

inC

3 r-

\\\ \ 2 r-

1 6

00'"

\ \\ <> 0 '" \ \ \

I

0

\ 0

\ I

-

-

-

9

Fig. 13. Heating rate as a function of the temperature required to achieve a specific relative density. An activation energy of 64.9 kcal/mol was obtained for the intermediate stage (~i/io = 0.07, 0.10 and 0.15) of the CRR process.


Fig. 14. The fracture surface of a compact heated at a rate of 5°C/min to l350°C. The average grain size was ~ 3 ~m and all pores were at the grain boundaries. Bar = 10 ~m.

CONCLUSIONS

To summarize, the monodisperse powder systems:

(1) justify the use of spherical particle models;

(2) allow more refined use of scaling law studies:

(3) reduce the extent of coarsening (and grain growth) as an interference in sintering research;

(4)

(5)

eliminate rearrangement and therefore allow the extension of two-sphere modelling to compacts; and

27 enhance the applicability of surface area measurements to study sintering kinetics.

It is perhaps not too optimistic to note that monodisperse powders offer an exceptional opportunity to tap the extensive literature on sintering models that has developed over the last thirty years and which has proved difficult to exploit in the past due to deficiencies in the available powder systems.

ACKNOWLEDGMENTS

This research was funded by DOE under contract DE-AC02-80ERl0588.


REFERENCES

1. S. Pejovnik, V. Smolej, D. Susnik, and D. Kolar, Powder Met. Intern., 11: 22 (1979).

2. R. L. Coble and R. M. Cannon, in "Processing of Crystalline Ceramics", Mat. Sci. Res., VoL 11, Eds. H. Palmour, R. F. Davis, and T. M. Hare, Plenum Press, NY (1978), pp. 151-170.

3. D. L. Johnson, in "Sintering Processes", Mat. Sci. Res., Vol. 13, Ed. G. C. Kuczynski, Plenum Press, NY (1980), pp. 97-106.

4. H. E. Exner and G. Petzow, Ibid, pp. 107-120.

5. E. A. Barringer, PhD Thesis, M.I.T. (1983).

6. G. C. Kuczynski, Trans AlME 185: 169 (1949).

7. F. W. Dynys and J. W. Hol1aran, J. Am. Ceram. Soc., 65: 442 (1982) •

8. C. Herring, J. App1. Phys., 21: 301 (1950).

9. R. L. Coble, J. Appl. Phys., 32: 787 (1961).

10. E. A. Barringer and H. K. Bowen, J. Am. Ceram. Soc., 65: C-199 (1982).

11. M. Yan, personal communication, 1982.

12. D. L. Johnson, J. Am. Ceram. Soc., 53: 574 (1970).

13. J. E. Burke and J. H. Roso10wski, in "Treatise on Solid State Chemistry", VoL 4, Ed. B. Hannay, Plenum Press, NY (1976).

14. M. Astier, G. Brula, F. LeComte, J. P. Reymond and P. Vergnon, in "Sintering - New Developments", Ed. M. Ristic, Elsevier Scient. Pub. Co., NY (1979), pp. 150-159.

15. G. R. Miller and O. W. Johnson, in "Processing of Crystalline Ceramics", Mat. Sci. Res., V<;>L 11, Eds. H. Pa1mour, R. F. Davis, and T. M. Hare, Plenum Press, NY (1978), pp. 181-191.

16. H. U. Anderson, J. Am. Ceram. Soc., 50: 235 (1967).

17. R. L. Coble and T. K. Gupta, in "Sintering and Related Phenomena", Ed. G. C. Kuczynski, et aL, Gordon and Breach, NY (1967), pp. 423-443.

18. R. L. Coble, J. Appl. Phys. 32: 793 (1961).


19. T. Vasi10s and W. Rhodes, in "Ultrafine-Grain Ceramics", Ed's. J. J. Burke, N. L. Reed and V. Weiss, Syracuse Univ. Press, Syracuse, NY (1970), pp. 137-172.

20. M. F. Yan, Mat. Sci. Eng., 48: 53 (1981).

21. D. N. K. Wang, Ph. D. Thesis, Univ. of Cal., Berkley (1976).

22. R. H. Bruce, in "Science of Ceramics," VoL 2, Ed. G. H. Stewart, Academic Press, NY (1965), pp. 359-367.

23. R. Haul and G. Dumbgen, J. Phys. Chem. Solids, 26: 1 (1965).

24. 1. B. Cutler, J. Am. Ceram. Soc., 52: 14 (1969).

25. W. S. Young and 1. B. Cutler, J. Am. Ceram. Soc., 53: 659 (1970).

26. D. A. Venkatu and D. L. Johnson, J. Am. Ceram. Soc., 54: 641 (1971).

27. R. M. German and Z. A. Munir, J. Am. Ceram. Soc., 59: 379 (1976).

A CELL MODEL FOR MICROSTRUCTURAL EVOLUTION DURING SINTERING

ABSTRACT

R.T. DeHoff

Department of Materials Science and Engineering University of Florida Gainesville, Florida 32611

A rigorous description of the geometric evolution of microstructure during sintering is presented, based upon two alternate spacefilling constructs: cells associated with the grains in the system, and bipyramids associated with the cell faces. Relations are derived between the rate of densification and the rate of annihilation of vacancies and also appropriate average concentration gradients in the solid phase at its surface. An efficiency factor is defined which describes the conversion of the volume of vacancies annihilated to the global volume shrinkage of the system. These relationships are free from simplifying geometric assumptions, and have potential application to all stages of powder processing.

INTRODUCTION

This paper reports the development of a new model for the description of the sintering process. It is distinguished from existing descriptions l - IO primarily in its attempt to maintain geometric and mechanistic rigor. The model connects the evolution of global geometric properties with specifically defined averages of diffusion fluxes, or, equivalently, concentration gradients in the system. The approach permits significant penetration of the problem of the description of sintering without important simplifying assumptions.

THE CELL STRUCTURE AND ITS PROPERTIES

At any instant of observation a partially sintered structure

23

24 R. T. DeHOFF

consists of a pore phase, which may be wholly or partially connected, or disconnected, and a solid phase, which contains a grain boundary network that may be disconnected, partially connected, or completely connected. A space filling cell structure may be visualized for such a system such that:

1. Each cell contains one grain in the po1ycrysta11ine structure; and 2. Each cell also contains the porosity that is associated with that grain.

The latter requirement follows because the cells fill space.

Figure 1. The cell construction, showing a grain and its associated porosity, at each stage of sintering.

Figure 1 illustrates constructions of the cell structure for sintered structures in each of the three primary stages of sintering. The surface that bounds a given cell is partially occupied by grain boundary facets, and partially by porosity. Unambiguous construction of individual cells requires the assumption that the grain boundaries are planar. This assumption is reasonably valid for the first stage when the grain boundary network is disconnected, and is not expected to be a serious approximation even in the late stages of sintering. Each cell in the structure is thus a polyhedron with flat sides.

Focus in the ith cell in the structure (grain i, with its attendant porosity). Locate the centroid of this cell for use as a reference point in evaluating its properties. [The centroid is chosen for consistency; any point within the cell could be used as a reference point.] Suppose this cell has Fi faces. Focus further on the jth face. Define the area of the face j to be Aj . Define the

MICROSTRUCTURAL EVOLUTION DURING SINTERING 25

perpendicular distance from the centroid of cell i to the jth face to be Pij; this property is called the pedal function for that face.

Figure 2. Associated with each face in cell i is a pyramid with base area Aj and altitude Pij'

Figure 2 shows that associated with face J 1S a pyramid with base area Aj and altitude Pij' The volume of this pyramid is

1 Vij = 3AjPij (1)

The volume of the ith cell is the sum of the pyramid volumes associated with each of its faces; the volume of the system is obtained by summing over all of the grains or cells in the system. Except for the assumption that the faces are planar, no approximations are required in carrying out this operation. It will be shown presently that an alternative, though related, summation of the pyramid contributions to obtain the total volume is more useful.

STRUCTURAL EVOLUTION

Sintering produces microstructural evolution that alters the cell structure. These changes may be described in terms of the motions of the cell bOllndaries relative to their centroids. The change in volume of the pyramid in cell i that is associated with face j is

dV ij = Aj dPij (2)

Motions of faces that result in rotations or expansions contribute higher order differentials to the volume change. Thus, equation (2) is a rigorous and complete evaluation of the first order change in the volume of the pyramid. The change in volume of the system may be obtained by summing over the faces in a cell, and over all of the cells in a system.

26 R.T.DeHOFF

Since the cell faces are generated from the grain boundary network in the system, motion of the cell faces is associated with motion of the grain boundaries relative to the centroids of their cells. The change in the pedal function, dPij in equation (2), may be unambiguously divided into two contributions:

1. decrease in Pij due to vacancy annihilation (VA) in the grain boundary, and 2. change in Pij not associated with vacancy annihilation; motions of this type are defined to be grain boundary migration (GBM).

Thus, in general,

(3)

Vacancy annihilation always decreases the pedal function and contributes to densification. Grain boundary migration may increase or decrease the pedal function, and does not contribute to densification.

An alternate formulation of the properties of the cell structure may be devised by focussing upon the cell faces rather than upon the cells themselves. The jth face is associated with two cells, labelled 1 and 2, and a pyramid in each cell.

Face j (Area A.)

J

Figure 3. Bipyramid construction associated with each face in the cell structure.

Figure 3 shows a face with its associated pyramids; call this element It has a face of the new, alternative cell structure bipyramid i.

area Aj and pedal functions Plj and P2j; its volume is


(4)

Grain boundary migration and vacancy annihilation result in changes in the pedal functions in each of the component pyramids that produces a change in the volume of each pyramid and hence the bipyramid cell:

= dVlj + dV2j = ~Ajdplj 1

= 3Aj[dPlj + dP2j]

Apply equation (3) to each of the component displacements

Thus,

dPlj (dPlj)VA + (dPlj)GBM

dP2j (dP2j)VA + (dp2j)GBM

(5)

Grain boundary migration cannot result in a change in the distance between centroids of the incident polyhedral cells:

(7)

The total change in pedal functions can be expressed in terms of the changes deriving from vacancy annihilation only:

(8)

The volume change of the bipyramid is thus

(9)

The change in volume of the system is obtained by summing the contribution from each bipyramid in the system:

F F dV = r dVj r Aj[(dPlj)VA + (dP2j)VA] (10)

j=l j=l where F is the total number of faces in the system.

DENSIFICATION AND VACANCY ANNIHILATION

The decrease in pedal function that contributes to densification is unambiguously associated with vacancy annihilation at the grain boundary o~the bipyramid face. Let the area of grain boundary on face j be Aj. This area is some fraction of the area of the cell face, Aj. Define an efficiency factor, fj for face j:

28 R. T. DeHOFF

(11)

This parameter varies from a very large value at the beginning of sintering when the grain boundary occupies a small fraction of the celi face to 1 in the late stages when faces become completely covered.

Let nAj be the rate of annihilation of vacancies on face j, with units of vacancies per square centimeter per second. It is evident that the rate of annihilation of vacancies over a single grain boundary facet will be constant, since departures from uniformity will tend to produce stresses that return the local rate to a uniform value. In a t~me ~nterval, dt, the volume of vacant sites annihilated on face j is RnAjAjdt, where ~ is the atomic volume. This volume of lattice sites annihilated corresponds to the removal of a slab of material of cross sectional area A~ and thickness (dPlj)VA + (dP2j)VA, i. e. ,

(12)

The minus sign derives from the convention chosen: a positive rate of annihilation of vacancies produces a decrease in the pedal function sum. Insert this result into equation (10),

F dV = - L A·[QQA·dt]

. 1 J J J= Substitute for Aj from equation (11):

dV F b. dt = - L fjA.llilA· (13)

j=l J J This equation may be rewritten

dV -. - = -~fn Ab dt A

where f

f -

is the average F b L f.uA.A.

j=l J J J F " • Ab L, nA ••

j=l J J

efficiency factor defined by

(14)

(15)

~A is the average rate of annihilation of vacancies in the structure, defined by

F ". Ab L, nA •.

j=l J J F L Ab

j=l j

(16)


and Ab is the total F

grain boundary area in the structure, given by

L: A~ j=l J

(17)

Inspection of equation (14) reveals that the quantity QfiAAbdt is the total volume of vacancies annihilated in the structure in time dt. The total volume change in the structure is shown to be larger than this quantity by a factor, t, defined in equation (15); the value of fj for each face is defined in equation (11). At the outset of sintering this factor is very large, approaching infinity as the contacting areas of grain boundaries between particles approach zero. It decreases smoothly during sintering, approaching a value of 1 as full density is reached. Thus, the volume decrease of the system is always greater than the volume of vacancies annihilated in any time interva1tO The factor by which it is greater is t, which might be usefully called an efficiency factor, since it reflects the efficiency with which vacancy annihilation is converted into volume shrinkage. The value of this factor is defined without significant approximation in equation (15).

DENSIFICATION AND DIFFUSION FLUXES

Vacancies that are annihilated to produce densification in sintering are supplied from pore-solid interface in the vicinity of the grain boundary upon which they are annihilated. Vacancies may be supplied from the surface through the lattice to the grain boundary, or they may travel in the zone of high diffusivity adjacent ot the grain boundary. Some of the vacancies generated at the pore-solid interface may find their way back to the interface, at a region of more positive local mean curvature, and be removed from the system at a pore surface sink, rather than at a grain boundary. The subset of vacancies that travel from surface source to surface sink aid the surface rounding process, but cannot contribute to densification.

---. Focus on an element of area of the pore-solid interface, dS,

Figure 4. This element may be represented by a vector that is locally normal to the surface with a magnitude equal to the area of the element. The geometry of the element is described by its two principle normal curvatures; the geometric factor of interest in thermodynamic considerations is the mean value, H = 1/2(K1 + K2) of these curvatures. The volume of solid adjacent to the surface is assumed to be in local equilibrium with the surface element, and possesses a vacancy concentration, cv, which is related to H. There also exists a vacancy concentration &radient, ~, and a corresponding vacancy diffusion flux vector, ~, in this volume element. In time dt, this local flux contributes ~ . ~dt vacancies into the volume of the solid phase. [The vector dot product in this expression gives the normal component of the vacancy flux into the solid; if there is a tangential component

30 R. T. DeHOFF

it lies in the surface and does not contribute to the solid phase.]

The total number of vacancies supplied to the solid phase from all of the pore surface in the system at time dt is:

~ ~

II Jv • dSdt s

It is valid to carry this integration over the whole surface because the value of II J v • dS for those elements that are involved in transferring vacancies from surface source to surface sink integrates to zero. If it is assumed that there is negligible accumulation of vacancies within the volume of the solid phase, then those vacancles that enter the system at the pore surface and do not re-emerge at the pore surface must flow to the grain boundaries, where their annihilation produces densification.

The intersection of grain boundaries in the system with the poresolid interface is a space curve. This curve is initially disconnected, becomes a connected network in the second stage, then disconnects again in the third stage, see Figure 1. This curve is a triple line, designated ssp, since it arises from the incidence of two solid grains and the pore phase. Let L be its total length in the system at any time. Grain boundary diffusion fluxes into the solid phase must originate from surface elements along this triple line.

---"'" ds

~

lie s

,.

Triple line (ssp)

Figure 4. Area elements, concentration gradients and fluxes associated with diffusional flows in sintering.


Focus upon an element of surface adjacent to this triple line, Figure 4. This element has a local mean curvature, H; the volume element of solid adjacent to it has a vacancy concentration, cv ' generally assumed to be in equilibrium with the element and its curvature. Th~volume element also has a concentration gra~ent of vacancies, Vc ,and a corresponding vacancy flux vector, J. These

v ---vectorp have components in the plane of the grain boundary, VCb and Jb. These components are related by Db, the grain boundary diffusion coefficient for vacancies •

... Let b be a vector that is normal to the grain boundary, and has

a magnitude that represents the thickness of the zone of enhanced diffusivity, roughly of atomic dimensions. Let at be an element of length of the triple line, pointing in the tangent direction. The area over which the ~r~n boundary componen~ of th~ vacancy flux acts is an element aSb = bXdL, Fig~e 4. Since band dL are normal to eac~other, the magnitude of dSb is. bdL; its direction, n, is normal to dL, and lies in the plane of the grain boundary. In time dt number of vacancies supplied to the grain~ound~y from the surface element associated with the line segment dL is Jb • UbdL. The total number of vacancies supplied to grain boundaries from the surface adjacent to the ssp triple line in time dt is

I ....... A

Jb • nbdLdt L

All of these vacancies move in along the grain boundary where their annihilation contributes to densification.

In time dt, the total number of vacancies supplied to grain boundaries from the pore-solid interface is

~ --'" -dNv = II J v • dSdt + I J b • UbdLdt (18) S L

The total number of vacancies annihilated at grain boundaries in the same time interval is

F xi.AjA~dt dN L iiA~dt (19) v j=l

The assumption that the accumulation of vacancies within the volume of the solid phase is negligible in comparison with the flow through the solid makes these two quantities identical:

-'0................. _ II J • dSdt + I Jb • nbdLdt = xi.A~dt S v L

Equation (14) relates the right side to the rate of volume shrinkage:

dV -T _ ....... - -dt = -QfnA~. = -QfI~1 Jv • dS + b{ J b • ndL] (20)

Introduce definitions of the average lattice flux over the surface,

32

J v

..... - ff J

S v

--11.. ds/ff dS

S and the average grain boundary flux over the triple line,

- ... Jb = f J b . ndL/f dL

L Equation (20) may be written:

dV = -~f (:J S + bJ L] dt v b

R. T. DeHOFF

(21)

(22)

(23)

The fluxes in the equations are evaluated at the pore-solid interface. Their values are related to the concentration gradients in the volume elements adjacent to the interface through the appropriate forms of Fick's laws:

...... ....... J = -D IJC

v v s (24)

The averaging process applied to the fluxes also applies to the gradients:

IJC - ff VC s S s

dS/ff dS S

Thus, equation (23) may also be written

or,

dV = ~frn IJC S + DblJCb bL] dt - v s

alternatively,

:~ = ~fDv\7Cs S[l + ~b v

• bL • IJCb S

ndL/f dL L

(25)

(26)

(27)

Dominance by volume diffusion or grain boundary diffusion is determined by the value of the second term in the brackets in this equation. If that term is large in comparison to 1, equation (27) be-comes

and shrinkage is controlled by grain boundary diffusion. If the term is relative to 1,

dV = ~fD IJC S (29) dt v s

results, and volume diffusion controls densification.

DISCUSSION

The primary results of this formulation are contained in


equations (14), (23) and (27). The only simplifying geometric assumption introduced is that the cell faces are approximated as planar. Thus, quantities computed from these equations may be expected to reflect the behavior of the system with reasonable accuracy.

Table 1. Computed vacancy annihilation rates for a 48 micron powder loose-stack sintered at lOOO°C.

Vv ca3 dV c.3 s~b c .. 2 f - 1/AAfract i'iA[ --r-] seconds monolayer

c.3 tit p::;ec c.3 em -Bee

0.42 _380x10-4 - 0 - SO - -0.34 7S 40 12 20x1016 0.07

0.33 64 SO 10 13 0.12

0.27 17 140 6 7 0.6

0.23 8 170 4 2 20

0.22 6 210 4 2 20

0.20 S 240 4 1.4 SO

0.16 1.9 250 3 0.2 270

O.lS 1.7 230 3 0.2 370

0.14 1.2 220 2 0.2 320

0.09 O.S 140 2 0.07 370

0.06 0.3 100 - 1 0.07 170

Table 1 presents computations based on stereological measurements applied to loose stack sintering of a 48-micron copper powder sintered at lOOO°C. The efficiency factor was estimated from measurements of the area fraction occupied by solid on an SEM projected image of a fracture surface. Densification rate was computed analytically from a semi-logarithmic curve which describes the change in volume fraction with time and reasonable precision. It is evident that the average vacancy annihilation rate varies significantly with time. This quantity may alternatively be expressed as the rate of annihilation of a monolayer of sites, or the time required to annihilate a monolayer.

The model may also be used to compute concentration gradient averages. Comparison with model computations that make simplifying assumptions will permit assessment of the validity of earlier approximations and their range of application.

Stereological measurments demonstrate that the path of microstructural change is insensitive to the sintering temperature, so long as sintering is carried out near the melting point. Thus, a comparison of densification rates at different temperatures may be undertaken, since purely geometric factors in equations (28) and (29) are invariant.

34 R. T. DeHOFF

The model presented in this paper is a rigorous description of the system at all stages of sintering. It also has potential application to sintering after cold compaction, and to hot pressing, so long as plastic deformation is negligible. Some of the parameters contained may be difficult to estimate; nonetheless, the description presented identifies the appropriate parameters whose values are to be sought.

SUMMARY

A cell model is presented which describes geometric evolution during sintering from beginning to end without important geometric simplifications. The model connects volume shrinkage and vacancy annihilation rates, and makes further connections with appropriate averages of diffusion fluxes or their associated concentration gradients. It is demonstrated that the change in volume of the system in any time interval is always larger than the volume of vacancies annihilated, and defines the efficiency factor that connects these two quantities. The approach has significant potential for providing more general insights into the processes that occur during microstructural evolution in many aspects of powder processing.

ACKNOWLEDGEMENTS

The author is indebted to the Army Research Office, which provided sponsorship for this work.

REFERENCES

1. J. Frenkel, J. Tech. Phys., Moscow 9~5 (1945). 2. B. Pines, J. Tech. Phys., Moscow 16:737 (1946). 3. G.C. Kuczynski, Trans. AIME 185:169 (1949). 4. W.D. Kingery and M. Berg, J. App1. Phys. 26:1205 (1955). 5. B. Alexander and R.W. Ba1uffi, Acta Met. 5:666 (1957). 6. R.L. Coble, J. Amer. Ceram. Soc. 41 ~ 55 (1958). 7. D.L. Johnson and I.B. Cutler, J. Amer. Ceram. Soc. 46:541 (19631. 8. D.L. Johnson and T.M. Clarke, Acta Met. 12:1173 (1964). 9. L. Berrin and D.L. Johnson, in Sintering-and Related Phenomena,

G.C. Kuczynski, N.A. Hooten and C.Y. Gibbon, editors, Gordon and Breach Sci. Pub., New York (1967) 369.

10. R.L. Eadie, G.C. Weatherby amd K.T. Aust, Acta Met. ~:759 (1978).

ANhLYSIS OF INITIAL STAGE SINTERING BY COMPUTER SIMULATION

ABSTRACT

K-S. Hwang and R. M. German

Materials Engineering Department Rensselaer Polytechnic Institute Troy, New York 12181 U.S.A.

The sintering of a row of spherical particles is computer simulated by a method which eliminates geometric approximations. Results for neck growth, and the rate law exponent for evaporation-condensation, surface diffusion, volume diffusion and grain boundary diffusion have been simulated and compared with those obtained from integrated sintering equations by others. The sintering involving five major mechanisms simultaneously is also simulated. The result shows that significant errors could occur if geometrical approximations are involved. It also shows that the rate law exponent is dependent on variables like heating rate, sintering temperature and atmosphere.

INTRODUCTION

Various types of material transport including viscous flow, plastic flow, evaporation-condensation, surface diffusion, grain boundary diffusion, and volume diffusion may occur during sintering. Models and sintering equations with a circular neck shape assumption have been proposedl-7 to describe these mechanisms. In general, by making some crude geometric approximations, neck growth rate equations were integrated giving general power laws as follows:

Bt (1)

in which X is the radius of the neck, A is the radius of the sphere, B is a temperature dependent constant which incorporates such properties as atomic volume and surface energy. The exponents n, m depend on the sintering mechanism as shown in Table I. These results have

35

36 K-S. HWANG AND R. M. GERMAN

TABLE I

Constants n,m in Equation 1 for Different Sintering Mechanisms

The first character of the abbreviation denotes the vacancy sink. (S: surface, G: grain boundary). The second character denotes the transport path. (S: surface diffusion, V: volume diffusion, E: evaporation-condensation, G: grain boundary diffusion).

Mechanism n m n-m Ref.

S.S 7 3 4 2 S.V 5 2 3 2 E.V 3 1 2 3 G.G 6.22 2.22 4 5 G.V 4.12 1.12 3 5

been repeatedly compared with model experiments. Based on the fit to experimental data, conclusions were drawn with regard to the governing sintering mechanism and the value of the diffusion coefficient.

This method was later shown by several authors 5 ,7,8,9 to be unreliable, since multiple mechanisms could operate simultaneously during sintering. The crude approximations involved in deriving sintering equations and the difficulty in measuring experimental results make this method even more questionable.

This paper proposes a computer method which eliminates problems of both geometric approximations and multiple mechanisms. The sintering of a row of spheres is computer simulated and a re-analysis is performed on the neck growth, rate exponent n, and shrinkage. The effects of such variables as heating rate, sintering temperature and material condition upon the sintering kinetics are also determined in this analysis.

GEOMETRIC APPROXIMATIONS FOR TWO-SPHERE MODELS

In general, sintering mechanisms can be classified into two different categories. The first is a non-densification or adhesion system in which material transport is from the particle surface to the neck region. Transport is through evaporation-condensation, volume diffusion or surface diffusion. Since there is no material removed from the contacting area between particles, no densification occurs. In the other case, the interparticle grain boundary serves as the vacancy sink and material moves from the contacting area to the neck region. The two active mechanisms are either grain boundary diffusion or volume diffusion. This causes the centers of the contacting particles to approach each other. Most sintering equations developed in the past for these two cases used geometric approximations to obtain the final integrated form as shown in equation 1. In the adhesion case, approx-

SINTERING BY COMPUTER SIMULATION 37

imations involved were radius of curvature 'TI2X3 3

of the neck AR = A' volume of the neck

2A 2 of the neck lip = X2' area

'TIX4 3 V = 2A' and thus

dV = 2A'TIx 3 which is directly related to the dX neck growth rate equation

as shown in the equation for the surface diffusion case.

• dV XadX

1 + 1) aD aAREA/p A X s (2)

where y is the surface energy, ~ is the atomic volume, k Boltzmann's constant and T the absolute temperature.

These approximations are compared in Figures 1 to 4 with exact values which are obtained by solving the following set of equations .

3

.06.-------r-------r------" ..... -_ .. TJ,is Study

_ . -X2/ 2A ) Adhe-$ion

- - - - Ihi,Study .04 ____ X2/ 4A ) Densilicl!ltion /

9 / A .. / "

.02 ... / ,,'

~.:~~~""" 0L---~~.~1~-----.~2------~.3-

X / A

.03.-------r-------r---------.--, .•••• , . 1'hi"t. Siudy, AdM-lion

- - - - This StvdV,Densllkolio"

-- TTX".t2A

.02

.01 " "

, ,

OL-------.~I~X=/=A~~------~ .3

2

. 3.------,---,....-----.."

.2 - - - - nus Study) __ n2x3/ 2A O~nsifit:otion

.1

0L-------~.1~-----.~2------~.3 X/ A

.15 r------...,--------,.------;----:n ... , .... This Study. Adh9sion

- - - - this StYCiy,o.",illIl:Ohon .-

10 --2T1X3'A

dV/dX A2 , ,

.05 , , ,

4 0 .1 2 .3

X/A

FIGURES 1,2,3,4: Comparison between approximations and exact values for radius of curvature of the neck P, neck area, neck volume and d(Vol)/dX.


Vol = ~TfA 3 3

26ZiTfY~(Z)dZ + }TfAT3 ~ }Tf(Zi-A+AT)(3Y~(Zi) + (Zi-A+AT)2)

(3) Zi

p

Ys(Zi)

A (4) AT+p

Yn(Zi) (5)

where p, Zi, AT, Ys, Yn are defined in Figure 5. Since there are only three unknowns (p,AT,Zi) in this equation system, they can be solved numerically by a computer package based on the Newton-Raphson method.

In the other case where interparticle distance changes, the ap-X2 3 Tf2X3 3

proximations involved are p = 4A' A = ~, and V is the same as in

the previous case. These approximations are also compared in Figures 1 to 4 with exact values which are solutions of the following set of equations.

4 Vol = -TfA3 3

Zi = A-lIL p A+p

Y (Zi) = Y (Zi) s n

where A, lIL are defined in Figure 6.

After p, AT, Zi or p, lIL, Zi were found, the area AR can be expressed by

and dV/dX can be described by

or

dV) dX S

dV) dX G

,

,

adhesion

= av le. + ~ aAT + ~ dZi ap ax aAT ax aZi ax

densification

(7)

(8)

(9)

(10)

(11)

The comparisons in Figures 1 to 4 show that the errors are

significant especially for p and for ~~ in the adhesion case. The

deviation for p amounts to 50% for ~ = .3 and :~ is over 100% for ~ = .2.

COMPUTER METHOD

In practical cases, both adhesion and densification mechanisms


v v

A

--z

z;

FIGURE 5 FIGURE 6

Two-dimensional representation Two-dimensional representation of two spheres sintered by nondensification mechanisms.

of two spheres sintered by dens ification mechanisms.

are operating simultaneously. This is simulated in this study by incrementing the geometry with very small time steps. The neck growth rates for both cases are calculated separately,

. ... X adhesion XSS + XSV + XSE

X densification *GV + *GG

(12)

(13)

where the subscripts are denoted in Table I and the rate equations for the five major mechanisms are selected as shown in Table II. The simple flow chart given in Figure 7 shows how these rate equations are used for the simulation.

TABLE II

Neck Growth Rate Equations for the Five Major Sintering Mechanisms

Mechanism

S.S

S.V

S.E

G.G

G.V

* F

X

· X

· X

· X

Rate Equations

* 1 1 2 ** D ·F·(- - - + -)·2·n·X·8 /(p·dV/dX) s p X A

1 1 2 *** Dv'F'(p - X + A)'AREA /(p'dV/dX)

P 'F'(! -! + 1)'AREA'(M/2nKT)Yz/(TD'dV/dX) o p X A

8.F'Db·(X + p)'n'8/(p'X'dV/dX)

4F·D ·(X + p)·n v !(p·dV/dX) AREA" 1TX2

** 8 = atomic diameter

Ref.

2

2

3

5

5

rSl/(K'T) *** AREA see Equation 9 - Other symbo1s- See Table III


° At any time t, the X adhesion is calculated based on the geometry and temperature at that moment. After a time increment t.t, the neck size increases by i adhesion °t.t. Accordingly, the geometry also changes due to the neck growth and this is calculated by the same method described earlier. Based on this new geometry, a new i densification is found which leads to an increase in neck size by iot.t. By iterations of small time steps, inversely dependent on the rate i, the centers approach, radius of neck curvature, and other geometric changes can be found as sintering continues.

SELECTION OF MATERIALS

Based on the past experimental work2 ,3,4,8 copper was selected as the material for simulation testing. The properties of copper selected for the simulation are listed in Table III.

~ Xu P. n..... • • Zi Xgv -- --+ Xsv _X+X.61 -+ AT -! Xse VOL Xgg .. AREA

L L_ Hi;..J VOL AREA

FIGURE 7: Flow diagram of the computer simulation method.

RESULTS AND DISCUSSIONS

Single Mechanism: The isothermal sintering of a row of copper spheres at 1050°C by each of the five individual sintering mechanisms is simulated before addressing multiple mechanisms. The neck growth curves shown in Figure 8a indicate the surface diffusion mechanism has the highest growth rate and evaporation-condensation has the lowest. The rate law exponent n as described in Equation 1 for each mechanism is shown in Figure 8b. It is noted that these exponents are not constant, they increase with sintering time. The range of rate law exponents are listed in Table IV and are compared with conventional values as shown in Table I. Among these values, the exponent n for the sur~ face diffusion mechanism differs most. After IOO-minute sintering at I050°C a value of n = 8 is obtained, which is much higher than the value obtained by Kuczynski2 and Rockland. 6 The other values are comparable to those obtained in previous studies.

The values of n listed in Table IV are not frequently expected because more than one mechanism is normally operative. iS The curves indicated by "alln in Figures 8a and 8b were simulated for a situation when all five mechanisms are simultaneously operative. As expected., the neck size for multiple mechanism sintering is greater than that of any single mechanism. However, the rate law exponent given in Figure


TABLE III: Data for Copper

Property Value Ref.

Atomic Volume, n(m3 ) Melting Point, (K) Density, (g/cm3), TD Surface Energy,y,(J/m2 ) Frequency Factor,Volume Diffusion,Dov '

(m2 /sec) Activation Energy,Volume Diffusion, Qv

(KJ/mole) Effective Surface Thickness,os,(m) Effective Grain Boundary Thickness,ob,(m) Frequency Factor,Grain Boundary Diffusion,

Dog 'og (m3 /sec) Activatlon Energy,Grain Boundary Diffusion,

Qg(KJ/mole) Frequency Factor,Surface Diffusion,

Dos'os(m3/sec) Activation Energy,Surface Diffusion,

Qs(KJ/mole) Pre-Exponential, Vaporization, Po(}ffi/m2 ) Activation Energy,Vaporization,

Qvap(KJ/mole)

1.18 x 10-29

1356 8.96 1.72

6.0 x 10-5

3 210 -10 x 10_10

5.12 x 10

5.12 x 10-15

105

6.0 x 10-10

205 1.23 x 105

324

10

11

11 12 12

12

12

13

13 14

14

'cO ,:=:.~1==±=::1::::=:=1 Iss

ex: , -: x

se

~-r------~--~~~+---~~-r .1 1. 10. 100.

a TIME MIN

z

b

a 11----______ _

W 99 ----------------------

se----__________________ __

N ~----~41--~~--1~----~ . 1 1. 10 .

TIME MIN 100.

FIGURE 8: The neck size ratio X/A (a) and the rate law exponent N (b) as a function of sintering time for a row of 108 ~m copper spheres isothermally sintered at 1050°C. The abbreviations are denoted in Table I.


TABLE IV: Calculated Rate Law Exponents

Mechanism n (this work) n (prior work) Reference

S.S 7.4 - 8.0 7 2 S.V 5.1 - 5.5 5 2 S.E 3.0 - 3.1 3 3 G.G 6.1 - 6.4 6.2 5 G.V 5.1 - 5.5 4.1 5

8b shows that it decreases from 7.2 to 6.7 between times of 6 sec and 100 min. This is because the relative importance of the surface diffusion mechanism decreases from 100% to 55% as shown in Figure 9. The trend of these curves also suggests that as time increases beyond 100 min. surface diffusion will become less important than volume diffusion.

FIGURE 9: The relative importance of individual sintering mechanism when 108 ~m copper spheres are sintered isothermally at 1050°C.

Effect of Heating Rate: In a sintering experiment, isothermal conditions can never be obtained without heating. It is therefore necessary to check the effects of heating rate. Three different heating rates, 5000°C/min, 1000°C/min and 200°C/min were incorporated into the computer program to check their influence on the neck growth and the rate law exponent n of copper sintered at 1050°C.

The curves in Figure lOa show that neck size is quite independent of the heating rate when the sintering time is over 30 min. However, the time exponent n at 30 min is quite different, with values of 6.8, 6.6 and 5.7 for 5000~C/min, 1000°C/min and 200°C/min, respectively, as shown in Figure lOb. According the Figure lOb, the starting time at which experimental measurements can be accurately conducted for a time exponent method is inversely dependent on the heating rate. For a slow heating rate such as 200°C/min, the experimental data should only be collected after 100 min. For a fast heating rate such as 5000°C/min, the measurement can be started after 10 min. The need for rapid heating to ensure accurate sintering results has been shown earlier. 16


....:

a

z

1. 10. 100. .1 1. 10. 100. TIME MIN TIME MIN

( a ) (b )

FIGURE 10: The effect of heating rate on X/A and N for a row of 108 ~m copper spheres sintered at 1050°C. a: 5000°C/min, b: 1000°C/min, and c: 200°C/min.

According to Ashby~2 the sintering diagram also shows that several materials including copper have different dominant mechanisms at different sintering temperatures. Therefore, when a time exponent method is to be used to indentify the dominant sintering mechanism a high peating rate must be applied to avoid the influence of other mechanisms during the non-isothermal period.

Effect of Sintering Temperature: Since some material constants are strongly dependent on temperature, two different temperatures, 1050°C and 900°C, were used to check their influence on the sintering kinetics. Figure 11a shows that the neck growth of copper sintered at 1050°C is larger but its n value (Figure 11b) is smaller than when sintered at 900°C. The lower value for n at 1050°C is because the relative importance of surface diffusion decreases with temperature as shown in Table V.

Effect of Material Constants: It should be noted that the accuracy of the simulations performed in this study depends on the accuracy of selected equations and the material properties involved. Such factors like atmosphere and impurity of the material could change the value of surface energy or the diffusion coefficients and consequently could alter the simulation results. Two simulations were conducted to examp1ify this effect. The curves marked "a" in Figures 12a and 12b result from applying the constants shown in Table III. The curves marked "b" result from using one-tenth of surface diffusion coefficient Dos and one-tenth of surface energy y of that applied in curve a. Since the neck growth rate is much slower curve b is much smaller than curve a in Figure 12a. The exponent n is also smaller for curve b in Figure 12b because volume diffusion overshadows surface

44 K-S. HWANGAND R. M. GERMAN

00

b

a b to

:z

...

~ . 1

• ~- ..• 'HI~---+-<~+--~~.....j-1. 10 . TIME MIN

100. a

N~----~4--------+------~ b .1 I. TIME MIN 10. 100.

FIGURE 11: The effect of sintering temperature on X/A and N for a row of 108 ~m copper spheres heated at 5000°C/min then sintered isothermally. a: 1050°C b: 900°C

TABLE V

The relative importance of individual sintering mechanism for copper spheres heated at 5000°C/min and sintered at 1050°C

and 900°C for 100 min.

Hechanism Relative Importance % lOSO°C 900°C

S.S 55 68 S.V. 11 7 S.E a a G.V 31 18 G.G 3 7

diffusion. Obviously, if other constants, such as the grain boundary diffusion coefficient, differ from those listed in Table III, different results can be expected. It should therefore be understood that the function of this computer simulations is essentially a qualitative re-analysis of the sintering kinetics instead of a quantitative one.

Shrinkage: This computer program also simulates the shrinkage of a row of sintered spheres. Figure 13 shows the shrinkage as a function of time when powders are heated at 5000 o /min and sintered at 1050°C (curve- a) and 900°C (curve b).


cO C!

a a c.ri b b

cr: z ...... -: x

..r

a 1. 10. TIME MIN

100. b . 1 1. 10 .

TIME MIN 100.

FIGURE 12: The effect of material constant on X/A and N for a row of 108 ~m copper spheres heated at SOOO°C/min and sintered at 10SO°C. a: material constant uSing Table III b: D and yare one-tenth of that in Table III. so

Figure 14 also shows the time exponent n of the shrinkage equation

(14)

where ~L/L is the shrinkage and C is a constant. Both curves in Figure 14 give a value of about 4.6 at 100 min . This is close to that predicted by Johnson5 who reported .49 for volume diffusion mechanism and .33 for grain boundary diffusion. The value obtained in this study is reasonable since volume diffusion is more significant than grain diffusion as shown in Table V.

Herring's Scaling Law: All sintering equations listed in Table I conform with the Herring scaling laws. li As a consequence, it is necessary to check if the computer simulations performed in this study also follow this law. Copper spheres 72 ~m in diameter were simulated and compared with the results presented previously for 108 ~m copper spheres sintered at 10SO°C isothermally.

Table VI shows the neck size each mechanism reaches after 100 min sintering time for 108 ~m copper spheres. The time needed for spheres 72 ~m in diameter to reach the equivalent neck size ratio are also listed in Table VI. From the Herring scaling laws, tID8 = An- m ·t72 where t is time, A is the scaling factor (A = 1.S) and n-m is calculated as shown and matches exactly with those predicted by Herring for the adhesion system. Although Herring did not predict n-m for the densification system (because this system was not avail-

46

W L> a: ><z· H a::: :r: U;

1. TIME

a

b

10. MIN

K-S. HWANG AND R. M. GERMAN

z

100. 1. TIME Ml

10. 100.

FIGURE 13: Shrinkage as a FIGURE 14: Value of the time exponent n in the equation (~L/L) = C·tn .

function of time for a row of lOS copper spheres heated at 5000°C/min and sintered at 1050°C.

TABLE VI: Data for Herring Scaling Laws.

Mechanism X/A tlOS(min) tn (min) n-m

S.S .235 100 20 4 S.V .164 100 30 3 S.E .028 100 45 2 G.G .164 100 20 4 G.V .230 100 30 3

able at that time) it can be derived in the same way as he derived for adhesion systems.

CONCLUSION

A computer program which eliminates geometric approximations and incorporates multiple mechanisms was constructed to re-analyze the sintering kinetics based on simple two-sphere models. The simulation results show the significant errors in the rate exponent caused by past approximations. These results also show that the rate law exponent is not a constant, rather it is a function of sintering time, temperature, material condition and heating rate.


ACKNOWLEDGEMENT

The authors gratefully acknowledge valuable discussions with Prof. F. V. Lene1. One of the authors (Hwang) also acknowledges a Fellowship (Allegheny Ludlum) which supported this work.

REFERENCE

1. J. Frenkel, J. Phys. U.S.S.R., 9, No.5, 1945, p. 385. 2. G. C. Kuczynski, Trans. AIME, 185, 1949, pp. 169-178. 3. W. D. Kingery and M. Berg, J. App1. Phys.,26, 1955, pp. 1205-1212. 4. R. L. Coble, J. Am. Ceram. Soc., 41, 1958, pp. 55-62. 5. D. L. Johnson, J. App1. Phys., 40, 1969, pp. 192-200. 6. J.G.R. Rockland, Acta Met., 14, 1966, pp. 1273-1279. 7. J.G.R. Rockland, Acta Met., 15, 1967, pp. 277-286. 8. T. L. Wilson and P. G. Shewmon, Trans. TMS-AIME, 236, 1966,

pp. 48-58. 9. H. E. Exner, Reviews Powder Met. and Physical Ceram., Vol. 1,

p. 22, Freund Publishing House, Tel-Aviv, Israel, 1979. 10. H. Jones, Meta11. Sci. J., 5, 1971, p. 15. 11. K. Hoshino, Y. Iijima and K. I. Hirano, Acta Met., 30, 1982,

pp. 265-271. 12. M. F. Ashby, Acta Met., 22, 1974, pp. 275-289. 13. J. Y. Choi and P. G. Shewmon, Trans. TMS-AIME, 224, 1962, pp.

589-599. 14. S. Dushmann and J. M. Lafferty (Eds.), Scientific Foundations of

Vacuum Technology, Wiley, New York, 1962. 15. R. M. German and Z. A. Munir, Inter. J. Powder Met. Powder Tech.,

12, 1976, pp. 37-44. 16. R. M. German, Powder Met., 22, 1979, pp. 29-30. 17. C. Herring, J. App1. Phys., 21, 1950, pp. 301-303.

CHANNEL NETWORK DECAY IN SINTERING

ABSTRACT

F.N. Rhines and R.T. DeHoff

Department of Materials Science and Engineering University of Florida Gainesville, Florida 32611

The development of the topological model of sintering is reviewed. It is pointed out that the decay of the topological network of channels and junction pores (i.e., sintering) is directly comparable to other network decay processes, such as that of grain growth in a polycrystalline aggregate, wherein surface tension both drives and directs the geometric changes that occur. Through this analogy some unfamiliar, though important, features of sintering have been deduced.

INTRODUCTION

Some 30 years ago, onp. of the present writers proposed a topological model of sinteringl , which brought thinking closer to reality through its ability to deal conceptually with a system composed of particles of mixed sizes and shapes. By viewing the sintering mass as a network of contacting particles, interpenetrated by a network of porosity, contracting under the forces of surface tension, it provided, for the first time, a standpoint from which the entire sequence, from loose powder to a dense mass, could be visualized. An essential parameter of this model is the topological connectivity (G) of the mutual surface of the two networks, which can be expressed in terms of its number of branches (B) and its number of nodes (K), thus:

G = B - K + 1 (1)

For the case of one-component solid state sintering, there is a first

49

50 F. N. RHINES AND R. T. DeHOFF

stage during which local adjustments in surface contour and interparticle spacing culminate in a minimal surface.area and balance of surface forces, that is contingent upon the topological connectivity. In a second stage, this balance is maintained as the coordinating connectivity decays spontaneously toward a third stage where the network begins to fragment into isolated pores. The present paper is concerned with the mechanism of topological network decay, by which the connectivity decreases is second stage sintering, in partnership with the pore volume and pore surface area.

At about that same time, the present authors undertook to find means by which we might measure'the geometric changes of sintering. While most of our colleagues in sintering resea2ch were concerning themselves with questions of material transport , without asking the crucial question: over what path should the material be conveyed; we were directing our attention to the field of quantitative microscopy, as a tool to penetrate the mystery of sintering by discovering its precise path from powder to dense bodY.3 Progress came first with the finding by Duffin, Meussner, and Rhines , of the measurement of total length of lineal feature in unit volume (LV) and total area of surface in unit volume (SV). Unknown to us, at the time, these relation~ had been discovered five years earlier by the Russian'5 Saltykov. We moved ahead of the Russians, however, when DeHoff developed the measurement of total integrated surface curvature in unit volume (Mv). Our set of quantitative relationships also included the volume fraction of phase (VV), which had been known among mineralogists for a century or more.

The first penetration of the mechanism of sinte6ing with these tools came with the observation by DeHoff and Rummel of the constancy of the ratio vv/Sv (i.e., volume fraction to surface area in unit volume), throughout second stage sintering. Its value is established by the initial connectivity and remains constant while the connectivity is decreasing by the process of topological decay, which is the subject of this paper. A geometric consequence of this relationship is that the channels of the pore network retain a constant diameter as densification proceeds. This can be seen in microsections through sinter-bodies, where it appears that the pores become fewer, though of the same diameter, while densification is in progress. The ratio also implies that densification occurs by the removal, one at a time, of similar units of void space, without alteration in the diameter of the remaining pores. This is characteristic of topological changes, which always occur in whole units, as distinguished from fractions of a unit.

A decade later, DeHoff and Aigeltinger7 undertook a study of sintering by serial section analysis. Measuring the connectivity of the pore network in this way, they found that the connectedness decreases in direct proportion to the loss of pore volume, during

CHANNEL NETWORK DECAY IN SINTERING 51

the second stage of sintering. This confirmed the conjecture that densification proceeds in discrete steps, as units of pore structure are eliminated.

Concurrently, Gregg and Rhines8 succeeded in measuring the contractive force of sintering (F) in unit area (a) and demonstrated that it is related to the surface tension (y) and to three parameters of qu~ntit~tive microscopy (MV, VV' and SV) through the fundamental re1at~onsh~p :

(2)

This is an exact natural law involving only fundamental quantities. It is descriptive of the state of the system at any point in second stage of loose stack sintering, but it does not, in itself, define either the path of geometric change, or its rate of change.

When the sintering force (F) is measured with progress of loose stack sintering, it is found to increase almost in proportion to the density, Figure 1. This is a surprising result in that it means that the sintering force becomes larger as the volume of pores diminish. The geometric ratio (~.Vv/SV)' being directly proportional to the sintering force, equat~on (2), also increases with decrease in pore volume. Since the ratio (VV/Sv) is demonstrably constant in second stage sintering, the increase in (~~.VV/SV) must be ascribed to an increase in the surface curvature (MV)'

1I00r--------------,

i ~IOOO

~

o z

CO"II POWO(. sau", 1III

o U, 6 loP o ......

o

o

B coo

!

./ /' ~ . ~. 0

zoo

Figure 1. sintering sintering powder at

OlNSITY(c.". "'5)

Variation of the measured force with density during of three sizes of copper lOOO°C.


In the terminology used in this paper, larger curvature means more negative curvature. Convex particles are considered to be enclosed by positively curved surface, isolated pores by negative surface. At the loose powder stage, the initial total curvature may be positive, or negative, depending upon the particle shape and size distribution, see Figure 2.

(x ,6")

Sphertcal

DerdntlC

b

5

4

o Spherocal J

2

o~--------------r----------

-1

2

-3

-4

-5~~~~ __ ~ __ ~~~~ __ ~ ___

0.13 0·7 0·6 0.5 0.4 0.3 0.2 0.1 0

._ ---f~1- I ~ ~~~III 1'II r: ~ Figure 2. Total curvature per unit volume versus volume fraction of porosity for 48 micron spherical and dendritic copper powders (Aigeltinger and DeHoff).

With the onset of sintering, saddle surface begins to form at particle contacts and this becomes increasingly negative as it grows at the expense of surrounding positively curved surfaces, until a channel network is developed. During subsequent network decay, the channels become fewer but longer, so that the negativity of surface increases while its area is diminishing. As the isolation of pores begins, however, their lesser curvature tends to mask the increasing negativity of the channels and there is a reversal in the total curvature as measured metallographically. The sintering force continues to increase, Figure 1, because it is derived from the channels and receives little if any contribution from th~ isolated pores.


TOPOLOGICAL TRANSFORMATION IN STEADY STATE SINTERING

The kind of shape evolution that is exhibited in second stage sintering is recognizeable as a typical behavior in the decay of topological networks, where surface tension provides the driving force. Examples exist in the collapse of foams and in g.rain growth in polycrystalline aggregates, where growth is effected by a decrease in the number of grains. One of the most obvious characteristics of surface tension controlled networks is that their branches tend to meet at nodes where four, and only four, branches join at mutual angles of 109°, Figure 3.

Figure 3. Quadruple point and triple lines in a polycrystalline grain structure.

In pursuit of this criterion9 , several partially sintered samples of copper powder were penetrated with a solidifying medium and then fractured to reveal the structure of the channel network by scanning electron microscopy, Figure 4. In this way it was verified that the channels of a sintering body do, indeed, prefer to meet in sets of four, just as do the edges of a polycrystalline aggregate.

With this confirmation of the topological nature of steady state sintering, it becomes reasonable to presume that sintering will display other features of topological decay, as seen in such processes as polycrystalline grain growth. Grain growth has br5n shown to occur by the collapse of three-edged crystal facets ,under the force of surface tension, Figures 5a, band c. When this event has occurred 13 times in the network of grain boundary, one grain, on the average will have been reduced to having a single bounding surface


Figure 4. Fracture of a pratly sintered copper sample, showing replicas of channels meeting in groups of four.

Figure 5. Illustration of the collapse of a three sided face during grain growth.


(i.e., an isolated body) which is capable of spontaneous collapse. At the same time 13 new three-sided facets are generated out of those formerly having more than three edges, thereby perpetuating the process.

It can be shown that this is the only topological process that can proceed within the grain boundary network, spontaneously under the driving force of surface tension, because only three-edged faces can shrink to zero with an uninterrupted expenditure of surface energy and without violating the geometric restrictions of surface tension. All other processes involve an increase in surface area somewhere within the network, or resolve into a series of three-sided collapses. When a three-sided face closes, the system loses exactly two edges (branches) and one corner (node). This is necessarily true of any network existing under the directing force of surface tension, as are both grain growth and sintering.

In the case of sintering, the channels correspond to the edges of the grains. These are so connected as to form closed circuits, corresponding to the facets of a grain, Figure 6.

Figure 6. Surface tension equilibrated pore network, with pores meeting at quadruple points. Note similarity to grain edge network.


The smallest circuits are composed of three channels and there are curcuits of 4, 5, 6 and more channels. A closed shell of circuits defines the volume of a metal particle. At the beginning, the particle is the original powder particle, but as sintering progresses, some particles will disappear, while others grow larger, until, at the end, the sinterbody becomes one large particle.

An altogether analogous process to that for collapse of the triangular facet, depicted in Figure 5a, b, and c, is illustrated for the case of the sintering channel network in Figure 7.

a b c

Figure 7. Illustration of the collapse of a triangular circuit during network decay.

The top sketch represents a three-channel loop, composed of three quadruple junctions connected by three channels. When the threecircuit collapses, under the force of surface tension, Figure 7b, there exists momentarily a single junction from which six channels emerge. This is an unstable configuration which, in order to establish equilibrium 109 0 angles, must divide into one composed of two quadruple junctions connected by a single channel, Figure 7c. The number of externally connected channels remains at six throughout this transformation, so that no change in the network structure external to the three channel circuit is called for. But, internally two channels and one quadruple junction are lost. Their elimination requires the average channel to become a little longer, thereby contributing a little more to the total negative curvature of the network, as a whole. The removal of a quadruple junction also increases the negativity of surface curvature by subtracting some positive curvature. In this way, the sintering force is increased by a specific


amount with each step in topological decay.

It will be apparent that the topological mechanism of network decay requires substantial realignment of the channels, as well as some lengthening, first, to close the triple circuit in the course of transformation and, then, to reestablish a balance of surface forces in which the 109 0 angles are resumed. Each topological event destroys the stress equilibrium locally and sends out a wave of readjustment throughout the system. The result can be seen in the microstructure, where the spacing of the porosity increases progressively, but the pattern of distribution remains the same. Such change necessitates a rather large transport of material. Recent studies by S.S. Chang9 have indicated that this requirement is satisfied mainly by gaseous diffusion in the channel network, as was suggested in the original paper on the topological model l .

Geometrically, an increase in density can be realized only by moving the particles bodily together. The result of such contraction is a shortening of the channels. In the network, each channel has an unbalanced lengthwise tension which can act to shorten the channel by conical shear. The system must contract in concert, else the shortening of anyone channel would be obstructed by the failure of connecting channels to do likewise. Thus, densification follows the reestablishment of surface equilibrium and occurs only to the extent that the curvature is increased by loss in connectivity. As the density increases, the cross sectional area of metal, against which the stress must operate, becomes larger, requiring an ever increasing sintering force to overcome the rising resistance to creep.

It may now be asked, what process holds the overall control of the rate of densification? The mechanism has its origin in the existence of three-channel circuits, which tend to collapse spontaneously, under the influence of surface tension, implemented by diffusion. The rate of diffusion is not fixed, because it must increase as the circuit is shrinking, becoming catastrophic as final closure is approached. Relief of the curvature imbalance, created by this event, is expected to begin rapidly and taper off as the wave of adjustment spreads. Only in the sense that the same pattern is duplicated at each site of topological transformation, can the diffusional transport be considered regular. With approaching equalization of the surface stress the sintering force rises and the pore volume is reduced by contraction in creep. The volume change is proportional to the volume of one topological unit, composed of two channels and one connecting four-channel junction. The creep rate is throttled by the sintering force, accelerating, or deccelerating, according to the degree of lead of this force. Since the change in the sintering force depends on the change in connectivity, which in turn is paced by diffusion, it follows that the process, as a whole, should be controlled by the rate of diffusion. This conclusion is hardly surprising, because sintering has long been recognized as a


process having the thermodynamic characteristics of rate control by diffusion. The factor which is new is the interconnection between structural evolution under the control of diffusion and densification through creep, provided by topological decay of the pore network.

It has already been mentioned that the channel network exists as a system of shells (or baskets) that enclose each original powder particle, Figure 4, and that these have been likened to the net of edges and facets that enclose the grains of a po1ycrysta11ine aggregate. As the elimination of triangular facets results in grain growth, so the elimination of three-circuits will cause some particles to disappear while others grow. The final event in the elimination of a particle may be imagined to occur when a particle is reduced to enclosure by a shell composed of four three-circuits, Figure 8a. This is a tetrahedral form which is capable of spontaneous collapse. Two paths are available. Either a three-circuit may close, whereupon the remaining structure is unstable, Figure 8b, and will go to a simple quadruple junction, Figure 8c, or a channel may break, being too long for its diameter, Figure 8d, and the unstable configuration will go to a simple quadruple junction, Figure 8e.

In this way the particle size of the system can grow as the channel network decays. This gives rise to an appearance of the microstructure in which the pores seem to maintain the same distribution pattern while their number diminishes. This is suggestive also of a characteristic of polycrysta1s, where the number of facets is proportional to the relative grain volume. Before the channels have disappeared altogether, there comes a third stage of sintering in which some of the porosity is observed to be isolated, often as spherical cavities. Speculation on the mechanism of pore isolation has taken the form of a catastrophic rupture of channels that have become too long to be stable. This idea is supported to some degree by the expectation, derived from ano10gy with po1ycrysta11ine aggregates, that the channels tend to maintain a common length and so might become unstable almost simultaneously.

SUMMARY

Second stage sintering is that interval during which the connectivity (G = B - K + 1) of the channel-pore network is undergoing decay through the stepwise loss of branches and nodes. With the occurrence of each step in this sequence, there is (for a given system) a specific reduction in pore volume and in surface area (in the ratio VV/SV)' and a specific increase in the sintering force and in the negativity of surface curvature, which are connected by the relationship (F/a = y MV·VV/SV). This fixed pattern of change is driven by the coordinated action of two processes, both of which are energized by the surface tension (y) and paced by the change in connectivity (G). One of these processes is a minimization of surface area,

CHANNEL NETWORK DECAY IN SINTERING

remove this triangle

/ a

Unstable

b

I particle gone

e

Figure 8. Illustration of two possible paths of the collapse of a tetrahedral circuit during network decay.

59


effected by the diffusional transport of matter from higher to lower energy sites, as distinguished by their curvature. The other is a minimization of pore volume by plastic creep acting to the limit that is set by the sintering force as opposed to the existing solid-pore ratio.

The mechanism of topological decay in sintering is similar, in most respects to other topological network decay processes, such as polycrystalline grain growth, in which surface tension provides the driving force. The branches of the network meet at each node in groups of four, standing at mutual angles of 109°. The network may be regarded as being composed of many circuits, composed of closed loops of branches, ranging upward from three-branch circuits. Threebranch circuits are special in the fact that they are the simplest that are relatively stable and also in the fact that they are the only circuits that can collapse spontaneously with a monotonic loss of surface area. When they do so, they subtract branches from more complex circuits, creating, on the average, one new three-circuit for each one collapsed. With each such collapse, two branches and one node are lost and the connectedness is decreased by one. When the branch angles have readjusted throughout the system, the average branch length will have been increased slightly and with it the negativity of curvature. In this way the sintering force is increased, activating creep, which reduces both the pore volume and surface area toward their new values consistent with the new connectivity.

As circuits are removed from the net in this way, the shells become simpler, on the average, and an occasional shell may be reduced to a mere tetrahedon, enclosed by four three-circuits. At this stage the shell is subject to total collapse. removing one particle from the system and leaving the average particle a little larger. If repeated indefinitely, this process would culminate in the elimination of all but one particle, which would be ideally dense. In fact, however, second stage sintering is overtaken by a third stage in which much of the porosity becomes isolated. The mechanism by which the network is broken into separate pores has yet to be elucidated.

ACKNOWLEDGEMENT

The authors are grateful to the International Copper Research Association whose sponsorship fostered the development of the concepts presented in this paper.

REFERENCES

1. F.N. Rhines, A New Viewpoint on Sintering, Trans MPA (1058):91-101; Plansee 3rd (1958).

2. G.J. Kuczynski, Self Diffusion in Sintering of Metallic Particles,


Jnl. of Metals 1 (2) (1II):169-l78 (1949). 3. R.J. Duffin, R.A. Meussner and F.N. Rhines, Statistics of Parti

cle Measurement and of Particle Growth, Carnegie Institute of Technology, Technical Report No. 32, CIT-AF8A-TR32 (April 1, 1953).

4. C.A. Saltykov, Stereometric Metallography, Moscow (1958). 5. R.T. DeHoff and F.N. Rhines, Quantitative Microscopy, McGraw Hill,

New York (1968) 316. 6. R.T. DeHoff, R.A. Rummel, H.P. LaBuff and F.N. Rhines, The Rela

tionship Between Surface Area and Density in the Second Stage of Sintering, Modern Developments in Powder Metallurgy, Vol. 1, Fundamentals and Methods, Plenum Press, New York (1966) 301-331.

7. R.T. DeHoff and E.H. Aigeltinger, Quantitative Determination of Topological and Metric Properties During Sintering of Copper, Met. Trans. 6A:1853-l862 (1975).

8. R.A. Gregg and F.N. Rhines, Surface Tension and the Sintering Force in Copper, Met. Trans. i:1365-l374 (1973).

9. F.N. Rhines, R.T. DeHoff and S.S. Chang, Progress Report to INCRA (1978-1981).

10. F.N. Rhines and K.R. Craig, Mechanism of Steady State Grain Growth in Aluminum, Met. Trans. 5:413-425 (1974).

THE APPLICABILITY OF HERRING'S SCALING LAW TO

THE SINTERING OF POWDERS

H. Song and R.L. Coble

Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139

R.J. Brook

Department of Ceramics University of Leeds Leeds, England

I. INTRODUCTION

Herring's scaling law(l)considers the particle size dependence of microstructural change, and notably of sintering during the processing of power compacts. On the basis that the driving force, transport path length, transport area and the volume to be transported are proportional to R- 1, R, R2, and R3, respectively, where R is the particle size, the times for equivalent geometric change among particles of different sizes can be formulated as:

(1)

where subscripts 1 and 2 represent two different powders of initial particle size Rl,Q and R2,Q, respectively, and m is an integer. When particle size ratio is maintained throughout the sintering process, the integer m corresponds to a certain transport mechanism (i.e., m = 1: viscous flow; m = 2: evaporation and condensation; m = 3: volume diffusion; m = 4: surface diffusion or grain boundary diffusion).

Owing to the general approach used in its derivation, the scaling law has several advantages over the more specific analytical models which have been commonly used to determine transport mechanism on the basis of different time dependences. It can, for example, be applied

63

64 H. SONG AND R. L. COBLE

to any shape of powder and to the intermediate and final stage as well as to the initial stage of sintering because it does not contain any geometrical detail in its derivation. As a consequence, the law is potentially one of the most reliable guides to mechanisms and to process control (particle size selection) in sintering.

In considering the range of conditions for which the law may be applied, a number of aspects that stem directly from the derivation can be identified. Thus the law required (i) that the particle size ratio in the two compared systems remain the same throughout their respective microstructural changes. In addition, it is assumed (ii) that the form of microstructural change, e.g.,particle shape change or particle coordination number change, remain similar in the two systems. It is also required (iii) that the transport coefficients be similar, i.e., comparable system chemistry and finally (iv) that, for the observation of simple integral values of the exponent, a single mechanism dominate the transport processes throughout the microstructural change.

In this study, the applicability of the law has been examined with respect to the pressureless sintering of different alumina powders. In making the comparison, emphasis has been given to powders of different size and different shape, the system chemistry being held constant.

II. EXPERIMENTAL

Two commercial powders (Norton 38-900 and Alcoa A-17) were used as starting powders. The Norton powder was separated into several particle sizes using an air classifier (Acucut (R) Model A12, Donaldson Co). The sized powder fractions were passed through a plasma arc torch in which the starting particles of irregular shape were changed into spheres. Owing to the coalescence of particles during the fusion process the spheroidized powders were subsequently sized by gravitational sedimentation in distilled water as a dispersion medium. During sedimentation, a small amount of hydrochloric acid was added to the medium to obtain the proper pH (-3) for dispersion. For the irregular shaped powders, different compacting pressures (5,000 and 30,000 psi for the 11.7 and 3.0~ powders, respectively) were applied to obtain compacts of the same green density. For the spherical shaped powders, 30,000 psi was used for compaction for all sizes. The compacts were then sintered at 16000 C in an air atmosphere. The heating and cooling rates were 50oe/min., except each specimen was held for 20 minutes at 6000 e to remove the organic compacting aid. Bulk densities of sintered compacts were measured using the Archimedes method. The sizes of the powders were measured by sedimentation (Sedigraph, Micrometritics Instrument Co.).

A slightly different procedure was employed for the Alcoa powders. The starting powder was sized by gravitational sedimentation in isopropyl alcohol. Sized powders were calc.ined at 4000 e for 24 hrs.

HERRING'S SCALING LAW TO SINTERING OF POWDERS 65

to remove the dispersing agent. Depending on the particle sizes such as for the Norton irregular shaped powders, different pressures (5,000, 35,000 and 55,000 psi for the 2.2, 4.6 and l.l~, respectively*) were applied to obtain the same green density (0.54). The compacts were sintered at 15500 C in a hydrog~n atmosphere. The heating and cooling periods were less than 5 mins for each sample. The sizes of the different powders and average grain areas on fractured surfaces of the sintered compacts were measured with an automatic image analyzer (Magiscan 2, Joyce-Loebl Co.). The av~rage grain size (G) was determined from the measured average area (A) by the relation(2):

G = 2.239 (A)1/2 (2)

following the procedure for polished surfaces. The sizes of powders were also measured by sedimentation for comparison with the result of the image analyzer.

II. RESULTS

1. Particle Size

The results of size measurements for Norton and Alcoa powders are summarized in Table I. Table II. shows the corresponding size ratios which are actually used in interpreting the scaling law experiments. In Fig. 1 and 2 scanning electron micrographs of the irregular and spherical shape Norton powders and three sized Alcoa powders, respectively, are shown.

In order to obtain an accurate value of the exponent of the scaling law, the particle size should be determined correct~. The result of Table I shows that the measured particle sizes and their distributions depend on the technique and parameter used. The discrepancy comes from the irregular shape of the powders, which can be one of the important sources of error when evaluating the exponent. In the present study, the particle size as measured by areas was used for comparison with the grain sizes in the respective sintered compacts.

2. Evaluation of the Exponent of the Scaling Law

The densification rate was not affected by the particle shape for the coarse Norton aluminas as shown in Fig. 3. However, the densification rate of coarse powders was so slow that the exponents of the scaling law could only be calculated for a limited range of the property (i.e. bulk density) under the given experimental conditions. When the exponents of the scaling law were calculated from the best fitting curves of Fig. 3, the values of exponents approached each other to the value about 3.5. The result (Fig.4),

* Note: TIle pressure sequence needed is not monotonic with the size sequence.

Fig

. 1

. S

can

nin

g ele

ctr

on

m

icro

gra

ph

s o

f N

ort

on

3

8-9

00

(a

) siz

ed

in

to

a siz

e ra

ng

e o

f 1

1

-1

5 ~

an

d

(b)

afte

r p

lasm

a

arc

fu

sio

n

(l,O

OO

x)

A1

20

3

Ol

Ol

I en

0 z G) » z 0 ;II :- n 0 OJ r m

Fig

. 2

. S

can

nin

g ele

ctr

on

m

icro

gra

ph

s o

f th

ree siz

ed

A

lco

a p

ow

ders

(a

) fi

ne

(b)

med

ium

(c

) co

ars

e

I m

:0

;;!

Z

Gl en

en

(") ~

r Z

Gl r ~ :E -I

o en

Z

-I

m

:0

Z

Gl o "T1

."

o :E o m

:0

en

en

'-I


Table I. Particle Size Distributions of Sized Powders

Powderl Sedimentation Technique (llm)

A1coa* F M C

Norton** IC IF SC SF

1.1±0.2 2.2±0.6 4.6±1.0

11.7±4.3 3.0±1.1

12.0±3.8 4.8±2.2

Area

0.85±0.26 1. 54±0. 49 3.88±1.01

Image Ana1ysis***(llm)

Length

1.14±0.27 1. 91±0 .63 4.93±1.46

Breadth

0.83±0.20 1.39±0.41 3. 59±1. 06

Perimeter

1.14±0.43 1. 72±0 .56 4.25±1.17

* F,M and C are fine, medium and course powders, respectively. ** IC,IF,SC and SF are irregular coarse, irregular fine, spherical

course and spherical fine powders, respectively. *** The diameters of the particles were converted from the measured

average area (A), longest dimension (L), shortest dimension (B) and perimeter (P).

Table II. Particle Size Ratios of Sized Powders

Ratiol Sedimentation Image Analysis technique

Area Length Breadth Perimeter

Alcoa M/F 2.0 1.8 1.7 1.7 1.5 c/M 2.1 2.5 2.6 2.6 2.5 C/F 4.2 4.6 4.3 4.3 3.7

Norton Ic/IF 3.9 SC/SF 2.5

however, showed different tendencies; for spherical shape powders the value of exponent decreased with densification and for irregular shape powders the value of exponent increased with densification (with no correction for any grain growth that might have occurred during densification).

For the Alcoa a1uminas which had smaller particle sizes than those of Norton a1uminas, the exponent of the scaling law could be calculated for a wider range of density changes. In this instance, the logarithm of density change versus the logarithm of sintering time was plotted as shown in Fig. 5. Fig. 5. shows that the slopes of two of the powders, M and C. are the same within the error range,

HERRING'S SCALING LAW TO SINTERING OF POWDERS

J.6

• spherica I powders

X irregular powders

= ::I 2.4 '"

2.0

20 40 60 Time(hrs)

80 100 120

Fig. 3. Bulk density in Norton aluminas compacts with sintering time. The compacts were sintered at l6000 C in air.

.., c C1I c o a.

4.5

4.0

• spherical x irregular

~ 3.5

3.0

2.5 2.6 2.7 2.8 Bulk Density(g/cm

Fig. 4. Change of the scaling law exponent with densification.

69

70 H. SONG AND R. l. COBLE

but that the slope for powder F is much smaller than those of powders M and C. It is often observed that a different transport mechanism dominates the sintering process depending on the particle size. In this case, the slow kinetics observed in compacts made by powder F may well be due to the different stage of sintering. Because the bulk density of the first data point of powder F is at about 90% of the final density, the sintering geometry of powder F probably corresponds either to final stage or to the transition from intermediate stage to final stage.

~ ... !

'.2. / . •

/: y. o.u.: - o.o~

!

• /II: 'I • 0.2'. - 0.)1

-0.2

/

- 0 .4 . .

L.OQ t ,,",ln~.}

c: 'I .. 0.25,: - J.02

,.: le;(p - Fo) II: 110 t

Fig. 5. Bulk density change in Alcoa alumina compacts with sintering time. The compacts were sintered at 1,550oC in HZ'

tble (:II tcY' rains.) far C(J:)

10 "

12

10

. .

Fig. 6. Grain growth in alumina compacts with sintering time. Notice two different scales of x-axis.

When the two data sets follow straight lines and are representative of the same stage, the average value of the exponent in the scaling law can be calculated from the intercept of the lines. At the same value of density change the logarithm of the time ratio for two powders of different size is:

~t2 intercept 1 - intercept2 log

slope (3)

The expression for the logarithm of time ratio can be obtained from Herring's equation (i.e., Eq.l) as:

log (4)


The value of the exponent was found to be 4.7 following the above procedure. The same procedure could not be applied to the Norton aluminas because the values of the slopes were different in the same tyre plot as Fig. 5.

71

The grain sizes at various densities were measured for the Alcoa samples and the result is shown in Fig. 6. The experimental results cannot be fitted with the customary power law for grain growth:

G n + Kt o

(5)

where G and G are the grain sizes of the sintered and initial materials, n ~s an integer, K is some constant, and t is the sintering time. As a result, continuous comparison at various densities was not possible; however, the ratio of grain sizes could be obtained at densities of 2.65 g/cm3 and 3.20 g/cm3 (refer to Fig. 5) because at those densities the data points of both powder M and powder C were measured. The ratio of grain sizes at 2.65 g/cm3 was 2.5 which was the same as that of the loose powders. However, the ratio was increased to 4.0 at the bulk density of 3.20 g/cm3 • In this case, the error caused by the conversion factor from the twodimensional fractured surfaces to three-dimensional grain sizes can be neglected because at the same porosity level the conversion factor can be assumed to be the same.

IV. DISCUSSION

The results obtained with the alumina powders lead to two conclusions, namely, first that the value of the scaling law index varies with densification especially for the early stage of densification, and secondly that high, non-integral values of the index are found with powders of narrow size distribution for the class.

In seeking an explanation for these findings, it is helpful to review some of the circumstances that can cause deviation from simple values of the index. These are considered in the following paragraphs.

1. Variations in Driving Force: Hot-Pressing

The scaling law was derived for changes driven by surface energy reduction, the driving force being then dependent on particle size according to a term of the order y/R where y is the specific surface energy for the system. In hot-pressing, the applied pressure adds to the driving force a term which is independent of the particle size leading to a total driving force of the form (3)

f(y/R) + g(a ) a


where 0a is the pressure applied to the system during hot-pressing. As a consequence, under conditions where the driving force arises predominantly from the applied pressure rather than from the surface energy term, the driving force becomes constant rather than proportional to R-l. The value of m accordingly changes. Under conditions of low pressure hot-pressing, say 10 MPa where both applied pressure and surface energy reduction make significant contributions to the driving force, intermediate and density dependent values of the index m may be expected. Note, however, that the index takes values lower than those for pressureless sintering by the same transport mechanism, (e.g., <3 for volume diffusion) during hot pressing. Therefore even were it used,hot pressing would not explain high (experimental) values of the index.

2. Interface Controlled Processes

Under certian circumstances, interface reactions (i.e., formation or annihilation of vacancies at the neck surface or at the grain boundaries) may control the sintering process. For such cases the scaling law can also be applied if the dependence of the driving force on particle size is known. The only modification required is that the dependence of the transport path length on the particle size be then omitted in these cases.

In crystal growth(4) and creep(5,6) processes where the controlling step is the interface reaction, the rate of the process is related to the driving force, D.F. by (DF)l or (DF)2. Assuming that the same relationships hold for sintering, the index 2 is obtained with linear D.F. and 3 with parabolic D.F. However, owing to the threshold stress which is usually found in interface reaction controlled processes, index values may deviate from the values (two or three); higher values of the index are to be expected. When the two particles sizes being compared lead to driving forces (-y/R) respective}y, above and at or below the threshold value, the index goes to infinity.

3. Simultaneous Densification and Grain Growth

Where the scaling law is being applied to microstructural change in the form of density change, changes in grain size arising from simultaneous grain growth can undermine one of the main assumptions behind the law, namely, that the particle size ratio remains constant throughout processing in the systems being compared. Grain growth is such a general occurrence during sintering that the impact of growth on the scaling law index deserves closer analysis.

Following the formulation adopted by Herring, the total material flow in infinitesimal time dt is

flow(t) = flux(t) . area(t) . dt (7)

where the t in parenthesis means that the given quantities are


functions of time. The corresponding geometric change is proportional to flow/G3 because the volumes to be transported are given by aG3 where a is a constant which includes a shape factor. Therefore, for an equivalent geometric change in two systems, 1 and 2, the following equation is valid:

(8)

where tl and tz are the elapsed times for the change in systems 1 and 2, respectively.

The grain growth effect can be taken into account by way of the customary power law given in equation (5). A grain growth law of this form has been commonly observed experimentally and normal grain growth models have shown that a variety of mechanisms lead to laws of this form with n taking integer values. (7,8) If the case where the flow leading to densification occurs by volume diffusion is examined as an illustrative example, Eq. (8) reduces to:

dt (9)

In this equation, the common factors such as volume diffusivity and shape factor have been eliminated from both sides. When the exponent n in Eq. (5) is 3, Eq. (9) becomes:

(10)

which upon integration, gives

(ll)

This result is the same as the original Herring equation. It is also found that when densification flow occurs by grain boundary diffusion the exponent in the grain growth law is 4. In this general case, when the absolute values of the powers in the integrand of Eq. (8) and in the grain growth Eq. (5) coincide, the scaling law is obeyed and can be extended to sintering with simultaneous grain growth. Physically, this case corresponds to such a rate of grain growth in the two systems, that although the grain sizes are changing with time, the size ratio is constant at comparable degrees of microstructural change (densification). The assumption made by the law is accordingly obeyed.


Returning to the case of densification by volume diffusion, and considering those instances where the exponents n in Eq.(5) have values different than 3, if is found that the time ratio does not follow the scaling law given in Eq. (11). Using the general value n, Eq. (9) becomes:

which after integration, results in:

(G n+kt {n-3)/n_G n-3 = (G n+kt )(n-3)/~G n-3 1,0 1J 1,0 2,0 2 2,0 (13)

In order to assess the significance of this for the applicability of the scaling law, Eq. (11) is modified to:

(14)

Using the relationships

A > 1 (15)

k~ (16)

(17)

Thus the value of x in Eq. (14) represents the exponent of the scaling law that would be calculated if the original grain sizes were used in making the comparison of the process times. Fig. 7 shows the exponent x plotted as a function of log (t1) for various n values. The initial condition used is A = 2.5 and each curve in the plot corresponds to a certain value of k~. (See appendix) Thus the grain growth constant k for each curve can be calculated by Eq. (16) using the initial value of G1 O.

Several trends may be recognized from'Fig. 7. If x-3 is defined as the error, namely, as the extent to which the index departs from the value expected in the absence of grain growth that the sign of this error is positive when n < 3 and is negative when n > 3. As expected, the error increases as the value of In-31 increases. The error is also very sensitive to the value of k except when n ~ 3. The error goes to zero at small k where the assumption of the scaling law is then approximately met. The error is also a function of the initial particle size ratio, A, as shown in Fig. 8, although the dependence is not as strong as on variations in n or k.


n = 3.5 n = 3 .01

6

X- x - 4 ~ 4 ., " 10-7 " OJ k' OJ k' 10- 5

" " 0 ] &.3 '" x x

105 '" '" k' 2

k' = 105

2 2 6 7

L09(t1' (sec. , L09(t1 ' (sec . )

n . 2 . 99 n = 10 - 4

6 6

5

x X-- 4 - 4 .....

105 .... c k' " ., ., c " &. 3

10-5 0 3

10 - 8 k' '" k' x

'" x '" 2 2

2 6 7 5 6 7

Log ( t 1 ) (sec.) Log(t1 ) (sec . )

Fig 7. Variation of exponent (x) with sintering time (tl) of system 1 for various nand k .... Successive lines represent one order of difference in k ....

76

Fig. 8.

H. SONG AND R. L. COBLE

• s l • 10

Variation of exponent (x) with sintering time (tl) in system 1 for various A values. In each plot k~ = 10 3-10-7 (from top line to bottom line), and n = 2.9.

., e

6

5

n= ~=2.5

~ k'

~ 3 ~::~==============::::::::::: '"

2

~~~~ii~iiii~~~~~~~k' 105 . 5 . 7 .9

Relative Density

Fig. 9. Variation of exponent (x) with densification.


A final trend is that the error depends on the span of microstructural change examined (as measured by the parameter t), being least when very small changes can be observed. To emphasize this meaning of the x axis, tl can be converted into equivalent density changes if a particular system is considered.

In Fig. 9 the case of A1203 is represented with densification assumed to occur by volume dittusion and grain growth assumed to occur by pore drag controlled by surface diffusion (i.e., n = 4). The initial green density is taken as 50% of the theoretical density, and the density change is calculated according to the intermediate stage sintering model(9) proposed by Coble:

6p t (18)

Here 6p is the change of density observed, D is the volume diffusivity, 0 is the molaO volume, R is the gas constant and T is the temperature; T = 1600 C and GO = 5jJm are assumed for Fig. 9. Since the model for Eq. (18) is derived on the basis of zero grain growth, the time t given by Eq. (18) corresponds to an ideal minimum time required to achieve the given density change.

Using this approach, the error can be presented in terms of the extent of microstructural change (6p) used in measuring the index. Furthermore, the range of experimental conditions over which the ideal scaling law indices may be reported can be obtained by way of Figs. 7,8, and 9 coupled with an experimentally determined k value for the material .and conditions of interest.

To summarize, the changes in the scaling law exponent in the presence of grain growth are dependent on

1) the relative exponents for grain growth and the scaling law, i.e., the mechanisms involved,

2) the rate of grain growth, 3) the span of microstructural change observed, and 4) the initial particle size ratio. In terms of the present findings, the high values that have been

experimentally determined would require a lower grain growth exponent than the ideal index value, e.g., lattice diffusion controlled pore drag and grain boundary diffusion controlled sintering. The form of expected curve is, however, not in convincing agreement with the data, and it would be premature to propose simultaneous grain growth as the only basis for the observed results.

4. Absence of Comparability

This includes such factors as different chemistry, different particle coordination, different mechanisms, different particle shapes (depending on the particle size) all of which c.an cause departure from the simple law. Generally, in planning experiments, the attempt is made to avoid those factors such as by use of ~owders


from the same precursor, by the use of similar green densities, and by the use of narrow spans of microstruct.ural change and small values of the particle size ratio. These are not trivial as experimental problems.

V. CONCLUDING REMARKS

The values of the scaling law index that have been measured for alumina are high, a finding which in principle can be explained in a number of ways as, for example, by simultaneous grain growth where the grain growth exponent is less than the expected index or by interface reaction controlled processes where a threshold for the driving force is encountered. The choice of possible explanation is suf.ficiently wide that a clear identification of the controlling factor cannot be made with confidence for the present results. However, the discussion has identified the conditions and experimental circumstances that define some effects of grain growth on the expected results when using the scaling law and the most likely sources of error if those factors are ignored.

VI. APPENDIX: ESTIMATION OF THE EXPERIMENTALLY OBSERVABLE RANGE OF k~

The power law for grain growth given in Eq. (S) can be expressed in terms of k~ (Eq.(lS» by dividing both sides of Eq. (S) with G n as

o

= t,

which is then identical with

by the definition of k~. Therefore, if the experimental limitations of the grain size

ratio and sintering time are given, the observable range of k~ can be estimated by the above equation. For example, if the experimental limitations are:

10 3 > GIGo> 1.1 24 hrs > t > 1/2 hr

then i) when n 3.S k~min S x 10-6 (sec-I)

k~max 2 x 10-7 (sec I )

ii) when n 2.S k~min 3 x 10-6 (sec-I)

k~max 2 x 101+ (sec-I)


ACKNOWLEDGEMENTS

This work was supported by the U.S. Dept. of Energy under Contract No. DE-AC02-76ER02390.

REFERENCES

79

1. C. Herring, "Effect of Change of Scale on Sintering Phenomena", J. Appl. Phys. 21, 301 (1950).

2. N.A. Haroun and D.W. Budworth, "Effects of Additions of MgO, 2nO and NiO on Grain Growth in Dense Alumina",Trans. Br. Ceram. Soc. 69, 73 (1970).

3. R. L. Coble, "Diffusion Models for Hot Pressing with Surface Energy and Pressure Effects as Driving Forces", J. Appl. Phys. 41, 4798 (1970).

4. W.B. Hillig and D. Turnbull, "Theory of Crystal Growth in Undercooled Pure Liquids", J. Chern. Phys. 24, 914 (1956).

5. M.F. Ashby, "On Interface-Reaction Control of Nabarro-Herring Creep and Sintering", Scripta Met. 3, 837 (1969).

6. B. Burton, "Interface Reaction Controlled Diffusional Creep: A Consideration of Grain Boundary Dislocation Climb Sources", Mat. Sci. & Eng. 10, 9 (1972).

7. F.A. Nichols, "Theory of Grain Growth in Porous Compacts", J. Appl. Phys. 37, 4599 (1966).

8. R.J. Brook, "Controlled Grain Growth", Treatise on Materials Science and Technology, 9, 331. Edited by F.F.Y Wang, Academic, New York (1976).

9. R.L. Coble, "Sintering Crystalline Solids 1. Intermediate and Final State Diffusion Models", J. Appl. Phys. 32, 787 (1961).

ON THE MECHANISM OF PORE COARSENING

ABSTRACT

D. Kolar*, G. C. Kuczynski and S. K. Chiang

Department of Metallurgical Engineering and Materials Science University of Notre Dame Notre Dame, IN 46556

Pore coarsening, frequently observed during sintering, is usually regarded as a consequence of pore migration with the grain boundaries. Experimental observations on grain growth and pore coalescence during heat treatment of copper, reported in the present 'work, however support the conclusion that the major mechanism of pore coarsening is Ostwald ripening by a grain boundary diffusion process rather than grain boundary controlled pore migration.

1. INTRODUCTION

Heat treatment of porous bodies generally results in pore shrinkage and average pore size growth. Two basic mechanisms are postulated for pore growth, i.e. pore coalescence by migration of pores with the grain boundaries (1-3) and pore coarsening due to the difference in curvature between small and large pores (Ostwald ripening) (4,5). Theoretical treatments of ceramic microstructures usually assume pore coalescence by a grain boundary drag mechanism (6). However, experimental evidence of pores being moved with the grain boundaries is ambiguous. Microstructures of sintered specimens do not allow differentiation between coalescence and Ostwald ripening mechanisms.

The present work was undertaken to supply experimental evidence of the mode of pore coarsening in the intermediate and final

* On leave from E. Kardelj University, Ljubljana, Yugoslavia.

81

82 D. KOLAR ET AL.

stage of the sintering process. To achieve this goal, artificial grain boundaries, with numerous pores, were created. These grain boundaries were easily distinguished from other microstructural features, enabling the study of their characteristics after various heat treatments.

2 . EXPERIMENTAL

Artificial grain boundaries were produced by swaging copper wire of initial diameter 1.59 mm inserted in a copper tube of slightly larger diameter. The copper was of OFHe purity. Swaging was done in several steps with intermittent annealing at 800°C for 1 h. In the final swaging step, sample diameter was reduced by 28% and 37%, respectively. The annealed samples (1 h, 800°C) were heat treated for periods ranging from 0.5 hour to 40 hours in purified argon atmosphere. After heat treatment, the samples were sectioned and polished for microstructural examination.

3. RESULTS AND DISCUSSION

Fig. 1 shows a cross section of a sample after annealing at 800°C for 1 h (a), and then heated at 1050 0 e for 5 hours (b). Annealing after swaging resulted in recrystallized structure with a clear boundary between the central wire and the tube. Some of the pores in this artificial grain boundary are not yet "spherodized" and are visible as elongated cracks. These cracks break up into discrete pores which spherodize after high temperature annealing as depicted in Fig. 2. Heat treatment at higher temperature (5h, 10500 ) caused grains to reach the size of several hundred ~m. The position of the original grain boundary between the wire and tube is still clearly visible, although in some places the grain boundary has moved away from the original position, leaving the pores behind at their original locations. The pores visible in metal outside the artificail grain boundary resulted from recovery of the heavily cold worked tube on annealing.

The microstructure examination of samples heat treated under various conditions strongly indicates that the grain boundary moves after being detached from the pores and the pores are not dragged by them. This can be seen in Figs. lb, 3a, 3b, 4a, and 4b. This conclusion does not necessarily contradict the pore coalescence theory because it could be argued that all cases observed are in the detachment field of Brook's diagram (8). If so, the pore coalescence process should occur on very rare occasions.

The photomicrographs reproduced in Fig. Sa show the deformation of a pore from which a grain boundary is just being detached. It seems that during this process the dihedral angle is preserved. In Fig. 5b, a pore just after detachment, already assumed spherical

MECHANISM OF PORE COARSENING 83

.. ' ,. , .~ .. • .. .. ,

I . • ,

'" I

• • J

" ." '. • , ." , ... .:..~ .. ' .. -'.

a b

Fig. 1. Cu wire in Cu tube reduced 27% by swaging, a) annealed at 800°C for 1 hr X50, b) after annealing at l050°C for 5 hr X50.

:/---.... , ,

/

. \ "

... ~ - ,.-."".' ......... -.... ..

~

I I

\

i t

I

• I

Fig. 2. Breaking up of elongated pores after annealing at l050 0 C for .5 hr X50.

84

\

. .

I

.-.

. '.

a

D. KOLAR ET AL.

• ..

• .' ....

b

Fig. 3. Cu wire in Cu tube prepared as the specimen in Fig. 1, then annealed at 10S0°C for 5 hrs. a) XSO, b) XIOO •

. .

a

. ~

' . ..

•• • ••

, .'

• • •• • .~

b

Fig. 4. Cu wire in Cu tube prepared as the specimens in Figs. 1 and 2, then annealed at lOOOoC for 40 hrs. a) XSO, b) X200.

MECHANISM OF PORE COARSENING

a b

Fig. 5. Pores at or near the grain boundary on the specimen swaged and annealed at 10000e for 20 hrs. a) before grain boundary .detachment from the pore X200 • b) after detachment X600.

Fig. 6. Lenticular pores on the grain boundry after annealing at 950 0e for 100 hrs. X400.

85

86

Fig. 7.

D. KOLAR ET AL.

a b

Pores originally in the artificial grain boundary annealed at a) 950°C for 40 hrs. X50, b) 1050 0 C for 5 hrs. X50.

shape, like all pores found inside the grains. The pores located on the grain boundaries have lenticular shape as depicted in Fig.6.

Another observation, documented in Fig. 7 is the coarsening of pores located on the grain boundary. The observed coarsening can not be dU'e to pore coalescence, as the coarse pores usually remain on a grain boundary which does not move. The only cause of their coarsening seems to be Ostwald ripening with the principal mechanism of grain boundary diffusion. The largest pore sizes were observed in samples heat treated for a long time at 950°C, Fig. 7a, when the shrinkage was the smallest. On the other hand, annealing at 1050°C resulted in a smaller pore size, Fig. 7b, a consequence of pronounced shrinkage. It has been estimated that the pores annealed at 1050°C grow with a rate of about 2~m/h, which is about 100 times faster than that of the pores isolated in single crystals, observed by Watanabe, where coarsening was by volume diffusion (7).

It has been argued (1) that Ostwald ripening process of the pores located on grain boundaries cannot proceed by grain boundary diffusion, because the grain boundaries act as effective vacancy sinks, and thus cannot transmit the vacancies from pore to pore. However, this statement based on the premise that grain boundaries act as perfect sinks of vacancies, has been frequently challenged. Ashby (9) postulated interface reaction as a critical step to explain the slowing or inhibition of sintering when a fine disper-

MECHANISM OF PORE COARSENING

sion of particles of a second phase are present, and to account for observation that fine dispersion of a second phase can change the rate of Nabarro-Herring creep. Kuczynski (10) suggested that whereas at high temperatures, near the melting point, the structure of grain boundaries may resemble that of undercooled liquid and therefore act as a near perfect sink of vacancies. At lower temperatures the structure of the grain boundaries resembles that of glass and in such a case, cannot be regarded as a perfect vacancy sink anymore.

87

Thus grain boundaries which are less effective or ineffective to act as vacancy sinks/sources may serve as relatively fast diffusion paths for vacancy transport among the pores which lay on them. Pores growing by grain boundary diffusion will therefore increase in size faster than pores which coarsen by volume diffusion as demonstrated in our experiments.

4. CONCLUSIONS

Using an artificial grain boundary created by swaging a copper wire inside a copper tube, it has been found that:

a) The pores (1-20 )lm diameter) never moved with the grain boundaries attached to them.

b) The grain growth proceeded by detachment of a grain boundary from the pores leaving them inside the grains.

c) At low temperature annealing (950°C) pores coarsened without detectable shrinkage and those annealed at 1050 0 e shrunk appreciably, although they also underwent Ostwald ripening.

d) At 1000°C the pores remaining in the grain boundaries coarsened about 100 times faster than the pores inside the grains.

e) Although the pores in the grain boundaries have familiar lenticular shape, they spherodized rapidly as soon as the grain boundary was detached from them.

REFERENCES

1. W. D. Kingery and D. Francois, Amer. Cer. Soc. ~ (10) 546-47 (1965).

2. F. A. Nichols, J. Appl. Phys. ]2, (13) 4599-4602 (1966). 3. R. J. Brook, J. Amer. Cer. Soc. ~,(l) 56-57 (1969). 4. F. H. Rhines, C. E. Birchenal and L. A. Hughes, Trans. AIME 188,

378 (1950). 5. G. C. Kuczynski, Powder Metallurgy 12, (1963).

88 D. KOLAR ET AL.

6. M. A. Spears, A. G. Evans, Acta Meta11. 30, 1281-1289 (1982). 7. R. Watanabe, K. Tada, Y. Masuda, Z. Meta11kunde ~, 619-624

(1976) . 8. R. J. Brook, pp. 261-275, in Ceramic Fabrication Processes,

edited by F. Y. Wang, Treatise of Materials Science and Technology 9, Academic Press (1976).

9. M. F. Ashby, Scripta Met 1, 837-842 (1969). 10. G. C. Kuczynski, H. Ichinose, Z. Meta11kunde 69, 635-638 (1978).

THE INFLUENCE OF GREEN DENSITY UPON SINTERING

M. A. Occhionero and J. W. Halloran

Case Western Reserve University Cleveland, Ohio 44106

The primary characteristic of a ceramic compact prior to sintering is its green density. The green density obviously determines the amount of shrinkage required to densify a ceramic, but its influence upon the densification rate or the microstructure of the ceramic is not well understood. A full description of microstructure development must include the role of green density. Green density effects are also important in understanding processing-related defects. Green density inhomogeneities on a microscopic scale have recently figured in models of the development of strength-limiting flaws in ceramics [1,2].

According to Coble [3] in the absence of re-arrangement, green density should have no effect upon initial stage sintering kinetics. Experimental data in the literature seems to indicate that early stage sintering kinetics are insensitive to green density if it is sufficiently high, but dependent upon green density in more porous compacts. Greskovich [4] examined the early stage sintering kinetics of an aggregated Linde alumina powder and found no difference in the shrinkage behavior of compacts with green densities between 47 and 50%, but below 45% he observed a decrease in shrinkage rate with decreasing green densities. A similar observation was made by Woolfrey [5] who examined ADU urania powders. In this case the rate constant for shrinkage rate vs. shrinkage was nearly the same for compacts with green densities between 50% and 40%, but the rate constant and shrinkage rate decreased substantially as green density fell below 40%. Related to this is the observation of Bruch [6] that sintering is retarded or "subnormal" if the green density is too low. Bruch also noted a green density effect in the "normal"

89

90 M. A. OCCHIONERO AND J. W. HALLORAN

sintering regime. In the intermediate and final stage of sintering, he found the densification rate to be very strongly dependent upon green density, with the rate of densification slower for higher green densities. This apparent discrepancy with Greskovich and Woolfrey is a consequence of the fact that Bruch is describing the approach to full density of specimens between 90 and 99+% dense. At any particular point in time, the compacts which originally had higher green densities now sinter more slowly because they are nearly fully dense.

If we restrict our attention to the higher green density regime which is of practical significance, the consensus of the literature is that we should expect little effect on sintering kinetics. If we consider microstructural development, however, we would expect an effect of green density upon grain and pore coarsening. In this paper we will concentrate upon the influence of green density, in the range of "normal" sintering, upon pore and grain coarsening during the intermediate stage of sintering.

Green density will affect microstructure development in the intermediate stage if it changes the extend of grain growth during sintering. It is convenient to display this as a plot of average grain size, G, vs. volume fraction porosity, V. The form of this plot can be inferred by noting that the grain size depends upon both porosity and time. The slope of G vs. V must be negative, since both terms on the right hand side of

dG aG I + OG I dt d\l = aV t at V dV

(1)

are negative in the case where the grain size is limited by porosity according to the Zener limit. By evaluating the second derivative one can see the curvature of G with respect to \I is positive.

Therefore one expects a plot of G vs. V to have a negative slope and is convex in shape with respect to the origin. Note G can only be a linear function of porosity if dG2 /dv 2 = a which seems unlikely

Previous observers have noted what appears to be a linear relationship between grain size and density in the intermediate stage of sintering [7-12]. DeHoff et al. [7] explain this linear relationship in a theory which is based on the assumption that for every unit of material transported, M, during densification there is a constant decrease of free energy, ~F.

INFLUENCE OF GREEN DENSITY UPON SINTERING

Succinctly stated, they suggest that

dllF = B dm

Where B is a constant. Unfortunately, the factor B is never a constant for sintering. Let us evaluate B using Gibbs Thompson equation to describe ~F in terms of surface tension y, and curvature K.

lIF = yK

if a quantity of matter, m, is transported this shows that

dllF dm

dK YJm

91

(2)

(3)

(4)

so the alleged constant actually depends upon how the transported matter changes the curvature. For a spherical pore of radius R in a material of density p.

dK _ ( IT R4) - 1 - - -lP dm

(5)

so that the decrease in free energy per unit mass is much greater during the later stpges of sintering. Hence this explanation cannot be correct.

While the data of these observers [7-12] might be perceived as linear in the intermediate stage, a closer examination reveals the slight upward curvature which is expected on the basis of the discussion in the previous section.

Yan, Cannon and Chowdhry (YCC), derived a model for microstructure evolution in which grain size and densification occur simultaneously [13]. The model used for the microstructure was that of Kelvin bodies with spherical pores at all grain corners. This model is a good representation of the final stage microstructure but not adequate for the intermediate stage.

A similar model for the intermediate stage of sintering can be developed by following the procedure of Yan, Cannon and Chowdhry using for an intermediate stage geometry, Kelvin bodies with cylindrical pores at all grain edges. The volume fraction pores in this case is

2 v = 1.06 (f) (6)


Here V is a function of pore radius, r, and pore length, 1, and by geometry is a function of pore radius and grain size, G, [14]. The time derivitive of volume fraction pores is the densification rate:

dv = 2vdG (dlnr -1) dt Gdt dInG

(7)

Densification and grain growth compete in the evolution of a microstructure. Pore size is a function of both grain size and volume fraction porosity. The rate at which a pore size changes can be represented by the total derivitive of pore radius with respect to time

(8)

The first term on the right hand size of eq. (8) describes coarsening, and the second term represents densification. From eq. (7) the grain coarsening term in eq. (8) can be written

and eq. (8) can be re-written

dr _ r OGI + or1 dt - G Tt" v li G

(9)

(10)

Eq. (10) will be solved once the grain growth and densification partial derivitives have been evaluated. As in the Y.C.C. model, to achieve this one must consider specific controlling mechanisms for densification and grain growth.

In the system under investigation (A1203 powder doped with MgO), it is believed that grain boundary diffusion is the major densification mechanism [15]. Using Coble's equation for grain boundary diffusion for an intermediate stage microstructure, and taking the time derivitive of the pore radius, on~obtains

or I _ -2 OgbDgbQrs li IG - 3' ~Tr21 (ll)

for grain boundary diffusion whereOgbDgb is the grain boundary diffusivity, n is the atomic volume, y is the surface energy and ~T is thermal energy and 1 the pore l~ngth [19].


If grain growth is limited by pore mobility [16], and if surface diffusion is rate limiting in the pore mobility, one obtains

OGI 8tv TIGM Y b p g

36

93

(12)

the grain growth rate at constant porosity for the intermediate stage microstructure [17]. Where the pore mobility M is

p

M P

<5 D Q s s

where sDs is surface diffusivity, 6 is the effective diffusion and Y gb is the grain boundary energy eqs. (12) and (13) can be combined

<5GI 8tv TIGy bO D Q g s s

172

using eq. (10) and (13) in eq. (9) yields

dr dt =

TIy bO D Q g s s

and dividing eq. (15) by ~~ and multiplying and dividing both sides by G and r respectively yields

dlnr = 1 _ 2:!!.. dInG aTI

where a is the ratio of coarsening to densifying kinetics

(13)

(14)

(15)

(16)

(17)

The solution to eq. (16) for porosity with respect to grain size is

p 1 - v [Q] -72/ (Ita) o G

o (18)


where Vo and Go are starting porosity and grain size respectively. Equation 19 is except for the value of a of identical form to the Y.C.C. final stage model for the same controlling mechanisms

Different choices of controlling mechanisms yield different expressions, but the general behavior is similar [13]. For the present purposes this one example will suffice.

When the ratio a is small densification kinetics dominates and the microstructure follows a path with little grain coarsening. When a is large grain coarsening kinetics dominate and the microstructure follows a path with little densification. This microstructural behavior is in fact seen in A1203[13,18,19,20], MgO [21] and the data for NaCl [22] shows similar behavior although the mechanisms for densification and coarsening are different. For similar samples under similar firing conditions, differing in green densities one expects the value of a to be the same, since a has no dependence on porosity. These microstructures may however follow different paths for varying green densities involving different Vo values.

Note that in general, a should be temperature-dependent, reflecting in this case the difference in the activation energy for grain boundary and surface diffusion. The consequences of this have been discussed by Y.C.C. [13] and Brook [19].

A similar dependence of grain size upon density in the intermediate stage is predicted from the statistical theory of sintering developed by Kuczynski [9], [23]. For this case the expression describing the pore geometry in terms of volume fraction por~~ity v, pore length per unit volume Lv' and mean square pore radius r .

dlnL dl- 2 _._v_+~ dlnv dlnv 1

is integrated under the condition that the term x defined as

x

(19)

(20)

is held constant. This assumption permits eq. (20) to be integrated to yield an expression which, combined with Zener's relation for the growth of grains of mean size G, predicts that grain si~e varies with porosity as:

%0 (*J«X+l)/2) = 1 (2la)

INFLUENCE OF GREEN DENSITY UPON SINTERING 95

which can be re-written as

p = 1 - VO (%J (-2/(x+l» (2lb)

to compare with eq. (17). Let us note however, that while a in eq. (18) is explicitly a temperature dependent exponent, the statistical theory asserts that x as defined by eq. (21) is independent of temperature.

EXPERIMENTAL PROCEDURE

Two highly sinterable a-A1203 powders* were used to examine the effects of green density on the microstructure evolution. Both powders were sub-micron size with quite narrow particle size distributions. The Sumitomo powder had a stated purity of greater than 99.99%, while the Reynolds powder was 99.7% pure and contained an "optimal amount" of MgO dopant.

Samples were pressed in a 2.54 cm diameter single action steel die an appropriate quantity of powder used in pressing so that samples with various green densities all had a 1:5 diameter to height ratio. All sintering was performed in air using a MoSi2

o furnace at temperatures between 1300 and 1500 C. Specimens were pre-sintered for one hour to facilitate handling during density measurements and SEM examination.

Density determinations were made by both standard water displacement technique and by geometrical measurements.

Grain size determinations were performed by examining fracture surfaces in SEM. At least 50 grains were measured on each fracture surface to determine the average grain size. The 95% confidence interval for each grain size determination were less than ± 20% of the normalized grain size. The initial grain size, G , was determined to be 0.55 ± 0.01 microns for the Reynold~ powder and 0.37 ± 0.03 microns for the Sumitomo powder. These values agree very well with the manufacturer's particle size analysis.

Isothermal dilatometry was used to obtain shrinkage kinetics in the range of 1 to 10% linear shrinkage. The dilatometer featured a high resolution LVDT interfaced with a microcomputer for data acquisition and manipulation. When used in the isothermal mode, the procedure was to thermally equilibriate the specimen and sample tube at 9000 C (where no detectable shrinkage occurred) before plunging the specimen into the hot furnace at the sintering

*Reynolds Aluminum Co. RC-172-DBM, Sumitomo Chemical Co. AKP-30


temperature. Sample heat-up time was approximately 60 seconds. Sintering temperature was maintained within 30 C. Details on the dilatometer apparatus and data analysis software are given elsewhere [17].

Mercury porosimetry was used to examine intrusion pore size distribution using a Micromeretics Model 910 porosimeter. Data was analyzed with the standard Washburn equation.

RESULTS AND DISCUSSION

We used mercury porosimetry to examine the intrusion pore size distribution of Reynolds alumina compacts sintered at l3000 C to produce a range of densities in the intermediate state of sintering. The data for the median pore diameter and relative grain size appears in Table I. Note that median pore diameter changes relatively little as the 49% green density compacts sinter. The median changes from 60 nm in the green compact to 57 nm at 73% density. Apparently in this case, the shrinkage expected from the 24% decrease in pore volume is nearly compensated by the more than 2-fold increase in grain size.

Pore volume frequency curves were obtained by differentiating the non-normalized cumulative volume curves so that the area under the frequency curves is proportional to the total pore volume. Figure 1 displays these distributions for the 49% green density compacts. Notice that the larger pores present in the green compact have mostly disappeared in the 63% dense specimen.

To examine the influence of green density upon pore structure, we have compared the pore size distribution in specimens with identical sintered densities. Figure 2 shows these distributions in three specimens sintered to 67% density at l300 0 C. These specimens were prepared with green densities of 49%, 54%, and 57%. Even though the total porosity is the same for these specimens, the pore size distributions are strikingly different. The specimen which started at the highest green density has a relatively narrow pore distribution centered at small pore size. The specimen with the lowest green density has a much broader size distribution extending to larger pore sizes. Table I includes the median pore diameter for these specimens. Note that the median pore size decreases significantly as green density increases. Relative grain size behaves similarly.


TABLE I

Median Intrusion Pore Diameter of Bayer Alumina Compacts Sintered at l3000 C

Green Densit~ Sintered Densit~

49% 49 63 49 73 lj9 67 54.5 67 57 67

1300'C 14

I:: Ll: !8 > 6 (I)

~4

2

0 01'

Figure 1: Pore distribution in 49% green density compacts sintered at 1300°C. Reynolds powder.

Median Pore Diameter (nm) G/Go(Go=0.55

60 + - 5 51 + 5 57 + 5 50 + 5 46 + 5 39 + 5

30

~"

6

51'11.TO

1 1.45 2.28 2.3 1.5 1.2

p=67%TD 1300·C

]lm

Figure 2: Pore distribution in compacts sintered to 67% density for three green densities. Reynolds powder.


Grain size vs. density data were collected for the Reynolds powder compacts prepared at 493 52, and 54.5% relative green densities and sintered at 1400 C to intermediate stage densities. Sumitomo powder compacts, with 52% green density, were also sintered at l4000 C. Some Reynolds compacts, with 49% green density were sintered at 1300 and l5000 C. These data were plotted as grain size vs. density so that they could be fit the modified YCC model of eq. (18).

Equation (18) requires two parameters, the ratio of kineticfactors, a, and the starting density, po. An attempt to fit this data using the green density for the value of po required a different value of a for each set of data. This is physically unreasonable since a must be only a function of temperature and composition. Instead we fit the data with a single a for each temperature, choosing as the starting density po the value of density at which grain growth commences. Note that this is the same as the starting density that appears in Kuczynski's statistical theory.

Figure 3 shows the data for the Sumitomo powder fit with an a of 20 and a starting density of 70%. Equation (18) represents the data well, reproducing the upward curvature of GIGo vs. p. Unfortunately the grain size changes only a factor of two, over a rather short range of densities, so that this data cannot be used for a convincing confirmation of the model.

3 o

~2 CJ

1

T= 1400·C

p.= 62%10

Po =70%10

Sunitomo Powder

0=20

Q

/ /

/ /

o-----------__ ~------------------

50 60 70 60 90 P %10

Figure 3: Grain size vs. density for Sumitomo compact with 52% green density. l4000 C.


3

T= 1400 ·C

50

RC-l72-DBM

Il. -Sold Points

10 p%TD

a=20

80 90

Figure 4: Grain size vs. density for Reynolds compacts at 49, 52, and 54.5% green density. l400oC.

The same value of a represents the Reynold's powder data at l4000 C as well. Fig. 4 shows the data for compacts with green densities of 49, 52, and 54.5%. Although this range of green densities is quite narrow, there is a clear separation between

99

the behavior of the lower and higher green densities. It is interesting to note that the starting densities po obtained from Fig. 4 increase with green density, being 65, 70, and 75% for green densities of 49, 52, and 54.5%, respectively. This observation suggests that one effect of green density upon sintering is to change the point during densification at which grain growth commences.

The data at 1300 and l5000 C was also fit to the model by choosing appropriate values of a and po. Fig. 5 shows the result.

o The a values at 1300, 1400, and 1500 C were 25, 20, and 15 respectively, suggesting that the relative rates of coarsening compared to densification is somewhat lower at high temperatures. Such a trend is expected since densifying kinetics should dominate at the higher temperatures. It is also apparent from Fig. 5 that the starting density po depends upon temperature. These compacts had the same green density, but the po at which grain growth began was 49% at l300oC, 65% at l400oC, and 70% at l500oC. Apparently coarsening is delayed to significantly higher densities as temperature increases. Notice that fitting the data with different a values in Fig. 5 would correspond to requiring temperature-dependent x-values in Eq. (2lb).

100

3

~2 "

RC-172-oBM

M. A. OCCHIONERO AND J. W. HALLORAN

'/ I

I / / I

/ 14OO"C/ / / a=~ /

~o ///6~~ ~o 0

1 ---_=---0 --------~---------

eo 70 eo 110 P "10

Figure: Grain size vs. density for Reynolds compact with 49% green density at 13,00, 1400, l500oC.

The results of the isothermal sintering kinetics experiments are shown in Figure 6, which shows the shrinkage vs. time for Reynolds powder compacts prepared at 41, 49, 52, and 54.5% green density. Note that there is no difference in the shrinkage behavior of these compacts during the first 8% linear shrinkage. This indicates that the green density range is sufficiently high that sintering kinetics are unaffected by green density.

1ltvE (miMes) 10 1e

12 T = 140dt 41,49%TD

~--*-o

~ 8 52%TD 54.5%TD

4

OIW-~--~~~~~400~~--'800~--~'800~----~I~~--~-J

TM: (seconds)

Figure 6: Isothermal shrinkage of compacts of Reynolds powder at 41-54.5% green density. l400oc.


CONCLUSIONS

The shrinkage rate is independent of green density in the range 49-54.5% green density. The green density affects the pore size distribution during the intermediate stage of sintering. Grain growth vs. density behavior can be adequately described by a Y.C.C. type model. The density at which grain growth commenses depends upon green density. High green density delays the onset of grain growth. Grain size vs. density hehavior is temperaturedependent.

REFERENCES

1. A. G. Evans, J. American Ceramic Soc. 65, (10), p. 497-501 1

(1982) . 2. F. F. Lange and M. Metcalf, "Processing Related Fracture

Origins", J. American Ceramic Soc. (in press). 3. R. L. Coble, J. American Ceramic Soc., 41, (2), p. 55-62,

(1958) • 4. C. Greskovich, Physics of Sintering, 4, (1), p. 33-46, (1972). 5. J. L. Woolfrey, J. American Ceramic Soc., 55, (3), p. 383-

387, (1972). -6. C. A. Bruch, Ceramic Bulletin, 41, (12), p. 799-806, (1962). 7. R. T. DeHoff, R. A. Rummel, H. P. LaBuff, and F. N. Rhines,

p. 310 in Modern Developments in Powder Metallurgy, Vol. I, H. H. Hausner, ed., Plenum Press, N.Y., (1968).

8. F. N. Rhines, R. T. DeHoff and R. A. Rummel, in Agglomeration, p. 351, Interscience Pub 1. , N.Y. (1962).

9. G. C. Kuczynski, p. 217 in Sintering and Related Phenomena, Mat'ls. Science Research, Vol. 6, ed. G. C. Kuczynski, Plenum Press, N.Y., (1973).

10. T. K. Gupta, J. American Ceramic Soc., 55, (5), p. 276-277, (1972). -

11. S. C. Samanta and R. L. Coble, J. American Ceramic Soc., 55, (11), p. 583, (1972).

12. T. K. Gupta and R. L. Coble, J. American Ceramic Soc., 51, (9), p. 525-528, (1968).

13. M. F. Yan, R. M. Cannon, and U. Chowdhry, "Theory at Grain Growth During Densification", discussed in M. F. Yan, Materials Sci. and Engr., 48, (1), p. 53-72, (1981).

14. R. L. Coble, J. Applied Physics, 32, (5), p. 787-799, (1961). 15. D. L. Johnson and 1. B. Cutler, i:---American Ceramic Soc., 46,

(11), p. 545-550, (1963). --16. W. D. Kingery and B. Francais, J. American Ceramic Soc., 48,

(10), p. 546-547, (1965). 17. M. A. Occhionero, M. S. Thesis, Case \{estern Reserve U, (1983). 18. M. F. Yan, unpublished work. 19. R. J. Brook, Proc. British Ceramic Soc., 32, (3), p. 7-24, (1982). 20. D. L. Johnson and I. B. Cutler, J. Americ~ Ceramic Soc., 46,

(11), p. 541-545, (1963).


21. B. Wang and J. A. Pask, J. American Ceramic Soc., 62, (3-4), p. 141-146, (1979).

22. R. J. Thompson and Z. A. Munir, J. American Ceramic Soc., 65, (6), p. 312-316, (1982).

23. G. C. Kuczynski, Z. Meta11kunde, £I, p. 606-610, (1976).

AN OVERVIEW OF ENHANCED SINTERING TREATMENTS FOR IRON

ABSTRACT

Randall M. German

Materials Engineering Department Rensselaer Polytechnic Institute Troy, New York 12181 USA

The fundamental sintering behavior of iron is examined to determine possible success in enhancing the rate or improving the properties. Within this scope, both liquid phase and activated sintering treatments are considered. Various additions are discussed in terms of diffusivity and phase diagram data. Small concentrations of additions like B, C, Nand P are identified as candidate additives for enhanced sintering when combined with various refractory or transition metals.

INTRODUCTION

There are two cornmon non-pressure based approaches to sintering enhancement of metal powders, activated sintering and liquid phase sintering. Both liquid phase and activated sintering use the presence of second phases during the cycle to increase the sintered properties. The fundamental difference is that liquid sintering uses a wetting liquid which flows between particles while activated sintering relies on a high diffusivity solid phase segregated to grain boundaries. The current interest in enhanced sintering treatments results from the often observed property benefits obtained with higher sintered densities. In this regard, many of the approaches available for enhanced sintering of iron are evaluated in this review in terms of their influences on mechanical properties.

Enhanced sintering refers to any special process aimed at improving the sintering rate of a powder compact; that is, to effectively lower the sintering temperature, shorten the sintering time,

103

104 R.M.GERMAN

or improve the sintered propertiesl Enhanced sintering has had its greatest advancement in the refractory metals. The problems associated with understanding conventional sintering studies are compounded in enhanced sintering studies by the presence of a second phase or supplemental treatment Z- 4 • Most enhanced sintering studies have been conducted with little or no advanced theory to predict beneficial treatments. The eventual success of this approach cannot be denied. However, lack of a sound theory to explain enhanced sintering is a clear detriment.

Enhanced densification results from an increased driving force through physical or chemical treatments. Many such enhanced sintering processes are well known. While most of the attention has been focused on tungsten, several other materials have been investigated. Enhancement of the sintering process is generally relegated to one or more changes in the fundamental material properties resulting from a special treatmentS. The strongest effects are those associated with changes in the interfacial properties. A less common means is to induce the operation of a normally dormant mass transport mechanism. To the ceramist, many of these phenomena are commonplace. It is well known that both impurities and stoichiometry departures can provide enhanced sintering of many ceramic materials. Likewise, the sintering atmosphere can have a profound influence on the sintering rate as well as on the sintering mechanism. As can be imagined, any change in material under study which induces an enhanced defect concentration, higher atomic mobility, or promotes the operation of new mass transport processes, is an example of enhanced sintering.

MODELS FOR ENHANCED SINTERING

With respect to activated sintering some generalizations are possible based on the prior experimental data. First, there is an optimum activator concentration which produces the maximum benefit. The optimum activator corresponds to relatively small additive concentrations on the surface of the metal powder. The process is sensitive to the uniformity of the activator distribution. The mechanisms of material transport are similar to those encountered in single phase, solid state sintering. The dominant processes are diffusion of the base metal through grain boundaries rich in additive, with some surface diffusion on free surfaces. The additive provides a high mobility phase for rapid base metal transfer. The interparticle activator layer provides a short circuit diffusion path which allows rapid mass transport to form the sinter bond. The role of the sintering activator is to lower the process activation energy for diffusive transport. In general, it is observed that activated sintering occurs when the additive remains segregated as a grain boundary phase6 • For this segregated phase to be most effective as a sintering activator, the additive typically forms a low melting

OVERVIEW OF ENHANCED SINTERING TREATMENTS FOR IRON 105

temperature phase. Additionally, a decreasing liquidus and solidus temperature as the concentration of additive increases aids segregation. The wetting of the grain boundaries and the continuity of this layer are additional criteria for activated sintering. It is hypothesized that moderate solubilities of the base metal in the additive are optimal for activated sintering. These various criteria for enhanced sintering are satisfied in systems typically involving elements from differing parts of the periodic chart.

Densification during sintering can also be enhanced by the presence of a liquid phase. The accelerated sintering occurs in three stages, with the influence of the liquid phase decreasing in each successive stage. Generally, the liquid is formed from constituents of the powder mass during heating. The surface tension associated with the liquid phase provides a capillary force which induces either swelling due to melt flow between parti.cles and grains, or rapid densification through rearrangement. Subsequently, diffusional flow through the liquid and microstructural coarsening act in opposite manners to develop the sintered microstructure. Similar to activated sintering, liquid phase sintering is frequently applied to the refractory metals. Extensive observation has defined the mass transport mechanism and given adequate theories for the process. From a practical standpoint, liquid phase sintering has both positive and negative aspects. Typically, it is associated with a large second phase content. Thermal exposures are limited because the liquid could reform and result in component failure. Also, fabrication of these materials can prove to be very difficult. Problems such as liquid phase runout and shape distortion during sintering are obvious difficulties. Even so, the technique has been applied to a number of materials.

During recent years, theoretical and experimental developments in liquid phase sintering have paralleled one another7 . The theories have been based on various precipitation models, considering the added involvement of the liquid phase. In general, there are two types of liquid phase of concern8 ; that which only undergoes a slight reaction with the solid powder, and that which forms an alloy. As would be expected, this latter case is more complicated to model, but is also more important. For best liquid phase sintering, there are three recognized criteria. The solid phase should be soluble in the liquid, but the solubility of the liquid phase in the solid phase must be very low. In the iron-copper system, iron is soluble in copper and a high density results. Alternatively, in the tungsten-copper system there is no significant solubility, and a low density results independent of the volume fraction of liquid. Thus, the solubility of the solid is an important first concern. If there is a high reverse solubility (liquid phase in the solid), then it is possible that the liquid phase will be traJsient and will lose its effect as homogenization takes place. As a second concern, the melting point of the solid must be considerably higher than the liquid phase formation temperature. In

106 R.M.GERMAN

this respect, liquid phase sintering is similar to activated sintering and exhibits the same phase diagram features as noted earlier. Furthermore, in order to achieve complete wetting of the solid particles, it is necessary for the solid-liquid surface energy to be much less than the solid-solid surface energy. Otherwise, wetting angle effects are considered slight with respect to process kinetics. As these three liquid phase criteria are satisfied, the shrinkage rate should increase. As the latter sintering stages are approached, the solidliquid surface energy and the ratio of the solid-vapor surface energy to the solid-liquid surface energy become important. A volatile liquid phase would promote rapid liquid rearrangement and a high homogeneity in the resulting sintered compact.

BASICS OF IRON SINTERING

Before opening a discussion on the enhanced sintering treatments for iron, it is appropriate to first overview the fundamental sintering behavior. There are many variables which play important roles in the sintering of iron powders. Each powder differs in chemical composition, particle size, particle size distribution, and particle shape. Factors such as the alpha to gamma phase transformation, differences in the diffusion rates in these phases, grain size and grain growth, also effect the sintering process for iron9- l7 . These powder characteristics have a considerable influence on the sintered properties. Commercial grades, in addition to surface oxides (0.3 to 1.0%), contain other impurities on the order of 0.2 to 0.6%. The impurities as well as alloying may effect the alpha to gamma phase transformation in addition to retarding diffusion.

Iron sintering is initially dominated by surface diffusion, with subsequent dominance by grain boundary diffusion. It is important to realize that surface diffusion provides for growth of interparticle diffusion joints but does not contribute to compact densification. The observed rapid grain growth in the gamma phase (face-centered cubic) hinders final sintering densification. Grain growth inhibits the sintering rate, and for th~s reason sintering in the face-centered cubic range is often considered detrimental. However, density does not necessarily control the grain size in iron, as has been suggested in other sintering systems.

Within the scope of this paper, the concern is with enhanced densification treatments. Therefore, dominance by surface diffusion is viewed as a negative event. The surface serves as both the mass source and sink, and fails to contribute to densification. For the practical powder metallurgist, surface diffusion may not be detrimental since it provides for compact strengthening with good dimensional control. Of greater concern to this study is the effect of various additives on the sintering of iron. Diffusion data demonstrates that sintering is much faster in the alpha phase than in the


gamma phase. Since our overall consideration is high densification for properties, we would probably emphasize higher sintering temperatures to enhance processes such as volume diffusion. However, the crystallographic change from alpha to gamma acts against this inclination. On the basis of diffusion datal8 , strong potential sintering enhancers at l200°C are Ag, Al, Ge, Si, Ti, and U. It is noteworthy that little attention has been given to some of these additions in spite of the favorable diffusivity. In addition to these additives, it is well recognized that phases incorporating the interstitial elements like C, B, P, and N are favorable. The next section describes the past experimental observations with respect to densification and mechanical properties using sintering enhancers.

THE EFFECT OF VARIOUS ADDITIVES

This section provides a concise review of the literature on various additives and their effects on the sintering and mechanical properties of iron. Additives treated in this review include copper, tin, sulfur, phosphorus, carbon, nickel, boron, titanium, and various carbides. Combinations of such additives are common, and an attempt has been made to sort out the main influences in such cases. Because the body of literature is extensive, very few references can be cited within the space limitations of this article. It is intended that a thorough review of greater length will be available soon to detail the current state of the fieldl9 . There is a body of past research which has been reduced to common practice such as with silicon, molybdenum and graphite additions. These additions will not be specifically addressed in this review since the focus is on the more recent developments in the field. Finally, specific attention has been given to combining the theoretical, mechanistic studies with the more applied efforts. This approach allows identification of the properties and an explanation of how they were obtained.

Copper

The Fe-Cu system has been investigated in great detail, representing both its commercial and theoretical significance. The Fe-Cu-C system represents the best understood example of enhanced ferrous powder sintering. Liquid phase sintering occurs at temperatures over l096°C when the iron is fully saturated with copper, at concentrations over 9.5 wt.%. Cannon and Lenel20 note that densification occurs in the first twenty minutes after liquid formation. The degree of densification depends on the amount of copper (i.e. on the amount of li~uid phase, which indicates the regrouping mechanism). Eremenko, et al review the main parametric influences and early literature on the iron-copper system. Multiple stages are observed with successively decreasing shrinkage rates. The solution-reprecipitation stage is the dominant time dependent process. It controls both densification and microstructure. In general, densification is enhanced by an increase

108 R. M. GERMAN

in the sintering temperature, longer sintering times, increases in the liquid content, and smaller particle size.

In general, for the Fe-Cu system, the first stages of liquid formation and flow are the most important to densification. Temperature, time, particle size, as well as percent liquid are all major factors. A direct correlation has been made between the copper penetration into iron and expansion/shrinkage. The relationship between dimensional stability and properties could be better established. The influence of powder purity and characteristics has yet to be fully developed, even in the basic studies. Many instances of apparent disagreement could be cleared by better design and control of the experiments. In spite of the volume of past efforts, full exploitation of the properties of this system via appropriate selection of processing parameters is still to be made.

Tin

Tin provides a low melting point addition for iron which has been proposed as an alternative to copper. The phase transformations occurring during sintering of iron-tin and iron-copper-tin powder mixtures have received considerable study. Esper, et a12l review early dilatometric work on these systems and provide a comprehensive examination of the phase relations. Tin stabilizes the body-centered cubic ferrite structure. With tin additions, the first sintering reactions begin in the 420 to 460°C range giving swelling. The degree of dilation increases with increasing tin content. X-ray diffraction shows these dilations correspond to reaction of alpha-iron with liquid tin giving FeSn. At higher temperatures the formation of the intermetallic phases also contributes to dilation. Enhanced sintering of iron results from the solid state reactions involving tin in the 1000 to l200°C range. However, intermetallic phases can be precipitated in sintered bodies with more than 9% Sn during cooling, causing embrittlement. For sintering temperatures between 820 and 1100°C, maximal strength occurs at approximately 2 wt.% Sn22 . One of the main benefits of tin additions is as a substitute for copper with a concomitant reduction in the sintering temperature or time.

Sulfur

The addition of sulfur to iron should provide for liquid phase sintering, but also embrittlement. Sulfur forms a low temperature liquid with iron at temperatures above 988°C. Sulfur has been used in a few instances for enhanced sintering. However, there are several detrimental aspects in using sulfur with iron in terms of compact ductility as well as sulfur contamination of sintering furnaces.

Phosphorus

Phosphorus forms a eutectic with iron which can aid sintering at


temperatures above 1049°C. Supplemental alloying additions can further lower the liquid formation temperature. Optimal properties are observed with 0.45 wt.% P. Phosphorus is a potent sintering enhancer, with a positive effect on both the magnetic and mechanical properties23- 27 • Molybdenum further contributes to an improved impact strength while nickel causes a decrease in ductility; both elements provided for strengthening when combined with phosphorus. Ductility in 0.45 wt.% P alloy requires a finer iron particle size and higher sintering density. Additionally, phosphorus slows grain growth during sintering. The use of sponge iron further enhances the effect of phosphorus. Formation of a liquid phase is an important reason for the effect of phosphorus. However, its high diffusivity, ferrite stabilization, and solubility in iron are all important contributions to compact properties.

Nickel

Nickel has a major effect on sintered properties of iron when used in conjunction with other alloying additions. The addition of 2 wt.% Ni to the Fe-Cu-C system reduces the needed copper for optimal strength. Furthermore, nickel reduces the net dimensional change and contributes to a higher toughness. Nickel as an alloying addition contributes to an improved hardenability, fatigue strength and toughness, as is well recognized in conventional steels.

Boron

Boron additions have been made to ferrous P/M compacts to enhance densification and properties. The use of boron falls into two categories. The first is iron-boride materials produced by infiltration techniques. The second category includes premixed powders. It has been demonstrated that boron based ternary systems offer some benefits, but it is evident optimization will require more extensive research25 . Boron based compound additions, like boron-carbide, which form a liquid phase definitely exhibit merits worthy of further study. Neither boron nor carbon seriously degrade the mechanical properties. Formation of liquid phases can be controlled and used to enhance densification. Microstructural coarsening is a definite disadvantage to boron based additions. It would appear that both processing and alloying must be optimized to fully exploit such systems. The combinations reported to date have not succeeded in simultaneously attaining high ductilities and high strengths. Unpublished research at RPI has found that boron and carbon are very effective sintering enhancers and make major contributions to strength when combined with certain refractory or transition metals.

Carbon

Sintered steels based on combinations of iron and carbon (graphite) have received extensive attention. Some of the early work is

110 R.M.GERMAN

reported by Squire28 . Experiments using carbonyl iron powder coated with colloidal graphite and moderate sintering temperatures (1175°C), show a transient liquid phase is formed during compact homogenization29 . A 0.4% carbon composition exhibits a yield strength of 270 MPa and 20% elongation. No data is given for dimensional control for such a technique, although it is very evident that high densities can be achieved with graphite coated powders.

Carbide

Most carbon or carbide systems work rather well as transient liquid phase sintering additions25 ,30-32 Some efforts have been reported on maintaining dimensional control through additions such as Cu, although this appears to have negative ductility consequences. The use of complex carbide master alloys obviously enhances strength and density. Mechanical properties for those systems are quite high and appear to be somewhat linked to the degree of homogenization. Loose sintering gives some large densifications, but shape control is hard to envision under such conditions.

Titanium

Like many other systems exhibiting enhanced densification, the iron-titanium binary has two low melting point liquid phases. Kieback and Schatt33 mixed Fe-Ti powders to provide for liquid phase sintering and precipitation hardening. Densification is enhanced because titanium has a high oxygen affinity, with an eutectic at 1086°C. Titanium has merits as a sintering enhancer for iron and will have a greater effect when combined with other additives.

Halides

Preliminary experiments have used halide additions either to the sintering atmosphere or directly to the compact34- 36 Improvements are noted in both the strength and ductility due to pore shape changes. At equal sintered densities, the halides, like chlorine, appear to effect the pore shape. A pore smoothening occurs with a small addition of a halide because of vaporization/condensation involving ironchlorides. Thus, the chloride additions improve the sintered properties without directly contributing to densification.

S~RY

The sintering of iron is dominated by surface diffusion for most powders, with some grain boundary diffusion contributions at the latter sintering stages. As a consequence of these diffusion processes, small shrinkages are common in the sintering of ferrous compacts. In some respects, low shrinkages are an advantage because of minimal distortion and dimensional change from the die dimensions. Alternatively,


the mechanical properties of powder metallurgy compacts are dominated by the sintered density. Thus, high sintered densities are an advantage when seeking better performance characteristics. Densification by compaction is not fruitful above pressed densities of 90% of theoretical; hence, the attention to densification during sintering. This article provides a review of the basics of the two prominent approaches to sintering enhancement, liquid phase and activated sintering.

One class of effective sintering enhancers are the nonmetals such as C, B, and P. These additions to iron provide both improved strength and ductility through microstructure and density effects. Additionally, in low concentrations, these elements do not degrade the grain boundary cohesive energy, and thereby avoid embrittlement. A further advantage with an element like P is the possible enhancement of volume diffusivity by stabilization of the body-centered cubic (alpha) ferrite phase.

The homogeneity of the addition is important to optimizing densification. A fine particle size of the additive proves most useful. In terms of the various candidate additives, the conventional additions to iron have little influence on sintering densification. Additions such as cobalt, nickel, and manganese have little sintering effect. Their main attributes are as solid solution strengthening additions. With copper the. effects .are less traditional since there is the formation of a liquid phase. The iron-copper system is well explored, as evidenced in this review. Graphite provides a useful addition in combination with copper since it aids dimensional control and strength, and minimizes swelling as induced by copper. The further addition of nickel lowers the required copper level to obtain attractive properties and raises the sintered toughness. These additions to iron represent the traditional approach to enhanced sintering of ferrous powders. Beyond these traditional additives, several other treatments are covered in this review.

Tin represents an alternative addition with a favorable low melting temperature.. Tin provides good dimensional control and rapid sintering at low concentrations. However, there is a high sensitivity to the sintering time and temperature with tin additions to iron. Additionally, at concentrations over roughly 0.5 wt.% there is rapid compact embrittlement due to tin. Titanium is one of the few metallic additions which has merit as a sintering enhancer for iron. It provides for rapid sintering homogenization, liquid phase formation, ferrite stabilization and precipitation hardening. This addition should be examined in greater detail in the future although it will require special atmosphere control. Additions like sulfur, phosphorus, boron and certain carbides show the characteristic phase diagram features associated with enhanced sintering. Sulfur is probably not an acceptable additive because of negative effects on the furnace. Phosphorus is of recognized merit because of the stabilization and

112 R. M. GERMAN

hardening of the ferrite phase. Additionally, it exhibits good wetting and flow as a liquid, and is available in several forms. Boron forms a liquid which has demonstrated densification benefits, but also leads to shape distortion. Carbon and carbides are effective additives and may be beneficial as supplemental additions with boron. By inference, it is possible that certain nitrides would also prove useful as sintering additives for iron. The halide additions like chlorine are viewed as secondary in importance. The main effect appears to be in changing the pore shape, which is generally not as important as attaining higher sintered densities.

As a general conclusion, additions which form a low melting phase with iron during sintering appear to be potential sintering enhancers. Often these additions are based on the nonmetallic elements and contribute to embrittlement while aiding densification. Thus, their concentration must be balanced to optimize properties. A solubility for iron and wetting of iron are necessary criteria for successful enhancement. A moderate solubility for the additive in iron appears to provide a secondary hardening benefit. Multiple element additions offer possible control over the various concerns for shape control, densification, strengthening, microstructure and ductility. As a generalization, the best sintering additions for iron are the ferrite stabilizers. Future research should explore the synergistic effects possible by combining elements like C, B, N, and P with various refractory and transition metals.

REFERENCES

l. R.

2. A.

3. A.

4. J.

5. A.

6. z.

7. V.

8. F.

M. German and Z. A. Munir, Activated Sintering of Refractory Metals by Transition Metal Additions, Reviews Powder Met. Physical Ceram., 1982, Vol. 2, pp. 9-44. S. Reshamwala and G. S. Tendolkar, Activated Sintering Part 1, Powder Met. Inter., 1969, Vol. 1, pp. 58-61. S. Reshamwala and G. S. Tendolkar, Activated Sintering Part 2, Powder Met. Inter., 1970, Vol. 2, pp. 15-19. Barta, Activated Sintering, Powder Met. Inter., 1970, Vol. 2, pp. 52-57. J. Shaler, Activated Sintering- A Review, Sintering and Related Phenomena, G. C. Kuczynski, N. A. Hooton and C. F. Gibbon (eds.), Gordon and Breach, New York, NY, 1967, pp. 807-823. A. Munir and R. M. German, A Generalized Model for the Prediction of Periodic Trends in the Activation of Sintering of Refractory Metals, High Temp. Sci., 1977, Vol. 9, pp. 275-283. N. Eremenko, Y. V. Naidich and I. A. Lavrinenko, Liquid Phase Sintering, Consultants Bureau, New York, NY, 1970. Eisenkolb, Sintering in the Presence of a Liquid Phase, Powder Metallurgy, W. Leszynski (ed.), Interscience, New York, NY, 1961, pp. 75-95.


9. S. L. Forss, Some Aspects of the Sintering of Iron Powder, Modern Developments in Powder Metallurgy, Vol. 2, H. H. Hausner (ed.), Plenum Press, New York, NY, 1966, pp. 3-11.

10. F. Thummler and W. Thomma, The Sintering Process, Metallurgical Reviews, 1967, Vol. 12, pp. 69-108.

11. M. J. Koczak and A. Lawley, The Effect of Particle Size and Shape on the Mechanical Properties of Sintered Iron Compacts, Powder Met. Inter., 1972, Vol. 4, pp. 186-191.

12. M. Oxley and G. Cizeron, Application of pilatometric and Microfractographic Methods to the Study of the Sintering of Iron, Inter. J. Powder Met., 1965, Vol. 1, No.2, pp. 15-27.

13. A •. R. Poster and H. H. Hausner, Alpha and Gamma Phase Sintering of Carbonyl and Other Iron Powders, Modern Developments in Powder Metallurgy, Vol. 2, H. H. Hausner (ed.), Plenum Press, New York, NY, 1966, pp. 26-43.

14. H. F. Fischmeister and R. Zahn, The Mechanism of Sintering of Alpha-Fe, Modern Developments in Powder Metallurgy, Vol. 2, H. H. Hausner (ed.), Plenum Press, New York, NY, 1966, pp. 12-25.

15. E. Aigeltinger and J. P. Drolet, Third-Stage Sintering of Carbonyl Iron Powder, Modern Developments in Powder Metallurgy, Vol. 6, H. H. Hausner and W. E. Smith (eds.), Metal Powder Industries Federation, Princeton, NJ, 1974, pp. 323-341.

16. H. F. Fischmeister, Densification and Grain Growth in the Later Stages of Sintering of Alpha-Iron, Iron Powder Metallurgy, H. H. Hausner, K. H. Roll and P. K. Johnson (eds.), Plenum Press, New York, NY, 1968, pp. 262-283.

17. F. B. Swinkels and M. F. Ashby, A Second Report on Sintering Diagrams, Acta Met., 1981, Vol. 29, pp. 259-281.

18. J. Askill, Tracer Diffusion Data for Metals, Alloys, and Simple Oxides, IFI/Plenum, New York, NY, 1970.

19. R. M. German and K. A. D'Angelo, Enhanced Sintering Treatments for Ferrous Powders, Submitted Inter. Metals Rev., 1983.

20. H. S. Cannon and F. V. Lenel, Some Observations on the Mechanisms of Liquid Phase Sintering, Proceedings First Plansee Seminar, F. Benesovsky (ed.), Metallwerk Plansee, Reutte, Austria, 1953, pp. 106-l2l.

21. F. J. Esper, K. H. Friese and R. Zeller, Sintering Reaction and Radial Compressive Strength of Iron-Tin and Iron-Copper-Tin Powder Compacts, Inter. J. Powder Met., 1969, Vol. 5, No.3, pp. 19-32.

22. R. Duckett and D. A. Robins, Tin Additions to Aid the Sintering of Iron Powder, Metallurgia, 1966, October Issue, pp. 163-167.

23. W. F. Jandeska, Activated Low Temperature Sintering of Iron Powder Structures, Prog. Powder Met., 1981, Vol. 37, pp. 233-253.

24. P. Lindskog, J. Tengzelius and S. A. Kvist, Phosphorus as an Alloying Element in Ferrous P/M, Modern Developments in Powder Metal~, Vol. 10, H. H. Hausner and P. W. Taubenblat (eds.), Metal Powder Industries Federation, Princeton, NJ, 1977, pp. 97-128.

114 R. M. GERMAN

25. K. S. Hwang and R. M. German, High Density Ferrous Components by Activated Sintering, Processing of Metal and Ceramic Powders, R. M. German and K. W. Lay (eds.), The Metallurgical Society, Warrendale, PA, 1982, pp. 295-310.

26. M. Hamiuddin and G. S. Upadhyaya, Effect of Molybdenum on Sintering of Iron and Iron-Phosphorus Premix, Powder Met., 1980, Vol. 23, pp. 136-139.

27. P. Lindskog and I. I. Ivanova, Investigation of the Activated Sintering of Iron Powder, Modern Developments in Powder Metal~, Vol. 2, H. H. Hausner (ed.), Plenum Press, New York, NY, 1966, pp. 45-61.

28. A. Squire, Iron-Graphite Powder Compacts, Trans. AIME, 1947, Vol. 171, pp. 473-484.

29. J. Klein, A Preliminary Investigation of Liquid Phase Sintering in Ferrous Systems, Lawrence Berkeley Laboratory, University of California, Berkeley, CA, Report LBL-3549, April 1975.

30. S. Banerjee, V. Gemenetzis and F. Thummler, Liquid Phase Formation During Sintering of Low-Alloy Steels with Carbide-Base Master Alloy Additions, Powder Met., 1980, Vol. 23, pp. 126-129.

31. S. M. Kaufman, The Use of Master Alloys for Producing Low Alloy p/V Steels, Modern Developments in Powder Metallurgy, Vol. 10, H. H. Hausner and P. W. Taubenblat (eds.), Metal Powder Industries Federation, Princeton, NJ, 1977, pp. 1-13.

32. H. P. Aksas and A. Kobylanski, A Dilatometric Study of Sintering Iron-VC, WC Composites, Modern Developments in Powder Metal~, Vol. 14, H. H. Hausner, H. W. Antes and G. D. Smith (eds.), Metal Powder Industries Federation, Princeton, NJ, 1981, pp. 335-345.

33. B. Kieback and W. Schatt, The Application of Momentary Liquid Phase Sintering for the Manufacture of Fe-Ti Sintered Alloys, Planseeber. Pulvermetall., 1980, Vol. 28, pp. 204-215.

34. M. Eudier, Note on the Activated Sintering as Influencing the Theories of the Sintering Mechanism, Sintering and Related Phenomena, G. C. Kuczynski, N. A. Hooton and C. F. Gibbon (eds.), Gordon and Breach, New York, NY, 1967, pp. 829-839.

35. I. M. Fedoechenko, I. G. Slys, I. I. Odoienko and B. Y. Kosov, Activated Sintering of Atomized Kh18N9 Steel Powder, Soviet Powder Met. Metal Ceram., 1976, Vol. 15, pp. 919-922.

36. R. D. McIntyre, The Effect of HCl-H2 Sintering Atmospheres on the Properties of Compacted Iron Powder, Trans. Quart. ASM, 1964, Vol. 57, pp. 351-354.

VAPOR TRANSPORT AND SINTERING OF CERAMICS

D. W. Readey, J. Lee, and T. Quadir

The Ohio State University Columbus, Ohio 43210

INTRODUCTION

There is a significant difference in the important processing steps between metals and ceramics. Most of the microstructure development and control which are used to vary properties in metallic systems occur during post-consolidation thermal and mechanical treatments such as recrystallization and precipitation. Only recently are similar techniques being applied to ceramics. For example, a great deal of effort is underway in trying to increase the work of fracture of ceramics by transformational toughening1 and microcracking2 • Nevertheless, if the fracture str'ength of such materials is determined by large random processing flaws, even though the average strength is increased by toughening, the sample to sample variation will still make the systems designer reluctant to utilize the material.. Therefore, an improved understanding of ceramic microstucture development is the most critical area which will lead to new, improved, and more widespread use of high technology ceramics.

Thus the goal of the ceramic engineer, given the task of producing a specific ceramic material, is to be able to start with a powder and sinter to essentially theoretical density with a controlled grain size. If he or she can do this, then intermediate densities and microstructures are possible. This paper will focus on microstructure development in single phase materials in which densification is produced entirely by solid state diffusion processes. In other words, multiphase materials, liquid phase sintering, and vitrification will not be considered. Many of the high technology ceramic materials are of this type.

The current understanding of ceramic powder processing has led

115

116 D. W. READEY ET AL.

to the following description of the desired powder and transport processes which lead to high density3:

l.small, nonagglomerated, monodisperse, spheri~al powders, 2. uniform, dense(close-packed) packing of powder, 3. mass transport during sintering by volume or grain boundary diffusion, no transport by surface diffusion or vaporization and condensation, 4. fire in an atmosphere of rapidly diffusing gas such as hydrogen or oxygen and avoid nitrogen, argon, etc.

Usually, one and frequently all of these requirements are not satisfied in practice. There is a great deal of research in progress today attempting to produce ideal powders by many processes4- 10 .However, there are other many equally important processing steps and variables which must be controlled between the powder preparation step and the final fired microstructure, one of which is the sintering atmosphere.

There are many atmosphere effects which are important and play critical roles in the powder processing and microstrucrure development in high technology, single phase, ceramic materials. It is impossible to cover all of them in a single paper. Therefore, only the area of vapor transport during microstructure development is discussed in detail. The effects of vapor transport are on good theoretical grounds and new experimental data are becoming available. Therefore, the effects of vapor transport will be emphasized. The role of point defects on diffusional processes and microstructure developoment and how they are affected by the atmosphere is an important area. Unfortunately, the experimental data clearly relating point defect chemistry to changes in sintering behavior are lacking. Therefore, rather than speculate further, point defect chemistry and how it affects sintering is not covered.

VAPOR TRANSPORT AND DENSIFICATION

1. Observations and Importance Both vapor transport and surface diffusion can lead

to neck growth without densification and are thus undesirable. However, vapor transport and its effects on the densification kinetics and micro~tructure development of ceramics has been probably the most neglected transport phenomenon both from an experimental and theoretical point of view. Nevertheless, it is an ideal process with which to study microstuctural development in powder compacts since the transport coefficients are easily controlled, are readily available in the literature or easily calculated. This is in contrast to the lack of control over solid, surface, and boundary diffusion coefficients for which there is

VAPOR TRANSPORT AND SINTERING OF CERAMICS 117

also a paucity of good data. Furthermore. it is well known that many ceramic materials lose weight by sublimation during sintering which clearly implies a significant vapor pressure of the subliming species. For example. if the weight loss is by evaporation. the rate is determined by gaseous diffusion through some boundary layer of thickness & around the sample. The flux density. J. is then given by:

where Co is the equilibriua concentration at the solid-gas interface. ~ is the concentration of the subliming species in the gas far from the surface. and D is the gaseous diffusion coefficent. If we consider the rate of weight loss from a spherical compact. expressing the gas phase composition in terms of pressure and assuming that ~ = 0 we obtain:

! !m = _!JHL p m dt r&dRT 0

where M = molecular weight r = sphere radius m = sphere mass d = solid density R = gas constant T= temperature

Po = equilibrium partial pressure.

For weight losses on the order of 1~ per hour. the equilibrium partial pressure of the subliming solid is 102 N/m2 if the other parameters are typical for ceramic materials in the above equation. As will be discussed later. this is a retatively large vapor pressure compared to that nocessary for vapor transport to contribute significantly to morphological changes within a powder compact. Many ceramic materials lose weight by sublimation during sinteringll.12.13 which clearly implies a significant vapor pressure of the subliming species. Therefore. certainly in those cases in pure materials in which a percent or more of weight is lost during sintering. vapor transport can play a significant role in densification and microstructure development. The presence of at least one volatile component is quite common in ceramics such as PbO in zirconate-titanatesI4 • Cr203 in chromiteslS • and Na20 in beta aluminal6 •

2. Vapor Transport and Sinterins Models Kuczynskii7 and Kingery and Bergi8 examined vapor

transport as a mechanism of neck growth in the intitial sintering model shown in Figure 1. In this model vapor transport and surface diffusion can only contribute to neck growth and not shrinkage.


Figure 1. TWo-sphere model of initial stage sintering.

Similar considerations and conclusions can be reached with intermediate stage sintering models since only the geometry is different. Therefore, in the following discussion, only the initial stage will be discussed. These derivations17 ,18 for vapor transport are unique among the sintering models in that they assume that the gas transport rate is rapid and that the rate-limiting step is the evaporation or condensation step at the solid surface. That is, they assume that the surface reaction is rate-controlling while all the other transport models assume diffusion is rate controlling. For this case, the flux density at the neck surface (see Figure 1) is given by:

cu!Ut ~ M /1/2 J = dpRT 0 /27fRT \

where a = sticking or accomodation coefficient T = surface energ~ p = neck radius M = molecular weight d = solid density

Po = vapor pressure

and Rand T have their usual meaning. The rate of neck growth, xv' in this case is given by18:

_ 7f",M ~ M ~1/2 Xv - ~ -- Po 2pd2RT 27fRT

On the other hand, we can assume that diffusion through the gas phase is rate-limiting and obtain:


and

. Xv

where D = gaseous diffusion coefficient r = sphere radius.

119

Equating these two fluxes we can obtain an estimate of the particle size at which gaseous diffusion becomes rate controlling:

r = D !lM 7tRT

For typical values of the gas diffusion coefficient (D g 1 cm2/s), the temperatures over which sintering is important for ceramics (T g 1000 - 20000 C), the range of molecular weights for ceramics (M g 20-200 g/mole), and an accomodation coefficient of one, we find that r g one micrometer which is typical of the size particles undergoing sintering in a powder compact.

3. Vapor Transport and Volume Diffusion In order to obtain an estimate of the importance of vapor

transport relative to the other transport processes possible during sintering, we shall compare the vapor transport contribution to neck growth with that of volume diffusion19 • A significant problem is that our knowledge of diffusive transport coefficients in ceramics is quite poor. The data are perhaps better for volume diffusion than for surface and grain boundary diffusion. Therefore, the comparison with volume diffusion is justified. For bulk diffusion, the rate of neck growth is given by17:

• 2Dy'Y~ xD = RTp

where Dv o

volume or bulk diffusion coefficient molar volume.

Therefore, the ratio of the rate of neck growth for vapor transport to that for volume diffusion, which gives a measure of the importance of vapor transport during densification, for typical sintering conditions is given by:


for vapor diffusion control and

for reaction rate control where Po is in dynes/cm2 and Dv in cm2/s. As mentioned earlier. for particles larger than about one micrometer. vapor diffusion is rate ontrolling. For a shrinkage on the order of one percent. since AL/Lo ~ p/r ~ x2/4r2 = 0.01:

This implies that for systems which exhibit weight loss due to sublimation. ie. Po = 10-3 atm. ~ 102 N/m2 • vapor transport dominates unless Dv ) 10-7 cm2/s which is a very large volume diffusion coefficientl Even for Po = 10-6 atm ~ 0.1 N/m2 • vapor transport will playa dominant role in neck growth for all shrinkages greater than 1% unless D ) 4x10-10 cm2/sl As shall be discussed below. there are many way~ in ceramic systems to obtain partial pressures on the order of 0.IN/m2 •

Of course. the undesirable feature of vapor transport during initial sintering is that it contributes to neck growth without shrinkage. hence. if present. will decrease the rate of sintering or densification. Since the ratio of vapor transport to diffusional neck growth is proportional to the particle size. vapor transport is more important for larger size particles. Therefore. it should be more readily observed in sintering large spheres rather than powder compacts. Because of this particle size dependence of vapor transport. it has largely been ignored as being a significant transport process during sintering of powder compacts.

Vapor transport has been observed to contribute to neck growth but no shrinkage in sphere-to-sphere sintering experiments on NaC118.20 and Zn021 with calculated partial pressures on the order of 10 N/m2 • Nevertheless. both Zn022 •23 and NaC124 powder compacts can undergo densification even though weight loss may occur during sintering indicating significant vapor transport24 • One of the most interesting materials from the standpoint of the relation between densification and vapor transport is Cr20312.25.26 and the chromites15 in which significant volatilization or weight loss occurs at all oxygen partial pressures. At high pressures. the following reaction dominates:

2Cr03(g)

and at low pressures


Interestingly, densification can o~ybe achieved at low oxygen partial pressures.

4. Vapor Transport and Atmospheres For the present, assume that the effect of vapor transport

121

is merely to contribute to neck growth and hence retard densification or shrinkage by volume diffusion processes. What are the possible atmospheric effects on vapor transport and densification? First there are compounds such as NaCI which have a high vapor pressure. In this case, the relative importance of vapor transport will depend primarily on the relative temperature dependencies of the vapor pressure and the relevant solid state diffusion coefficient which controls densification. The gaseous diffusion coefficient can only be slightly changed by changing the ambient gas. However, for materials such as MgO or ZnO which vaporize as atomic species:

MgO(s) = Mg(g) + 1/202(g)

the equilibrium pressure, Po' and the rate of vapor transport can be controlled by the oxygen partial pressure. For example, in hydrogen,

and at 20000 K in very dry hydrogen, p(Mg) ~ p(H20) ~ 300 N/m2 27 which is certainly large enough to produce significant vapor transport. On the other hand, in vacuum, Po = 0.3 N/m2 and in air, Po = 10-3 N/m2 • Therefore, the amount of vapor transport during sintering of MgO should depend critically on the atmosphere, being very important in a reducing ambient but of little consequence in air or oxygen. It has been shown that the rate of reaction of MgO and Al203 to form spinel is higher in hydrogen due to rapid vapor transport of Mg028 •

Vapor transport can be enhanced in a reducing atmosphere by the formation of volatile suboxides as in the case of alumina29 :

Clearly, one of the main problems which impedes the densification of covalently-bonded ceramics is the difficulty in preventing vapor transport. The densification of silicon30 and silicon-containing compounds such as SiC and Si3N4 is inhibited by the formation of the volatile SiO species31 :

8iC(s) + 8i02(s) 38iO(g) + CO(g).


For this reaction at 18000C. p(SiO) = 103 N/m2 so if any residual silica is present. vapor transport will clearly be important. Even with no residual silica. if the gas contains only 1 ppm of oxygen. vapor transport will be significant in these systems I

s. Impurities and Vapor Transport An example of one effect of impurities is vapor transport

via halides. Halides are frequently present in oxide powders as impurities since precursor materials are often precipitated from halide solutions. Volatile halides are easily formed by reactions such as the following:

The free energy for this reaction is such that for halide impurity concentrations on the order of 1 ppm the partial pressure of MgCl2 will be on the order of 0.1 N/m2 • There have been no extensive studies performed on the effect of halide impurities on vapor transport or densification kinetics. However. it is part of the folklore of ceramic processing that the presence of residual halide and other anion impurities is to be avoided. One qualitative piece of evidence that this mechanism is operative is that removal of chloride impurities in Zr02 lowers the temperature for densification on the order of 1000C32.

6. Vapor Transport and Particle Coarsening Another important effect of vapor transport is that it may

contribute to or be responsible for the grain growth or Ostwald ripening that occurs during the initial and intermediate stages of sintering. For Ostwald ripening by diffusion in the surrounding gas phase33- 37 :

3 8 Dy02 t r = 9" (RT)2 Po

and for an interface controlled reaction:

where r = average particle radius K = surface reaction rate constant Po equilibrium partial pressure.

In addition. a characteristic of the classical Ostwald ripening theory is that the particle size distribution reaches a steady state distribution that is skewed to small particle sizes36 • Again. in this case. if vapor transport significantly affects the


rate of particle coarsening it would again decrease the rate of densification due to the reduction of surface area which, of course, is the driving force for densification.

VAPOR TRANSPORT IN MULTI COMPONENT SYSTEMS

1. Introduction Vapor transport in a multicomponent system can provide a

123

rapid transport path for one or more of the constituents during sintering. There are two distinct situations to consider in a multicomponent system: 1. initial chemical uniformity and equilibrium between the constituents except for the surface energy driving forces, and 2. chemical heterogeneity and a nonequilibrium distribution of the constituents. The driving force for sintering is relatively small and can be completely overshadowed by nonequilibrium compositional inhomogeneities. This implies that any densification study in which additives are used, great care must be exercised to characterize the nature, distribution, and equilibrium or nonequi1ibrium state of the system in each stage of the sintering process in order to determine the true effect of any additive. Unfortunately, in far too many sintering studies with ceramics, additives have been used rather indiscriminantly giving results which are difficult if not impossible to analyze. In what follows we shall examine the first of these two situations, namely, an initially chemical homogeneous and equilibrium system.

2. Solid Solution For the sake of simplicity, consider a stystem of two

components, A and B, which could of course be two compounds, which form an ideal solid solution. Nonideal solid solutions will not show radically different behavior. The chemical potentials of the two components are given by:

I1A I1A + RTlnXA + pO

PB PH + RTI~ + pO

where XA and XB are the mole fractions, and the pressure, p, will be assumed to be produced by the surface tension force at the neck region. Thus, the gradients in chemical potentials are:

RTVXA + ovp XA

= RTVXB + ovp. XB

If one of the species, say B, moves rapidly via the vapor phase, then the gradient in chemical potential of B can approach zero and there will be a composition gradient between the neck region and the bulk of the material given by:


G

A B

Figure 2. Free energy-composition diagram for an ideal solid solution in which component B is rapidly transported through the vapor phase. The dashed curve shows the free energy curve at the neck region lowered by surface energy. ~ is the free energy of component B which is assumed to be constant. Alb is the composition difference between the neck region and the bulk.

G

A

I ' I , I I I

I\~I I \ I G

I \ b

B

Figure 3. Free energy-composition diagram for a system which exhibits a two phase region. The dashed lines correspond to the change in free energy brought about by surface tension in the neck region. As a result, composition II, originally in the single phase alpha solid solution , region is shifted to II which is now in the two phase field, and beta will precipitate at the neck.


VX_ = _ OXBVP. IJ RT

For typical values of the parameters for oxides at 20000 K and a neck radius on the order of 10 nanometers, the concentration difference, ~, would be:

125

or less than a ten percent increase in concentration. As the neck size becomes larger, the concentration difference of course becomes smaller. Figure 2 shows schematically how this increase in concentration can be explained with a free energy compostion diagram. The curve for an ideal solution is lowered by the surface tension neck stress and the tangents to both curves must intersect the chemical potential of B at the same point since the gradient in the potential of B is assumed to be zero.

3. Multiphase System If instead of a single phase solid solution system, the

phase diagram consisted of one or more possible phases, then rapid transport of constituent B could cause the appearance of a second phase at the neck region as depicted schematically in Figure 3 and has been observed experimentally in metal systems in which one constituent diffuses through the bulk more rapidly than the other38 • The dashed lines in both the free energy composition diagram and the phase diagram show the effect of the surface tension stresses at the neck region. In order to have a second phase appear, the initial composition must be very near the phase boundary. Of course, a second phase could occur at the neck region without rapid transport of one of the species if the beta phase had a larger molar volume thean the alpha phase. Then the free energy compost ion curve for beta would be lowered by the neck curvature stress more han that of alpha so that the alpha composition now lies in a two-phase region. This would be a stress-enhanced precipi ta tion.

In any event, in principle, neck stresses alone, or in combination with rapid vapor transport, can lead to chemical inhomogeneities during sintering a powder compact. Certainly, such an inhomogeneity at the neck will affect grain boundary migration and resultant coarsening. It is interesting to speculate that some additives in solid solution which enhance densification may very well be efficacious for these reasons. The above considerations hold true, of course, regardless of the rapid transport mechanism of component B, be it vapor phase, volume, boundary or surface diffusion. These considerations are likely to be of importance in many ceramic systems of technical importance which contain one or more volatile component such as LiFeSOS and PbZrxTil-x03' Certainly, it is expected that such vapor transport effects must


playa role in any multicomponent ceramic system in which the ambient vapor pressure of one of the species such as PbO must be controlled to prevent weight loss and compositional changes. Howeve~no careful study on the precise effects of vapor transport on microstructure development in such systems has been performed.

VAPOR TRANSPORT AND THIRD STAGE GRAIN GROWTH

As discussed above. the mechanism of grain growth in very porous compacts in the initial and intermediate stages of sintering is widely believed to be an Ostwald ripening process via transport down the open pores rather than by grain boundary migration. The exact modeling of this important growth process has not been completely satisfactory as yet nor has it been experimentally verified. However. in the final stages of sintering. when pores are isolated. grain growth takes place by boundary migration and has been well-modeled and studied. In this case. the residual pores and their mobility can have a significant effect on the attainment of high density. As Brook has summarized39 • the grain boundary velocity can be expressed as the product of a grain boundary mobility. M. and a driving force. F:

For intrinsic boundary motion limited only by grain boundary diffusion under the driving force of boundary curvature. this gives:

where G is the grain size. Impurity segregation. second phases. and pores at grain boundaries all reduce boundary mobility and grain growth rates. As Brook40 and Carpay41 have shown for pores moving with a grain boundary:

boundary velocity force on the boundary boundary mobility pore mobil ity

number of attached pores per boundary.

Depending on the relative values of the mobilities. either the pores control boundary velocity or the boundary itself does. Pore control is the more interesting case in that as grains grow and porosity decreases. pores are less effective in controlling


boundary motion and the boundary may break away from the pores leading to secondary or abnormai grain growth with pores entrapped within the grains. Pore mobility is determined by volume diffusion, surface diffusion, or vapor transport42 ,43,44. If the assumption is made that the grain size is proportional to the pore size45 then:

for diffusion through either the vapor or solid phases and

for surface diffusion. When the pores move with the boundary:

and the pore mobilities are given by:

for vapor diffusion,

M - Db D p, b - nr3RT

for volume diffusion,

for surface diffusion,

where Dg , ~, and Ds = gaseous, solid, and surface diffusion coefficients respectively, and a = the thickness of the surface diffusion layer.

The maximum force a grain boundary can exert on a pore is43 F =nyr which in combination with the mobilities leads to the expressions for boundary velocities and G(t) relations given above.

Although Brook39 equates the equilibrium partial pressure with the gas pressure in the pore, variation in the equilibrium partial pressure, Po' inside the pore can usually be neglected since p = po(I-2yD/rRT) where 2yD/r is the change in free energy due to surface tension. Taking y - 1000 ergs/em , D - 20cm3/mole, and r ~ 1 micrometer, at T = 1500oC, p ~ po(I-3xl0-3).


Clearly, as shown by the above equations, the mobility of pores can be increased by enhanced vapor transport by increasing the equilibrium product gas partial pressure. Figure 4, for example, shows that the region for pore-grain boundary separation can be extended

10'

10~

E ::I...

102 Q,I N

(j) C '0

10 ' t5

10°

10' 10' Kf 10 ' 102 10~

Pore Size (JLml

Figure 4. Calculated regions of pore-grain boundary separation in Fe203-air and Fe203-BCI.

to much larger grain and pore sizes in Fe203 in the presence of BCI in which the vapor pressure is enhanced through:

Therefore, during the third or final stage of sintering, the tendency for pore-grain boundary separation can be decreased by enhancing pore mobility through increased vapor transport. Therefore, secondary or abnormal grain growth and the attendant pore entrapment can be avoided which allows sintering to a higher density. Thus, in the Fe203 example cited above, sintering in air to about 8S~ of theoretical density followed by sintering in an atmosphere containing BCI can, in principle, retard secondary grain growth and lead to higher densities.


ENHANCED VAPOR TRANSPORT: EXPERIMENT

Enhanced vapor transport has been studied in the Zno-H246 and the Fe203-HC147 systems. Enhanced vapor transport occurs via the following reactions:

and

129

These were chosen as model systems because of the availability of reasonably nonagglomerated monodisperse powders. low reaction temperatures. and easily enhanced vapor transport. The results in both systems are virtually the same. As Figure 5 shows. enhanced vapor transport decreases the densification rate and can prevent shrinkage completely. As Figure 6 dramatically shows. the decrease in densification is not due to simply neck growth but to tremendous particle coarsening. As predicted by classical Ostwald ripening theory33-37. r3 is proportional to time. as shown in Figure 7. However. since r3 is proportional to Po' where Po is the equilibrium partial pressure for the reaction. i.e.:

where AHo is the standard free enthalpy for the reaction. AHo = 27 kcal/mole. Thus. for very dry hydrogen in which p(Zn) :; p(H20).

the apparent activation energy is AHo/6 = 4.5 kcal/mole. If the hydrose~ is wet so that p(Zn) « p(H20). then the activation energy is AHo/3 = 9 kcal/mole. As Figure 8 shows. the high temperature observed activation energy agrees well with that predicted for dry hydrogen. At lower temperatures. the apparent activation agrees more with that for grain growth22 • The same reults are observed in the Fe203-HCl system. Furthermore. the typical particle size distributions are skewed to large particles while the classical Ostwald ripening distribution is skewed to small particles. These results strongly suggest that the Greskovich-Lay48 mechanism of coarsening illustrated in Figure 9 is operative at lower temperatures. That is. at low temperatures. the major mass transport process is still via the vapor phase but the rate at which particles coarsen is determined by how fast the grain boundaries move. This conclusion. if correct. has significant implications for the effect of vapor transport on the type of microsturcture developed. For materials such as Fe203' ZnO. etc •• in which the diffusive processes controlling grain boundary

130

~ ... c:

'" ."

C U

~ o .. :: .~ ;; 'ii 0:

D. W. READEY ET AL.

1150·C Air

PH2 - 1.2 alms

0601~----~~ ____ ~ ____ ~ ______ ~ ____ -L ______ L-~ o 10 20 30 40 50 60

Time (mins)

Figure S. The effect of enhanced vapor transport on the shrinkage of ZnO.

Figure 6. Large grain size iron oxide obtained with no shrinkage by firing at 12000 C for S hours in 0.1 atm. BCl. 360X magnification.


motion are almost as rapid as vapor transport, rapid coarsening with the concomittant decrease in shrinkage results. For materials such as SiC, AlN, etc., in which vapor transport can be significantly more rapid than boundary diffusion, then only neck growth occurs producing the porous, elongated microstructures observed in these systems49 ,SO. Furthermore, since coarsening is generally detrimental to densification, then these results clearly indicate that coarsening can be controlled by controlling boundary mobility. Therefore, grain boundary mobility control is critical in all stages of sintering and not just the last stage.

As further evidence for the operation of this mechanism and the control of boundary motion on coarsening rate, we have purposely added A1203 to ZnO to form ZnA1204 as a second phase. In principle, if the zinc aluminate phase is present at the grain boundaries, th,n it should impede boundary migration and the rate of coarsening. ?reliminary results indicate that this is indeed the case. The rate of particle coarsening still follows a time to the one third power dependence and the activation energy remains the same. However, with up to about five mole percent addition of alumina, the rate of coarseing is decreased almost an order of magnitudeS1 • Furthermore, since coarsening is generally detrimental to densification, then these results clearly indicate that coarsening can be controlled by controlling boundary mobility. Therefore, grain boundary mobility control is critical in all stages of sintering and not just the last stage.

CONCLUSIONS

Vapor transport is thought to be undesirable during sintering because it can lead to neck growth and particle coarsening both of which inhibit densification. Nevertheless, it can be controlled far better than other mass transport processes operative during microstucture development in ceramic powder compacts. Therefore, enahnaced vapor transport is an ideal tool for examining certain transport phenomena on sintering and grain growth in ceramics. Furthermore, vapor transport is probably important in many ceramic systems of technical importance and may significantly affect microstructure development in these systems. Some recent experimental results clearly show that enhanced vapor transport largely inhibits densification by greatly increasing particle coarsening. Although, the rate of coarsening follows the third power time dependence as predicted by classical Ostwald ripening theory, the particle size distributions and the activation energies for the process do not. It is tentatively concluded that the rate of coarsening in some systems is controlled by the rate of grain boundary motion, ie. the Greskovich-Lay48 mechanism of particle growth. These results suggest that inhibition of grain boundary motion is important during all stages of sintering and not just the final or grain growth stage.


Firing Temp. Slope

1200"C 0.41

I 150°C 0.35 E

0.36 3- 30 I!I in 20 Q)

~ L-

10 e. ~

5 Q)

~

2

Time(min)

Figure 7. Grain size versus time for hematite sintered in BCI.

o

-0.8

6.8 8.2

Figure 8. Temperature dependence of the rate of coarsening of zinc oxide fired in pure hydrogen.


Figure 9.

RaP&'dVapar 8 Q Transport

----- -Rapid Bounda Motion Particle Growth

~ ;>~~~, Boundary

~~ (j "E Ion gated " Structure

:. Relative Rates of Vapor Transport and Boundary Migration Determine Direction of Microstructure Development

The Greskovich-Lay mechanism is thought to control the rate of particle coarsening. That is, grain boundary motion can control the rate of particle growth and and the relative rates of vapor transport to boundary migration will determine the details of the microstructure.


ACKNOWLEDGEMENTS

This work was sponsored by the office of Naval Research.

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8. V. Suyama. T. Mizobe. and A. Kato. Ceram. Int. ~ 141 (1977).

9. Y. Ando and R. Uijeda. J. Am Ceram. Soc. 64 C-12 (1981).

10. Y. Suzawa. et al.. Ceram. Int. ~ 84 (1980).

11. V. J. Tennery. T. G. Godfrey. and R. A. Potter. J. Am. Ceram. Soc. 54 327 (1971).

12. P. D. Ownby and G. E. Junquist. J. Am. Ceram. Soc. 55 433 (1972) •

13. H. F. Priest. G. L. Priest. and G. E. Gazza. J. Am. Ceram. Soc. 60 181 (1977).

14. J. J. Dih and R. M. Fulrath. J. Am. Ceram. Soc. 60 92 (1977) .

15. H. U. Anderson. J. Am. Ceram. Soc. 57 34 (1974).

16. R. S. Gordon. p. 231 in Ceramics for Energy Applications. U. S. ERDA Report No. CONF-751194. Nov. 1975.

17. G. C. Kuczynski. Trans. AIME 185 169 (1949).

18. W. D. Kingery and M. Berg. J. Appl. Phys. 26 1205 (1955).


19. T. L. Wilson and P. G. Shewmon. Trans. AINE 236 48 (1966).

20. J. B. Moser and D. H. Whitmore. J. Appl. Phys. 31 488 (1960).

21 L. F. Norris and G. Parravano. J. Am. Ceram. Soc. 46 449 (1963).

22. T. K. Gupta and R. L. Coble. J. Am. Ceram. Soc. 51 521 (1968) •

23. Y. Moriyoshi and W. Komatsu. J. Am. Ceram. Soc.53 671 (1970).

24. A. A. Ammar and D. W. Budworth. Proc. Brit. Ceram. Soc. 12 251 (1969).

25. J. W. Halloran and H. U. Anderson. J. Am. Ceram. Soc. 57 150 (1974).

26. J. M. Neve and R. L. Coble. J. Am. Ceram. Soc. 57 274 (1974).

27. D. R. Stull and H. Prophet. et al •• JANF Thermochemical Tables. 2nd edition (U. S. Govt. Printing Office. Washington. D. C.). 1971.

28. R. E. Carter. J. Am. Ceram. Soc. 44 116 (1961).

29. D. W. Readey and G. C. Kuczynski. J. Am. Ceram. Soc. 49 26 (1966).

30. N. 1. Shaw and A. H. Heuer. Acta Met. 31 55 (1983).

31. C. Greskovich and J. H. Rosolowski. J. Am. Ceram. Soc. 59 336 (1976) •

32. C. E. Scott and J. S. Reed. Bull. Am. Ceram. Soc. 58 587 (1979) •

33. A. E. Nielsen. Kinetics of Precipitation. (MacMillan. N.Y.).1964.

34. G. W. Greenwood. Acta Met. ! 243 (1956).

35. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19 35 (1961).

36. C. Wagner. Z. Electrochem. 65 581 (1961).


37. H. Fischmeister and G. Grimvall. Maters. Sci. Res. ! 119 (1973).

38. G. C. Kuczynski. G. Matsumura. and B. D. Cullity. Acta Met. ! 209 (1960).

39. R. J. Brook. p. 331 in Ceramic Fabrication Processes. F. F. Y. Wang. ed •• Vol. 9 in Treatise on Materials Science and Technology. (Academic Press. N. Y.). 1978.

40. R. J. Brook. 1. Am. Ceram. Soc. 52 56 (1969) •

41. F. M. A. Carpay. 1. Am. Ceram. Soc. 60 82 (1977) •

42. P. G. Shewmon. Trans. AIME 230 1134 (1964) •

43. F. A. Nichol s. 1. Nucl. Maters. 30 143 (1969) •

44. T. R. Anthony and R. A. Sigsbee. Acta Met. 19 1029 (1971).

45. W. D. Kingery and B. Francois. p.471 in Sintering and Related Phenomena. G. C. Kuczynski. N. A. Hooten. and C. F. Gibbon. eds •• (Gordon and Breach. N.Y.). 1967.

46. T. Quadir and D.W. Readey. to be published.

47. J. Lee and D. W. Readey.in this volume

48. C. Greskovich and K. W. Lay. J. Am. Ceram. Soc. 55 142 (1972) •

49. S. Prochazka. C. A. Johnson. and R. A. Giddings. p. 366 in Factors in Densification and Sintering of Oxide and Nonoxide Ceramics. (Tokyo Inst. of Tech •• Tokyo. Japan). 1979.

50. S. Prochazka and C. F. Bobik. p. 321 of ref. 14.

51. T. Quadir and D. W. Readey. to be published.

EFFECTS OF OXYGEN PRESSURE AND WATER VAPOR ON SINTERING OF ZnO

O.J. Whittemore and S.L. Powell

University of Washington, Seattle, Washington 98195

ABSTRACT

ZnO compacts were sintered at 650 to 7500C. in dry air, dry argon, argon \'iithupto 50% oxygen , and air-water vapor mixtures. The progress of sintering was measured by mercury porosimetry from which linear shrinkages, volume shrinkages, surface areas, and pore diameters were derived. In the water free atmospheres, initially about 80% loss in surface area and small pore growth occurred, followed by more rapid shrinkage than predicted with relation to surface area reduction. No relation was found with oxygen pressure. The presence of water vapor in air caused pore growth at 6500C. rel ated 1 i nearl y with shri nkage but without relation to the water vapor pressure.

INTRODUCTION

The sintering of ZnO has been studied by several workers. Shrinkage and gra ingrowth of compac ts has ~e3n one method of study 1 wll i 1 e the loss of surface area has been another' . Komatsu and MoriYRshi have both shrinkage and grain growth in various oxygen pressures ,5 and in hel i urn and nitrogen . Util i zi ng mercury poros imetry, pore sizes, surface areas, and densities have been measured on compacts after sintering in roomair 7, and indryairwithcontrolled watervaporpressures8. This work describes further studies by mercury porisimetry of compacts sintered in various oxygen pressures in argon as compared with dry air and air with various water pressures.

EXPERIMENTAL

(1) Sample Processing

"French process" ZnO with a reported mi ni mum of 99.8% ZnO was usedt . This material is made by oxidizing Zn vapor, is not aggregated and has a rel ati ve ly un iform parti c 1 e size of 0.24 llm as measured from SEM photomicrographs. Surface area by nitrogen adsorption was determined as r.4 m2jg which indicates an average particle diameter of 0.25 llm. tSt. Joe Resources Co., ~10naca, Pa.

137

138 O. J. WHITTEMORE AND S. L. POWELL

Compacts were pressed without binder at 4.1 MPa in a steel mold and then isostatically at 213 MPa. The compacts were sintered in an alumina boat in a mu11ite tube with one closed end in an electric furnace. Sintering atmospheres were 1.5 L/minute flowing mixtures of argon and oxygen, both of which had passed through molecular sieve dessicants, or of similarly dried air, or air with water vapor pressures controlled by bubbling through a gas washer.

The boat containing the compacts was first heated in a zone in the tube at about 400°C. for about 30 minutes while the gas mixture was allowed to flow. Then the boat was pushed into the zone of the furnace at the desired temperature and left for the desired time.

Compacts were sintered in atmospheric pressures of pure argon and argon containing 1,20 and 50 volume percent of oxygen at 650 and 750°C. for from 15 to 240 minutes. Characterizations of these compacts will be compared with those previously sintered isothermally for from 1 to 240 minutes in dry air at 650, 700 and 725°C. or in air with various partial pressures of water vapor at 650°C.B

(2) Characterization

The principal method of characterizing the sintered samples was by mercury pore size distribution (PSD). Bulk densities were determined by difference from the total pore volume and also by mercury displacement. Relative volumetric and linear shrinkages were obtained, as follows:

= p/p - 1

= (~V/V + 1)1/3 - 1 o

(1)

(2)

where ~V/Vo is the relative volumetric shrinkage, ~L/Lo is the relative linear shrinkage, Po is the initial bulk density, and P is the density at time t.

From the PSD were determined the mid-pore diameters, defined as the pore diameter when half of the pore volume has been intruded by the mercury.

Surface areas were calculated from the PSD curves using the re1ationshi p9:

S f~P P dvIYm cos e

o (3)

EFFECTS OF OXYGEN AND VAPOR ON SINTERING OF ZnO 139

where S is the total surface area, v is the cumulative volume intruded at pressure P, Ym is the surface tension of Hg, and e is the effective contact angle between Hg and the sample (137°). Good agreement was reached with surface areas determined by nitrogen adsorption.

SEM photos were made of compact fracture surfaces.


All relationships described below involve the state of the initial compact. The initial bulk density was 3.57 g/cm3 which is 63.7% of theoretical density or near the density termed "random close packing" for spheres, the maximum attainable by vibratory compactionlO . Figure 1 shows the structure of the initial compact. The particles can be seen to be fairly equiaxial and uniform in size but not aggregated and these properties are probably due to the method of manufacture by oxidation of Zn vapor. The high compact density can be attributed to non-aggregated equiaxial particles. Gupta and Cable used a similar material and had green compact densities of 66 to 68%, the higher value probably being due to a wax binder and a higher compaction pressure. However, Komatsu et al. used calcined zinc carbonate and their lower initial compact density of 50% may have been due to particle aggregation.

Fig. 1. Fracture surface of ZnO compacts before sintering (left) and after 240 min. at 750°C. in 50% argon - 50% oxygen (right).


The other initial compact properties were: mid-pore diameter, 0.124 ~m; surface area, 3.6 m2jg; and particle size, 0.25 ~m.

Shrinkage rates for compacts sintered in dry air are plotted in Fig. 2 together with those for compacts sintered in dry argon and in argon containing 1%, 20% and 50% oxygen at 650 and 750°C. No systematic progression with oxygen pressure was noted. Log-log plots of shrinkage vs. time showed an initial curved portion as reported by Moriyoshi and Komatsu4 and also their slope of 0.31 for the 750°C. samples but a slightly higher slope for the 650°C. samples. They associated grain growth with the initial curved portion. Another explanation could be particle rearrangement as recently shown for MgO.11

0.10 r---.--,.----,--,-----::1

%02 inAr

.J 0 0 ::J 0.08 /::, I <I + 20 ai 0>

..£ 0.06 c: . .:

.s::. f/)

o 50

o

250

time (min)

Fig. 2. Shrinkage rates of ZnO compacts sintered at 650°C. and 750°C. in dry air and in dry argon with various oxygen contents.

The relationship between densification and pore size (from PSD) is shown in Fig. 3 where relative volumetric shrinkage is plotted vs. the relative mid-pore diameter for samples sintered in water-free atmospheres. The straight line represents shrinkage of pores at the same rate as the sample volume. Inall cases, an initial pore growth occurred probably due to surface diffusion. At 700 and 725°C. in dry air, the curves paralleled the theoretical line. At 650°C. in all dry atmospheres, no systematic change occurred so points are not linked. Pore diameters appear to

EFFECTS OF OXYGEN AND VAPOR ON SINTERING OF ZnO

change little in size as shrinkage continues. At 750°C. in dry argon and in argon with various oxygen pressures, similar nonsystematic behavior was noted.

o ::: 0.3.----,-------,----.-------.---.----, > <l

'r-~ 0.2 .c VI +

o

%02inAr x-dry air o 0 0

'" I + 20 o 50

U o or-~

-i-> QJ E ::::s r- 0.1 0 > QJ

>

o

+ o

x

0 0 + x

650°C '" D ~+

x

x x~--~----~--~--~~--~ 0.2 0 -0.2

relative mid-pore diameter3, (d/do)3_1

141

Fig. 3. Relative volumetric shrinkage vs. relative mid-pore diameter cubed of ZnO compacts sintered in dry air at 650, 700 or 725°C. or in dry argon with various oxygen contents at 650 or 750°C. at times from 1 to 240 minutes. The solid line represents homogeneous pore shrinkage.

However, when water vapor is present in air and irrespective of the amount, the pores in samples sintered at 650°C. grow while the sample shrinks. This relationship is shown in Fig. 4. In dry air, after an initial 7% of pore growth, the pore diameter remains approximately constant while shrinkage proceeds to 4%. In air containing water vapor up to maximum (101.3 kPa), pores grow linearly with shrinkage. Pore growth was reported in ZnO compacts sintered in room air for 1 to 63 hours at from 450 to 600°C.7 It is now believed that this pore growth was caused by the water present in room air.

Another method of demonstrating the effects of sintering on microstructure of compacts is to follow the rate of surface area reduction. If the total surface area loss is due to neck growth,


o ...J "-

0 .06

0 .05

<! 0 .04

'" 0> o ~ 0 .03

g 0 .02 ~

0 .01

o

I r o 0 kPo o 8.7 kPo x 16.0 kPo o 49.3 kPo 6 101.3 kPo

01

I • I

o I 6

I I

01 x

o ' 0/ .1

o I~

I 0 I.

o 100

I x oox,6

o~_~~ __ ~~~~ __ ~~~~--~ o 0.1 0 ,2 0.3 0,4 0.5 0 .6

relotive pore growth, dido-I

Fig. 4. Linear shrinkage vs. relative pore growth of ZnO compacts sintered at 650°C. in dry air or air with various pressures of water vapor for 1 to 240 min.

surface area and neck size have been related12 as 2 !S/So = Nc .(x/2r) (4)

where !S/SQ is the relative reduction of surface area, Nc is the mean coordlnation number per particle, x is the neck size, and r is the particle radius.

The coordination number increases with relative density and a linear approximation is13 :

Nc = 16 p/Pt - 2 (5)

where P is density and Pt is the theoretical density.

By combining equations (1), (2), (4), and (5), Varelall derived the following relationship between reduction in surface area and linear shrinkage:

!S/So = [16 po/Pt (~L/Lo + 1)3 - 2] (~L/Lo) (6)

EFFECTS OF OXYGEN AND VAPOR ON SINTERING OF ZnO 143

This relationship is plotted as a solid line in Fig. 5. The actual relationship for ZnO compacts sintered in dry air for 1 to 240 min. a~ from 600 to 725°C. was found to follow the dashed line of Fig. 5. At first, some surface is lost without associated shrinkage and this could be due to surface diffusion. Then, linear shrinkage proceeds at a faster rate than predicted by eq. (6) and crosses the line at 3% shrinkage. A combination of particle rearrangement with densifying diffusional mechanisms could explain this behavior. The samples sintered in argon or argon mixed with up to 50% oxygen also follow the same relationship with no correlation with oxygen pressure.

O.IOr---r----,---,....----r------r--,----r-=O----,

o ...J "-...J 0.08 <1

Q)

0-

~ 0.06 .S ~

..c: on

20.04 c

Q)

> ::§ 0.02 ~

% O2 in Ar o 0 t:. I + 20 o 50

/ / 0

/ + /

/. 0 /+

/0 ...-::

relative decrease in surface area, AS/So

o

-0.8

Fig. 5. Relative linear shrinkage vs. relative decrease in surface area of ZnO compacts sintered in various 02 pressures at 650 and 750°C. for from 15 to 240 min. The dashed line represents similar data for sintering in dry air at 600 to 725°C. for from 1 to 240 min. The solid line is the plot of equation (6).

It should be noted that the geometrical assumption i2 eq. (4) was that the variation of surface area is given by S = ~ x which limits the validity of eq. (6) to ~S/So ~ 0.5.

CONCLUSIONS

After about 8% loss of surface area and an initial small pore growth probably due to surface diffusion, relative linear shrinkage of ZnO compacts was found to increase more rapidly with relation to reduction in surface area than predicted by equation (6)


derived for surface area loss due to neck growth when sintering was conducted in (1) dry air, (2) dry argon, and (3) argon mixed with up to 50% oxygen. This relationship was interpreted to be due to a combination of rearrangement with densification mechanisms.

In water free atmospheres, after the initial small pore growth, pore dimensions remain relatively constant in size while shrinkage proceeds to at least 4%. However, at 650°C. in air, the presence of water vapor causes pore growth related linearly with shrinkage but without relation to the proportion of water vapor.

There appears to be no relation between oxygen pressure in argon with shrinkage, pore size, or surface area reduction in ZnO compacts sintered from 15 to 240 minutes at 650 and 750°C.

ACKNOWLEDGEMENT

The authors gratefully acknowledge the support of this work by the National Science Foundation, grant no. DMR 8,111,111.

REFERENCES

1. T. K. Gupta and R. L. Coble, J. Am. Ceram. Soc. 51,9,521-25 (1968).

2. T. J. Gray, J. Am. Ceram. Soc. 37, 11, 534-39 (1954). 3. D. Dollimore and P. Spooner, Trans. Faraday Soc. 67, 9, 2750-59

(1971) . 4. Y. Moriyoshi and W. Komatsu,J. Am. Ceram. Soc. 53, 12, 671-75

(1970). 5. W. Komatsu and Y. Moriyoshi, Yogyo-Kyokai-Shi 76, 31-35 (1972). 6. Y. Moriyoshi, Y. Ikuma, O. Maruyama and W. Komatsu, Z. phys.

Chemie, Leipsig 261, 825-28 (1980). 7. O. J. Whittemore and J. A. Varela, J. Am. Ceram. Soc. 64, 11,

C154-155 (1981). 8. O. J. Whittemore, J. A. Varela and E. S. Tosaya, 5th Inter

national Meeting on Modern Ceramics Technologies, Italy, 1982. 9. H. M. Rootare and C. F. Prens1ow, J. Phys. Chern. 71,8,2734

(1967) . 10. R. K. McGeary, J. Am. Ceram. Soc. 44, 10, 513-522 (1961). 11. J. A. Varela and O. J. Whittemore, J. Am. Ceram. Soc. 66,1,

77-82 (1983). 12. R. M. German and Z. A. Munir, J. Am. Ceram. Soc. 59, 9-10,

379-83 (1976). 13. F. B. Swinkels and M. F. Ashby, Acta Meta11. 29, 259-81 (1981).

MICROSTRUCTURE D~VELOPMENT OF Fe203 IN HCL VAPOR

J. Lee and D. W. Readey

The Ohio State University Columbus. Ohio 43210

INTRODUCTION

During sintering. particles and pores change size and shape to decrease the interfacial energy of the system. The pores shrink and the grains or particles grow. Since surface energy is the driving force for both processes. their comparative rates determine the densification rate and microstructure evolution. Since the goal of sintering is to obtain a desired microstructure. it is critical to understand the relationship between the two processes.

The four mass transport mechanisms operative in sintering of crystalline materials are lattice. grain boundary. and surface diffusion. and vapor transport1 •2 •3 • The former two produce densification and the latter morphological changes only with no densification. Among these processes. vapor transport is probably the least studied yet is the only mechanism which can be easily controlled by the experimental conditions4. Thus. enhancing vapor transport permits the observation of controlled microstructure development with the intent of obtaining an improved fundamental understanding of the sintering process rather than an immediate improvement in densification kinetics or final density. This paper reports some effects of enhanced vapor transport on microstructure development during the early stages of densification of Fe203 powder compacts.

In the final stage of sintering when pores are isolated. grain growth takes place by grain boundary migration. Ideally. pores move with grain boundaries. However. when pore mobilities are sufficienty low so that the pores can not keep pace with the moving boundaries. pore separation occurs leading to secondary grain growth and pore entrapment. Since vapor transport is one of the

145

146 J. LEE AND D. W. READEY

several possible mechanisms for pore migration, increased pore mobility is expected with enhanced vapor transport. Some preliminary results of experiments to enhance pore mobility to retard secondary grain growth by controlling vapor tranport are also reported.

Vapor transport can be increased in Fe203 by the introduction of BCl gas to increase the vapor pressure of the product species:

FeCl3 and FeCl2 are also possible vapor species, the vapor pressure of each iron chloride depends on the temperature and water vapor content of the ambient BCl gas. For the above reaction, the equilibrium constant, Ke , is given by:

The equilibrium constant can be calculated from thermodynamic data5 • Thus, by varying the BCl pressure in the system, the product gas pressures can be calcuated and the amount of vapor transport controlled.

EXPERIMENTAL One of the reasons Fe203 was chosen for investigation

was that the product gas pressures achievable at reasonable temperatures and BCl pressures are quite high ensuring significant enhancement of vapor transport. Another reason was the availability of a relatively pure, nonagglomerated commercial powder(Baker Reagent grade) having an average particle size around 0.2 ~.

Pellets 1.4 cm in diameter and approximately 0.3 cm thick were made by pressing in a steel die at 5000 psi to a green density of 48 percent of theoretical. The pellets were prefired at 5000 C for one hour to provide some green strength. After firing at various temperatures and times in different atmospheres, the shrinkage was measured and the microstructure examined. To avoid severe weight loss due to vaporization, samples fired in high BCl pressures were encapsulated in fused silica ampules. The resultant porous samples were impregnated with a lead-borosilicate glass in vacuum to minimize pull-outs during polishing and the polished sections were analyzed quantitatively by semiautomatic image analysis (Zeiss Videoplan). Pore sizes were determind by mercury porosimetry. Belium was used as an inert carrier gas.

For the experiments to attempt to increase pore mobility by

MICROSTRUCTURE DEVELOPMENT OF Fe2031N HCL VAPOR 147

vapor transport during the final stage of sintering. pellets were first fired in air to 70 to 90 percent of theoretical density before the introduction of HCl vapor. With this procedure it was hoped to introduce the reactant gas before pore closure yet not so early in densification to prohibit further shrinkage to the closed pore stage.


Early Stage Microstructure Development Shrinkage versus time data are shown in Figure 1 as a function

of the ambient HCl pressure at 9000 C. As expected. as the HCl pressure and the amount of vapor transport increases. densification decreases. For HCl pressures in excess of 0.1 atm. there is no shrinkage at all. However. as Figure 2 dramatically shows. the reason for this decrease in densification is due to particle coarsening via vapor transport and not due to neck growth between particles. Figure 3 shows a typical polished section used for quantitative microstructure analysis •

.:J 20 ~ "- 90 .0;

...J <J c

~ a> Air 80 en "0 0

¥ .:c; c ·c ~ c-

10·'HCI 70 g en C c-

f-a>

~ e If 60 ~ a.

10·'Hel

50 IO·'HCI

47 3 10 30 100 300

Time (min)

Figure 1. Typical shrinkage curves for Fe203. 9000 C.

Figure 4 demonstrates that the particle or grain size grows as the one third power of time in agreement with classical Ostwald ripening by diffusion through the gas phase6 •7 •8 • Figure S gives


Figure 2. Fracture surface of Fei03 sintered at 12000 for 5 hours. in air(left). and in 10 percent HCl(right).

Figure 3. Glass encapsulated and polished sample fired at 12000 C for 5 hours in 10 percent HCl. polarized light.

MICROSTRUCTURE DEVELOPMENT OF Fe2 0J IN HCL VAPOR

Firing Temp. Slope

1200°c 0.41

1150°c 0.35 E

I 100°C 0.36

-=- 30 I!:l iii 20 Q)

;g c£ 10

6. e 5 Q)

> <t

2

Time(minl

Figure 4. Particle size versus time for Fe203 sintered in 10 percent HCI.

1.0

~ 1200°C U'i 10-1 HCI c '0 ....

0 <!> 0 0 ....... 0.5 0 0 Cll N

U'i .::£ 0 Cll Z

0 ,L

10' 102

Time(min)

149

Figure S. Ratio of interparticle neck size to particle size as a function of time.


the ratio of the interparticle neck size to the particle size as a function of time and shows that it remains constant during the times of measurement. This implies that the interparticle necks quickly grow to a steady state ratio and then the entire structure coarsens uniformly. This occurs apparently very rapidly. certainly within the first three minutes of the firing. Since the entire structure coarsens uniformly. it might be expected that the pore size would also coarsen as the one third power of time. Figure 6 shows typical pore size distributions obtained by mercury porosimetry. Note the sharpness of the distributions and invariance of their shape. Figure 7 illustrates that the average pore size does indeed grow as the one third power of time.

As mentioned above. the one third power dependence of the particle coarsening with time is typical of Ostwald ripening via vapor phase diffusion since:

-3 _ ~ Dyn; p t r - 9 (RT) 0

for diffusion and for an interface controlled reaction:

(8~ K n2 r2 = - U-2 P o t 9 (RT)

where r average particle radius K surface reaction rate constant n molar volume D gaseous diffusion coefficient R gas constant T= temperature Po = equil ibrium

In the above equation for exponentially temperature pressure of the diffusing FeC12' FeC13' or Fe2C16.

partial pressure.

Ostwald ripening by diffusion. the only dependent term is the equilibrium partial gaseous species which in this case is For the latter.

if the ambient water vapor pressure in the HCl is much lower than that produced in the reaction. If the reverse is true. then

This implies that the apparent activation energy for the coarsening process is either AlJ,o/40r AHo where AHo is the standard enthalpy for the reaction. Taking into account all three possible iron chloride gaseous species and both high and low ambient water vapor pressures in the HCl. the predicted activation

MICROSTRUCTURE DEVELOPMENT OF Fe2 031N HCL VAPOR

c 100 .E I- o IAtm HCI

1050·C

0

Yf r

.J 10' 10°

Pore Size (fLm)

lI.300mln o30m,n. O3m,n

10'

Figure 6. Pore size distributions for different firing times obtained by mercury porosimetry.

l lo' w N

en w

& "'C 10 ~

Te"" SlOpe o 1200·C 037 l> 1150·C 026 o IIOO·C 029

Temp SlOpe OI050·C 032 e IOOO·C 027 ... 900·C 029

151

Figure 7. Mid pore size versus time showing a one third power dependence.


energy lies between 6 and 24 kilocal/mole5 • In Figure 8 is plotted the temperature dependence of the particle coarsening rate with an apparent activation energy of 58.0 kilocal/mole which is much larger than that expected from tabulated thermodynamic data. As a result. the classical Ostwald ripening model of this coarsening must be questioned. Furthermore. the observed particle size distributions. as shown in Figure 9. are strongly skewed to large particles which is completely opposite to that expected from Ostwald ripening theory6.7.8. Thus. it must be concluded that some other process with a higher activation energy is controlling particle growth just as in the case of Zn09 • Specifically. the data tend to indicate that coarsening may be controlled by grain boundary migration even though the major mass transport is via the vapor phase. This is the Greskovich-LaylO mechanism which has been proposed to explain grain growth in porous compacts.

One of the advantages of vapor phase transport processes is that all of the parameters of the system. such as the gaseous diffusion coefficient. should be either available in the literature or calculable. This is quite different than transport by solid state diffusion processes for which there is a paucity of reliable diffusion coefficient data for ceramic materials and those which do exist may vary by several orders of magnitude from investigator to investigator. As a result. experimental results of vapor transport can be quantitatively compared with the models as a further evidence for a rate controlling mechanism far more easily than can solid state diffusion processes. In this case for example. taking y ~ 500 erg/cm2 • and D ~ 1 cm2/s the calculated particle size at 12000 C in pure HCl after 10 minutes is 11 ~ and that measured. 6~. This is extemely good agreement considering the approximate values of y and D used and the uncertainties in the model. Nevertheless. it reinforces the argument that gaseous diffusion is major mass transport process leading to particle growth while grain boundary migration may be rate controlling.

Final Stage Sintering When the pores move with the boundary. the pore velocity. vp'

and the grain boundary velocity. vb' are the samell.12.13 and are determined by the force on the pore. F • caused by the boundary curvature and the pore mobility. ~14.15.16:

The pore mobilities are given by:

for vapor diffusion.

MICROSTRUCTURE DEVELOPMENT OF Fe2 031N HCL VAPOR 153

-12

Qo 58.0 keol/ mole

- 13

Figure 8. Temperature dependence of the rate of particle coarsening in 10 percent HCI with an activation energy larger than that predicted by the gas transport model.

300',---,----,----,----,----,

50

Groin Size(fLm)

Figure 9. Typical particle size distribution, S hours at 10S0oC in 10 percent HCI.


M b =~ P. ~

for volume diffusion.

M = DsaO P. s rrr4RT

for surface diffusion.

where Dg• ~. and Ds = gaseous. solid. and surface diffusion coefficients respectively. a = the thickness of the surface diffusion layer. r = the pore radius. and M = the molecular weight.

Comparing pore mobilities for vapor transport and volume diffusion at 14000 C by taking Db = 1.5xl0-lO cm2/s17 and Dg = 1 cm2/s. ~.v/Mp.b = 4.4 for an HCI pressure of 10-4 atm. Therefore. for any HCI pressure greater than this. pore mobility should be greatly enhanced and secondary grain growth retarded. Figure 10 is the calculated pore-grain boundary stability diagram after Brookll in 10-3 HCI showing that secondary grain growth should be retarded by enhanced vapor transport.

However. the theoretical prediction was not verified by experiment. Secondary grain growth could not be retarded with HCI pressures up to 10-2 atm if it were added at fired densities between 70 and 90 percent of theoretical. The reason for the lack of grain growth retardation is not clear at present.

Two very interesting observations were made however. First, 10-3 and 10-2 atm HCI pressures had no affect on retarding densification when added at 85 percent of theoretical density as shown in Figure 11 which should be contrasted with the data in Figure 1 which shows that these HCI pressures inhibited densification if added at the start of sintering. Second. the major factor affecting the occurence of secondary grain growth. regardless of the atmosphere. was the green density of the compact. Figure 12 shows a micrograph of a sample with a green density of 48 percent exhibiting secondary grain growth in contrast with a sample of 51 percent green density showing no secondary grain growth. Fifty percent seemed to be about the critical green density below which secondary grain growth always occured. Why the initial green density is so critical is not known but certainly must be related to the densification path in grain size-density space.

MICROSTRUCTURE DEVELOPMENT OF Fe10JIN HCL VAPOR

Figure 10.

>. 95 -iii c 8 "0 u ~ \-

90 0 Q) .c I-~ 0

85

103

E ::t. 2

a; 10 N

iJ'J c

~ 10'

Pore-Boundary SeporallQr'l RegIOnS

10' L----L-__ -"-=-__ '-c-_--'--:-_---L;-'

10' 10' Id Pore Size (I'-ml

Caloulated grain-pore size plot showing pore, grain boundary separation regions in both air and HClll.

IV' IV'

10

Time{minl

0 0 0 t:,.

\l

r:r--

100

Air 2x 10' Aim HCI 10'AIm HCI IO' Alm HCI I AIm HCI

155

Figure 11. Density versus time plots after initially firing in air to 8S peroent density at 10S0oC for one hour.


Figure 12. Fe2~ samples fired in air for 15 hours at 12000 C. left 51 percent and right 48 percent green density.

SUMMARY AND CONCLUSIONS

1. Vapor phase transport of Fe203 is enhanced in HCI vapor.

2. Vapor transport of Fe203 retards sintering primarily by particle coarsening.

3. The entire microstructure coarsens uniformly. 4. Both the particle size and the pore size follow a one third

power dependence on time. 5. Pore size distributions are very narrow. 6. Grain boundary motion controls the rate of particle

coarsening. 7. Secondary grain growth could not be eliminated by enhancing

vapor transport during the final stage of sintering. 8. Enhanced vapor transport was far less effective in limiting

densification kinetics during the later stages of sintering.

9. Green density has a significant effect on the final microstructure with green densities less than 50 percent of theoretical leading to secondary grain growth.

ACKNOWLEDGEMENTS The assistance of L. Tiffenbach with the pore size and particle

size measurements is appreciated. This research was sponsored by the Office of Naval Research.

MICROSTRUCTURE DEVELOPMENT OF Fez031N HCL VAPOR

REFERENCES

1. G. C. Kuczynski, Trans. AIME 105 169 (1949).

2. W. D. Kingery and M. Berg, J. Appl. Phys. 26 1205 (1955).

3. R. L. Coble and R. M. Cannon, p. 291 in Vol.l1 of Materials Science Research Processing of Crystalline Ceramics, (Plenum, N. Y.), 1978.

4. D. W. Readey, J. Lee and T. Quadir, this volume.

157

S. D. R. Stull and H. Prophet, et al., JANF Thermochemical Tables, 2nd edition (U. S. Govt. Printing Office, Washington, D. C.), 1971.

6. G. W. Greenwood, Acta Met. i 243 (19S6).

7. I. M. Lifshitz and V. V. Slyoz, J. Phys. Chem. Solids 19 35 (1961).

8. C. Wagner, Z. Electrochem. 65 581 (1961).

9. T. Quadir and D. W. Readey, to be published.

10. C. Greskovich and K. W. Lay, J. Am. Ceram. Soc. 55 142 (1972) •

11. R. J. Brook, p. 331 in Ceramic Fabrication Processes, F. F. Y. Wang, ed., Vol. 9 in Treatise on Materials Science and Technology, (Academic Press, N. Y.), 1978.

12. R. J. Brook, 1. Am. Ceram. Soc. 52 56 (1969).

13. F. M. A. Carpay, 1. Am. Ceram. Soc. 60 82 (1977) •

14. P. G. Shewmon, Trans. AIME 230 1134 (1964) •

15. F. A. Nichols, 1. Nucl. Maters. 30 143 (1969) .

16. T. R. Anthony and R. A. Sigsbee, Acta Met. 19 1029 (1971) •

17. V. I. Izvekov, et ai, Phys. Metals and Metallog. 14 30 (1962) .

MICROSTRUCTURE EVOLUTION IN Sn02 AND CdO IN REDUCING ATMOSPHERES

T. Ouadir and D. W. Readey

The Ohio State University Columbus. Ohio 43210

INTRODUCTION

Microstructure control during sintering of ceramics is necessary in order to tailor the microstructure to obtain the properties desired in the final material. Such control can only be achieved through a thorough understanding of the relative contributions of the mass transport mechanisms of bulk. grain boundary. and surface diffusion. and vapor transport. Unfortunately. there is a paucity of diffusion data in the literature making it difficult to compare experimental results to sintering models1 •2 • On the other hand. vapor phase transport coefficients exist or can easily be calculated permitting comparison between experiment and models if vapor transport is the dominant transport mechanism3 •

In this research. the microstructure evolution during the sintering of CdO and Sn02 powder compacts was studied with vapor transport enhanced in reducing atmospheres containing hydrogen. CdO and Sn02 were chosen for study because of the high vapor pressures which could be generated at relatively low temperatures thus ensuring the dominance of vapor transport over other mass transport processes.

EXPERIMENTAL

Relatively nonagglomerated reagent grade(Baker) CdO and Sn02 powders having average particle sizes on the order of a few tenths of a micrometer were pressed at 10.000 psi into pellets 1.4 cm in diameter. A green density of 61 percent of theoretical was obtained with CdO and SS percent with Sn02. The pellets were fired in air at temperatures below SOOOC to provide some green

159

160 T. QUADIR AND D. W. READEY

strength. Pellets were placed into fused silica ampules which were then evacuated and dried until a dew point of -320 C or less was achieved. The ampules were then filled with dry hydrogen at an appropriate pressure so that the pressure at the firing temperature would be in the neighborhood of one atmosphere. The pellets were fired for different times at various temperatures. After firing, samples were removed and their dimensions measured to determine shrinkage and their fracture surfaces examined by scanning electron microscopy. Quantitative microstructure determinations were made with a semi-automatic image analyzer(Zeiss Videoplan). At least 60 particles or grains were measured for each data pOint and over 300 measured to obtain particle size distributions.


Cadmium Oxide The densification rates of CdO in air and hydrogen are

compared in Figure 1. Note that significant densification was observed in air at 7000 C while no shrinkage occured in hydrogen. It might be noted that densification was observed as low as 3000 C in air. Results at other temperatures were similar except that at the highest temperatures studied, some densification occured even in the pure hydrogen atmosphere. As can be seen in Figure 2 the reason that densification does not occur in hydrogen is due to particle coarsening similar to that observed for ZnO in hydrogen4 and Fe203 in BCIS. Figure 3 demonstrates that the particle or grain size follows a time to the one third power dependence as

90

~ CdO "(ji 80 700°C c Air Q) 0

V Q) 70 > :;::: PH2 =1.2Atm 0

& 60 C B

50 ... &

0 10 20 30405060 70 80 90 100

Time (min)

Figure 1. Density versus time for CdO fired in air and hydrogen.

EVOLUTION IN SnOz AND CdO IN REDUCING ATMOSPHERES

Figure 2. CdO fired at 7000 C for 100 minutes in air(left) and hydrogen(right).

05

CdO 04 Ave. S/ope:033

03

02

E 0 1 :>. u; " ~ 0

Q 038 C1' -01 .5 030

-02

-03 030 " IIOO'C o IOOO·C

-04 • 900°C · 800'C · 700"C

-05 0 15 20

Log,o Time (min)

161

Figure 3. Particle radius versus time for CdO fired in hydrogen.


observed in the other systems4 •S• This is predicted by the classical Ostwald ripening models of coarsening by diffusion through the surrounding fluid phase6 •7 •8• namely:

On the other hand. for an interface controlled reaction:

where r average particle radius K surface reaction rate constant n molar volume D gaseous diffusion coefficient R = gas constant T = temperature Po = equil ibrium partial pressure.

In the above equation for Ostwald ripening by diffusion. the only exponentially temperature dependent term is the equilibrium partial pressure of the diffusing gaseous species. The reaction of importance for CdO in H2 is:

which gives for the equilibrium constant. Ke:

If the ambient hydrogen gas is very dry. as it is believed to be in these experiments. then the only water vapor in th.e system is a product of the reaction so p(H20) ~ p(Cd). This leads to the following temperature dependence of the equilibrium partial pressure of the diffusing gaseous species:

where AHo is the standard enthalpy for the above reaction. On the other hand. if the ambient water vapor pressure in the system were much larger than that produced from the reaction. then p(H20) » p(Cd) and.

Po = p(Cd) «Ke « exp( -AHo/RT).

From above. the rate of particle coarsening can be written as:

r = nl/3.

EVOLUTION IN Sn02 AND CdO IN REDUCING ATMOSPHERES

Since K ~ Pol/3. if the log of the intercepts in Figure 3 are plotted versus lIT. the apparent activation energies are AHol6

163

and AHo/3 for the low and high ambient water vapor pressures. Figure 4 shows the temperature dependence of the rate of coarsening with an apparent activation energy on 8 kilocal/mole. The standard enthalpy for the reduction of CdO in H2 is 5 kilocal/mole9 • Thus the observed activation energy is much larger than is predicted by the gaseous diffusion model of coarsening. These results are similar to those obtained in other systems4 •5 which have been explained3 by the Greskovich-Lay model of particle coarsening in porous compacts10 • The major mass transport is by gaseous diffusion. but the actual rate control is by migration of the grain boundary. Unfortunately. there are no grain growth data for CdO available in the literature with which to compare the observed activation energy for grain growth obtained here.

Furthermore. as Figure 5 shows. the measured particle or grain size distributions are strongly skewed to large particles which is just the opposite to the predictions of the classical Ostwald ripening models6 •7 •8 • These results are again similar to those observed in Zn04 and Fe2035 and give further support to the postulate of grain boundary migration rather than gaseous diffusion being the rate controlling step in the coarsening process.

Tin Oxide The Sn02 exhibited rather unusual behavior in that even in

air no shrinkage was observed over the temperature range studied while in pure hydrogen the samples actually expanded as shown in Figure 6. Again. the major microstructural effect of the enhanced vapor transport was particle coarsening as can be seen in Figure 7. Also. the Sn02 particles exhibited a great deal of faceting even at the highest temperatures studied. That the Sn02 expands can be explained by the fact that the particle growth or coarsening is probably not isotopic since tin oxide is tetragonal. As a result. the particles become somewhat elongated leading to expansion.

Figure 8 demonstrates that the Sn02 grains also grow as the one third power of time as predicted by the Ostwald ripening models6 •7 •8 • In this case. the reaction is thought to bell:

As in the case of CdO. since there are only the two product gases the same considerations hold. namely:

in very dry hydrogen and.

164

o

"§ -0.2 ...... E ::l.. ~

r:J -0.4 .3

-0.6

T. QUADIR AND D. W. READEY

CdO

-0.8 '--_'-----lL----l_---l_---"_---"_-' 7.0 7.5 8.0 8.5 9.0 9.5 100 105

I/Txl04 (OK)

Figure 4. Temperature dependence of the rate of coarsening for CdO fired in hydrogen.

Figure S. Particle diameter(micrometers) distribution for CdO fired at 7000 C for 100 minutes in hydrogen.


?:' Sn02 .~ 75 1275°C ~ Q) 65

.!:! Air "5 55i".... -~ L ........

45 ----__ .-------~~--~ C ~ 35 &

o ~ ~ ~ ~ ~ ro m 00

Time (min)

Figure 6. Density versus time for Sn02 fired in air and hydrogen.

Figure 7. Sn02 fired at 127SoC for 80 minutes in air(left) and hydrogen(right).

165


0 .5

04

0 .3

02

E 01 ::l. U;

:::l '6 0 ~

0 0 .37 a; -01 0 .37 0 0 .33 -.J 0 .31

-02 0.30

o1275°C -03 . 12SOOC

o 1225°C

-0.4 .12000C o 1175°C

-0.50'----'------',...------',...----::"-,...---->

Log,oTime(min)

Figure 8. Particle radius versus time for Sn02 fired in hydrogen.

Po = p(SnO) ~ Ke ~ exp( -AHO/RT)

in wet hydrogen. Again. AHo is the standard enthalpy for the reaction which in this case is 43 kilocal/mole9 • The expected apparent activation energy of the rate of coarsening for this system should likewise be AHo/6 or AHo/3 for dry and wet hydrogen respectively. From the data in Figure 9. an apparent activation energy of 10 kilocal/mole is obtained which lies directly between the two expected activation energies. Thus. in this case it is more difficult to conclude that the rate of coarsening is not controlled by gaseous diffusion but rather by grain boundary migration. In fact. the particle size distribution observed for the Sn02 do not seem to be as strongly skewed to the larger particle sizes as in the case of CdO as seen in Figure 10. However. the particle size distributions still do not fit those expected from the Ostwald ripening models. There have been


-0.20,---,--__ ,--__ ----.--,

-0.25

c -E Q = 10kcai/moie .......

1. -0.30

a r:ii .3

-0.35

Figure 9. Temperature dependence of the rate of coarsening of Sn02 fired in hydrogen.

100

80 >. 0 c 60 Q) ::J

I 40 (J) Ql «

20

0 I 4

5n02

60 mins_

I • • 6 8

167

Figure 10. Particle diameter(micrometers) distribution for Sn02 fired at 127SoC for 60 minutes in hydrogen.


modifications of these models for the case when the volume fraction of the growing particles is large12 ,13 which do lead to distributions more similar to those commonly observed in other systems exhibiting coarsening14 • However, these models do not completely explain the observed distributions and are not even valid when the coarsening particles are in contact as they are in a powder compact. Thus, the rate controlling step in the case of Sn02 is perhaps somewhat more uncertain than in the case of CdO.

CONCLUSIONS

Enhanced vapor transport in the CdG-H2 and Sn02-H2 systems leads to reduced shrinkage and exaggerated particle coarsening as in the ZnG-H2 and Fe203-HCl systems. In the case of Sn02' the powder compacts actually expand which can be explained by nonisotropic par~icle growth. Also as observed in these systems, the particles coarsen as the one third power of time following the classical Ostwald ripening models of particle growth controlled by diffusion through the surrounding fluid phase. However, neither do the particle size distributions fit the models nor do the observed activation energies, particularly for CdO. Unfortunately, really no quantitative coarsening model exists for the case in which the particles or grains are in contact as they are in a powder compact. However, given the generally larger activation energy observed than expected. it is tentatively concluded that the Greskovich-Layl0 model is operative in CdO. That is, the rate of grain boundary migration is controlling the rate of grain or particle coarsening. For Sn02' the evidence is less convincing.

ACKNOWLEDGEMENT

This research was sponsored by the Office of Naval Research.

REFERENCES

1. G. C. Kuczynski, Trans. AIME 105 169 (1949).

2. W. D. Kingery and M. Berg, J. Appl. Phys. 26 1205 (1955).

3. D. W. Readey, J. Lee and T. Quadir, this volume.

4. T. Quadir and D. W. Readey, to be published

5. J. Lee and D. W. Readey, this volume.

6 G. W. Greenwood, Acta Met. ! 243 (1956).

7. I. M. Ufshitz and V. V. Slyozov, J. Phys. Chem. Solids 19 35 (1961) •

EVOLUTION IN SnOz AND CdO IN REDUCING ATMOSPHERES

8. C. Wagner, Z. Electrochem. 65 581 (1961).

9. o. Kubaschewski and C. B. Alcock, Metallurgical Thermochemistry, 5th ed., (Pergamon, N. Y.) p. 267, 1979.

10. C. Greskovich and K. W. Lay, J. Am. Ceram. Soc. 55 142 (1972).

11. H. H. Kellogg, Trans AIME 236 602 (1966)

12. A. J. Ardell, Acta Met. 20 61 (1972).

13. C. K. L. Davies, et al., Acta Met. 28 179 (1980).

169

14. Y. Masuda and R. Watanabe, p. 3 in Vol. 13 of Materials Science Research, Sintering Processes, (Plenum, N. Y.), 1980.

REACTIVE SINTERING OF DIAMOND-TITANIUM SYSTEM UNDER HIGH PRESSURE

ABSTRACT

I. Kushtalova, I. Krstanovic, I. Stasyuk, S. M. Radic and M. M. Ristic Institute of Technical Sciences of the Serbian Academy of Sciences and Arts, Belgrade, Yugoslavia and Institute of Superhard Materials of the Academy of Sciences of Ukr. SSR, Kiev, USSR

The reactive sintering of diamond with titanium was studied. The experiments were carried out at pressures of 4.3 and 7.0 GPa in a "TOROID" type pressure chamber. Under these conditions it was possible to investigate reactive sintering at temperatures up to 1973°K without graphitization of diamond.

INTRODUCTION

Sintered diamond-metal systems have wide applications in modern technology. These materials have high resistance against abrasion. The effectiveness of these materials to resist abrasion and wear depends to a large extent on the structure at the interface between the diamond and the metal matrix.! A number of factors may be of importance; the reaction between diamond and the metal, dissolution of carbon (diamond) in the metal, the formation of interphases, adhesion and the phase transformation of diamond to graphite. 2

A. B. Nozhkina2 showed that the sintering of diamond with transition metals, within the temperature range 573-2123 K depends upon the interfacial energy between diamond and the metal. In the case of diamond the wetting of the surface. by titanium is considerably higher on the (100) plane than on the (ll'l) plane. This may have considerable effect on the sintering mechanisms.

171

172 I. KUSHT ALOVA ET AL.

ExpEalMENTAL PROCEDURE

For the sintering studies particles of diamond and high purity titanium, of 10~m and 3~m respectively, were homogeneously mixed together with a volume ratio of 70:30 (diamond/titanium).

The sintering was carried out in a high temperature "TOROID" type pressure chamber. A pressure of 4.3 GPa was used in the temperature range 973 to 1573 K and a higher pressure of 7 GPa was used for temperatures between 1573 and 1973 K. The time at maximum temperature was 120 seconds. Also some samples were sintered at a pressure of 4.3 GPa for intervals of time ranging from 30 to 480 seconds.

X-ray diffraction was used to determine the structure of new phases produced during the sintering process. A philips PW 1051 X-ray diffractometer was used for these studies. To simplify the identification of new phases, standards were made by subjecting the pure starting materials and pure powders of titanium carbide to the same condition of pressure and temperatures as were used for the sintering reaction experiments.


It was found that reactive sintering between diamond and titanium started at a temperature of 973 K. Figure 1 shows the effect of sintering temperature at a pressure of 4.3 GPa on the sintering reaction between diamond and titanium. It can be seen that as the temperature was increased from 973 to 1573 K there was a reduction in intensity of the Ti diffraction peak. The unit cell dimension of the TiC phase produced by the reaction was determined from the diffraction peaks to be 0.4283 nm.

Increasing the pressure from 4.3 GPa to 7 GPa under the same sintering conditions (973K, 60 secs) was found to reduce the amount of titanium carbide produced (Figure 2). This may be due to the fact that the titanium carbide lattice is larger than that of pure titanium.

4 Kis1i et a1. also reported that the reactive sintering re-action between diamond and titanium could first be observed at a temperature of 973K even though their experiments were carried out at much lower pressures (1.3 x 10-3 Pa).

It can be seen from Figure 1 that the rate of reaction between diamond and titanium is considerably increased by increasing the sintering temperature. Table 1 shows that lattice parameter of titanium carbide is increased as the sintering temperature is increased.

SINTERING DIAMOND-TITANIUM SYSTEM UNDER PRESSURE

Ti{!qt)

r ..

TiC

base stock

CD ~ TiC

TiC

Ti.

~

f-'''--

~

..,J

CD

./

S,

A

f-etc 25 degree)

riC T;G

~

lML T,C T,C

.@ll!<

0v T.C 'I.....---

T.e 1473K

~L To( TIC

~

U"----20 15

173

Fig. 1. X-ray spectra of reaction products in diamon-titanium system under a pressure of 4.3 GPa for 120 sec.

174 I. KUSHTALOVA ET AL.

Table 1. Dependence of the Unit Spacing of Crystalline Lattice of Titaniu~Carbide on Temperature Interaction (t=60 sec.)

Temperature Sintering Pressure (K) 4.3 GPa 7.0 GPa

a(nm) a (nm)

973 0.4283

1073 0.4288

1173 0.4293

1213 0.4297

1373 0.4306

1473 0.4314

1573 0.4310

1673 0.4318

1773 0.4321

1873 0.4323

1973 0.4324

The experiments on the effect of time of sintering on carbide formation at a constant temperature of 1273 K show that the fastest rate occurs during the first minute of heating (Figure 3). A considerable amount of carbide is formed in 30 sec. After 60 seconds the amount of carbide does not change appreciably with time up to 480 sec. However the lattice parameter (a) of the carbide does continue to increase with time3 as can be seen from the data presented in Table 2.

Table 2. Dependence of the Lattice Parameter (a) of Titanium Carbide on Sintering Time and Temperature at a Constant Pressure (p=4.3 GPa).

Temperature a{nm) (K)

30S 60S 120S 240S 480S

1273 0.4287 0.4294 0.4297 0.4299 0.4301

1573 0.4311 0.4313 0.4318 0.4320 0.4321

SINTERING DIAMOND-TITANIUM SYSTEM UNDER PRESSURE 175

1l

4.3Gta.

Tr

' .. T;

Fig. 2. X-ray diffraction spectra of reaction products in diamondtitanium system at temperature of 973 K during 120 sec. for pressures of 4.3 GPa and 7.0 GPa.

The high initial rate of reaction of titanium carbide and the subsequent slowing down of the rate, which was also observed by Kisli et al. 4, can be explained as follows. The initial stage of the reaction is controlled by reaction at the interface between diamond and titanium. This reaction occurs very rapidly in powders. Once the initial carbide layer is formed then the process becomes more complex due to carbon diffusion through the carbide layer. The rate of carbon diffusion through the carbide is reduced as the pressure is increased from 4.3 GPa to 7.0 GPa.

According to the equilibrium phase diagram for diamond,S the graphite phase should be stable at 1573 K at a pressure of 4.3 GPa. However, since the transformation from diamond to graphite is diffusion controlled, an appreciable amount of graphite is only formed after 480 seconds under these conditions of temperature and pressure.

176

Fig. 3. Influence of time on reaction in diamond-titanium system at temperature of 1273 K and under the pressure of 4,3 GPa.

Ti T., T<

~ r.

~

TIl '- '" '" 2

'" ~

'0< '- "' ~ ,

18731<

I. KUSHT ALOVA ET AL.

. '" Q.S'

,., '. n< T<

..

1973K

Fig. 4. X-ray spectra of reaction in diamond-titanium system under the pressure of 7 GPa during 120 sec.

'i< c.,


At higher temperatures 1673 and 1773 K. the time to produce an equivalent amount of graphite at 4.3 GPa is reduced to 240 and 120 seconds respectively. However to retain the stability of the diamond phase, it was necessary to increase the pressure to 7.0 GPa to continue the sintering study at higher temperatures.

It can be seen that the X-ray spectra shown in Figure 4, obtained from a sample that was sintered at 1673 K under a pressure of 7 GPa is identical to that of a sample that was sintered at a temperature of 1573 K under a pressure of 4.3 GPa (Figure 1). At 1873 K, under a pressure of 7 GPa, the amount of titanium carbide formed is at a maximum. The use of higher temperatures under this pressure will result in graphitization of the diamond. This observation is somewhat surprising since the equilibrium phase diagram for carbon indicates that diamond phase should be stable to 2273 K at a pressure of 7 GPa. 5 The reduction of the graphitization temperature appears to be connected with the melting of titanium under these conditions of temperature and pressure. Some catalytic effect of metals that form carbides on graphitization of diamond was found in the paper by Nozhkina. 2

It was found that the unit cell dimension of titanium carbide increased by about 0.0041 nm during reaction sintering from an initial value of 0.4283 nm. According to the results of Koso1anova7 a change in lattice parameter of 0.0038 nm occurs when the C/Ti ratio changes from 0.5 to 1.0. It may be concluded, therefore, that the titanium carbide reaches the stoichiometric ratio C/Ti = 1.0 during the reaction sintering process.

It is apparent from these results that the reactive sintering of diamond with titanium occurs in two stages:

1) Reaction and formation of titanium carbide 2) Sintering of titanium carbide.

Both of the above stages are presented schematically in Figure 5.

178

initia I state

titanium diamond

beginning of sinter

I. KUSHT ALOVA ET AL.

titanium- ca rbide

end of n g

Figure 5. Schematic presentation of reaction sintering of the diamond titanium system.

REFERENCES

1. N. V. Novikov, N. V. Capin, A. L. Maistrenko, I. F. Vovchanovski, Sverhterdye kompozicionnye a1mazosoderzhashchie materia1y na osnove terdyh sp1avov, in "Sverhtverdye materia1y"("Superhard materials"), Vol. 1, p. 219; AS USSR, Kiev (1981), (in Russian)

2. A. V. Nozhkina, Vzaimodeistvie a1maza s metal1ami pri izgotov1enii i eksp1uatacii a1maznogo instrumenta, in "Sverhtverdye materia1y" ("Superhard materials"), vol. 1, p. 221; AS USSR, Kiev (1981), (in Russian).

3. E. Storms, The Refractory Carbides, Academic Press, New York, (1967).

4. P.S. Kis1i, I. P. Kushta1ova, S. N. Kuzmenko, A.F. Nikityuk, Tverdofaznoe vzaimodeistvie karbidoobrazuyushchih metal10v s a1mazami, in "Kompozicionnye sverhtverdye materia1y" ("Composite superhard materials"), p. 42; ISM AS USSR, Kiev (1979), (in Russian).

5. F. P. Bundy, Direct conversion of graphite to diamond in static pressure apparatus, J. Chern. Phys., ~, 631 (1963).


6. A. V. Kurdyumov, A. N. Pi1yankevich, Fazovye prevrashcheniya v ug1erode i nitride bora (Phase transformations in carbon and bor nitride), Naukova Dumka, Kiev (1979), (in Russian).

7. T. Ya. Koso1anova. Karbidy (Carbids), Meta11urgiya, Moskva (1968), (in Russian).

APPLICATION OF X-RAY DIFFRACTION

TECHNIQUES TO STUDY THE SINTERING OF CATALYSTS

Abstract

Robert J. De Angelis, Ashok G. Dhere, James D. Lewis and Hai-Ku Kuo*

Department of Metallurgical Engineering and Materials Science University of Kentucky Lexington, Kentucky 40506

*Institute of Materials Science and Engineering National Sun Yat-Sen University Kaohsiung, Taiwan Republic of China

An x-ray diffraction single profile analysis method is presented which allows the calculation of the particle size distribution function (PSD). This method is verified by using it to analyze simulated diffraction profiles from single, duplex, triplex, and normal distributions of particle sizes. This method is employed to study the sintering of a nickel catalyst.

A method is developed to unfold x-ray diffraction patterns of metal to obtain the pattern from particles residing on a crystalline support. This method is employed to produce the x-ray pattern of cobalt containing particles in a 9.5% Co-ZSM-5 catalyst. The resulting pattern indicates the metallic cobalt particles contain a high density of basal plane faults.

INTRODUCTION

Metal catalysts are generally employed in the form of small metal particles or crystallites dispersed on high surface area supports. In this form, a high proportion of metal atoms exists on the surface and an active catalyst results. The support also serves

181

182 R. J. DeANGELIS ET AL.

the function of physically separating the small metal particles, and tends to inhibit agglomeration of the small particles into larger particles. Strong interaction between the support and the metal particles also inhibits agglomeration. This agglomeration, known as sintering, occurs very rapidly in unsupported metal catalysts and leads to fewer metal atoms at the surface of the particle with consequent loss of catalytic activity. Sintering also occurs at high temperatures in supported metal catalysts and is the main source of catalyst thermal deactivation. The process of sintering, by definition, requires changes to occur in the particle size distribution. The sintering behavior of a metal catalyst depends on the initial particle size distribution, and knowledge of the progressive changes in the particle size distribution during sintering can assist in elucidating the mechanism of sintering in metal supported catalysts. 1

Therefore, a reliable determination of the initial particle size distribution (PSD) function and the changes occurring in the PSD during sintering becomes essential if the sintering process is to be understood and ultimately controlled. A reliable x-ray diffraction method for determining the PSD will be reviewed.

X-ray diffraction experiments on catalyst systems in which the support material is crystalline present a difficult problem because of the superposition of two diffraction patterns. The relatively strong pattern from the support is superimposed on the broad weak pattern of the metal. In such cases it is necessary to unfold the entire diffraction pattern to isolate the pattern of the metal particles.

In this paper a method to obtain the particle size distribution (PSD) from a single x-ray diffraction profile will be presented and a method to unfold diffraction patterns will also be discussed. The single profile method will be verified by employing the method to analyze a number of profiles from simulated particle size distributions. The changes in PSD observed during the sintering of a nickel catalyst supported on silica will be presented. The pattern unfolding technique will be applied to patterns obtained from a 9.5% Co on ZSM-5 catalyst to obtain a detailed x-ray diffraction pattern of C0304, the metal-containing phase prior to reduction, and of cobalt metal following reduction of 16 hrs. at 3500C under flowing hydrogen.

THEORY

Single Profile Analysis Technique

The single x-ray diffraction profile analysis technique is based on the work of Gangulee2 and Mignot. 3 The stokes corrected cosine coefficients~ from an (hkl) x-ray diffraction profile are composed of two components, a size coefficient At and a microstrain or distortion coefficient AE; their relationship can be expressed as

DIFFRACTION TECHNIQUES TO SINTERING OF CATALYSIS 183

(1)

where ~ are the Stokes corrected cosine coefficients at a given L, where L is no. Here, n is the harmonic number and 0 is a distance normal to the diffracting planes inversely related to the Fourier interval. Defining a variable X = l/De, where De is the effective diffracting particle size for small values of nand 0, where the values of L are small and such that the number of diffracting domains in the specimen with this dimension is insignificant, the particle size term of the Fourier coefficients can be expanded as:

~ = (1 - LX) (2)

The distortion coefficients can be expanded for small values of n, as:

(3)

where K is 2n2/d2, d is the (hkl) planar spacing and <Et> is mean square of the micros train averaged over all distance in the diffracting specimen spaced L apart.

2 Letting YL = K <EL>' the small L value cosine coefficient can be written as:

(4)

Eq. (4) can be solved for X if the functional form of YL is known. In this way the particle size can be separated from the micros train terms. The problem then resolves to determination of the most suitable forms of YL. Assuming the form of the strain function to be 5- 6

YL = (C/L)oK (5)

leads to an expression for AL of

~ = 1 - L(X + CoK) + L2 (XCoK) (6)

The expression for AL has the form of a second order polynomial in L.

Using a least square fitting to the actual cosine coefficients the values of X and C are obtained and from these the average diffracting particle size, De' and the average value of the micros train <€t> are determined. 7 The values of the particle size portion of the cosine coefficients are retrieved from 8 :

S 2 2 -2 2 Ai = ~/exp (-2n L d <EL» (7)

and the particle size distribution function is calculated using:


(8)

The single profile analysis method gives particle size results which compare well with double order methods of analysis; however, there has been difficulty in obtaining reliable strain values. Very recent work by Nandi et al. 9 develops a most encouraging method for arriving at meaningful values of strain.

Pattern Unfolding

If an x-ray pattern from a mixture of two crystalline components (metal particles and the support) is obtained, it can be represented by;

f . (28) = f (28) + f (28) m1X m s (9)

which after suitable scaling of the patterns 10 has a Fourier transform,

F . (s) = F (s) + F (s) m1X m s (10)

The x-ray pattern of the metal particles is obtained from

F (s) = F . (s) - F (s) m m1X x (11)

The inverse transform of Fm(s) gives the diffraction pattern of the metal particles sitting on the support, f m(28). One pattern can be shifted, an amount a, to another by multiplying all coefficients of the pattern by exp(-2TIisa) which is a simple operation and gives this technique a great advantage over direct subtraction. 10

EXPERIMENTAL AND RESULTS

Verification of Single Profile Method

A computer program was coded to produce intensity as a function of two theta for a one dimensional interference function of the form sin2Nx/sin2x, where N is the column length or particle size. This program was used to simulate diffraction patterns from single particle sizes of 10, 50 and 90 nm. The program, with the addition of appropriate summations and normalizations, was then employed to simulate diffraction patterns from 50/50 mixtures of 10 and 30 nm, 30 and 50 nm, 50 and 70 nm and 70 and 90 nm and 33/33/33 mixtures of 30, 50 and 70 nm and 50, 70 and 90 nm. Finally the program was used to simulate diffraction patterns from normal distributions of particle sizes. The following six distributions of mean particle size and

DIFFRACTION TECHNIQUES TO SINTERING OF CATALYSIS

standard deviation were simulated; (10 nm, 1 nm), (10 nm, 2 nm), (50 nm, 5 nm), (50 nm, 10 nm), (90 nm, 9 nm) and (90 nm, 18 nm).

185

The simulated diffraction patterns were analyzed using the single profile analysis method. The average diffracting particle sizes obtained from the analysis are tabulated in Table 1. There is excellent agreement in all the cases investigated. All of the agreements are within five percent, with one exception (10 and 30 nm; 50/50).

The computed distribution function for the cases; 90 nm single size; 50/50-30 nm and 50 nm; 33/33/33-50 nm, 70 nm, 90 nm; and three normal distributions are shown in Figs. 1 to 6. The distribution functions from the 90 nm single size particle is a broadened distribution function centered at 90 nm (Fig. 1). Similar results were obtained from other single size particle simulations and analysis (see Table 1). The distribution function from the 50/50-30 nm and 50 nm mixture of two sizes of particles is very bimodal in character with the two maxima at the values of the particles used to simulate the diffraction profile (Fig. 2). In the 33/33/33-50 nm, 70 nm, 90 nm mixture of three particle sizes the computed distribution functions broaden into a single smooth function with a maximum at 70 nm (Fig. 3). The 50/50 and 33/33/33 mixtures were employed with other sizes which give similar results (see Table 1).

Table 1. Results of Single Profile Analysis of Simulated X-Ray Diffraction Profiles

Particle Size and Average Particle De From Distribution (nm) Size (nm) Single Profile (nm)

10 single size 10 9.8 50 single size 50 48.5 90 single size 90 87.8 10 and 30; 50/50 20 16.8 30 and 50; 50/50 40 39.9 50 and 70; 50/50 60 60.1 70 and 90; 50/50 80 81.4 30, 50 and 70; 33/33/33 50 47.7 50, 70 and 90; 33/33/33 70 67.2 (10, 1) normal 10 9.8 (10, 2) normal 10 10.1 (50, 5) normal 50 49.8 (50, 10) normal 50 49.4 (90, 9) normal 90 91.6 (90, 18) normal 90 88.0

186

T II> ON ... •

o ZN o

..... W ZII>

~-Z o

..... 0 :::;) ... en a: ..... VI ... Oll>

LI.J N ... VI

20

R. J. DeANGELIS ET AL.

SIZE=900

40 60 80 100 120 140 160 l(RNGSTRDHSJ .10'

Fig. 1. PSD function determined from the analysis of the simulated diffraction profile from 900Ao particles.

R 0 'N o -•

10 z ... o

I-W ZN

~-Z o

50

SIZE=lOO RND 300

100 150 200 250 300 350 400 L(RNGSTRDHS)

Fig.2. PSD function determined from the analysis of the simulated diffraction profile from O.50-l00Ao and O.50-300Ao particles.


'" z-c I-W zN

~-z c .... ::Jw III

cc I-~

0 ....

w ....

MERN=100,S.D.=20

o Normol Distr ibution used for

Profile Simulo lion

x Distribution Function Determined from Single

Profile Analysis

o~ N' o -• '" -z

C

IW

N%

-~ z c .... I-

co::J III

cc I~

.... 0

w .... ~-4~~~'-~~*-~~----r-----~-----r----~--*--+0 ~

0 0 20 40 60 80 100 120 140 160 ~

L(RNGSTAOMSl

187

Fig. 3. PSD function determined from the analysis of the simulated diffraction profile from 0.33-500Ao; 0.33-700Ao and 0.33-900Ao particles.

T ~ o

-o

ZN C

I-W ZU')

~-z c .... 1-0 :::1-m

cc I-~

oU'l

w .... ~

20

SIZE=SDO.7DD,900

40 60 80 100 120 140 160 LIRNGSTROMS) _la'

Fig. 4. PSD function determined from the analysis of the simulated diffraction profile from particles with the normal distribution shown.

188

T ~ o --

N zC"> C

..... W Z ... ~N Z C ..... ..... '" ::l_ 00

a:: I-en

000

20


MEAN=SOO.SIGHA=100

40 60

o Normal Distribution used for Profile Simulation

x Distribution Function Determined

from Single Profile Analysis

80 100 120 140 LIANGSTRCHS) -la'

~T o i

N C">Z

C

..... W

.....z N~

Z C

w ..... _::l

00 .... a:: ..... en

!DO

UJ .... .... en

Isif


T ~ o

-w

zc 0-W

~N lL..-

Z C

I::lCXl 00

a:: I-

'" c ....

UJ N

MEAN=900.S.D.=180

o Normal Distribution used for Profile Simulation

x Distribution Function Determined from Single Profile Anolysis

°T NO --

z c ..... W

N~ -It..

z c .....

oo::l CD

a:: ..... en

.....0

UJ .... '" °0~~"4rO----8~0-----lr2-0~~16~0~~2~0-0----2r40----2~8-0----+32if

en

L(ANGSTROHS) -10'



In the normal distribution cases the results of single peak analysis of the simulated diffraction patterns gave particle size distribution function shown in Figs. 4 to 6. The distribution functions employed to simulate the diffraction profile are shown in the figures together with the distribution functions determined from the analysis. It is easily seen that the computed distributions compare very favorably with the distribution functions employed to simulate the diffraction profiles. The best results were obtained from 10 nm average size distribution. This indicates the smaller the average particle size the more closely the analysis produces the true distribution function.

Application to the Study of Sintering of Nickel Supported on Silica

The silica-supported catalytic material (C1S0-1-01) used in this investigation, supplied by United Catalysts Inc., Louisville, Kentucky, contained Sl.7% Ni, Z.94% C and 0.06% S. It has a nickel surface area of ZllmZ/g, a pore volume of 0.34 cm3/g and a density of 1.OS g/cm3• The catalytic material NiO/SiOZ was produced by a co-precipitation process. This is one of the four catalysts reported in a previous investigation. 7

The particle size distribution functions obtained by x-ray diffraction technique for the silica-supported nickel catalyst C1S0-1-01 on sintering up to ZO h at temperatures between SOO to BOOoC in nitrogen atmosphere are given in the form of isochronal plots in Figs. 7-9. The sintering behavior observed in hydrogen atmosphere was very similar to the nitrogen atmosphere results. All of the PSD functions are log-normal in form. 11 Sintering occurs very rapidly at short sintering times and proceeds much more slowly at longer times. The effects of sintering temperature on the PSD are much more pronounced than the effects of sintering time. There appears to be a limiting particle size which increases with increasing sintering temperature. These effects can be seen in Fig. 10 which shows the kinetics of sintering. The distribution functions show a definite formation of tails to larger particle size side. This type of tail formation supports a sintering model based on a particle migration mechanism. 12 13 The lack of formation of particles smaller than the original particles tends to indicate that an atomic migration mechanism1~ was inoperative.

In order to independently check the validity of particle size distribution functions determined by the x-ray diffraction method, transmission electron microscopy work was done on specimens from five selected runs to obtain the PSD's by direct observation. 1S

Comparisons of the normalized PSD's determined by x-ray diffraction and transmission electron microscopy for catalysts that were; reduced and sintered SO h at 7000 C in NZ and HZ; 100 h at 7000 C in NZ and ZO h at BOOoC in HZ, have been reported. 1S The agreement

190

... CD

~:1 ~ol l1..

~~ I ~o1 t- CD (fl --: _

_ °1

~ I _0

CATALYS ~ - 25 REO. ')( - 16 REO . ... - 19 REO. .. ' 35 ~EO .

Cl - 20 REO.


CISO-I-OI 3I1RS. qT SOOC 3I1RS . Rr sooe & SINT. ~I1RS. qr saaelNI 3HRS. qr sooe & SINT. 10HRS. qr saOCINI 3HAS. Rr SOOC & S I NT. 20HRS. qT SOaC(NI 3HRS. qT soae & S I NT. ~aHRS. RT SOOC I I

<f1 O ... ___ h--_ r----.~-~R ... - --.__---r_, ----I ct. 00 20. 00 --4~J. 00 cO. 00 80. 00 I '00. 00 120. 00 140. 00

L (RNGSTR~MS )

Fig. 7. PSD functions of catalyst elSO-l-Ol reduced at soooe for 3 hand sintered at soooe for times indicated.

CD ...

z 0 ....

N

W N

CATALTS T " .2S REO. x _77 REO. ... . 70 REO . A -31 REO. Cl . 33 REO. I!l -34 REO.

CISO-l-Ol 3HRS. Rr sooe 3HRS. Rr sooe 3HRS. Rr SOOC 3HAS. RT sooe 3HRS. Rr sooe 3I1RS. Rr SOOC

& SIN!. ~I1RS. Rr 700CIN I & SINT. 10HRS. Rr 700CINI & SINT. 20HRS. Rr 7 00C I NI & SINT. SOHRS. Rr 7 00C (NI & SINT. IOOMRS. RT 700C IN I

_ 0 1 .J.l:~~~~~~--..--------, (flO ...

ct. 00 30. 00 cO. 00 90. 00 120. 00 LSD. 00 180.00 2L O. 00 L ( RNGSTR~MS )

Fig. 8. PSD functions of catalyst elSO-l-Ol reduced at soooe for 3 hand sintered at 7000 e for times indicated.


... CD CATRlYS

¢ . 2S AEO. X . 71 AEO. + . /3 A€O. .. . H REO. (!) . 75 AEO. I!l . 76 RED.

(I SO -I -0 I 3HAS. ~T SOOC 3HAS. AT SOOC 3HRS. R! SOOC 3HRS. RI 500C 3HIIS. RI SOOC 3HAS. ~T sooe

, SlhT. IHRS. , S I NT. ~HRS. , 51 I. 10HAS. , 5 I NT. 20HR5 . , 51 I . SOH RS.

RT BOOCI N' R BoDe I , RI BOOCIN' RT BOOC INI ~I BOOC t 1

Fig. 9. PSD functions of catalyst elSO-l-Ol reduced at soooe for 3 hand sintered at BOOoe for times indicated.

100

90 Cotaly.t CI50-I-OI

05 80 Reduced 3/'1' • . at 500·C

In Hlotm . .. Sln .... d a t 8oo·C (V ) 1 700·C (O )

! 70 600·C(O) 0 500·C(ll.) 0

:: In HI aIm.

iii 60

~ i 0..

50

• go ~ 40 ~

30

20

0 20 40 60 80 100 SIn"r!nO Time (hra.)

191

Fig. 10. Average particle size as a function of sintering time for catalysts elSO-l-Ol at sintering temperatures indicated.


between the results obtained from the two techniques was found to be excellent. IS

Cobalt on ZSM-S

ZSM-S is a crystalline support material with an orthorhombic structure with lattice constants of a = 20.1, b = 19.9 and c = 13.4 angstroms. In this case the support gives Bragg profiles throughout the range of diffraction. Diffraction patterns from 9.S% cobalt on ZSM-S and pure ZSM-S are shown in Fig. 11. The catalyst is in the calcined condition putting the cobalt in the C0304 oxidation state. Unfolding the pattern of the mixture employing the technique described produced the cobalt oxide pattern shown in Fig. 12. The detail in the unfolded diffraction pattern is revealed, producing a diffraction pattern of the metallic component which can be used for phase identification or profile analysis. Scherrer analysis of the C0304 (311) profile in the pattern in Fig. 12 gave an average oxide diffracting particle size of 3S nm.

This calcined sample was reduced for 16 hrs. under hydrogen at 3S00C in a "in situ" camera attached to a Picker X-ray Diffractometer. The x-ray diffraction pattern of the reduced catalyst after unfolding from the ZSM-S pattern is shown in Fig. 13. It is clear that there still exists some small amount of CoO after the reduction treatment. Also the Co (002) profile is sharp compared to the Co (101) profile. Using the same unfolding technique the Co (110) profile was recovered from the 9.S%Co-ZSM-S pattern in the reduced condition. The Co (110) was sharp, similar in appearance to the Co (002). The Co (110) sits along with no interference from neighboring profiles while the Co (002) sits near Co (100) and Co (101). The Co (110) was used to compute the PSD function of cobalt particles shown in Fig. 14. The PSD function obtained from analysis of the Co (101) is shown in Fig. IS.

The Co (002) and Co (110) profiles broadening is due only to particle size effects, but the broadening of the Co (101) is due to a combination of small particle size and faults on the basal plane. 16

The average particle sizes for the reduced catalyst from Co (110) and Co (101) are 17 nm and 3.5nm respectively. Particle size data indicate a faulting probability of 0.07 to 0.08, or on the average one out of every twelve basal planes are faulted which gives an average fault spacing of 2.5 nm. Transmission electron microscope observations made on these samples revealed the cobalt particles to contain faults on the basal planes with a spacing of about 2.S nm. 17 ,18 This agrees with the fault spacing determined from the unfolded x-ray pattern.

In summary, two analysis techniques have been presented which extend the usefulness of x-ray diffraction as a method to study the structure and sintering behavior of catalysts.

~ ~

9.

SZ

CO

BA

LT

-W

ATE

R ,C

A2

00

-!

~l

+

ZS

,,-S

:R

35

0-

16

COJ~ ..

(3U

)

o o ~

~~

:~

~

II: ~g

K.

~=

> _0

_

0

"',;

z·

w·

~g ~

'0

......

.... :J

:::

,.. "'

• •

0 ."

>: •

~.

: »-~

i .

. ...

........

Cos

O ..

(22

2)

I

,,,,

+~

~I ",

' ,

, ,

, ,

, ,

, ,

";7

.00

111.

00

S

t. 0

0 4.0

.00

U.

OO

U.O

O ..s

o 00

u.O

D .. S

.OO

46.

00

41.0

0

48.0

0

d.O

O 50

.00

S

I.OO

S:

Z.O

O 5

'.0

0

St..

DO

S5.0

0 5S

, DO

A

NG

LE (

DE

GR

EE

S!

Fig

. 1

1.

X-r

ay d

iffr

acti

on

p

att

ern

s fr

om calc

ined

9.

S%

co

balt

on

ZS

M-S

an

d p

ure

Z

SM-S

.

0 :;l 0 0 <;! o·

00

~-; ":

g",

."

' O

N

~- :: ~~

~~

z

0 0 :oj 0 ,,"~O

0 TI

TI

:0

» ()

-I

5 z -I

m

()

:x:

z is c m

CJ)

-I

0 CJ)

Z

-I

m

:0

Z

G)

0 TI

() » -I

» r -<

CJ)

en CD

W

o ~ o o ~ . " _0 ~~

Zo

::

>0

Gio

0:

::::

~ .. .. g

:;;

0 ~.

Z -g

~ o

9.5

"t.C

OS

ALT

-W

ATE

R: C

A-2

00

-1

Co

sO ..

(311

)

! ..

rv--J

Co

,O.{

40

0,

I ~

x- -

CD

.j:>.

~t 00

,i.

oo

,i. 0

0 4

0.0

0

It C

O 4

'.00

4

',00

,t.

oo

45

.00

.1.

. ....

. .1.

~..

. .:.~

.. -~

Fig

. 1

2.

X-r

ay d

iffr

acti

on

patt

ern

of

Co

304

aft

er

un

fold

ing

th

e d

iffr

acti

on

patt

ern

sho

wn

in

~

Fig

. 1

1.

~

c CD » z G)

m

!::

en

m

-l » :-

o o ;1 -gl

'" 'i

~~

z :::> '0

C

Do

0::

. a:

0

-~

... ~ _0

",0

zo

...,0

~~

z

9.

SZ

CC

BA

L T

-~RTEA :

CA

20

0 -

1.A

3S

0 -

16

C

o(o

02

)

I x • x

x x I x C

oIIO

O)

x I

Co

O(2

00

) 'It

1 I

:'*\.~

';.AXx

""

VI"

l'\fj('~

x x

x x

Co(

lOI!

x

1

~~~ x~~

oK

~)()(

o o

:.. ....

. 'I<r~

••• :-..

•

• ..

.. '\

!~-.

~~-.

....:...

,;:.;..,

. .......

.. P.'

x

'*",-

'I< x

x --

'l"!:.

>I'

o o gl

, ,

, ,

, i

, ,

, ,

, ,

.,

, ,

, ,

N,O

. 0

0

".0

0

'l.O

O

43. D

O ..

. DO

'5.0

0

.6.0

0

17.

DO

.8.0

0

'9.0

0

50

.00

5

1.0

0

52.

DO

53

.00

54

.00

5

5.0

0

56.

DO

51

.0

ANG

L E

I DE

GAE

E 5

)

Fig

. 1

3.

X-r

ay d

iffr

acti

on

patt

ern

of

co

balt

meta

l in

9.

S%

Co-

ZS

M-S

cata

lysts

aft

er

un

fold

ing

.

Q

"TI

"TI

::D >

(')

-I

5 z -I

m

(') :r:

z o C m

en

-I

o en

Z

-I

m

::D

Z

Gl o "TI

(') >

-I

>

r -< en en to

(11

196

N 9.S%COBRLT-ZSM-S:R3S0-1S

Cl ~ Cl

• z ." ~CD I-W Z ~ IL

Z'" X ."

I-~ CD - ... a:: IIn

Cl

x

x

x

x

x

x

SIZE (ANGSTROMS)


CClBRLT(110)

Fig. 14. PSD function obtained from single profile analysis of Co (110) profile.

• z ." ~ ... I-W Z ~ IL

zC"> o I~ CD -N a:: IIn

Cl

9.5I.CClBRlT-ZSM-5:R350-1S COBRl T (101 I x

• x

x x

x

x

x x

x

x

x x

20 40 SO 60 100 SIZEIRNGSTROMSJ

Fig. 15. PSD function obtained from single profile analysis of Co (101) profile.


Acknowledgements

One of the authors (A.G.D.) acknowledges STI/MIC of the Brazilian Government for the financial support. (J.D.L.) was supported by an IBM Corporation Grant through the University of Kentucky. This research was also partially supported by the Department of Energy on Contract No. DE-AS05-82ER12098.

References

1. S. E. Wanke and P. C. Flynn, Catal. Rev. 12 (1):93 (1975). 2. A. Gangulee, J. Appl. Crystallogr. 7:434 (1974). 3. J. Mignot and D. Rondot, Acta Met. 23:1321 (1975). 4. A. R. Stokes, Proc. Phys. Soc. 61:382 (1948). 5. R. L. Rothman and J. B. Cohen, Advan. X-Ray Anal. 12:208 (1969). 6. B. E. Warren and B. L. Averbach, J. Appl. Phys. 21:595 (1950). 7. P. Ganesan, H. K. Kuo, A. Saavedra, and R. J. De Angelis, J.

Catal. 52:310 (1978). 8. B. E. Warren, Prog. Metal Phys. 8:152 (1959). 9. R. K. Nandi, J. Kuo, W. Schlosberg, G. Wissler, J. B. Cohen,

and B. Crist, Jr., submitted for publication. 10. A. G. Dhere and R. J. De Angelis, to be published in J. Catal.

81 (1982). 11. H. K. Kuo and R. J. De Angelis, J. Catal. 68:203 (1981). 12. E. Ruckenstein and B. Pulvermacher, AICHE J. 19:356 (1973). 13. E. Ruckenstein and B. Pulvermacher, J. Catal. 29:225 (1973). 14. P. C. Flynn and S. E. Wanke, J. Catal. 34:390, 400 (1974). 15. H. K. Kuo, P. Ganesan, and R. J. De Angelis, J. Catal. 64:303

(1980). 16. B. E. Warren, in "X-Ray Diffraction", Addison-Wesley Publishing

Company, Reading, Mass. (1968). 17. A. G. Dhere, Ph.D. Thesis, University of Kentucky (1982). 18. A. G. Dhere, R. J. De Angelis, J. Bentley, and P. J. Reucroft,

to be published in J. of Mol. Catal.

THE EFFECT OF INTERACTIONS AMONG ~TAL, SUPPORT AND ATMOSPHERE ON

THE BEHAVIOUR OF SUPPORTED ~TAL CATALYSTS

ABSTRACT

E. Ruckenstein

Department of Chemical Engineering State University of New York at Buffalo Amherst, N. Y. 14260

The paper is mainly concerned with wetting and spreading in catalyst-substrate systems and with the roles played by the interactions among catalyst, atmosphere and substrate in the above phenomena. The first part of the paper analyzes the thermodynamics of spreading, using three different approaches. The first of these considers a thick film on a substrate, the second one improves on the first by considering the film thickness to be smaller than the range of the interaction forces between a catalyst atom and the substrate across the film, and the third one starts from a given loading of the catalyst and tries to obtain information, for given interaction forces, on the organization of the catalyst atoms on the substrate. The analysis indicates when a two-dimensional phase of single atoms of catalyst dispersed over the surface of the substrate exists alone, and when it is in equilibrium with a large crystallite. The Ostwald ripening mechanism of sintering occurs only when a two-dimensional surface phase can exist, while migration and coalescence of the crystallites is the mechanism of sintering . when such a phase does not exist. Conditions are identified under which the crystallites spread over the surface of the substrate to extended planar shapes with a steep variation of angle near the leading edge. This happens when the interactions with the substrate are moderately strong and is a consequence of the fact that the wetting angle at the leading edge is larger than the thermodynamic macroscopic wetting angle which is reached at a distance of a few nanometers from the leading edge. This means that total spreading can occur at some distance from the leading edge, while the atoms near the leading edge still have a finite wetting angle with the substrate. When the above interactions are

199

200 E, RUCKENSTEIN

strong, the crystallite will disintegrate and disperse over the surface of the substrate. The second part of the paper contains an explanation of the higher mobility of the catalyst atoms on the surface of the crystallites above the so called Tammann temperature. The third part presents a selection of experimental results obtained in this laboratory which provide evidence for the extension of the crystallites during heating in O2 followed by contraction during subsequent heating in H2 , as well as on their splitting and change in shape.

INTRODUCTION

Sintering is a deactivation phenomenon in catalysts containing metal particles supported on refractory metal oxides, wherein the average size of the metal crystallites increases, thereby decreasing the surface area of metal exposed to the chemical atmosphere and the number of sites available for reaction. This happens either during the catalytic reaction itself, or during secondary reactions the function of which is to reverse coking or poisoning. It is important that the decrease in the exposed surface area of the catalyst be minimized or even reversed by redispersion.

Several mechanisms for the sintering process have been sug

gested: (1) migration of crystallites and their coalescence l

(2) emission of single atoms by small crystallites and capture of

single atoms by large ones2- 6 j (3) a combination of (1) and (2)4. For mechanism (2), two possibilities have been emphasized. In one of them, a large number of crystallites are involved in the process, and the small crystallites lose atoms to a two dimensional phase of single atoms dispersed over the substrate, while the large ones capture atoms from this bulk. In this case, the bulk surface phase of single atoms is supersaturated with respect to the large crystallites and undersaturated with respect to the small ones.

In the other caseS, atoms released by a small crystallite move directly to a neighboring large crystallite, even though the bulk surface phase of single atoms is not supersaturated with respect to the large crystallites. While the first process has a global character (since it involves many crystallites) the second is local, involving two or only a few neighboring particles. The first

h ' 'k ld' , 2-4,6 h'l th d mec an1sm 1S nown as Ostwa r1pen1ng , w 1 e e secon , sug-

gested more recently by Dadyburjor and RuckensteinS , is called direct ripening.

Redispersion can take place by spreading of the crystallites , 1 1,7,8 over the surface of the substrate to a smaller wett1ng ang e ,

BEHAVIOUR OF SUPPORTED METAL CATALYSTS 201

and/or by emission of single atoms to a bulk surface phase of single atoms which remains undersaturated with respect to a large part

, t 1,3,4,9,10 of the size distribut10n spec rum •

Direct experimental evidence that crystallites can migrate on substrates under certain conditions can be found in the early work

11 12 of Bassett and Masson et al. • While a number of authors con-sider the migration of crystallites (of all sizes including single atoms) and their coalescence as the main mechanism of sintering, others attribute the main role to Ostwald ripening. Recent transmission electron microscopy experiments have revealed that

, 'f II' d" 13,14, both m1grat10n 0 crysta 1tes an r1pen1ng occur D1rect

, , b f ch ' 13 Of d d' r1pen1ng appears to e a requent me an1sm course, epen 1ng on the conditions, either of the mechanisms may dominate the process.

However, sintering and, in particular, redispersion are not as simple processes as previously considered. For instance, redispersion during heating in 02 does not occur only by emission of

single atoms by the crystallites. Transmission electron microscopy

experiments? have shown that the Pd crystallites spread during heating in 02 on the substrate to a smaller wetting angle, change

their shape, and exhibit tearing or even fragmentation. In fact, the increase in the exposed surface area during redispersion might be, at least in some cases, the result of spreading to a new wetting angle (because of the change in composition of the crystallites and/or the substrate) and of the associated tearing and fragmentation rather than the result of emission of single molecules to a bulk surface phase.

The emphasis of the present paper is on the phenomena associated with wetting and spreading. The first part of the paper is concerned with the thermodynamics of spreading and presents three different approaches of increasing degree of realism. The first approach is based on the traditional treatment of spreading of a thick film of metal on a substrate, the second one improves on the previous one by considering the film to be thin (i.e. it has a thickness smaller than the range of the interaction forces between a catalyst atom and the substrate across the film), and the third one uses thermodynamics to obtain the organization of a given number of atoms on the substrate under the influence of the interaction forces existing among them and with the substrate. While the latter treatment is the most realistic, it will be shown that the other two also provide useful insight into the problem of sintering and redispersion. This part of the paper is also concerned with the extended planar shape which crystallites can take on the substrate when their interactions with it are sufficiently strong.

202 E. RUCKENSTEIN

The second part of the paper contains some explanations of the higher mobility of the metal atoms on the surface of the crystallites above the Tammann temperature.

The third part of the paper, based on transmission electron microscopy, brings experimental evidence concerning: a) extension of crystallites on an alumina substrate during heating in O2 and

their recontraction when they are subsequently heated in H2 , and

(b) the change in shape and splitting of crystallites.

I. THERMODYNAMIC CONSIDERATIONS

I.l Thermodynamics of a Thick Catalyst Film on a Substrate

For the sake of simplicity, let us start with a thick film of metal transferred from a large reservoir to a substrate. The specific free energy of formation Of of the film on a uniform sub-

strate is given by:

° +0 -0, (1) cg cs gs

where the subscript 00 indicates that the film is thick, 0 .. denotes 1J

the surface tension between phases i and j, and subscripts c, g and s denote crystallite, ~as and substrate phases, respectively. We note that the thermodynamic considerations contained in the present paper are, in general, more appropriate for liquid droplets than solid crystallites. Nevertheless, they provide some insight into the behaviour of solid crystallites as well. Eq. (1) can be rigorously applied to systems involving solids if the 0 .. are the

1J corresponding free energies. If °00 < 0, the material composing

the film wets the substrate and spreads completely over its surface. In the opposite case, i.e., °00 > 0, the material does not wet the

substrate and therefore islands with a distribution of sizes will form. In order to decrease the free energy of the system they will tend to coalesce into a single island, forming with the substrate an angle 8 which is given by Young's equation

° cos8 = ° - ° ( 2) cg gs cs

Kinetically the approach to equilibrium takes place by one or several of the mechanisms enumerated in the Introduction. The kinetic process can however be so slow that thermodynamic equilibrium is not achieved during the lifetime of the supported metal. Each "droplet" can however achieve the equilibrium wetting angle


in a time which is short compared to the lifetime of the supported catalyst.

In vacuum or in any inert atmosphere, metals have high surface tensions. For instance, platinum has a surface tension of 2340 dyne/cm in vacuum at 1310o C. Such values are several times higher than those of metal oxides. Consequently, metals do not wet refractory metal oxides which are usually used as substrates in catalysis. If the supported metal crystallites are oxidized, the crystallite-gas surface tension is decreased and the crystallite will spread over the substrate forming a new equilibrium contact angle. Of course, if its surface tension is decreased sufficiently, Eq. (2) can lead to cose > 1. Under such conditions, no equilibrium angle exists and the crystallite spreads completely over the surface of the substrate. Alternatively, the atmosphere can react with the substrate and thereby increase the surface tension ° Under these

gs conditions also, the crystallites will spread to a new equilibrium angle. In this respect, it is of interest to mention that when Pt supported on titania is heated in H2 , the Pt crystallites spread

. . h 15 . to form thln planar structures hexagonal ln s ape ThlS appears to happen because, in the presence of Pt, H2 reduced Ti02 to the

lower oxide Ti 40 7 , thus increasing the surface tension 0 gs However,

this explanation is incomplete because a planar shape for the crystallite implies a macroscopic thermodynamic wetting angle equal to zero and hence a total spreading of the metal on the substrate. Why this should not occur had earlier been predicted by Ruckenstein

arid Lee16 , who showed theoretically that, if the interaction potential between a molecule of liquid and a molecule of the substrate is moderately strong, a droplet of liquid will have a planar configuration but with a rapid variation of angle near the leading edge. The detailed explanation of this behaviour is presented in the next section. We note that extended planar crystallites can also occur on alumina during heating in 02'

Experiments carried out in this laboratory have shown that this happens during heating in 02 with Fe crystallites supported on alumina.

Let us also note in passing that because oxides can wet metals, the latter can, in principle, constitute excellent substrates, since they allow high dispersion of oxide catalysts.

I.2 Strong Interactions and the Shape of the Crystallites

The thermodynamic approach on which Young's equation is based involves the existence of a macroscopic wetting angle defined on a scale which is large compared with atomic dimensions. Nevertheless, on the basis of statistical mechanics, one can demonstrate

204 E. RUCKENSTEIN

that within a (short) distance of a few nanometers from the leading edge, the (internal) angle between the horizontal and the line connecting the centers of two successive molecules at the liquidgas interface varies rapidly from some value e at the leading

16 0 edge to the smaller thermodynamic value e The calculations have been carried out by using the following simple expression for the interaction potential, ¢ .. , between two molecules (atoms) of

1J species i and j whose centers are at a distance r apart:

¢ij

fj. . _ 2.2

00

6 r

r > a .. 1J

r < a .. 1J

( 3)

where a is the sum of the atomic radii of species i and j (which

is a me~~ure of the size of the repulsive core' between species i and j) and S .. characterizes the strength of the attractive inter-

1J actions between them. For the particular interaction potential (3), the rapid variation of angle is caused by the hard-core exclusion between the molecules of the liquid drop and the substrate which enters via the value of a£s' At the leading edge, where the

molecules of liquid and solid are in close proximity, the effect of this exclusion (repulsion) is the greatest and consequently the angle the largest. Approximate calculations lead to the following expressions for the angles e and e

o

and

where

1 + cose

1 + cose o

(4)

( 5)

< 1 , (6)

n. is the density of phase j expressed in number of molecules per J

unit volume, the subscript £ refers to the liquid and the subscript s to the solid.


Since e is the angle between the line connecting the centers o

of two successive molecules situated at the leading edge of the liquid-gas interface and the horizontal, values of cose > 1, which

o result from Eq. (5) when nsB~sK/n~B~~ > 1, are not compatible with

the presence of a second layer of molecules on the first layer. Consequently, spreading will generate individual molecules of liquid in contact with the solid when

( 7)

However, if the value obtained for cose is larger or equal to unity, while that of cose is smaller than unity, i.e., if

o

nsB~s 1 --- >

n~BH -( 8a)

and

n B~ ~K < 1, n~BH

( 8b)

then spreading will generate an extended thin planar drop whose profile changes rapidly in the region of a few nanometers from the

. 16 Th b h . 1 . f h lead~ng edge e above e av~our can occur on y ~ t e amount of liquid is sufficiently small. When the amount is large, the liquid will cover the entire surface of the solid, in both situations examined above. Of course, if the amount of liquid is so small that the size of the droplet is of the order of the distance over which the shape varies rapidly, then the droplet will have no planar region even if inequality (8a) is satisfied.

Even though the behaviour of metal crystallites cannot be described accurately by the interaction potential (3) and by the liquid droplet approximation, the observed phenomena can be explained qualitatively within the framework of the above considerations. In conclusion, we emphasize that planar extended droplets require that there be moderately strong interactions between the atoms of the droplet and those of the substrate. They must be strong enough for inequality (8a) to be valid, but not so strong that the inequality (8b) cannot also be satisfied. If instead the above interactions are so strong that inequality (7) is valid, then spreading of single molecules will occur (if the loading is equivalent to a submonolayer). One may, however, note that the anisotropy of

206 E. RUCKENSTEIN

the surface tension in crystalline solids also contributes to the former behaviour.

1.3 Thermodynamics of a Thin Film

The metal loading of the substrates in a supported metal catalyst is, in general, low. If one assumes that the catalyst covers the substrate as a film, its thickness h in some cases may correspond to no more than a submonolayer. It is therefore clear that the above considerations, which are valid for thick films,

cannot be applied under such conditions. In ref. 17 an expression for the free energy of formation of was derived which involves a "thin" film, i.e. a film whose thickness is smaller than the range of the interaction forces between one catalyst atom and the substrate across the film, but is still large compared with atomic dimensions. Consequently, the expression obtained is still not entirely adequate for our purpose here. However, compared with the equations of the previous section, it contains a new element namely the film thickness, and one may expect that it will yield at least some qualitative insights into the present problem. In addition, as shown below, this expression can be corrected qualitatively so that it more nearly describes the actual situation. Assuming for the sake of simplicity, a Lennard-Jones potential, one can establish

the following expression for 0£17

2 8 °00 + alh - Blh - °00 + f(h) , (9)

where h is the thickness of the film, a is related to the strength of the attractive components of the interaction potential between two atoms of the crystallite and between a crystallite atom and a substrate atom, and B is related to the strength of the corresponding Born repulsion terms. Of particular interest is the case in which a thin film can completely spread over the substrate but a thick film cannot. This may happen when a and B are negative and °00 ,

while positive, is not too large. In Fig. 1, Of is plotted vs. h

for the latter case. Because when h + 0, Of has to be obviously

zero, Eq. (9) is replaced by the unbroken curve passing through the origin. In an approximate way this correction extends Eq. (9), which is valid for relatively large thicknesses, to the regime of atomic or subatomic thicknesses. The latter correspond to metal loadings in the submonolayer region, i.e. a two dimensional phase of single atoms. From Fig. lone can note that a is negative below h = h •

f c Because the repulsive (Born) interactions are short range, and the

term which accounts for them (-B/h8 ) is partly responsible for the

BEHAVIOUR OF SUPPORTED METAL CATALYSTS

1 0"00

Fig. 1. crf vs the Thickness h of the Film. Broken Curve, Lennard-Jones Potential for the Interaction; Full Curve, more Realistic Potential for h + O.

207

shape of the curve below h = h , we expect h to correspond to at m m

most a monolayer (or more likely a submonolayer) coverage, i.e., the two dimensional phase. For metal loadings corresponding to h > h , there will be two coexisting phases: a two-dimensional

m surface phase corresponding to thickness h and a single crystallite

m which includes the rest of the on the substrate. In this way minimized. On the other hand,

atoms and occupies a very small area the free energy of the system is for metal loading h < h there is a

m single, two-dimensional, phase alone.

208 E. RUCK EN STEIN

Eq. (9) shows that there are circumstances under which no wetting, partial wetting or total wetting occurs. If 0f(h) > 0,

no spreading will occur for any h and the droplets on the substrate tend to coalesce into a single drop. However, if the shape of the curve is like that of Fig. 1, total spreading will occur for h < h

m while for h > h partial spreading-the phase separation described above-will occ~r.

Let us now imagine that there are a large number of crystallites on a substrate. If 000 is so large that 0f(h) > ° for all values

of h even when a is negative, the crystallites will eventually acquire their equilibrium wetting angles. Further, because of the tendency of the system to reduce its free energy, the crystallites will migrate over the surface of the substrate and coalesce to achieve the smallest possible area. Although purely thermodynamic considerations predict the formation of a single crystallite, the rate at which this process occurs may be so slow that a large number of crystallites can survive for the entire life of the supported metal catalyst. Some metals supported on oxides, in general, have large values of 000 in vacuum, and probably also in a reducing atmosphere, and therefore 0f(h) may not become negative for any

value of h. In an oxidizing atmosphere 000 is, however, much smaller

and 0f(h) can become negative for h < hc ' Starting from metal

crystallites, heating in oxygen generates metal oxide which leads to a decrease of the -wetting angle but also to the emission of metal oxide molecules as a two-dimensional phase on the substrate. As long as the surface concentration of the two-dimensional phase is lower than the surface concentration in equilibrium with the largest crystallite present, all the crystallites will lose molecules to a bulk surface phase of single molecules. However, if the surface concentration is larger, then only the crystallites having sizes smaller than a critical value will lose molecules to the two-dimensional phase, while those with larger sizes gain such molecules from this two-dimensional bulk phase (Ostwald ripening) . The overall behaviour is redispersion if the exposed surface area of oxidized metal increases and is sintering if the exposed area decays. In conclusion one can say that Ostwald ripening can occur in systems in which a two-dimensional phase of the supported compound can coexist in equilibrium with a crystallite. Note that this does not mean that migration of crystallites and their coalescence cannot also occur. Indeed it may be an important mechanism of sintering if the Ostwald ripening process is too slow, and, if 0f(h) > ° for all values of h, it is the only mechanism of

sintering. We have already mentioned in a previous section that the atmosphere may react with the substrate, thus increasing the surface tension of substrate-gas. In this case also the metal can spread on the substrate.

BEHAVIOUR OF SUPPORTED METAL CATALYSTS

1.4 Thermodynamics of an Ensemble of Atoms Dispersed on a Substrate

209

In the previous sections the behaviour of supported metal catalysts was predicted from results obtained for the limiting case of a thick metal film supported on the substrate and for the more relevant case in which the film is "thin", i. e. its thickness is less than the range of interatomic forces between a metal atom and substrate across the film. In the present section, the problem is treated on the basis of a somewhat more realistic approach in which thermodynamics is used to predict the way in which an ensemble of metal atoms supported on a substrate tend to organize. The main thermodynamic problem is to predict the size distribution of the clusters that form.

At equilibrium the system consists of N' free sites of the s

substrate, Nl metal atoms, each occupying one site of the substrate, and N tridimensional clusters containing g atoms, each cluster

g occupying s sites of the substrate. Denoting by N the total

g s number of sites of the substrate, one can therefore write

N s

00

s N g g

const. (10)

Considering the clusters of different sizes as distinct chemical species, with negligible interactions among them, the free energy, G, of this dilute system is

00 N' Nl N'sa

0 L

0 + kT [N'Q,n s G + Nlfll + N ]J - + Nl Q,n s sg

g=2 g g s Nt Nt

00 N + L N Q,n f], (ll)

g=2 g t

where the entropy is approximated by that of an ideal mixture.

Here s is the surface area per site of substrate, flo are the standard chemical potentials,T is the absolute temperature and k is the Boltzmann constant. The subscript g associated with flo and N denotes cluster size, while associated with a refers to the gas. Nt' the total number of "particles" involved, is given by:

210

N' s

co

+ N1 + LN. g=2 9

E. RUCKENSTEIN

(12)

The minimization of G subject to the constraint (10), yields the size distribution

(s -g) 0 X xgx 9 exp (-gi'IG /kT) ,

9 1 s 9 (13)

where ,

Xl - N1/Nt X s - N /N

s t (13a)

and

o 0 0 [ 1 ~G = ~ /g - ~1 + a s 1 - (s /g)J.

9 9 sg 9 (Db)

Eq. (13) contains three factors: one of them, (N1/Nt )g, is

due to the entropy decrease caused by the reduction in the number of independent metal particles through clustering; the second,

(s -g)

X g , is due to the entropy increase caused by the greater s number of free substrate sites that become available because threedimensional clusters cover fewer sites on the surface than the atoms they contain; the third factor is due to the standard free energy change involved in clustering. Since X «X and Is -gl < g,

1 s 9 the first factor, xi, dominates the second. Note that the term 0sgS [1 - (Sg/g] in Eq. (13b) represents the substrate-gas surface

free energy change per atom which takes place because g metal atoms each occupying a single site on the substrate, are replaced by a three-dimensional cluster occupying only s sites. At low metal loadings of the substrate, N1/Nt is very small and the corresponding entropy decreases so prohibitive that almost no clustering occurs. The size distribution of clusters is in this case a monotone decreasing function of size. At sufficiently high loadings, Xg decreases with 9 for small values of g, but now increases at higher values because the exponential factor in which g~Gg < 0 becomes dominant (see Eq. (16a) as an approximate expression for ~Gg). Intuitively it is clear that as soon as the loading is such that Xg ultimately increases with 9 a "phase separation" occurs (Le. a large cluster forms in addition to the two-dimensional surface phase) •.


In order to determine the point at which phase separation occurs, let us note that this happens when the size distribution changes from a monotone decreasing function to one which has a minimum. Using Eq. (13), the value of Xl at which the transition occurs can be obtained from

ds £nX1 - £nXs + £nXs (~) dg

g -+ co

1 d(gL'lGo) ( g

- kT dg) = O.

g -+ co

(14)

Note that the slope dX /dg remains equal to zero for all values of g

Xl smaller than the transition value, even though d£nXg/dg f O.

This happens because below the transition value X -+ 0 for g -+ co. g

Treating the crystallite as a macroscopic body, an approximation which is certainly inapplicable to small clusters, one can write Eq. (13b) as:

gL'lGo = gL'lGo + s a + s (a - a ) + gsa , g cg cg cs cs sg sg

(15)

where L'lGo is the difference between the standard free energies of an atom within a large body and in the two dimensional phase on the substrate, and sand s are the surface areas of the crystallite-gas and 8~ysta11i~e-substrate interfaces. Considering that each cluster has the shape of a spherical cap of radius Rand wetting angle e with the substrate (Fig. 2),

2 s = 2TI (1 - cose) Rand s

cg cs R2 . 2e = TI Sln •

Since, in addition,

1/3 2 -1/3 R = (~) [(1 - cose) (2 + cose)]

TI

where v is the volume per atom (molecule) in the cluster, Eq. (15) becomes:

AGOO + 2/3 gL1 yg • (16a)

Here

212 E. RUCKENSTEIN

CTsg

Fig. 2. Crystallite on a substrate

y 3 2/3

(-2) [21T (1 - cosS) 0 + 1T 1T cg

(0 - 0 ) sin2SJ cs sg

2 -2/3 X [(1 - cosS) (2 + cosS) J (16b)

and

(16c)

Using Eq. (16a), and taking into account that

ds ds s (---!l) (~) 0 (/:'Go) /:'Goo

dg dg g __ g g--g-t<X>

and

d/:'Go

[g~J 0, g--


the value of Xl at which the transition occurs is given by:

Xl = 6.Goo J/,n X kT (17)

s

Since we assume that the loading of the substrate with catalyst is much smaller than N , Eq. (17) can be approximated by

s

6.Goo/kT e (17a)

It should be noted that Eqs.(17,17a) have the form of an equilibrium condition between a dilute two dimensional surface phase of single atoms (molecules) and a bulk phase of metal. The generality of this expression suggests that Eq. (17) should not be strongly dependent on the particular model used for the cluster. Indeed,

Eq. (17) could be derived without using a particular model for lGo , g

but only by observing that, for large values of g, 6.Go contains a g -n

term independent of g and a surface term proportional to g , with n > O. If the interaction between two atoms (molecules) in the large crystallite is much stronger than that between an atom

and substrate, then 6.Goo has a large negative value and the transition occurs at extremely small values of Xl. A large surface

concentration of the two-dimensional phase is expected when the interactions with the substrate are sufficiently strong, since, in

that case, 6.Goo has a smaller negative value. On an alumina substrate this can happen in particular in an oxygen atmosphere, because the molecules of the oxidized crystallite have a stronger interaction than the metal with the substrate. For metals the values of Xl at which the transition occurs are expected to be much smaller.

The qualitative conclusions of the present section are therefore similar to those of the previous one. It is also worth mentioning that the thermodynamic considerations summarized or developed in the present paper shed light on the relation between surface phenomena and various mechanisms possible for sintering or redispersion. Indeed the Ostwald ripening mechanism of sintering can occur only when a two dimensional surface phase can exist. Redispersion is a result of spreading of the crystallites to a new wetting angle and/or of emission of a two-dimensional surface phase (which is really equivalent to a two-dimensional spreading). It might be of interest to calculate the equilibrium size

214 E. RUCKENSTEIN

distribution in order to identify conditions under which clusters of various sizes and shapes are thermodynamically stable. Of course to carry out such calculations, more adequate expressions than Eq. (15) are needed to calculate /';Go for the smaller clusters.

g However, the approach to thermodynamic equilibriums is very slow and therefore may hardly ever be achieved in supported metals. The kinetic features of the problem have been treated in refs. 1 to 5. For a detailed review of these aspects see ref. 24.

II. THE SIGNIFICANCE OF THE TAMMANN TEMPERATURE

In connection with the mobility of atoms on the surface of a crystal, frequent reference is made to the so-called Tammann temperature, T , which is equal to a fraction (of about 0.5) of

Tam the melting temperature, T , of the bulk solid in OK. At this

m temperature the mobility of the atoms on the surface of the crystallite is greatly increased in comparison with that below this temperature. This enhanced mobility can be associated with the two dimensional melting of the surface of the solid catalyst, i.e. with the occurrence of a "liquid like" behaviour.

A theory of the two dimensional melting was developed by 18,19 d· b d th d· 1 . . Kosterlitz and Thouless an lS ase on e lS ocatlon palrs

model of melting. Although isolated dislocations cannot occur at low temperatures in a large system, because their energy increases logarithmically with the size of the system, pairs of dislocations with equal and opposite Burgers vector, which have finite energy, will occur because of thermal e~citations. (Note, however, that for the small crystallites isolated dislocations may also playa role). Melting occurs when the number of dislocation pairs of large separation becomes sufficiently large. The final result for the two-dimensional melting temperature is

T m,2

2e 2 a , (18)

where m is the atomic mass, h is the Planck constant, a is the lattice parameter and e is the Debye temperature (ke = hvD, vD

being the cutoff value in the frequency spectrum of the solid) .

A similar result was obtained by Lindemann20 for the melting temperature T of a three-dimensional solid, on the basis of the

10 3 hypothesis that fusion occurs when the amplitude of thermal vibra-tions of the atoms of the crystal reaches a certain small fraction of the lattice constant. Denoting by ~ the displacement of an atom


from its equilibrium position, one has ~2 kT 3 m,

2 2 (2'Tf) mvo

2 (Sa) , where

S is a number between 1/7 and 1/10. One thus obtains

T m,3

(19)

A comparison of Eqs. (18) and (19) shows that the two temperatures are proportional to one another. The proportionality constant is near to that which is used in the definition of the

Tarnrnann temperature if S = ~2' This is somewhat small. However,

the upper limit of the frequency spectrum has been used in obtaining (19); if instead a more appropriate average is used, the result will be displaced in the right direction.

Perhaps a better understanding is provided by a theory

d k 21 f ' , developed by Burton, Cabrera an Fran or the transltlon temperature at which significant roughness occurs on the surface of a crystal. In one of their calculations they assume that the molecule in the crystal surface is positioned at one of only two

, d 22 levels and use the results obtalne by Onsager for the two dimensional Ising model. The conclusion is that the above transition temperature is almost equal or even larger than T 3 when the

m, nearest neighbor interactions in the surface itself are the same as 'the nearest neighbor interactions inside the crystal. This happens for the (1,0,0) face in both cubic and face centred cubic lattices, as well as for the (1,1,1) face in the face centred cubic. However, for surfaces for which the nearest neighbor interactions in the surface include also some second nearest neighbor interactions in the lattice, as, for instance, (1,1,0) surface both for simple cubic and face-centred cubic lattices, the transition temper-ature can become lower than T In the latter cases,

m,3 kT "/¢l is a function of ¢2/¢1' where ¢l and ¢2 are the transltlon bond energies for the first and second neighbor interactions,

respectively. If ¢2/¢1 = 0.1, then Ttransition = ~ Tm,3 Finally,

for surfaces containing only second nearest neighbor bonds, such as (1,1,1) for simple cubic crystals, the transition temperature is very low, being of the order of ¢2/¢1 times the three-dimensional

melting temperature. The above considerations provide some meaning to the concept of the Tarnrnann temperature.

21 6 E. RUCKENSTEIN

III. EXPERIMENTAL

The method of preparation of thin films of y-alurnina of about

° 300 A thickness as well as the method of deposition of the metal on the substrate have been described previously13 Of the many results obtained in our laboratory on the behaviour of Pt, Ni, Fe, and Pd crystallites supported on thin films of alumina, we have selected 6 transmission electron micrographs for presentation here. Figs. 3a to 3f show the time sequence of the same region of a specimen of Ni on y-alumina. The specimen was heated alternately in 02 and H2 at 530°C. Fig. 3a shows the initial specimen, while

Figo 3b shows the same area of the specimen after heating in flowing 02 for 1/2 hr. The electron diffraction patterns indicate that Ni

is oxidized to NiO. The larger particles, with diameters greater ° than about 175 A, extended over the substrate, changing their shape

from spherical to toroidal. However, this torus is divided into a number of interlinked particles. Some of the torus like particles have (remaining) small particles inside the ring. Smaller particles

° with diameters of 50 to 150 A only extended over the surface of the substrate, the smallest among them even disappearing. Further heating in 02 for 2.5 hr. did not produce any major change (Fig.

3c). A few small crystallites extended over the substrate and the thickness of the rims of the larger particles decreased and their edges sharpened. Subsequently, the specimen was heated in H2' also at 530°C: for 1 hr. The electron diffraction patterns indicated taht NiO is reduced to Ni. At the same time the subunits of the torus cont~act to a greater wetting angle and the splitting becomes more obvious (Fig. (3d». Further heating in H2 for an additional one (Fig. 3e» or two (Fig. (3F» hours leads to an increasing degree of sintering.

The above behaviour of crystallites during heating in 02 is due to the better wetting of the substrate by NiO than Ni. In assition, an aluminate is formed between NiO and A1203' 23 It is therefore likely that aluminate forms at the bottom of the crystallites and that this aluminate also covers the substrate within the central cavity of the torus. A possible explanation for the accurrence of this torodial shape can be based on thermodynamics. Let us assume that the corresponding crystallite-gas and crystallite-support contact areas are the same for both the torus and the droplet configurations. Then, the toroidal shape is the more stable configuration when the interfacial tension between the aluminate covered alumina


Fig. 3. Behaviour of Ni Crystallites Supported on Alumina During Heating in 02 Followed by Heating in H2 • See Text for Details.

218 E. RUCKENSTEIN

Figure 3 continued


Figure 3 continued

220 E. RUCKENSTEIN

and gas, within the cavity of the torus. is smaller than the one between alumina and gas. Since the above assumption regarding the surface areas is not likely to be valid, it is plausible that the torus configuration is preferred to the droplet, when the interfacial tension of aluminate covered alumina is very much smaller than that of alumina. Calculations based on variational calculus are in progress, and, in addition, alternate explanations are being considered.

Similar phenomena have been observed previously during heating of Pd in °2 7 or during the alternating heating of Pd in 02 and H28 • During heating in 02 at SOO°C spreading of the oxidized crystallites to a smaller wetting angle was very extensive and spreading-induced tearing and fragmentation were observed. During alternate heating, most of the crystallites extended by spreading on the alumina surface and became irregular in shape during heati.ng in oxygen. Also pits and cavities developed on many of the crystallites. During heating in H2 , most of the crystallites which extended during the previous heating in 02 contracted to a more circular form. Some large crystallites grew in size. Some small crystallites disappeared during heating in 02 or H2 .

The present experiments as well as those already published confirm the opinion expressed a decase ago 1 that wetting, and the interactions that are involved among catalyst, substrate and atmosphere, playa major role in the behavior of supported metal catalysts.

CONCLUSION

The thermodynamic considerations of this paper show that Ostwald ripening is associated with a kind of phase separation in the sense that it can occur only when a two dimensional phase of single atoms (molecules) dispersed on the substrate can coexist with a large crystallite. When such a phase separation is not possible, migration of "crystallites" of all sizes including single atoms (or molecules) constitutes the mechanism of sintering. The atmosphere, the substrate and the temperature each play a role in the above proces~ ses. In addition, the same thermodynamic considerations indicate that, because of the chemical reactions between the atmosphere and the metal crystallites, and/or between the atmosphere and the substrate, the chemical nature of the crystallites and/or substrate change as do the interactions between them. As a consequence, depending on the conditions, the crystallites extend or contract to lower or higher wetting angles. These processes are associated with changes in shape, tearing or even fragmentation of the crystallites. There are conditions under which the crystallites take the form of extended planar configurations with a rapid variation of angle near the leading edge. It is shown that such configurations can occur if the interactions between substrate and catalyst are moderately strong


and some quantitative expressions are provided for this case. Experimental results are presented which illustrate some of the phen .. omena associated with wetting and spreading.

ACKNOWLEDGEMENT

The experiments have been carried out by Mr. S. H. Lee and Mr. I. Sushumna. I am also indebted to them and to Drs. J. Beunen and R. Nagarajan for useful comments.

REFERENCES

1. Ruckenstein, E., and Pulvermacher, B., J. Cata1. 29, 224 (1973). 2. Chakraverty, B. K., J. Phys. Chem. Solids 28, 240r-(1967). 3. Flynn, P. C., and Wanke, S. E., J. Cata1. 33, 233 (1974). 4. Ruckenstein, E., and Dadyburjor, D. B., J.-Cata1. 48, 73 (1977). 5. Ruckenstein, E., and Dadyburjor, D. B., Thin Solid Fi1ms,~,

89 (1978). 6. Lee, H. H., J. Cata1. ~, 129 (1980). 7. Chen, J. J., and Ruckenstein, E., J. Phys. Chem. 85, 1606 (1981). 8. Ruckenstein, E., Chen, J. J., J. Colloid Interface Sci. 86, 1

(1982). 9. Fiedorow, R. M. J. and Wanke, S. E., J. Cata1. 43, 34 (1976). 10. Ruckenstein, E., and Chu, Y. F., J. Cata1. 59, 109 (1979). 11. Bassett, G. A., in "Proc. Eurp. Reg. Conf. on Electron Micr.

Delft," Vol 1, p. 270 (1960). 12. Masson, A., Metois, J. J. and Kern, R., Surface Sci. 12, 463

(1971) . 13. Chen, J. J., and Ruckenstein, E., J. Cata1. 69, 254 (1981). 14. Arai, M., Tshikawa, T., and Nishiyama, Y., J. Phys. Chem. 86,

577 (1982). 15. Baker, R. T. K., Prestridge, E. B., and Garten, R. L., J. Catal.

22., 293 (1979). 16. Ruckenstein, E., and Lee, P. S., Surf. Sci. 52, 298 (1975);

J. Colloid Inteface Sci. 86, 573 (1982). --17. Ruckenstein, E., J. Crystal Growth~, 666 (1979). 18. Dash, J. G., Films on Solid Surfaces, Academic Press, New York,

1975. 19. Koster1itz, J. M. and Thou1ess, D. J., J. Phys. C: Solid State

Phys. 5, 124 (1972); 6, 1181 (1973). 20. Lindemann, F. A., Z. Phys. 11, 609 (1910). 21. Burton, W. K., Cabrera, N., and Frank, F. C., Trans. Roy. Soc.

(London) A243, 299 (1951). 22. Onsager, L., Phys. Rev. ~, 117 (1944). 23. Anderson, J. R., Structure of Metallic Catalysts, Academic Press

(1975). 24. Ruckenstein, E., and Dadyburjor, B. D., Reviews in Chemical

Engineering 1, No.3, 1983.

SINTERING AND REDISPERSION OF CONVENTIONAL SUPPORTED METAL

CATALYSTS IN HYDROGEN AND OXYGEN ATMOSPHERES

ABSTRACT

Sieghard E. Wanke

Department of Chemical Engineering, University of Alberta Edmonton, Alberta, Canada T6G 2G6

The average metal crystallite size in supported metal catalysts usually increases during use. This increase in average metal crystallite size, i.e. decrease in metal surface area, is one of the causes of catalyst deactivation. For some supported metal catalysts the average metal crystallite size in deactivated catalysts can be decreased by appropriate regeneration procedures. The processes by which increases in metal crystallite sizes occur is referred to as sintering, and processes which result in decreases in metal crystallite size are called redispersion.

In this paper, data obtained with conventional supported metal catalysts, i.e. metals supported on high surface area porous carriers, are examined with the aim of determining the mechanisms of sintering and redispersion. The systems examined will be restricted to platinum metals on carriers which do not react with the surrounding atmosphere, e.g. metals supported on carbon will not be included in the discussion. The data strongly supports the hypothesis that redispersion and sintering for these non-reacting systems occurs via transport of atomic or molecular species, and not by migration of entire metal or metal oxide particles.

INTRODUCTION

The commercialization of platinum reforming catalysts in 1949 opened a new area for catalysis; platinum reforming was the first industrial use of noble metal catalysts for the upgrading of petroleum l . One of the main reasons for the economic success of

223

224 S.E. WANKE

platinum reforming is the total useful life of Pt/alumina catalysts. In recent years the Pt/alumina catalysts have largely been replaced by bi-and multimetallic catalysts, notably Pt-Re/alumina2 and Pt-Ir/alumina3. These bimetallic catalysts have superior activity, selectivity and stability. However, all reforming catalyst still deactivate due to coking and sintering, but deactivated catalysts can be regenerated by coke burn-off and metal redispersion. Sintering, i.e. loss of metal surface area due to metal crystallite growth, can occur under reforming conditions and during coke burnoff. Metal redispersion, i.e. increase in metal surface area, is achieved by oxygen and oxychlorination treatments 4 .

This paper will deal with changes in metal surface areas of conventional supported noble metal catalysts. The term 'conventional' refers to metals supported on high surface area ceramic supports; the paper will not deal with metals supported on thin films, i.e. model supported metal catalysts. This paper is not a review of sintering and redispersion of supported metal catalysts, but it is an overview of results we have obtained during the past 10 years. Most of the results presented have been publishedS- 17 ,

but some recent, unpublished data are also included.

The emphasis in this paper will be on the changes in metal surface areas caused by treatment in oxygen and hydrogen at elevated temperatures. Results for various platinum group metals (Pt,Ir,Rh,Ru,Pt-Ir and Pt-Pd) supported on a variety of carriers (A1 20 3, SiO z ' Si0 2-A1 20 3 and MgO) will be discussed. Probable mechanisms for sintering and redispersion will be examined in the last part of the paper.

EXPERIMENTAL METHODS

Catalysts

Descriptions of the catalyst used in this study are given in Table 1. Aqueous solutions of metal chlorides were used for all catalysts, except Cat. 16, prepared by impregnation8 . For Cat. 16, a platinum acetylacetonate in acetone solution was used for the impregnation. This, as well as other, chlorine-free preparations were done in order to determine whether residual chlorine, from impregnations with metal chlorides, affects the sintering and redispersion behavior. The bimetallic Pt-Ir catalyst (Cat. 14) was prepared by co-impregnation.

Catalysts prepared by aqueous impregnation were dried in air at 110°C for 24 h. Shortly after drying, the catalysts were reduced in flowing hydrogen for 16 h at 150°C, 2 h at 250°C and 1 h at 500°C. The 500°C reduction was omitted for Catalysts 6 and 16. The drying step for Cat. 16 was done at 75°C rather than 110°C.

SINTERING AND REDISPERSION OF METAL CATALYSTS

Catalyst Number

1

2

3

4

5

6

7

8

9

Table 1. Description of Catalysts

Metal

Pt

Pt

Pt

Pt

Pt

Pt

Ir

Rh

Rh

Ru

Ru

Metal Loading Supporta (mass%)

1.0 Alon(!)

2.0 KA-20l(2)

1.0 Si02 (3)

1.0 Si02-A1 203(4)

5.0 MgO(5)

0.5 MgO(5)

2.0 KA-20l(2)

1.0 KA-20l(2)

0.5 Al 20 3(6)

1.0 KA-20l(2)

0.5 A1 203(6)

0.3 A1 20 3(6)

0.05 KA-20l(2)

Method of Preparationb

impregnation

impregnation

impregnation

impregnation

impregnation

impregnation

impregnation

impregnation

commercial

impregnation

commercial

commercial

impregnation

225

Initial HIM RatioC

(Do)

0.41

0.28

0.13

0.17

0.34 d

0.43d

0.42

0.33

0.37

(0.04)

(0.07)

0.32

0.15

10

11

12

13

14

Pt

Pt

Pt-Ir 1.0 Pt 1.0 Ir

Alon(l) co-impregnation 0.43

15

16

17

18

19

Pt-Pd

Pt

Pt

Pt

Pt

0.04 Pt A1 20 3(7) 0.04 Pd

0.5 MgO(5)

0.5 Alon(l)

1.0 Alon(l)

4.0 Alon(l)

ASee Table 2 for description of supports.

commercial

impregnation

impregnation

impregnation

impregnation

0.10

0.37d

0.29

0.33

0.31

BAqueous solutions of metal chlorides used in all impregnations, except for Cat. 16, for Cat. 16, Pt(C5H702)2 in acetone was used. Commercial catalysts, except Cat. 15, obtained from Engrlhard, Cat. 15 is General Hotors Type 78925 converter catalyst.

CHydrogen to metal ratio measured by dynamic pulse technique after reduction snd degassing at 500°C (no oxygen pretreatment).

DUydrogen uptakes after oxygen pretreatment at 550°C, and reduction at 300°C.

226 S.E. WANKE

Table 2. Description of Supports

Support Material

Supplier Surface Area Number (Designation) (m2 /g)

1 y-A1203 Cabot (Alon) 100

') y-A1 203 Kaiser(KA-20l) 200 ...

3 Si0 2 Alpha Products 220

4 Si02-A1203 Alpha Products 100

5 MgO Alpha Products 50

6 y-A1 203 Engelhard 100

7 y-A1 203 General Motors 85

The reduced catalysts were stored in air until use. It should be pointed out that the laboratory prepared catalysts were not calcined at elevated temperatures before reduction.

The properties of the supports are summarized in Table 2. The phase of all the alumina supports was identified as y-alumina by x-ray diffraction (XRD). All the alumina XRD patterns exhibited a doublet at 0.198 and 0.195 nm. This doublet, according to Spitler and PollockW, is the main distinguishing feature between y- and n-alumina. The surface areas reported in Table 2 were obtained by the BET method.

Thermal Treatment and Adsorption Procedures

Catalyst samples to be examined were placed into a Vycor or quartz U-tube and treated in flowing gas (oxygen or hydrogen) at the desired temperature. The size of the catalyst sample used varied from 1 to 10 g depending on the metal loading of the catalyst; the larger amounts were used for catalysts with low metal loadings, e.g. Catalysts 13 and 15. In situ reduction in flowing hydrogen, usually for 1 h at 500°C, and degassing in flowing nitrogen or helium at 500°C for 2 h followed the thermal pretreatment. MgO supported catalysts were reduced at 300°C and degassed for 1 h at 300°C and lh at 500°C.

Hydrogen and, for some catalysts, carbon monoxide adsorption uptakes were measured by the dynamic pulse method 19 . Nitrogen was used as the carrier gas for hydrogen adsorption and helium was used for carbon monoxide adsorption since a thermal conductivity cell

SINTERING AND REDISPERSION OF METAL CATALYSTS 227

was used to measure the amounts adsorbed. Previous publications 8,9,19,20 should be consulted for more detailed descriptions of equipment and treatment procedures.

Transmission Electron Microscopy and X-ray Diffraction

Catalyst samples, after various thermal treatments, were examined by conventional transmission electron microscopy (CTEM) using JEM 100B, Siemens EMl02 and Philips EM400T electron microscopes. Due to the nature of the samples reliable detection of metal particles less than 1 to 1.5 nm in size is not possible; the supports alone give areas of contrast in this size range which are not readily distinguishable from contrast due to metal particles. Other problems encountered when examining porous catalysts by CTEM have been discussed previously21 ,22 •

X-ray diffraction studies, for phase identification and metal crystallite size determination by line broadening, were done on a Philips diffractometer 17 .

EXPERIMENTAL RESULTS AND DISCUSSION

This section is divided into three parts. In the first part the influence of oxygen treatment on metal dispersion is discussed, the effect of hydrogen treatment on metal dispersion is presented in the second part, and in the final section bimetallic catalysts and the influence of metal loading are discussed.

The sintering and redispersion results presented below are normalized dispersion, DIDo, as a function of thermal treatment. D is the metal dispersion after thermal treatment and Do is the metal dispersion of the fresh catalysts. Metal dispersion is defined as the ratio of surface to total metal atoms. For all catalysts, except those supported on MgO, the values of D and Do were obtained from hydrogen adsorption measurements by assuming that one hydrogen atom adsorbs per surface metal atom, i.e. D is equal to HIM and Do is equal to (H/M)o. Values of Do are tabulated in Table 1.

The HIM ratio determined by the dynamic pulse method, is probably somewhat lower than the metal dispersion since it is likely that the hydrogen adsorption stoichiometry under dynamic adsorption condition is somewhat less than unity. This is certainly the case for the Ru catalysts (Catalysts 10 and 11) since hydrogen adsorption on Ru is activated. However, normalized dispersions are independent of hydrogen adsorption stoichiometry as long as thermal treatments does not alter the adsorption stoichiometry. Hence, normalized dispersions are a good indicator of the changes in dispersion brought about by thermal treatment.

228 S.E. WANKE

For Pt/MgO (Catalysts 5,6 and 16), HIM ratios are not a reliable measure of Pt dispersion since hydrogen uptakes are a strong function of reduction conditions 13 ,16. For these catalysts Pt dispersions were estimated from electron micrographs.

'J' 25 e. c: o "§ Q) a. '" Ci -0 10 ~:::::;""'" Ql

.!::! lii E 05

o Z

0 ~3~0~0--4~0-0--5~0-0--6~0-0--7~0-0--8~0-0~

Treatment Temperature (oq

Figure 1. Changes of Pt dispersion for Pt on various supports as a result of 16 h treatment in oxygen (see Table 1 for description of catalysts).

The Effect of Oxygen Treatments on Metal Dispersion

In Fig. 1 values of DIDo after oxygen treatment for 16 h at various temperatures are plotted for Pt on different supports. The data in Fig. 1 clearly shows that the nature of the support has a large influence on the sintering and redispersion of supported platinum. For silica (Cat. 3) and silica-alumina (Cat. 4) supported catalysts the DIDo values decrease with increasing treatment temperatures. The value of D never exceeded the value of Do for these catalysts, i.e. redispersion did not occur. For the alumina supported catalysts (Catalysts 1 and 2) the DIDo values increased with increasing treatment temperatures up to a maximum at temperatures of 500 to 550°C. Above 550°C the values of DIDo decrease sharply. For the MgO supported catalyst a large increase in DIDo,


as determined by CTEM, is caused by oxygen treatment at 500 to 700°C. Hydrogen adsorption results, after reduction at 300°C, show similar increases in DIDo. Studies are currently in progress to determine the effect of oxygen treatment on DIDo at temperatures below 500°C and above 700°C.

Sintering and redispersion of supported Pt undoubtedly occurs via the transport of platinum oxide species. The nature of the interaction of platinum oxides with the support governs the sintering and redispersion behavior of Pt. Strong Pt oxide-support interactions results in redispersion. Based on this interpretation, the sequence of decreasing strengths of Pt oxide-support interactions is

MgO > Al 20 3 > Si0 2-Al 20 3 ~ Si0 2

Details regarding a possible mechanism for the sintering and redispersion will be presented later in this paper.

It has been suggested23- 25 that the increases in H/Pt ratios as a result of oxygen treatment are not due to redispersion, but are due to metal-support interactions. This, however, is unlikely since the catalysts were reduced in hydrogen at the same temperature, usually 500°C, before and after oxygen treatment, i.e. D and Do were both measured after hydrogen reduction at elevated temperatures. Furthermore, carbon monoxide adsorption uptakes of reduced, alumina and magnesia supported Pt catalysts also increased as a result of oxygen treatment at temperatures between 500 and 550°C (see Runs 1 to 3, Table 3).

Additional, conclusive evidence of platinum redispersion as a result of oxygen treatment for alumina and magnesia supported catalysts was obtained by CTEM and XRD. Figure 2 shows electron micrographs of eat. 18 (1% Pt/Alon) after various thermal treatments. Reduction at 500 0 e of a freshly impregnated catalyst yields a catalyst with a surface average Pt particle size26 of approximately 3.7 nm (see Fig. 2AY. There is evidence for many Pt particles smaller than 1 nm, but these particles were not measured. Oxygen treatment at 550 0 e without subsequent reduction results in the disappearance of Pt particles (see Fig. 2B). Subsequent reduction at 500 0 e of the oxygen treated sample yields Pt particles with a surface average particle size of about 2.4 nm. Again there is evidence for many sub-nanometer particles. Similar CTEM observations have been reported for Pt/MgO catalysts 13,16. For Catalyst 5, oxygen treatment at 550°C, followed by reduction resulted in a decrease in surface average Pt particle size from 4.4 to less than 2.0 nm. As in the case for Pt/Alon,small Pt particles were detected on unreduced Pt/MgO samples following oxygen treatments. This indicates that the mechanism for redispersion of Pt on alumina and magnesia is similar.

230 S.E. WANKE

Table 3. Effects of oxygen treatment on adsorption uptakes of alumina and magnesia supported platinum

Oxygen Treatment Reduction Adsorption Uptakes Runa Cat. Temperature Time Temperature Hydrogen CO

(OC) i!!.L (oC)b (H/Pt) (CO/Pt)

1 12 none 300 0.33 0.31 none 500 0.41 0.29

550 16 500 0.79 0.36

2 13 none 300 0.l6 0.23 none 500 0.18

550 1 500 0.55 0.45

3 16 none 250 0.0 0.05 100 1 250 0.06 200 1 250 0.06 300 1 250 0.06 400 1 250 0.07 550 1 250 0.23 0.26

4 15 none 250 0.44 0.14 none 500 0.10 0.08

550 1 250 0.33 none 500 0.13

5 1 none 500 0.41 500 1 500 0.62 500 16 500 0.86

6 17 none 500 0.29 550 1 500 0.62 550 16 500 0.64

7 18 none 500 0.33 550 1 500 0.68 550 16 500 0.69

8 19 none 500 0.31 550 1 500 0.35 550 16 500 0.27

AA11 treatments for a given run were done sequentially on the same sample.

BDegassing done at same temperature as reduction (1 h reduction, 2 h degassing).


A

Figure 2. Electron micrographs of 1.0% Pt/Alon (Cat. 18) after various treatments (all micrographs at same magnification). A. Freshly reduced sample (no oxygen treatment), H/Pt=0.33;

° B. Sample after oxygen treatment at 550 C (unreduced); ° C. Reduced sample after oxygen treatment at 550 C, H/Pt=0.69;

D. Sample after hydrogen treatment at 700°C for 1 h, H/Pt=0.22.

232 S.E. WANKE

800

-en 600 ... C :s 0 (,) - 400 ~ ~ 'iii c CI) ... 200 C

0 36 38 40 42 44 46 48

Angle (26)

Figure 3. XRD patterns for 5% Pt/MgO (Cat. 5). Patterns obtained with CuKa radiation, step scanned at 4 s per step of 0.05° of 28. --- pure MgO;···freshly reduced 5% Pt/MgO; --- 5% Pt/MgO after oxygen treatment at 550°C and reduction at 500°C.

XRD line broadening studies of Pt/MgO (Cat. 5) and (Pt-Ir)/Alon (Cat. 14) also show that Pt redispersion occurs as a result of oxygen treatment at 500 to 550°C. The marked broadening and decrease in intensity of the Pt III and 200 lines (at 39.8 and 46.3° of 28) for Cat. 5 are shown in Fig. 3. Similar results have been obtained for the bimetallic Pt-Ir catalyst. The Pt lines become broader and the Ir lines become sharper as a result of oxygen treatment at 500°C 17 •

It has also been proposed4 that chlorine, as well as oxygen, is necessary for Pt redispersion. Most of the catalyst discussed above were prepared by impregnation with hexachloroplatinic acid, and the possibility exists that the residual chlorine from the platinum precursor may be responsible for the subsequent Pt redispersion. A chlorine-free Pt/MgO catalyst, Cat. 16, was prepared using a platinum acetylacetonate in acetone solution for the impregnation. Redispersion of Pt as a result of oxygen treatment at 550°C, similar to that observed catalysts prepared with chloroplatinic acid in water, was obtained for the chlorine free catalyst (see Run 3, Table 3). Redispersion was also observed for alumina supported Pt ~epared by impregnation with platinum acetylacetonate in chloroform .

The above results show, beyond doubt, that Pt redispersion can be obtained by oxygen treatment at 500 to 550°C in the absence of chlorine for alumina and magnesia supported Pt. Redispersion of Pt


J> 25 Calalysl 2) 0 2 (PI)

c: 20 V 7 (Irj 0 8 (Rh) .~

Q) 1.5 9 (Rhl a. (/)

0 "0 10 Q)

.!:! (ij 05 E (; z 0 300 400 500 600 800

Treatment Temperature (0C)

Figure 4. Effect of 1 h treatment in oxygen on dispersion of various metals supported on alumina.

was never observed for silica and silica-alumina supported Pt.

The influence of oxygen treatments on other platinum metals supported on alumina was investigated in order to determine whether redispersion can also be achieved9 . The results of this study, summarized in Fig. 4, show that a modest amount of redispersion is obtained for Ir/A1 2 0 3 at temperatures of about 400°C. No redispersion was observed for Rh and Ru on alumina.

The redispersion observed for Ir/A1203 is sensitive to the nature of the y-A1 20 3 support. For Cat. 7 (Ir on Kaiser y-a1umina) the maximum redispersion was observed after 1 h oxygen treatment at 400°C. The value of DIDo for this catalyst decreased to 0.51 if the oxygen treatment at 400°C was done for 16 h. For another Ir/y-A1203 catalyst (1% Ir on Alon) , the maximum redispersion was observed after oxygen treatment at 300°C; values of DIDo equal to 1.18 and 1.22 were obtained after oxygen treatment for 1 and 16 h, respectively. This indicates that the strength of the interaction between Ir oxide and alumina is less than that of Pt-oxides with alumina.

Based on the results shown in Fig. 4, the order of decreasing

234 S.E. WANKE

thermal stability of platinum metals on alumina is

Rh > Pt > Ir > Ru

However, the strength of metal oxide-alumina interactions probably have the following sequence

Pt > Ir > Rh > Ru

since redispersion requires metal oxide-support interactions.

The Effect of Hydrogen Treatments on Metal Dispersion

Hydrogen treatments at elevated temperatures were done on a large number of supported metal catalysts; results for Pt on various supports are presented in Fig. 5, and results for various metals supported on alumina are summarized in Fig. 6. The relative dispersion obtained after hydrogen treatments never exceeded unity, i.e. hydrogen treatment does not result in metal redispersion.

For all catalysts, except Cat. 6 (Pt/MgO), DIDo values were obtained from hydrogen adsorption measurements. It has been argued~ that decreases in hydrogen adsorption uptakes after hydrogen treatment at elevated temperatures are due to metal support interactions brought about by high temperature treatment in hydrogen. For Pt/MgO catalysts hydrogen treatment at temperatures of above 400°C certainly does result in decreased hydrogen uptakes without an increase in Pt

-0 0 ...... 0 c 0 'iii .... OJ C. en Ci "0 OJ

~ co E 0 z

10

05 Catalyst

0 1 (AI20~

0 2 (AI20~

.0. 3(51° 2)

• 4 (SI02-AI20;,)

A 6 (MgO)

0 L-5~0~0------6~00~--~7~0~0----~80~0~

Treatment Temperature (0G)

Figure 5. Effect of I h hydrogen treatment on dispersion of Pt on various supports.

10 -0 0 ...... 0

c .2 en .... OJ c. en Ci 05 "0

Catalyst

o 2 (Pt) OJ ,!::! t\1

v 7 (Ir)

.0. 8 (Rh)

E 0 Z

A 9 (Rh)

o 10 (Ru)

• 11 (Ru)

0~5~0~0----~60~0~--~7~O~0----~80~0-J

Treatment Temperature (0G)

Figure 6. Effect of I h hydrogen treatment on dispersion of various metals supported on alumina.


crystallite size 13 ,16; hence, CTEM was used to obtain D/Do for Pt/MgO catalysts.

For alumina, silica and silica-alumina catalysts, the decrease in H/M ratios caused by hydrogen treatment is largely due to growth of metal crystallites. This has been confirmed by CTEM. Comparison of Figs. 2A and D shows that for Cat. 18 (Pt/Alon) hydrogen treatment at 700°C for 1 h increases the surface average Pt particle size from 3.7 to 4.0 nm. This apparently small increase is deceiving because considerably more Pt is 'visible' by CTEM in the catalyst after the 700°C hydrogen treatment, i.e. the freshly reduced sample (Fig. 2A) contains many sub-nanometer Pt particles which largely disappear as a result of hydrogen treatment at 700°C. It is the incorporation of these small particles into the larger particles which is largely responsible for the decrease in the H/Pt ratio from 0.33 to 0.22. The disappearance of sub-nanometer particles and the relatively small increase in the average size of the remaining Pt crystallites is not detectable by XRD.

The sequence of decreasing thermal stability for Pt on various supports, according to Fig. 5, is

For the different metals supported on alumina, the sequence of decreasing thermal stability, according to Fig. 6, is

Ru > Ir > Rh > Pt

The two important conclusions resulting from the hydrogen treatment experiments are; one, redispersion does not occur as a result of hydrogen treatment, and two, hydrogen treatment at elevated temperatures does result in metal particle growth.

Bimetallic Catalyst and Metal Loading Effects

Two bimetallic catalysts, Pt-Ir (Cat. 14) and Pt-Pd (Cat. 15) on alumina were examined. The influence of hydrogen and oxygen treatments on the Pt-Ir catalyst have previously been described in detail 11 ,17. The results showed that the Pt-Ir catalyst does contain bimetallic, but not homogeneous, crystallites, and that the thermal stability in hydrogen is similar to that of Ir/A120 3 . Treatment in oxygen resulted in the segregation of Pt and Ir into monometallic crystals. XRD resultsVshowed that Ir02 crystallites formed during oxygen treatment at 400 to 800°C. Pt-oxides were never detected by XRD; in oxygen at temperatures of 600°C and above rapid growth of Pt crystallites was detected by XRD, i.e. Pt oxides on alumina are not stable at these temperatures.

The effects of hydrogen and oxygen treatments on adsorption

236 S.E. WANKE

capacities of the Pt-Pd General Motors converter catalyst (Cat. 15) was studied because we had observed27 significant increases in CO oxidation activity as a result of CO burn-off. Typical results showing the effects of reduction temperature and oxygen treatment on hydrogen and CO adsorption, are given in Table 3, Run 4. These results indicate that hydrogen treatment at 500°C, i.e. reduction, causes a decrease in hydrogen and CO adsorption uptakes. The adsorption capacities can be largely restored by oxygen treatment at 550°C. CTEM studies showed that these changes in adsorption uptakes are mainly due to changes in metal particle size. No metal particles were detected in the fresh catalyst reduced at 250°C. However, numerous metal particles in the 1 to 4 nm range were visible in the fresh and oxygen treated catalysts after reduction at 500°C. It is not known whether these metal particles were Pt, Pd or bimetallic particles.

Similar decreases in adsorption uptakes as a function of reduction temperature were not observed for the 0.05% Pt/A120 3 catalyst (see Run 2, Table 3). Increases in dispersion were, however, observed for this catalyst as a result of oxygen treatment. For the catalysts with very low metal loadings (Catalysts 13 and 15) the H/M and CO/M ratio are probably significantly lower than the metal dispersion. It is possible that a significant fraction of the metal in catalysts with very low metal loadings exists as atomically dispersed metal. The adsorption on these metal atoms or metal ato~surface complexes may be weak and/or activated; the dynamic pulse method does not detect weak or activated adsorptions. For catalysts with higher metal loading this problem is not serious because the fraction of metal in this undetected state, if it exists at all, is insignificant.

Metal loading, however, does influence the redispersion behavior. The effect of metal loading was studied for Pt/Alon with Pt contents of 0.5, 1.0 and 4.0 wt %. Results of these studies are shown in Table 3, Runs 5 to 8. For the 0.5 and 1.0% Pt catalysts, significant redispersion occurs as a result of oxygen treatment at 500 to 550°C. However, only a modest increase in dispersion is observed for the 4% Pt catalyst after 1 h treatment (Table 3, Run 8). Increasing the treatment time to 16 h causes a decrease in dispersion. This dependence of D/Do on treatment time at 550°C, i.e. an initial increase followed by a decrease, has been observed for other 4.0% Pt/Alon preparations. For magnesia supported Pt a different dependence on Pt loading was observed. Redispersion of Pt occurred for catalysts containing from 0.5 to 5.0 wt% Pt 13. Redispersion for Pt/MgO was also observed at 700°C in oxygen; Pt/Al203 catalysts sinter severely under these conditions (see Fig. 1). Although the behavior of alumina and magnesia supported Pt differ, the same mechanism of sintering and redispersion is believed to be operative. This mechanism is discussed in the following section.


THE MECHANISM OF SINTERING AND REDISPERSION

Two main mechanisms have been proposed for the sintering and redispersion of supported metal catalysts; one is the crystallite migration mechanism28 ,29, the other is the atomic or molecular migration mechanismS' 29. Since crystallite migration alone cannot account for redispersion, the hypothesis of crystallite splitting was introduced 30 • Wetting of the support by the metal, i.e. decreases in the metal-support contact angle, in oxidizing and reducing atmospheres have been used to explain some of the observed sintering and redispersion phenomena31,~. Decreases in metal-support contact angles (spreading of the metal particles over the support) do occur; however, this continuum phenomenon cannot explain the disappearance of metal containing particles (see Fig. 2B). Extended x-ray absorption fine structure studies on Pt/a1umina 33 have shown that exposure to oxygen, even at room temperature for highly dispersed catalysts, results in disruption of order in metal-metal distances. To obtain the disappearance of metal particles and disordering of metal-metal spacings requires random migration of metal atoms or metal oxide molecules. The concepts of wetting and contact angles becomes meaningless when dealing with isolated metal atoms or metal oxide molecules.

The mechanism which will be described in this paper and which is in agreement with all the results presented in the previous section is the atomic migration mechanism. In oxygen atmospheres the mechanism consists of the following steps:

1. Oxygen adsorbs on the surface of metal particles to form surface metal oxides or bulk metal oxide particles.

2. Metal oxide molecules become detached from the particles and move onto the support surface. (Transport of metal oxide molecules to the gas phase is insignificant for the systems and conditions studied in this paper with the possible exception of Ru at ~ 400°C and Ir at 800°C).

3. A metal oxide molecule diffuses over the support surface until it either

(i) encounters a site on the support which has a large interaction with the metal oxide. This metal oxide-support interaction will slow down or even stop the diffusion of the metal oxide molecules.

(ii) collides with a metal or metal oxide particle and becomes incorporated into the particle.

(iii) decomposes into a metal atom and oxygen. At the elevated temperatures the resulting metal atom diffuses rapidly of the support surface until it collides with and becomes captured by a metal particle.

4. Hydrogen treatment after the oxygen treatment results in (i) reduction of metal oxide particles to metal particles

238 S. E. WANKE

(ii) reduction of the metal oxide-support complexes formed in step 3(i) to individual metal atoms on the support. The metal atoms diffuse over the support surface until they are captured by metal particles. If no metal particles are present initially, collision of diffusing atoms will result in the nucleation of metal crystallites.

The sintering and redispersion behavior for a given metal-support system depends on the relative rates of the various steps in the above mechanism. Quantitative predictions for various rate controlling steps for a very similar mechanism have been presented previouslyS,6,lO. In the present paper only qualitative analyses of the data present in the Results and Discussion section will be presented.

The nature of the redispersion sites, i.e. the sites mentioned in Step 3(i) at which metal oxide-support interactions occur, will largely determine which step in the mechanism is rate controlling. We have postulated 12 that for Pt in oxygen the redispersion sites are basic sites on the support. Several cases, depending on the abundance of and interaction strength at the redispersion site, can be envisaged.

Case 1: No, or very few redispersion sites are present. In this situation the escape of metal oxide molecules from the particles (Step 2) becomes rate controlling and only sintering, and no redispersion, occurs, i.e. the metal oxide molecules on the support have a high mobility (see bottom curve in Fig. 4 of Ref. 6). This case applies to Pt supported on silica and silica-alumina and to Rh and Ru on alumina. It is also applicable to Pt on alumina at temperatures of 600°C and higher because the Pt oxides on the support decompose (Step 3(iii» and the resulting Pt atoms are very mobile.

Case 2: Redispersion sites which interact weakly with metal oxide molecules. Steps 1 or 2(i) or both are rate determining for this case. The interaction at the dispersion sites reduces the mobility of the metal oxide molecules on the support and this can result in transient increases in metal dispersion. This case is probably applicable to Ir on alumina.

Case 3: Medium strength interactions at redispersion sites with the number of redispersion sites exceeding the total number of metal atoms. For this case all the metal can be accommodated at the redispersion sites, but due to the strength of the interaction the metal oxide molecules retain some mobility. This situation is applicable to all the Pt/alumina catalyst listed in Table 1 except for Cat. 19 (i.e. the 4% Pt catalyst) at oxygen treatment temperatures ~ 550°C. Subsequent reduction of oxygen treated catalysts results in the formation of atomically dispersed metal which diffuses over the surface and nucleates into small crystallites (Step 4(ii». It is this nucleation step which governs the final dispersion. The formation of the Pt oxide-redispersion site complexes is rather rapid «1 h at


550°C) because the final Pt dispersion after oxygen treatment at 550°C and reduction is essentially independent of oxygen treatment time (see Table 3, Runs 6 and 7, and Fig. 3 in Ref. 8).

Case 4: Same as Case 3 except that the amount of metal exceeds the amount of metal oxide that can be accommodated at redispersion sites. This means that metal containing particles will remain present on the catalyst at all times. These metal particles will grow with increasing treatment times while the amount of metal in the dispersed phase will remain relatively constant. During reduction the atomically dispersed metal will migrate over the surface and either nucleate into small crystallites or are captured by the existing metal particles. The overall effect is similar to that described for Case 2, i.e. small redispersion for short treatments and sintering for larger treatments. This case explains the observed results for Cat. 19 (4% Pt/Alon).

Case 5: Strong interactions at redispersion sites with the number of redispersion sites exceeding the number of metal atoms. In this case all the metal can be complexed at redispersion sites, but the mobility of metal oxide species is very low due to the strong interaction. Complete redispersion of the oxide phase can be obtained, but the degree of redispersion is dependent on the length of the oxygen treatment. This case is applicable to all the Pt/MgO catalysts. Pt oxides on MgO also appear to be stable to at least 700°C; bulk Pt oxides decompose at much lower temperatures.

A similar mechanism also is in agreement with the results obtained for hydrogen treatments. The metal oxide molecules in the above mechanism are replaced by metal atoms for treatment in hydrogen. All the systems examined (Figs. 5 and 6) fall into Case 1, i.e. none of the supports studied have redispersion sites for metal atoms. The differences in the sintering rates for the different supports and metals are due to differences in the rates at which metal atoms escape from the metal crystallite to the support, i.e. the rate of Step 2 depends on the metal and the support. Although the mechanism can explain the experimental observations, it is not possible on the basis of the experimental data to exclude the migration of subnanometer metal particles as a contributing factor to the sintering of supported metal catalysts in hydrogen.

SUMMARY AND CONCLUSIONS

The experimental data show that redispersion of Pt can occur in oxygen without the presence of chlorine. Redispersion was never observed as a result of hydrogen treatments, only sintering occurs. All the sintering and redispersion observations are in agreement with the presented atomic or molecular migration mechanism.

240 S.E. WANKE

ACKNOWLEDGMENTS

P.C. Flynn, R.M. Fie do row , B.S. Chahar, A.G. Graham, J. Adamiec, B. Tesche, U. K1eng1er, W.C.S. Pick and J.A. Szymura made significant contributions to the material presented in this paper. I thank them for their contributions. I also acknowledge the support of this research by the National Sciences and Engineering Research Council of Canada. The donation of alumina supports by Cabot Corp. and Kaiser Corp. is appreciated.

REFERENCES

1. M.J. Sterba and V. Haense1, Catalytic Reforming, Ind. Eng. Chern. Prod. Res. Dev. 15:2 (1976).

2. E.M. Blue, Regenerab1e Catalyst Highlights New Rheniforming Process, Hydrocarbon Processing~ 48(9):141 (1969).

3. J.H. Sinfe1t, Polymetallic Cluster Compositions Useful as Hydrocarbon Conversion Catalysts, United States Patent 3,953,368 April 27,1976.

4. J.P. Franck and G. Martino, Deactivation and Regneration of Catalytic-Reforming Catalysts, in: "Progress in Catalyst Deactivation", J .L. Figueiredo, ed., Martinus Nijhoff, The Hague (1982).

5. P.C. Flynn and S.E. Wanke, A Model of Supported Metal Catalyst Sintering I. Development of Model, J. CataZ. 34:390 (1974).

6. P.C. Flynn and S.E. Wanke, A Model of Supported Metal Catalyst Sintering II. Application of Model, J. CataZ. 34:400 (1974).

7. P.C. Flynn and S.E. Wanke, Experimental Studies of Sintering of Supported Platinum Catalysts, J. Catal. 37:432 (1975).

8. R.M.J. Fiedorow and S.E. Wanke, The Sintering of Supported Metal Catalysts I. Redispersion of Supported Platinum in Oxygen, J. CataZ. 43:34 (1975).

9. R.M.J. Fiedorow, B.S. Chahar and S.E. Wanke, The Sintering of Supported Metal Catalysts II. Comparison of Sintering Rates of Supported Pt, Ir and Rh Catalysts in Hydrogen and Oxygen, J. CataZ. 51:193 (1978).

10. S.E. Wanke, Sintering of Supported Metal Catalysts: Application of a Mechanistic Model to Experimental Data, in: "Sintering and Catalysis", G.C. Kuczynski, ed., Plenum, New York (1975).

11. A.G. Graham and S.E. Wanke, The Sintering of Supported Metal Catalysts III. The Thermal Stability of Bimetallic Pt-Ir Catalysts Supported on Alumina, J. CataZ. 69:1 (1981).

12. J. Adamiec, R.M.J. Fiedorow and S.E. Wanke, Influence of Supports on the Thermal Stability of Supported Platinum Catalysts in Oxygen, 74th AIChE Meeting~ Fiche 59, New Orleans (1981).

13. J. Adamiec, S.E. Wanke, B. Tesche and U. K1eng1er, Metal-Support Interactions in the Pt/MgO System, in: "Metal-Support and Metal-Additive Effects in Catalysis", B. Imelik et al., eds., Elsevier, Amsterdam (1982).


14. S.E. Wanke, Sintering of Commercial Supported Platinum Metal Catalysts, in: "Progress in Catalyst Deactivation", J.L. Figueredo, ed., Martinus Nijhoff, The Hague (1982).

15. S.E. Wanke, Models for the Sintering of Supported Metal Catalysts, in: "Progress in Catalyst Deactivation", J.L. Figueredo, ed., Martinus Nijhoff, The Hague (1982).

16. S.E. Wanke, U. K1eng1er and B. Tesche, Effect of Thermal Treatments on Pt Crystallite Size for Pt/MgO Catalysts, in: "Proc. 40th Meeting EMSA", G.W. Bailey, ed., C1airtor's, Baton Rouge (1982).

17. W.C.S. Pick, S.E. Wanke and U. K1eng1er, The Characterization of Thermally Treated Pt-Ir/A1umina Catalysts by Transmission Electron Microscopy and X-ray Diffraction, Preprints 3 Div. PetroZ. Chern.~ ACS3 28(2):429 (1983).

18. C.A. Spitler and S.S. Pollack, On X-Ray Diffraction Patterns of n- and y-A1umina, J. CataZ. 69:241 (1981).

19. S.E. Wanke, B.K. Lotochinski and H.C. Sidwell, Hydrogen Adsorption Measurements by the Dynamic Pulse Method, Can. J. Chern. Eng. 59:357 (1981).

20. E. Kikuchi, P.C. Flynn and S.E. Wanke, Studies of the Enhancement of Hydrogen Adsorption During Hz-Oz Titration on Supported Pt Catalysts, J. CataZ. 34:132 (1974).

21. P.C. Flynn, S.E. Wanke and P.S. Turner, The Limitation of the Transmission Electron Microscope for Characterization of Supported Metal Catalysts, J. CataZ. 33:233 (1974).

22. M.M.J. Treacy and A. Howie, Contrast Effects in the Transmission Electron Microscopy of Supported Crystalline Catalyst Particles, J. CataZ. 63:265 (1980).

23. F.M. Dautzenberg and H.B.M. Wolters, State of Dispersion of Platinum in Alumina Supported Catalysts, J. CataZ. 51:26 (1978).

24. S.J. Tauster and S.C. Fung, Strong Metal-Support Interactions: Occurrence Among the Binary Oxides of Groups IIA-VB, J. CataZ. 55:29 (1978).

25. K. Kunimoro, T. Okouchi and T. Uchijima, Strong Metal-Support Interactions in Alumina Supported Platinum Catalysts, Chemistry Letters 3 1513 (1980).

26. C.R. Adams, H.A. Benesi, R.M. Curtis and R.G. Meisenheimer, Particle Size Determination of Supported Catalytic Materials: Platinum on Silica Gel, J. CataZ. 1:336 (1962).

27. D.T. Lynch and S.E. Wanke, Oscillations in the Catalytic Oxidation of Carbon Monoxide, Preprints, 8th Can. Symp. on CataZ. 46 (1982).

28. E. Ruckenstein and B. Pulvermacher, Kinetics of Crystallite Sintering During Heat Treatment of Supported Metal Catalysts, AIChE J. 19:356 (1973).

29. P. Wynblatt and N.A. Gjostein, Supported Metal Crystallites, Progr. SoZid State Chern. 9:21 (1975).

30. E. Ruckenstein and M.L. Malhotra, Splitting of Platinum Crystallites Supported on Thin, Nonporous Alumina Films, J. CataZ. 41:301 (1976).

242 S. E. WANKE

31. E. Ruckenstein and Y.F. Chu, Redispersion of Platinum Crystallites Supported on Alumina - Role of Wetting, J. Catal. 59:109 (1979).

32. E.G. Derouane, R.T.K. Baker, J.A. Dumesic and R.D. Sherwood, Direct Observation of Wetting and Spreading of Iridium Particles on Graphite, J. Catal. 69:101 (1981).

33. T. Fukushima and J.R. Katzer, EXAFS Study of H2 , O2 and CO Adsorption on Supported Platinum, in: "Proc. 7th Intern. Congr. Cata1.", T. Seiyama and K. Tanabe, eds. Kodansha Ltd., Tokyo (1980).

ULTRA-RAPID SINTERING

ABSTRACT

D. Lynn Johnson

Department of Materials Science and Engineering Northwestern University Evanston, Illinois 60201

A number of highly sinterable ceramic powders have been rapidly sintered by insertion of small samples into preheated furnaces, rapid heating of small specimens in low thermal mass furnaces, and passing tube-shaped samples through short hot zone furnaces. More recently, aluminum oxide has been sintered by passing through gas plasmas. Heating rates in the neighborhood of 100oK/s and densification rates >l%/s have been achieved in the plasma sintering. Sintering models and computer simulation shed some light on the effect of rapid heating on the various sintering mechanisms and the interplay among the sintering mechanisms.

INTRODUCTION

It has been known for many years that fine particle size sinterable powders can be sintered in a matter ofls~conds if heated sufficiently rapidly. Thus Vergnon et al. ' studied rapid heating of alpha and delta A1203 and Ti02 by rapid insertion into a preheated furnace, whicfi resulted in heating rates of about 100oC/s. They observed, for example, a linear shrinkage rate20f 0.75%/s for specimens of alumina having a surface area of 110 m /g which were inserted into a furnace at l300oC. Their specimens were of low green density, however, and the final specimen densities were not high.

3-5 Morgan et al. reported the densification of sinterable

243

244 D. L. JOHNSON

powders in which specimens were heated in a low thermal mass furnace at heating rates up to 300C/s with no isothermal hold at temperature. They observed, in many cases, densities which were dependent only upon the maximum temperature achieved, but independent of the rate of heating. Here again, high densities were not attained.

Wynn Jones and Miles6 sintered a-alumina tubes by passing them through a short high temperature induction heated furnace at 1.25 em/min, effecting zone sintering and rapid denstfication. The heating rate was about 2000C/min. Harmer et ale utilized a similar apparatus for sintering ~-alumina with and without MgO doping at heating rates up to 400/s. Wynn Jones and Miles and Harmer et ale observed densification to high levels, and the latter also reported grain sizes that were significantly smaller than those obtained by conventional sintering schedules. They, moreover, attributed the high densification rates and fine grain sizes to suppression of surface diffusion by rapid transit through the temperature regime where surface diffusion is important, thus avoiding the deleterious effects of surface diffusion. During conventional processing, considerable time is spent in the temperature range where the coarsening effect of surface diffusion outweigh the densification produced by grain boundary and lattice diffusion.

Johnson and Rizz08 used an induction-coupled plasma (rcp) to sinter eN-alumina in argon at translation rates up to 2 em/min. They reported high density, fine grain sizes, and rapid conversion to the stable e"-alumina form from the precursor powders.

Kim and Johnson9 ,lO used the rep to sinter tubes and rods of ~-A1203 at translation rates up to 6 em/min. Heating rates exceeded 1000 C/s. By quenching the plasma during translation of the specimen, the tapered zone of the specimen between the green and fired zones was preserved for analysis. They f~plored the shrinkage and grain growth rates in this tapered zone. For rods translated at 2 em/min, they observed a linear shrinkage rate for undoped powder of 0.83%/s, nearly constant from the onset of densification to about 18% linear shrinkage. For specimens d~ped with 0.25% MgO, the observed linear shrinkage rate at a translation rate of 2 em/min was just over l%/s. An undoped rod translated at 3 em/min had a linear shrinkage rate of 1.4%/s.

Their grain growth rates showed a maximum of about 0.2 ~m/s at the surface, and about half that at the interior of the specimens.

Their highest density was achieved in a thin wall tube

UL TRAcRAPID SINTERING

translated at 6 cm/min, with a resulting density of 99.5% of theoret ica 1.

245

The common thread running through all of these observations is that fine particle size materials can be sintered at very high rates if heated at very high rates. Usually, the final grain size is significantly less than the grain size of coventionally sintered materials. It is interesting to explore the possible explanations of such behavior.

DISCUSSION

The fine grain sizes typically observed for materials sintered to high density at high heating rates is undoubtedly due, in part, to the very short time the sample is at high temperatures. However, the result reflects in part, also, the apparent fact that the onset of final stage sintering commenced after minimal coarsening of the structure during the initial and intermediate stages. It is well understood that sintering mechanisms can be divided into two groups, those that produce coarsening without densification, and those that cause densification, as well. The former group includes surface diffusion, vapor transport, and lattice diffusion from the particle surfaces to the neck surface, while the latter includes grain boundary diffusion and lattice diffusion from the grain boundary to the neck surface between particles (during the initial stage of sintering). Although reliable surface diffusion data are rare, the usual trend is that the activation energy for surface diffusion, at least at low temperatures, is less than that for grain boundary diffusion which is, in turn, less than that for lattice diffusion. Thus coarsening by surface diffusion could take place at the lowest temperatures at which atom motion becomes significant.

Surface diffusion also is relatively more important for smaller particles than lattice diffusion. Although the atom fluxes during sintering by surface diffusion and grain boundary diffusion have the same particle size dependence, they do not have the same dependence on the degree of sintering; surface diffusion is favored at smaller neck sizes between particles. Thus, in general, surface diffusion will be the first mechanism operative during sintering. If it also has a lower activation energy than the densifying mechanisms, its relative importance at the onset of sintering will be even more accentuated.

Coarsening has two major direct effects which inhibit densification. As the structure coarsens, the local surface curvature decreases, thus decreasing the driving force for

246 D.LJOHNSON

sintering. At the same time the average diffusion distance for matter flow from grain boundaries to pores increases, causing a further reduction in the densification rate. An additional effect of coarsening is that grain boundary migration can occur, resulting in pore coalescence, which exacerbates both the reduction in driving force and the increase in diffusion distance. Rapid heating, then, provides an opportunity to carry a compact through the temperature range where surface diffusion-controlled coarsening occurs readily to a regime where the densifying mechanisms of grain boundary and lattice diffusion would predominate. The structure is thus taken, in a highly sinterable condition, to a high temperature where the grain boundary and lattice diffusion coefficients are relatively large and can cause extremely rapid densification because of the high driving force and short diffusion distance.

A cOffui2r code, used previously to simulate initial stage s inter ing , , was employed to explore the effects of heating rate on initial stage sintering. This program utilizes the circle approximations for cubic and hexagonal close packed spheres of equal sizes. The neck surface profile is assumed to be a circle tangent simultaneously to the grain boundary groove in the neck and the sphere surface. After an initial small neck size is assumed, the four flux equations for grain boundary and lattice diffusion from the grain boundary and surface and lattice diffusion from the particle surfaces are used to calculate an incremental volume of matter transported to the neck surface. The fluxes from the grain boundary determine an incremental shrinkage, and with this incremental shrinkage and the incremental volume, the ~ew neck profile is determined within the circle approximation constraints. Thus each of the four fluxes can respond to the instantaneous geometry, and vice versa, and the relative importance of neck growth versus densification will be determined by the particle size, the relative values of the various diffusion coefficients, and the instananeous geometry of the system. Although the circle approximation is not rigorous, the trends predicted by this simulation are probably accurate.

Table I displays the parameters employed for this simulation. These represent values from the literature for silver, although there is some liberty taken in the selection of the surface diffusion coefficient which seems to be most appropriate for the low temperature regime, and the lattice and grain boundary diffusion coefficients have been extrapolated to temperatures considerably below where they were determined. A particle radius of 0.5 ~m was chosen in order to approach the typical particle sizes employed in ceramic materials where ultra-rapid sintering has been observed. Heating rates of 0.1, 1, 10, and 100oK/s, with an isothermal hold at 800oK, were programmed.

ULTRA-RAPID SINTERING 247

Table 1. Parameters for Simula~ions Represented in Figures 1 - 4.

Surface tension

Atomic volume

2 1140 erg/cm -23 3 1. 70 x 10 cm

Surface diffusion coefficient13

D = 9.1 x 10-5exp (-8.4 x 103 /RT )cm2 /s s

Grain boundary diffusion coefficient14 4 3 Db = 0.12 exp(-2.l5 x 10 IRT)cm Is

Lattice diffusion coefficient15 4 3 DL = 0.40 exp(-4.4l x 10 IRT)cm Is

Figure 1 shows the diffusional fluxes for surface, J , and grain boundary. Jb , diffusion as functions of the lin:ar shrinkage, y. Lattice diffusion under these temperature and particle size conditions was negligible. Also shown are the fluxes calculated for instantaneous heating to 8000 K, followed by maintenance at that temperature. On this figure, the circle on each line represents the point at which the close-packed model breaks down, that is. the point at which adjacent necks in a close-packed array of spheres would impinge upon each other. The lines terminate at the point at which a simple cubic array of spheres would show adjacent neck impingement. It should be noted. with regard to this plot. that only the 1000 /s run reached the isothermal temperature before the simple cubic model breakdown point. The simple cubic model breakdown point occurred at 754°,596°. and 4600 K for the 10,1 and O.lo/s runs, respectively.

Figure 2 shows the fractional shrinkage versus the time from the onset of linear heating from 3000 K. Again, the circles represent close-packed model breakdown point, and the lines terminate at the simple cubic model breakdown point. Finally, Figure 3 displays the neck size as a function of shrinkage for each of these simulations. The line marked "minimum" represents the minimum neck size at any given shrinkage if no matter transport from the particle surfaces took place. The O.lo/s curve fell outside the range of this plot.

248 D. L. JOHNSON

I09r-----------r----------.r---------~~--------_.----------_,

I ."

Ag T max = eooOK a' O.5JA-m

y

Fig. 1. Atom fluxes for surface and grain boundary diffusion as functions of linear shrinkage at various heating rates. The circles represent model breakdown for close-packed particles, and the lines terminate at model breakdown for cubic close packed particles.

It can be seen from these figures that the heating rate for these chosen diffusion and particle size parameters has a very large effect on the sintering behavior. Excessive neck growth and model breakdown occurs much earlier in the sintering process for the slower heated specimens. Of particular interest is the very large difference between even a 1000 /s heating rate compared to infinite heating rate at the small neck sizes. However, the final shrinkage and neck size at model breakdown at 1000 /s are not greatly different from those for the infinite heating rate. Thus, at this high rate the system would pass into internlediate stage sintering with minimal coarsening. At the other heating rates, the intermediate stage would be reached before the isothermal sintering temperature was reached.

The regimes of surface diffusion predominance as a function of heating rate were further explored for particle sizes 10 and 100 times that of the above simulations. The results can be


Fig. 2.

t,s

Ag Tmax =800o K

a =O.5/Lm

Fractional shrinkage versus time from the onset of heating from 3000 K at various heating rates.

249

presented on a map of neck size versus homologous temperature, as presented in Fig. 4. This is somewhat different from the traditional sintering maps, and could be called an accessibility map in that it displays graphically the regimes that can be achieved in practice, given a set of diffusion coefficients, heating rates and other parameters. In this figure, the open circles represent the point at which the grain boundary diffusion flux equals the surface diffusion flux for each of the runs. The uppermost broken line represents the point at which the lattice and grain boundary diffusion fluxes are equal for 5 iJ.m radius spheres, and the dot-dash line is the same boundary for 50 iJ.m radius spheres. The dash-double dot line is the boundary between lattice and grain boundary diffusion if the prior history of the sample was not taken into account. Thus the surface diffusion that occurs during the linear heating pushes the boundary between lattice and grain boundary diffusion to higher temperatures and neck sizes. It is interesting to note that the transition from grain boundary to lattice predominance for the 50 iJ.m radius spheres was relatively insensitive to the heating rate from 0.1 to 100oC/s, indicating that ultra-rapid sintering, and its beneficial effects, is a phenomenon unique to fine particle sizes.

250 D. L. JOHNSON

0.6r----------.-----------r-------~___:J

0.5

0.4

Ag Tmax =8000 K 0= O.5JLm

y

/ I /

/ / /

! /

/ /

/ /

/ 51 ~I ~I ~/

/ /

Fig. 3. Neck size normalized to the particle size versus fractional shrinkage at various heating rates.

CONCLUSIONS

High densification rates can be achieved by high heating rates.

Rapid sintered specimens tend to have finer grain sizes than conventionally materials of comparable density.

The high densification rates are caused. in part. by minimal coarsening by rapid transition through the temperature regime where surface diffusion predominates.

ACKNOWLEDGEMENTS

This material is based upon work supported by the National Science Foundat ion under Grant IDMR-79 18403 • This work was conducted in the Ceramics. SEM and Metallography facilities of Northwestern University s Materials Research Center. supported in part under the NSF-MRL program (Grant No. DMR 79-23573).


0.8....---""""T""----r------r---....-------,

0.6

. 5 0.6 0.7 0.8 T/Tm

0.9

\ ,

'. ' .

1.0

251

Fig. 4. Sintering map (normalize neck size versus homologous temperature) for various particle sizes and heating rates. The circles represent points at which surface and grain boundary diffusion fluxes are equal. The isolated circle is for instantaneous heating to 800oK. The broken lines represent equal grain boundary and lattice fluxes (see text). A-D = 50 IJ.m radius, 100, 10, 1 and 0.loK/s6 12000 K hold. E-G = 5 ~ radius, 10, 1, and 0.1 K/s. H,I = 0.5 IJ.m radius, 100 and lOoK/6.

REFERENCES

1. P. Vergnon, F. Juillet, and S. J. Teichner, Effect of Increasing Rate of Temperature on Sintering of Pure Alumina Homodispersed Particles, Rev. Int. Hautes Temp. Refract. 3:409 (1966).

252 D. L. JOHNSON

2. P. Vergnon, M. Astier, D. Beruto, G. Brula, and S. J. Teichner, Sintering Qf Very Finely Divided Particles. II. Flash Heating Technique and Kinetic Study of Shrinkage in Titanium Oxide and Aluminum Oxide Compacts, Rev. Int. Hautes Temp. Refract. 9:271 (1972).

3. c. S. Morgan and C. S. Yust, Material Transport during Sintering of Materials with the Fluorite Structure, J. Nucl. Mater. 10:182 (1963).

4. c. S. Morgan, C. J. McHargue, and C. S. Yust, Material Transport in Sintering, Proc. Brit. Ceram. Soc. 3:177 (1965).

5. c. S. Morgan, Densification Kinetics During Nonisothermal Sintering of Oxides, in: "Kinetics of Reactions in Ionic Systems, Materials Science Research Vo 1. 4", T. J. Gray and V. D. Frechette, eds., Plenum Press, New York (1969).

6. I. Wynn Jones and L. J. Miles, Production of S-A12~3 Electrolyte, in: Proc. Brit. Ceram. Soc. va 1. 19, Stoke-on-Trent, Eng land (1971).

7. M. Harmer, E. W. Roberts, and R. J. Brook, Rapid Sintering of Pure and Doped a-A1203 , Trans. J. Br. Ceram. Soc. 78:22 (1979).

8. D. L. Johnson and R. R. Rizzo, Plasma Sintering of j"-Alumina, Am. Ceram. Soc. Bull. 59:467 (1980).

9. D. Lynn Johnson and Joung Soo Kim, Ultra-Rapid Sintering of Ceramics, in: "Material Science Monographs, Vol. 14", D. Kolar, S. Pejovnik, and M. M. Ristic, eds., Elsevier, Amsterdam (1982).

10. Joung Soo Kim and D. Lynn Johnson. Plasma Sintering of Alumina, Ceram. Bull. 62:620 (1983).

11. P. H. Shingu, Effect of Competitive Mechanisms Upon Densification During the Initial Stage of Sintering and Sintering Kinetics of Iron, Ph.D. Thesis, Northwestern University (1967).

12. D. Lynn Johnson, New Method of Obtaining Volume, Grain Boundary and Surface Diffusion Coefficients from Sintering Data, J. Appl. Phys. 40:192 (1969).

13. G. E. Rhead, Surface Self-Diffusion of Silver in Various Atmospheres, Acta Met. 13:223 (1965).

14. R. E. Hoffman and D. Turnbull, Lattice and Grain Boundary Self-Diffusion in Silver, J. Appl. Phys. 22:634 (1951).

15. C. Tomizuka and E. Sonder, Self-Diffusion in Silver, Phys. Rev. 103:1182 (1956).

CHARACTERIZATION AND INITIAL SINTERING OF A FINE ALUMINA POWDER

ABSTRACT

S. V. Raman, R. H. Doremus and R. M. German

Materials Engineering Department Rensselaer Polytechnic Institute Troy, New York 12181

Gamma and alpha alumina powders having an average particle size of 9.6nm and 20nm respectively were sintered isothermally and at constant heating rates. With increase in heating rate, the gamma-alpha phase change occurred at higher temperatures, and densification of pellets originally made of gamma powder was enhanced. Pellets made of alpha powder were not sensitive to change in heating rates. Initial densification was interpreted in terms of Coble creep and grain boundary diffusion of oxygen. In gamma pellets from l400°C to l800°C this mechanism was aided by dislocation climb, which reduces the activation energy by approximately 0.57 of the actual value of 441 kJ/mol calculated from shrinkage of alpha pellets at l200°C to l800°C. The dislocation climb was caused by transformation of gamma to alpha phase, so gamma pellets densified more (90% theoretical) than alpha (70% theoretical) at l800°C.

INTRODUCTION

Changes in fine powders during the initial stages of their sintering are essential in determining the final density and properties. Fine alumina powders precipitated from solution have the cubic gamma phase structure after heating at 1000°C (Lippens, 1970) and transform to the stable hexagonal alpha phase above l200°C. Different interpretations of the kinetics of transformation have been reported (Steiner et al., 1971; Badker and Bailey, 1976; Dynys and Halleran, 1982).

253

254 S. V. RAMAN ET AL.

The purpose of the pres~nt work was to examine the mechanism of transformation and evolution of structure and microstructure of a precipitated alumina powder. X-ray diffraction, dilatometry, surface area measurements and scanning electron microscopy were used to follow the sintering. The results are discussed in terms of various sintering models (Coble, 1958; Young and Cutler, 1970; German and Munir, 1975).

EXPERIMENTAL

Powder Synthesis

7.5% aluminum sulfate solution of pH 2 was treated with reagent grade ammonium hydroxide of pH 14. Aluminum hydroxide particles precipitated at pH 9 in the mechanically agitated solution, and particle size was reduced by aging the particles for 120 hours in the alkaline solvent. There was some volume reduction during aging, and the particle solvent mixture became a nearly colorless, transluscent sol. The sol was partly dehydrated and the particles were dispersed by repeated centrifuging and washing with ethanol. The precipitate turned into a fluffy aluminum hydroxide powder upon drying for 24 hours at 65°C. The powder was converted into gamma alumina by heating at 1000°C for 30 minutes.

Sintering

Isothermal sintering was restricted to gamma powder and was performed at l200°C and l400°C for short time intervals ranging from 3 to 20 minutes. Ball milling was avoided and the resulting sintered powders were examined for specific surface area by multiple point BET using nitrogen as the absorbate. The relative weight fractions of the two allotropic forms of alumina were determined from the ratios of (116) X-ray peak intensity (Cullity, 1967). Constant heating rate experiments of 5°C/min and a two hour isothermal hold time were adopted for sintering the pellets. The pellets of gamma, alpha and the hybrid powder of 43% alpha + 57% gamma were prepared in the double-action steel die with trichloroethylene as die wall lubricant. All the pellets were pressed to nearly the same green density of 0.82 to 0.85 g/cm3 • For sintering beyond l500°C a hydrogen tube furnace with molybdenum windings was used at 5°C/min heating rate. The sintering was done in air within the alumina tube that was placed inside the furnace. The other pellets were sintered in the di1atometer, where the heating rates were precisely controlled and accurate information on shrinkage and shrinkage rate as a function of temperature was obtained. Fractographs of sintered pellets were examined for microstructure using scanning electron microscopy.

SINTERING OF A FINE ALUMINA POWDER

>-l-ii) :2 w I-

~ >-« a:: X

~ e

T • 1400'C I" 5 Mm

T· 1400 'C t • 7 Min.

ORIGINAl.

TAI.O,

alii' I.%t .. 9SA-

16%0:

255

Fig. 1. The X-ray diffraction pattern shows formation of alpha phase from the original gamma alumina as a function of time at l400°C.

180 .-...

IX) -.... (\)~

140

al ~ Q)

100 ()

.:l • Gamma 9 Ul

5~+ () .. '" 60 431.A1pha .... '" • Alpha () Q) Po Ul

20

TIME (minutes)

Fig. 2. The specific surface area of the original gamma powder reduces gently without phase change at l200°C and sharply with phase change at l400°C.


RESULTS

X-Ray Diffraction

The gamma powder was characterized by broad, low intensity (400), and (440) reflections in X-ray diffraction (Fig. 1) from which a crystallite size of about 9.6nrn is calculated. The gamma alumina transformed into alpha upon heating at l400°C for 15 minutes. The transformation was complete with the development of (116), (124), and (030) reflections. This powder had a crystallite size of 20nm. The diffraction angle of the (116) alpha reflection shifted following heat treatment of gamma powder at l400°C for 5 minutes (Fig. 1). With continued heating for 15 minutes the compressive strain, indicated by a .02Ao decrease in the interplanar spacing was alleviated and the original position of (116) reflection in alpha restored. The transformation kinetics are of second order and similar to that reported by Dynys and Halleran (1982) for ball milled particles. These workers crushed the gamma powder to increase the rate of transformation. However, in the present work this higher rate was achieved by treating the powders isothermally at a higher temperature.

BET

The gamma and alpha powders had specific surface areas of 152 m2/g and 20 m2/g respectively. The kinetics of surface area reduction were remarkably sensitive to extent of phase change. A decrease in surface area from 152 m2/g to 130 m2/g for gamma alumina at l200°C accompanied a sluggish transformation. But at l400°C the area rapidly decreased to 20 m2/g in response to the formation of alpha phase following a short induction time of 4 minutes (Fig. 2).

Dilatometry

For gamma pellets the shrinkage commenced at 1100°C and increased to 40% at l800°C. For alpha pellets the shrinkage occurred in the temperature interval of l200°C to l800°C and reached a maximum of 20% at the maximum temperature (Fig. 3). Both the surface area reduction and the shrinkage rate are influenced by the gamma-alpha phase transformation at about l200°C, as indicated by the shrinkage rate peaks at l200°C, for a heating rate of 20°C/min and l150°C for a heating rate of 5°C/min (Fig. 4). The upper temperature for the transformation is also sensitive to the rate of heating. It is l300°C and l225°C for the higher and lower heating rates, respectively (Fig. 4).

Scanning Electron Microscopy

The differences in the evolution of a dense polycrystalline

SINTERING OF A FINE ALUMINA POWDER

40 Heating Rate 5°C/min.

Sintering Time 2 hours

• Gamma • 57%Gamma+43Wpha

• Alpha

1000 1200 1800

STNTERING TEMPERATURE (oC)

Fig. 3. Greater shrinkage of gamma pellet relative to alpha is apparent. The hybrid pellet composed of 43% alpha + 57% gamma shows intermediate shrinkage.

2.4 GamIna Alumi n&

2.0 Heating Rate

• 20oC/JIJin.

1.6 • 5OC/JIJin.

.., ~ 1.2 ..,

i .8 ffi rn

.4

o

500 700 900 1100 TntPERATURE (oC)

Fig. 4. Changes in the shrinkage rate, and the lower and upper limits of phase transformation during constant heating rate sintering.

257


microstructure for the two types of pellets alpha and gamma, are evident from the changes in the shrinkage as a function of temperature and time, and scanning electron micrographs. The SEM micrograph of gamma powder at lSOODC reveals small neck sizes of less than a micron and suggests that the smaller particles are becoming smaller and the larger ones larger (Fig. Sa). This step is followed by the development of necks and grain boundaries between coarser particles. Normal grain growth begins at about l600 DC (Fig. Sc) and the pellet densifies to 91% theoretical at l800 DC. At the same temperature an alpha pellet sintered to a lower density of 70% theoretical, and micrograph (Fig. Sd) shows that considerable pore coalescence as well as grain growth has occurred. The grains are devoid of intragranular porosity. The heating rate does not seem to influence the sintering of al~ha, but gamma pellets sintered to a higher density of 1.74 g/cm at lSOODC at 20 DC/min. The density for gamma alumina at this temperature and a lower heating rate of SOC/min is 1.40 g/cm3 . The micrographs (Fig. Sa and Sb) suggest that normal grain growth begins at a lower temperature when the heating rate is increased.

DISCUSSION

Phase Transformation

The change of gamma alumina to an alpha phase occurs by conversion of an inverse spinel structure to a corrundum type. Associated with this transformation is the breakdown of tetrahedral coordination of aluminum ions and formation of edge-shared octahedrq. The process is exothermic (Badker and Bailey, 1976) and results in the formation of a denser phase. The X-ray reflections suggest that the transformation is initiated by build up of compressional strain within the alpha embryo, which is alleviated with progressive formation of alpha phase. One possible explanation for the behavior is that the transformation occurs by positive dislocation climb within the metastable lattice. This is unlike diffusional creep in which alpha particles grow by reduction in the alpha-gamma boundary area, initiated by tensile stress within the alpha particle. Therefore, rapid transformation should be favored by a high dislocation density in the metastable lattice. This defect induced transformation is also suggested by the shift in the transformation temperature as a function of heating rate evident from shrinkage rate-temperature dependence (Fig. 4). At higher shrinkage rates the defects are sluggishly created and hence the relatively defect-free lattice is retained above the transformation temperature, and the transformation to alpha alumina occurs at a higher temperature. The situation is analogous to creation of low-energy dislocations by synchronized motion of A13+ and 02- ions at higher temperature where the strain rates are higher. Once the energy barrier is overcome a rapid rise in dislocation density occurs (Kingery et al., 1976).

SINTERING OF A FINE ALUMINA POWDER 259

Fig. 5. Scanning electron micrographs of sintered pellets. The pellets densify through normal grain growth. At lSOOoe the gamma pellet density is, (a) 38% theoretical at 5°C/min heating rate and (b) 43% theoretical at 20°C/min heating rate. At l600 0 e and 5°C/min heating rate, (c) the gamma pellet density is 45% theoretical and (d) the alpha pellet density, is 42% theoretical. Bar = 3 ]lm

260 s. V. RAMAN ET AL.

Dens if ica tion

The increase in density for gamma pellets is probably associated with an increase in dislocation density. Hence the density rises to 1.74 g/cm3 from 1.S2 g/cm3 with change in the heating rate from SOC/min to 20°C/min. This density change contrasts with the sintering behavior of many oxides, including MgO doped A1203 (Morgan and Tennery, 1980) where density decreases or remains unchanged with increases in heating rate. Another interesting difference arises when the density evolution as a function of temperature is compared with that reported by Badker and Bailey (1976). In the experiments of these authors a rapid rise in density occurs at lower temperatures (lOOO°C to l200°C) and culminates in a density plateau beyond l200°C. This decrease in the rate of densification was attributed to the gamma/alpha transformation, and is contrary to the observations made in this work, where density rises sharply above lSOO°C and gently changes below this temperature. In the absence of microstructural evidence and accurate information on particle size distribution a tentative conclusion is that the higher green density of 40% theoretical for gamma pellets in Badker and Bailey's experiments leads to the buildup of strai.n energy at the particle contacts which aids exaggerated growth of pores and grains.

A sharp discontinuity in the shrinkage rate-temperature dependence (Fig. 4) at 11SO°C and l300 0 C for the lower and higher heating rates points to the presence of alpha phase alone beyond these transformation temperatures. Yet the pellets originally made of alpha powder sinter to a lower density, although the trend of density variations as a function of temperature is similar to that of pellets that started as gamma phase. Thus the processes that are active in the initial stages govern the densification of alumina at higher temperatures. The commencement of sqr~nkage in alpha pellets at higher temperature and reduced shrinkage relative to gamma pellets (Fig. 3) leads to the development of larger necks with well defined grain boundaries at l600°C amidst coalesced pores, and is perhaps aided by surface diffusion (Fig. Sd). The gamma pellets, on the other hand show considerable shrinkage (Fig. 3) which, combined with microstructural features, suggests that volume diffusion (Coble, 19S8) is predominant in the development of smaller neck morphology (Fig. Sa).

Mass Transport Mechanism

The differences in the sintering behavior were further examined with surface area (German and Munir, 1976) and shrinkage (Young and Cutler, 1971) models. The exponent calculated from the time dependence of decrease in surface area of gamma powder has values of 1.03 and 1.07 at temperatures of l200°C


2.4

Heating Rate 20°C/mi n .

2.0

• Gamma

1.6 • 5~+ 4~ Alpha

• Alpha

'" ~ 1.2

'" ~ .8 H

~ '"

.4

0 - . 500

TEMPERATURE (oc)

Fig. 6. Changes in shrinkage rate as a function of original green pellet composition during sintering at 20°C/min.

8

Alpha Alumina. 7 Heating Rate 50C/min.

o~ nQ, = 147 kJ /mol

8 6 '-~o

r-I 5

4

9 10 11 12

- In (IU/L TOK) °

Fig. 7. An integral plot of shrinkage-temperature dependence for alpha pellet. The activation energy is similar to oxygen grain boundary diffusion by Coble creep mechanism.


and l400°C, which are characteristic of a plastic flow mechanism, since the vapor pressure of alumina is too low for evaporationcondensation. The activation energy for a plastic flow mechanism as calculated from the surface area measurement is 82 kj/mol and closely approximates the activation energy of 72 kJ/mol calculated from shrinkage-temperature dependence with a constant heating rate of 5°C/min and a volume diffusion model exponent of 0.5. This similarity in activation energy between the constant heating rate and isothermal experiments suggests that the plastic flow involves steady-state creep initiated by dislocation climb for gamma pellets below l400°C (Weertman, 1955). In the temperature interval of l400°C to l800°C the activation energy is 3.5 times higher at the same heating rate and signifies a change in the rate limiting mechanism, which is also associated with a sharp change in shrinkage rate at l400°C (Fig. 4). At the heating rate of 20°C/min the change in the mechanism is indicated at a lower temperature of l300°C from the temperature dependence of shrinkage rate and shrinkage (Fig. 4 and 3). This temperature shift is supported by the enhanced grain growth observed in the gamma pellet at l500°C (Fig. 5b).

While the mechanism below l300°C at 20°C/min heating rate is identical to that occurring at 5°C/min, at higher temperature the activation energies at the two heating rates differ for gamma pellets. Such differences are even more pronounced between alpha and gamma pellets at the heating rate of 5°C/min. The shrinkage rate of alpha lacks the alpha/gamma transition peak (Fig. 6) and non-linearly increases with temperature. Hence the shrinkagetemperature dependence is devoid of slope changes (Fig. 7), and gives activation energies of 441 kJ/mol and 368 kJ/mol for grain boundary and volume diffusion models, respectively. The former value falls within the range of 392 kJ/mol to 497 kJ/mol for grain boundary diffusion of oxygen by Coble creep mechanism (Lessing and Gordon, 1977).

If alpha pellets densify by grain boundary diffusion, it is unlikely that densification oi alpha phase in the gamma pellets above the transformation temperature occurs by another mechanism, even though the activation energy for the latter is lower at 250 kJ/mol. The microstructural differences are not large at 800°C and 5°C/min heating rate between pellets originally of either alpha or gamma phase. Therefore, an alternative suggestion is that the decrease in activation energy by a factor of .57 is aided by dislocations that form during densification and exothermic transformation of the gamma alumina. In gamma alumina dislocations are formed as it is annealed whereas in alpha alumina they annihilate with heating, decreasing the internal energy of the alpha grains. Dislocations probably are removed in alpha phase at temperatures below the commencement of shrinkage so that densifi-


cation of alpha occurs by grain boundary diffusion from l200°C to l800°C (Fig. 7). In gamma pellets dislocations anneal from l400°C to l800°C at SOC/min heating rate with lower activation energy of 250 kJ/mol, because densification is aided by dislocation motion.

The sintering of alpha+gamma hybrid pellets supports the role of plastic deformation on alpha sintering. Figure 6 shows that a 43% alpha + 57% gamma pellet has a transformation end point at l300°C. All the three pellets (alpha, gamma, and hybrid) have this same end point at 20°C/min heating rate and have shrinkage of .10, which deviates at other temperatures. The differences at low temperatures are explained by the presence of gamma phase. But at temperatures higher than l300°C, where alpha phase alone is present in all the pellets, the hybrid pellet is composed of two types of alpha phase. These are the 57% metastable alpha formed as a consequence of transformation and the 43% original alpha phase. Immediately following the transformation the shrinkage rate is predominantly influenced by the strain in the alpha phase, and the shrinkage rate follows the gamma pellet. As the strain is gradually alleviated with increasing temperature the shrinkage rate decreases under the influence of unstrained original 43% alpha beyond l400°C (Fig. 6).

ACKNOWLEDGEMENTS

This work was supported by contract no. DE-AC02-82-ER12069 from the Division of Materials Research, Division of Energy. We thank J. Dunlap for helping with dilatometry.

REFERENCES

Badker, P. A. and Bailey, J. E., 1976, The mechanism of simultaneous sintering and phase transformation in alumina, J. Mat. Sci., 11:1794.

Bruce, C. A., 1962, Sintering kinetics for the high density alumina process, Am. Ceram. Soc. Bull., 41:799.

Burke, J. E., 1957, Role of grain boundaries in sintering, J. Am. Ceram. Soc., 40:80.

Coble, R. L., 1958, Initial sintering of alumina and hematite, J. Am. Ceram. Soc., 41:55.

Cullity, B. D., 1967, "Elements of X-Ray Diffraction", AddisonWesley, Reading, MA.

Dynys, F. W., and Halleran, J. W., 1982, Alpha alumina formation in alum derived gamma alumina, J. Am. Ceram. Soc., 65:442.

Dynys, J. M., Coble, R. L. Coblenz, W. S. and Cannon, R. M., 1980, "Mechanism of atom transport during initial stage sintering in A1203" in Sintering Processes, ed. G. C. Kuczynski, Plenum, New York.

German, R. M. and Munir, Z. A., 1976, Surface Area reduction during isothermal sintering, J. Am. Ceram. Soc., 59:379.

264 s. V. RAMAN ET AL.

Greskovich, C. and Lay, K. W., 197Z, Grain growth in very porous A1Z03 compacts, J. Am. Ceram. Soc., 55:14Z.

Kingery, W. D., Bowen, R. K. and Uhlmann, D. R., 1976, "Introduction to Ceramics", John Wiley and Sons, New York.

Lessing, P. A. and Gordon, R. S., 1977, Creep of polycrystalline alumina, pure and doped with transition metal impurities, J. Mat. Sci., lZ:2291.

Morgan, C. S. and Tennery, V. J., 1980, "Magnesium oxide enhancement of sintering of alumina" in Sintering Processes, ed. G. C. Kuczynski, Plenum, New York.

Nichols, F. A., 1966, Theory of grain growth in porous compacts, J. Appl. Phys., 37:4599.

Ogbuj i, L., Mitchell, T. E., and Heuer, A. H., 1980, "Plas tic deformation during the intermediate stages" in Sintering Processes, ed. G. C. Kuczynski, Plenum, New York.

Oishi, Y. and Kingery, W. D., 1960, Self-diffusion of oxygen in single crystal and polycrysta11ine aluminum oxide, J. Am. Ceram. Soc., 33:480.

Rosokowski, N. R. and Greskovch, C., 1975, Theory of the independence of densification on grain growth during intermediate stage sintering, 58:177.

Steiner, C. J. P., Hasselman, D. P. H., and Spriggs, R. M., 1971, Kinetics of the gamma to alpha alumina phase transformation, J. Am. Ceram. Soc., 54:412.

Westwood, A. C. R., MacMillan, N. R., and Kalyoncu, R. S., 1973, Environment-sensitive hardness and machinability of A1203, J. Am. Ceram. Soc., 56:258.

Weertman, J., 1955, Theory of steady-state creep based on dislocation climb, J. Appl. Phys., 26:1213.

Whitemore, J., Jr., and Sipe, J. J., 1974, Pore growth during the initial stages of sintering ceramics, Powder Technology, 9 :159.

Walker, F. R., 1955, Mechanism of material transport during sintering, J. Am. Ceram. Soc., 38:187.

Young, W. S., and Cutler, U. B., 1970, Initial sintering with constant rates of heating, J. Am. Ceram. Soc., 53:659.

SINTERING BEHAVIOR OF OVERCOMPACTED

SHOCK-CONDITIONED ALUMINA POWDER

T. H. Hare, K. 1. More, A. D. Batchelor, and Hayne Palmour, III

Department of Materials Engineering North Carolina State University Raleigh, North Carolina 27650

INTRODUCTION

The use of highly dynamic shock waves to alter ceramic and metal powders to enhance sinterability has been described in the literature for a variety of materials (1-4). Recently, a group of target materials has been intensively investigated, with the use of alumina as one of these focus materials here at North Carolina State University (5-8).

It was found that the effect of increasing the shock-loading pressure not only increases the amount of induced strain and associated defects, but significantly alters the particle size distribution which is obtained, even after extensive processing (5,7-8). The production of these hard agglomerates occurs above a certain shock loading, hence the term "overcompacted".

The effect of the shocking and overcompaction has produced some very unusual densification kinetics and microstructural development which has been investigated in experiments whose results are reported here.

PARTICULATE AND COMPACT CHARACTERIZATION

Using procedures described elsewhere (9,10), compacts were fabricated from Baikowski CR-lO alumina and from a powder obtained from explosive shocking of the same material at 74KB. The shocked material was initially fabricated into a large (7.6 x 0.11 em) disk, shocked by a planar "mousetrap" apparatus at Battelle Columbus Laboratories (5), and reconstituted for sintering by intensive dry milling. It was hoped that the particle size distribution would

265

266 T. H. HARE ET AL.

remain essentially unchanged when comparisons were made between the processed CR-IO and the reconstituted shocked material. Table I shows some critical comparisons between the intensively milled CR-IO and the shocked material.

Table I. Powder Characterization (6)

Unshocked CR-IO Shocked at 74KB

Surface Area, 12.5 10.6 mig (BET)

Mean Dia., um 0.13 0.15 (BET)

Median Dia., um 0.35 0.35 (Sedimentary)

Major Impurities (ppm) NAA) Fe <10 <10

Mg <200 <200 Si <200 <200

Compact Density 0.62 0.64 (Frac. Avr.)

The difference in impurities as determined by NAA do not appear to be significant. especially in light of the experiments described below. although it is recognized that small variations of impurities can have a major effect on grain growth, especially in the late stages of sintering.

Although the characteristic particle size diameters calculated from the BET and sedimentary analysis are nearly equal, an important difference was observed in the size distributions indicated by sedimentary analysis. as shown in the cumulative distribution functions in Fig. 1.

Particle Size Distributions 100

C CD u 80 Ii 0. .. .. 80 II E CD ~ 40 • -; E

20 ,. 0

0 100 10 1.0 0.1

Equivalent sphsrlcal dlamstsr (I'm)

Fig. 1. Cumulative particle size distributions for (1) shocked CR-IO. 74KB and (2) unshocked, both intensively milled.

OVERCOMPACTED SHOCK-CONDITIONED ALUMINA POWDER 267

The principal difference in the two powders is in the presence of particle agglomerates in the 5-10 micron range, comprising at least 10% of the mass of the material. Materials compacted at a higher shock loading showed a larger percentage of this hard agglomerate material, those shock loaded at lower pressures do not (7). Intensive milling is sufficient to reduce agglomerates to this size range, but not completely to individual grains.

A typical agglomerate is shown in Fig. 2. From previous work (6,7) the best estimate of the fractional density of these agglomerates is in the range of D = 0.75-0.80. An SEM examination of the shock loaded powder showed a much higher concentration of these and even larger agglomerates than should have been seen (based on the sedimentary curve), perhaps due to settling in the can or some other procedure favoring a concentration effect.

Fig. 2. An example of a hard agglomerate present in CR-10 alumina shocked at 74KB.

As shown in Table I, compacts made from the shocked powders had a slightly higher initial fractional density, which is consistent with the presence of denser agglomerates and a wider pore size distribution, but are not so different as to preclude direct comparisons of the sintering kinetics. In our experience, when well processed, a wide variety of aluminas in this particle size range seem always to yield starting densities in the 0.60 - 0.63 range (9,10) .


DENSIFICATION KINETICS

Densification kinetics were obtained from dilatometric studies in an advanded computer controlled dilatometer (11) using a variety of heating rate schedules from 2K/min (to obtain low densification rates) to 20K/min, as well as several rate controlled sintering runs (12-14) in which the densification rate history of a particular sample is forced along a particular path believed to be nearly ideal for optimizing final microstructure.s. For aluminas, it has been observed (14) and was again observed in this study that recent densification rate history has no effect on the sintering kinetics of alumina until densities above 0.95 were reached.

In previous work (6,8) we have found it useful to examine the densification behavior by observing the change in densification rate as a function of density, particularly for linear heating rate schedules (6). In this plots the change in shape is sensitive to changes in sintering mechanisms and/or microstructure evolution as a function of density. Fig. 3a shows a comparison between the densification rates for shocked and unshocked CR-lO. The unshocked curve shows a typical form (except for densities above 0.95, where the temperature was held constant), which characterizes well processed alumina fabricated from this reasonably uniform fine grained material. The shocked material shows a drop and a reacceleration "hump" or shoulder which is quite characteristic of alumina shockloaded above 50KB.

The densification rate-time plot, Fig. 3b (the isothermal hold begins at 60 min) shows a similar form, except that the shocked material is shifted to longer times (higher temperatures) relative to the unshocked material at higher densities, an effect which is best described in the full kinetic plot described below.

Fig. 4 shows the densification kinetics plotted in Arrhenius form for five different densities for the two materials. It must be emphasized that the slopes of these fitted lines do not represent activation energies of a particular process, since they could only be strictly interpreted as such if only one mechanism was rate controlling, and if the pore and grain size distributions and morphologies were similar over the entire rate regime. The slope does depict empirically the sensitivity of the densification rate to temperature, and therefore such densification kinetics can be compared among materials (and processing methods, 9).


O . O~r-------------------~~~--------' O .02 r-------------------~=---------~

o . a: c o

rD' c

a FrUltlon. _ Denalt)'

; a: c o

~ 0 .01 . c . ~

b eo 70

Fig. 3. Comparative densification behavior of shocked and unshocked CR-lO alumina sintered at l5C/min to l803K, 30 min hold.

Temperature (OK) 1800 1700 1600

5 . 0r-~~~------~~--------+------------+---' 1500

-r:: E

~ 1.0 \ ~ '" a: r::

0 . 5 0

'" " "' r::

'" a

0 . 1

\

~ 0 .90 \ 0.90

0 .95 Unshoeked Shoe ked at 74 KB

0 . 05 L-----~----~----_4------~----~----~----~ 5 . 4 5 . 6 5 . 8 6 . 0 6 . 2 6 .4 6 . 6 6 . 8

Inv e r se T e mp erat u r e (OK- ' X10 4 )

Fig. 4. Comparative densification kinetics for shocked and unshocked CR-IO alumina.


It can be seen from Fig. 4 that, although the kinetics are roughly similar at low density (0.75), being offset only by an approximately constant temperature difference which may in fact be related to a strain-related energy release, large differences are observed at 0.90. For example, to sinter at an equivale.nt rate (O.OOI/min), roughly the rate achieved at 2K/min, requires 90K more temperature for the shocked material, a difference which narrows considerably at faster densification rates.

The isodensity lines at 0.95 (much more approximate than the others) show that there is a considerable difference in final stage kinetics, but not nearly the temperature difference observed in the later intermediate stage.

BPcause the spacing of the isodensity lines at constant densification rate can be related to grain growth (15), it was ('onjectured that grain growth related to shocking was in fact responsible for the unexpected result of retarded densification after shocking.

Fig. 5 shows fracture surfaces of the two material deliberately fired to about 0.90 at 20K/min. Examination of the microstructures resulted in the startling observation that the apparent grain size is the same or finer for the shocked material even though it requires a higher temperature to drive it at a given rate. Exactly similar microstructures were seen in fracture surfaces at fast heating rates, in duplicate experiments, and in all areas of specimens.

This anomaly was resolved by a combination of experiments described below.

Fig. 5. Fracture surfaces at lower density for CR-10 aluminas, (a) shocked, D=0.91 and (b) unshocked, D-0.90.


ANNEALING KINETICS OF SHOCKED ALUMINA

Because the thesis of shock conditioning is the possibility of alteration of the sintering kinetics by making use of the store energy (16) (though possibly deleteriously as a recrystallization and grain growth pehnomenon) present in the form of defects such as dislocations, it became obvious that the rate at which this energy is released as a function of time and temperature might shed light on the observed densification behavior, particularly to decide at what point during densification the defects which can induce X-ray line broadening will have annealed out.

Figure 6 shows the results of the annealing kinetics expressed as the fraction strain removed as a function of temperature and time.

1.o,-;p __ ----------~===---------------------_.

0.8 .., CD > o E ~ 0.8

.!: ~

U; " 0.4 £ <J

~ ... 0.2

•

•

o o 923K ·1073K o 1223 K ·1373K h 1623K

1223K

1073K

°0~---------670~---------12~0~--------'~8-0---------2~40 Time (min)

Fig. 6. Annealing behavior of CR-IO alumina shocked at 74KB.

A detailed analysis of this data is the subject of another paper (17), but the main conclusions suggest that the release occurs over a wide range of temperatures, even easily observed at 923K for short times. A wide variety of annealing models were employed to describe the kinetics, and, as is nearly always the case, those with enough parameters fit well. No single model of the common form

dE/dt n aE , and

a = aOexp(-Q/RT),

where a is a constant and E is the fractional rema~n~ng strain, could deal with all temperatures using a single exponent, whereas


almost any choice of exponent worked sufficiently well if the annealing was composed of two parts; a low temperature and high temperature component. This does not necessarily imply there are two or more or less kinds of defects, but that for annealing, a simple one-mechanism kinetic model will not do.

In any interpretation, several models were sufficiently accurate to allow the calculation of the amount of strain removed as a function of time for any firing schedule, and they showed little difference (17). Table II shows the calculated strain remaining for two heating rates employed in the kinetic study for one of these models (solid lines in Fig. 6). This strain was calculated by assuming the firing schedule was made up of very many isothermals of short duration, calculating the strain removed using the model, and using the new strain left to calculate the strain release rate at the next temperature. In Table II the density r,eported for the given heating rate is obtained directly from the dilatometer runs at those heating rates. Other models showed similar results.

Table II. Calculated Strain Remaining

Density 24K/min 20K/min Temp Remaining Temp Remaining (K) Strain (K) Strain

0.65 1273 0.29 1277 0.42 0.70 1426 0.04 1501 0.28 0.75 1490 0.01 1572 0.19 0.80 1553 0.01 1621 0.12 0.85 1622 0.00 1673 0.06

Because the kinetics of release favor fast densification rates for retention of some of the potential driving force, it was postulated that the faster heating rates might show a greater effect on the microstructure than slowly densified or annealed specimens. Despite the possibility of the persistence of the strain up into the middle of the intermediate densification stage at high heating rates, it became apparent that for this material, the excess strain energy was not the dominant factor determining the kinetic behavior.

THE PRE-ANNEALING SINTERING EXPERIMENT

Samples fabricated from shocked powder were annealed (a) 2 hours at l123K and (b) 1.5 hours at 1373K, schedules which were designed to remove most (a) or all (b) of the defects induced by the shocking procedure with only a small amount of densification. The samples were then heated at 20K/min to l873K and the densification behavior observed (Fig. 7).

OVERCOMPACTED SHOCK-CONDITIONED ALUMINA POWDER

! .. II:

" o .. ()

., " ., c

0 .02 r-____________ ~S~H~O~C~K~E~D~A~T~74~K~B~ ____________ _,

o~~~----~--------~~--------~------~~ 0 . 60 0.70 0 .80 0.999 0.90

Fractional Density

273

Fig. 7. Densification behavior of annealed and unannealed shocked CR-lO alumina.

It can be seen that the densification behavior at higher densities (above D=0.75) was not significantly affected by the anneal. Further, the final microstructures observed (Fig. 8) for the three runs at D=0.98+ were qualitatively identical, exhibiting uncontrolled grain growth, especially compared to the unshocked material sintered in exactly the same way. It is possible, and there is some evidence (14), that by using different rate histories this microstructure can be forestalled while still reaching high density, but the propensity of this and many similar materials for development of this fatal microstructure is evident, and has been observed countless times elsewhere.

Although the annealing of these samples has effectively removed the strain which could be present during intermediate stage sintering, the possibility that the defects act to alter the morphology at low temperature by changing the amount of rearrangement, local grain growth, etc., remained a real possibility.

AGGLOMERATE FORMATION BY PRESINTERING

To resolve the question of to what extent the primary microstructural development and kinetic effects are due to strain and what are due to the presence of agglomerates, large compacts (0.5 x 5 cm) with a starting density of about D=0.60 were fabricated and sintered to a density of D=0.65. These compacts were then crushed in an alumina mortar and pestle, screened with 325 mesh


Fig. S. Microstructures of shocked CR-10 (a) 15K/min to lS03K, 30 min hold, (b) annealed 2h l223K, then as in (a), (c) annealed 1.5h, l373K, then as in (a) and (d) unshocked, same schedule as (a).

nylon screens, and finally milled in a rather severe environment (alumina-lined SPEX mill) to produce a powder to which lubricant was added with a subsequent milling operation. A batch of asreceived powder was similarly treated for comparison. In addition, a batch blending the two materials in equal proportion was also processed.

The sintering behavior of the three 0.ifferently prepared materials is shown in Fig. 9.

It is readily apparent that the high density shoulder where the densification rate stays fairly constant is similar to the behavior of the shock-compacted material (Fig. 2). EVen diluting the agglomerate concentration by a factor of 2 does not appreciably alter the sintering behavior. As before, the densification kinetics (shown approximately in Fig. 10) show similarities with the previous comparison at D=0.90, although the formation of agglomerates by presintering has stalled the early stage densification which the shock-produced agglomerates do not. This must related to the relative surface areas possessed by the agglomerates; the surface area of the sintered agglomerates may have been much more reduced than that of the shocked ones.

OVERCOMPACTED SHOCK-CONDITIONED ALUMINA POWDER

! .. II:

c o .. u

.. c .. C

0 . 025~----------------------~~----------------'

o~~==~~--~--------~---------+~ 1000 1200 1400 1600

Temperature (DC)

275

Fig. 9. Densification behavior of SPEX-milled CR-10 alumina and presintered and remilled CR-10 material, 20K/min.

Tempor.lure (OK)

5.0r-~'8+0~0 ____ ~'~70~0~ ____ ~,e+0~0 _______ '_5~0_0-,

· i ;;; -1 . 0

· · a:

~O . 5

· ~ · · o

D. l

o.u

\ \ \\, \ \ \ '\ \ \ \\~,\ '\ ,\,.:.:5

0. 80 0 .86

o.eo o.eo

Original p, •• inl.red

0 .0 5.'-.• -----< • . >-6-----< • . -8---e-+.-o ---e .... 2----8 ..... . -----,-6<-:.6---::'8. 8

Fig. 10. Densification kinetics for (1) CR-10 processed in the SPEX mill, and (2) presintered to D=0.65, reground and as (1).


(a) (b)

(c) (d)

Fig. 11. Microstuctures for SPEX processed CR-IO (a) Normal CR-lO, l873K, 2K/min, D-O.997+ (b) Presintered CR-lO, l873K, 25K/min, D=O.975, (c) Normal, D=O.915 20K/min, Cd) Presintered, D-O.9l5, 20K/min.

The microstructural comparison shown in Fig. 11 (a,b) shows a striking similarity with the shocked-unshocked comparison previously discussed. The unagglomerated 'as received' batch produced a vet'y uniform microstructure and was about the best microstructure (and density) attained in this study, reaching a final density of better than 99.7% of theoretical and exhibiting considerable translucency, even while maintaining this microstructure, perhaps aided by a small amount of Mg contributed by the doped lining of the SPEX mill (all materials processed this way had about the same impurity levels). The fracture surface comparisons obtained at about D-O.92 also revealed a similar apparent grain size anomaly as discussed previously, although not as striking, in that there was not a particularly noticeable grain size difference between the two materials.

We have not measured the size distribution of the agglomerates remaining but a brief SEM examination of the reconstituted powder revealed the presence of many sintered agglomerates, some of which were larger than lOWm.


DISCUSSION AND CONCLUSIONS

The question of the final microstructure and its relationship to the shocking has been decided for this type of material by a combination of experiments. The main conclusion is that the presence of agglomerates, even if relatively few in number, can dramatically affect the microstructure which evolves during final stage densification. For materials as morphologically confounded as these, it appears that the release of strain energy even well into. the intermediate range of sintering has little to do with the main effects observed in the intermediate and late stage.

The puzzle of the grain growth (or lack of it) observed in the late intermediate stage (D=0.9l) in the agglomerated batch was finally resolved by the examination of polished sections at that density level. The large "grain" areas (present at both heating rates) shown in Fig. 12 are dense and have been growing and even changing shape (observed milled agglomerates are quite rounded) while the finer matrix which is only what is observed by the fracture surface (see Figs. 7 and 11). These regions were most obvious in the light microscope. It is important to realize that these dense regions are often larger than 100 wm and seem to grow from more humble beginnings. Although the dense regions revealed here appear to be large single grains, we believe they are not yet fully dense, nor are they all single grains at this stage.

One surprising effect is that the growth and densification of these regions appears to be progressing into areas where the porosity is connected and the samples are still absorbing considerable water during density measurements.

Fig. 12. Polished sections, 74KB-shocked, sintered alumina (a) 20K/min, D=0.92 and (b) 2K/min, D=0.92.


Workers at MIT (18,19) have produced fine. spherical powders which pack uniformly, even regularly, with a resultant minimal grain growth, because essentially all particles have like surroundings, like coordination, like neck growths, and therefore, instabilities which favor grain boundary movement do not develop.

In the cases presented here, we arrive at the opposite end of the spectrum, where we have introduced not a great variation in crystallite size in the starting compacts, but a great variation in local densities, neck sizes and pore distributions, characterized even as bimodal, with parts of the distribution coming from the interior of the agglomerates, and other parts due to their 'boundary' or matrix areas formed from the fine grains or the agglomerate 'grain boundaries' and lower density interstices. As any compact proceeds through the intermediate stage, regions of the sample arrive at a critical high density where they can begin to grow into the microstructure, a process which can convert the "fine" region observed in the fracture surfaces into denser regions (but still with pore entrapment), as is usually only observed much later. These denser areas then become ripe for the onset of exaggerated (or any other) grain growth at lower overall density.

In the case of overcompaction we have created a starting compact which, though reasonably uniform in crystallite size, has two populations of pore and neck sizes at the onset, so that the pore population becomes or remains, in some sense, bimodal, causing the late intermediate stage densification rate 'bump' that has been observed.

We believe strongly, and confirm the findings of Yan et. al (19), that the main microstructural effects seen throughout are very strongly influenced by packing geometry of the initial compact stage, and that both the over-compaction which was produced by the 74KB shocking and the formation of denser agglomerates formed by the presintering and regrinding of compacts give a very wide pore and neck size distribution at the start which do not produce great variations in average grain size, but produce great differences in densification kinetics and in the final stage microstructures.

Therefore any non-ideal compact should exhibit some aspects of what has been observed, so that the relationship between the final grain size attained must be a complex function of not just the initial grain size distribution, but also the pore size distribution and how the evolvement of the pore and grain network proceeds from the initial compact state.


ACKNOWLEDGMENTS

Supported by the U.S. Army under Contract No. DMKll-13-K~002. Special thanks are due to T. T. Fang. who reminded us who should know better that fracture surfaces are sometimes selective in what they reveal. Thanks also to K. Y. Kim, M. J. Paisley, T. Goudey, L. Freed, M. Bridges, J. Lebold and E. M. Gregory for their help in the laboratory.

REFERENCES

1. O. Bergmann and J. Barrington, J. A. Cer. Soc. 49(9), 502 (1966). 2. A. C. Greenham and B. P. Richards, Trans. Brit. Ceram. Soc. 69,

115 (1970). 3. R. Pruemmer and G. Ziegler, Powder Metall. Inst. 9 (1), 11-14

(1977) . 4. "Dynamic Compaction of Metal and Ceramic Powders," National

Materials Advisory Committee Study Report NMAB-394, National Research Council, 1982.

5. H. Palmour III, et. aI, p. 331-372 in C. F. Cline, Ed., First Quarterly Report, DARPA Dynamic Synthesis and Consolidation Program. Lawrence Livermore National Laboratory Report UCID-1963, August, 1982.

6. K. Y. Kim, A. D. Batchelor, K. L. More, and H. Palmour III in "Emergent Process Methods for High Technology Ceramics," to be published by Plenum Publishing Corp.

7. K. Y. Kim, Doctoral Thesis, N. C. State University, May 1983. 8. Y. Horie, H. Palmour III, and J. K. Whitfield, "Shock Compaction

and Sintering Behavior of Selected Ceramic Powders," in C. F. Cline, ed., 2nd Quarterly Report, DARPA Dynamic Synthesis and Consolidation Program, Lawrence Livermore Laboratory (in press).

9. T. M. Hare and H. Palmour III, pp. 307-320 in G. Y. Onoda, Jr. and L. L. Hench, eds., "Ceramic Processing Before Firing," John Wiley and Sons, New York, 1978.

10. H. Palmour III and T. M. Hare, and M. L. Huckabee, Final Technical Report, Contract N00019-73-C-0139, March 1974.

11. A. D. Batchelor, M. J. Paisley, T. M. Hare, and H. Palmour III, in "Emergent Process Methods for High Technology Ceramics," to be published by Plenum Publishing Corp.

12. H. Palmour III and M. L. Huckabee, U. S. Patent 3,900,542, December, 1975.

13. M. L. Huckabee and H. Palmour III, A. Cer. Soc. Bul. (8) 574-76. 14. H. Palmour III, M. L. Huckabee, and T. M. Hare, pp. 308-319 in

R. M. Fulrath and J. A. Pask, eds., "Ceramic Microstructures-'76" Westview Press, Boulder, CO (1977).

15. W. Beere, Metal Sci., (10) 294 (1972). 16. D. Lewis and M. Lindley, J. Nuc. Mat. (17) 347-349 (1965). 17. To be published.


18. R. L. Pober, E. A. Barringer, M. V. Parrish, N. Levay, and H. K. Bowen, in "Emergent Process Methods for High Technology Ceramics," to be published by Plenum Publishing Corp.

19. M. F. Yan, R. M. Cannon, U. Chowdry and H. K. Bowen, Bull. Am. Cer. Soc., 64, 19 (1981).

SINTERING OF LiF FLUXED SrTi03

ABSTRACT

Harlan U. Anderson & Marie C. Proudian

Department of Ceramic Engineering University of Missouri - Rolla Rolla, Missouri 65401

The densification of SrTi03 using LiF as a sintering aid was investigated. In the temperature range 700 to 900°C, the sintering kinetics of Yz to 2w% LiF doped SrTi03 appears to be controlled by liquid phase sintering. Densification was found to be a function of cation stoichiometry and temperature as well as LiF content. For example, 2w% LiF additions with 4 hour sintering at 910°C, specimens of composition SrI 03 Ti03achieved a density of 96% TD, whereas, for the same treatment of·tnose of compositions Sr 98 Ti03 achieved only 75% TD. The interaction between LiF and SrTi03 is very complex and both X-ray diffraction and weight loss measurements suggest that it might involve the formation of Li and F containing compounds.

INTRODUCTION

The influence of small quantities «2w%) of LiF on the densification of both MgO and BaTi03 has been the subject of several investigations (1-12). In these studies, it was shown that the LiF introduced a liquid phase at temperatures well below normal sintering temperatures which both lowers processing temperatures and improves densification. An additional characteristic of this sintering aid is that its volatility and solubility are such that most of the resulting liquid can be removed by annealing, thereby, removing many of the detrimental effects that can be attributed to the presence of a second phase in the grain boundary. The fact that BaTi03 and SrTi03 have quite similar properties makes one suspect that the addition of LiF to SrTi03 will substantially reduce sintering temperatures. This paper describes an investigation in which LiF was added to SrTi03 and the influence of densification assessed.

281

282 H. U. ANDERSON AND M. C. PROUDIAN

Experimental Procedure

High purity SrTi03 powders of varying Sr/Ti ratio were prepared using the "Pechini Process". (13) This process yielded powders of about O.ll1m crystallite size with purity levels of 99.9%. To these powdErs Yz to 2w% LiF was added by dry mixing in a vibrating mill. The resulting mixtures were moistened and dry pressed into 13mm diameter discs with green densities of about 55% of theoretical.

Weight change and densification measurements were made on specimens heated in box furnaces in the temperature range 690 to 910°C for periods of time up to 250 hours. The densities of the sintered specimens were determined by the buoyancy technique and shrinkage was measured by both a micrometer and dilatometer. Microstructural examinations were made of both fractured and polished SJrfaces using a scanning electron microscope. Both starting powders and sintered specimens were subjected to X-ray diffraction to ascertain the presence of phases other than LiF or SrTi0J..' Chemical analysis was used to determine the Li and F contents after the sintering process.

Results and Discussion

Since no phase equilibria data are available for the LiF-SrTi03 system, the temperatures at which LiF and SrTi03 mixtures start to interact were determined by heating mixtures in a Mettler TGA-DTA system and by making shrinkage measurements. It was found that thermal effects, weight loss and shrinkage began at temperatures below 600°C. Since this is far below the melting point of LiF (845°C), it was suspected that the LiF and SrTi03 were interacting to form either a low melting or high vapor pressure comPQund (or both) and that enhanced densification was occurring from either liquid phase or vapor phase reactions. To establish the presence of liquid at the sintering temperature, a careful scanning electron microscope study was made of both polished and fractured surfaces of sintered specimens. Figures 1-3 show quite conclusively that a glassy phase exists in specimens which were heated in the 700 to 900°C range. The composition of the glassy phase has not been established, however, EDS analysis shows that it contains about lOm% more Ti than does SrTi03. Also, it is evident that the amount of glassy phase decreases with both increasing sintering time and Ti content. If is also apparent that densification is enhanced as the Sr content increases (or liquid phase content increases). Changes of the surface morphology of the SrTi03 crystals are also quite good evidence of the action of either liquid or vapor transport occurring during densification.

The influence of LiF content and Sr/Ti ratio on densification and shrinkage is illustrated in Figures 4-7. As can be seen, sintering is very much dependent on both LiF content and Sr/Ti ratio. Supporting this conclusion Figures 1-3 indicate that the amount of liquid increases with both Sr content and temperature. Also, the fact that maximum densities are obtained for the highest Sr content (Srl. 03 Ti03) again suggests the presence of more liquid. (Fig 2)

SINTERING OF LiF FLUXED SrTiOJ 283

Figure 1

Figure 2

POLISHED SURFACES 2 W% LiF 6 HR

910°C

Scanning Electron Micrographs of LiF-SrTi03 Showing Glassy Phase.

POLISHED SURFACES

2 W% LiF 250 HR

9tO°C

Scanning Electron Micrographs of LiF-SrTi03 Specimens Showing Glassy Phase.


A/B=l.OO - 2W% LiF - FRACTURED SURFACES

___ ---=6'-'H'-'"'R -910oe __ _ 12 HR - 700oe

Figure 3 Scanning Electron Micrographs of LiF-SrTi03 Showing Second Phase Labeled A.

In the temperature range of 690 to 910°C, densification is only weakly dependent on temperature {Fig 4 & 5).Even though there should be more liquid present at 910°C than at 700°C, the maximum achievable densities only change by about 5% within this temperature range. For example, for 2w% LiF and composition SrLO::l Ti03. the densities obtained after 250 hours sintering were 90% and 96% TIYat 690 and 910°C respectively.

It should be pointed out that densities greater than 90% TD were achieved at 700°C which is about 700°C lower in temperature than is necessary for unfluxed SrTi03• (See Figures 4-5.) At temperatures as low as 700°C for 12 hours the gram size increased from O.hJm to about l]Jm and then changed little with additional time or temperature. In fact, the grain growth appears to be inhibited and does not appear to show much increase until the densities exceed 95% TD after which some exaggerated grain growth can be seen. (Fig 1,2 & 8.) It should also be noted that grain size is little influenced by temperature and time but is dependent on Sr content. (Fig 3,8.)

One of the most striking microstructural features is the rather distinct

SINTERING OF LiF FLUXED SrTiOJ

Figure 4

Figure 5

100

~ 90 • • '"

~ .. l- • ~ 80 • w 0

w • • ::: 70 • '" ~ .. ..J • .. • • 0.5 w1% LiF w a:

60 • .. 1.0 wl% LiF

• 2.0 wl% LiF

50 0.98 0 .99 1.00 1.01 1.02 1.03

Sr/Ti RATIO

Relative Density of Specimens Sintered for 250 Hours at 690°C.

100

• ;,!!90 .. -. Q

• • .,: I-

~80 w • 0

• .. w '" ?:70 • • • l- I> <[ ..J • • 0.5 wl% LiF w a: .. 1.0 wl% LiF 60

• 2.0 wl% LiF

50 0 .98 0.99 1.00 1.01 1.02 1.03

Sr/Ti RATIO

Relative Density of Specimens Sintered for 250Hours at 910°C.

285


w ~ ~ z cr I (f)

0.1

....J 0.01 <l: z o

~ a: u..

ll. Sr/Ti =0.98

o Sr ITi = 0 .99

<> Sr/Ti= 1.00

c Sr/Ti=1.01

v Sr/Ti= 1.03

0.001 '--;-----'_L.......L...J....I...L.LJ'"'---:-_.L..-..l...-L..l-.L..L.J...L.l...._....I...--I-.J....J...LJ..u.J

101 102 103 104

w ~ ~ z a: I (f)

0.1

....J 0.01 <l: z o

~ a:: u..

TIME (seconds)

o 695°e v 7500 e

c 8000 e

0.001 '-:---'L-.L.......I....J....IU-Lu......._..L-...l....-L....L...LU-LL_-I---L.....L...l...I...J...uJ

101 102 103 104

TIME (seconds)

A

B

Figure 6 Shrinkage as Function of Time for Specimens Containing 2w% LiF - A. 2w% LiF, 760°C; B. Sr/Ti = 1.01, 0.5w% LiF.

SINTERING OF LiF FLUXED SrTiO. 287

-----

•

• 0.5 wt% LiF • 1.0 wt% LiF • 2.0 wt% LiF

1.00 1.01 1.02 1.03

Sr/TI RATIO

Figure 7 Shrinkage of Specimens Sintered for 250 Hours at 690°C.

crystal shapes that were observed. Inspection of Figures 1, 2 and 8 shows grains that are both cubic and spherical in habitat. This is interpreted as additional evidence that liquid and/or vapor phase transport occurs during sintering.

In addition to the densification characteristics, one of the most striking features of this system is the weight loss. As can be seen in Figure 9, the amount of weight loss observed even at the lowest temperatures far exceeds the amount expected due to the loss of LiF. It is evident that the maximum weight loss is both LiF and Sr content dependent. The fact that the loss is highest for the composition Sr 03 Ti03 suggests that Sr has to playa role in the liquid as well as vapor formation. Figure 2 shows that the amount of liquid decreases with increasing time at 910°C and appears to be missing for the composition SrI 03 Ti03 after 250 hours at 910°C. For this composition the weight loss appears to be stabilized at about 5.5% for a 2w% LiF .addition for temperatures above 800°C. (Fig 9.)


2 W% LiF - 910°C - FRACTURED SURFACES

A/B=0.98 AlB = 1.00 AlB =1.03

Figure 8 Scanning Electron Micrographs of Specimens Sintered at 910°C Showing Influence of Time and Sr/Ti Ratio.

At 910°C, SrTiO alone shows no weight loss, however, the observed weight losses exceed the amount of LiF added by factors of 2 to 6 depending on LiF and Sr content (see Figures 9·H). Thus it is apparent that the reaction between LiF and SrTiOJ is producing a product which is volatile at temperatures below 910°C. As was previously mentioned, EDS analysis indicates that the glass formed by the reaction is enriched in Ti which suggests that part of the Ti is being dissolved. Chemical analysis of a number of sintered specimens indicates that nearly 80% of the F and 90% of the Li leave the system.

If the assumption is made that the Li found in the SrTi03 specimens substitutes into the structure for Ti and that all of the excess Sr and Ti that is removed from the structure forms a volatile oxyfluoride, then most of the observed weight changes can be taken into account. For example, for a specimen of SrI 0 Ti~ with Zw% LiF sintered at 910°C for 250 hours was observed to have·a ?s.5~fnOSS in weight. Based on chemical analysis and the above assumption, a weight lm:s of 4.8% was calculated.

X-ray analysis of part of the condensed volatiles show diffraction lines primarily of LiF with few additional lines which are yet to be identified.

SINTERING OF LiF FLUXED SrTiOJ

o

rJ)4.0 rJ)

0 ..J

I-:I: C)

iii ~

!z3.0 0

LtJ 0 0:: LtJ c..

2,0

o 51'0,98 TiO,

" Sro.u TiO,

V Srl .oo TiO,

a Srl.OI TlO, o Sr 1,0' TIO,

°O~~~--L-~~I~OO~L-~~--L-~ooo~~~-..!

TIME (hours)

Figure 9 Weight Loss as Function of Time for Specimens Containing 2w% LiF that were Heated at BOODC •

289

Chemical analysis needs to be made of the condensate before the supposition of a volatile Sr, Ti oxyfluoride can be proved or disproved. Thus it must be emphasized that the above calculation is based only on conjecture until the nature of the volatile components has been identified.

X-ray analysis of all of the SrTiO compositions after sintering with LiF shows the primary phase to be Srrl03' however, a few yet unidentified lines were observed. These lines might be related to the oxyfluoride phase as was suggested by Desgardin and co-workers. (10) Again, at the moment this is very weak evidence and much more study will be required before definitive statements can be made.

Conclusions

Lithium fluoride promotes the densification of SrTiO so that high densities can be achieved at temperatures as low as 700o~. The mechanism of sintering enhancement appears to be through the formation of a liquid phase whose amount depends both on temperature as well as LiF and Sr

290

Figure 10

(/) (/)

9 5: (!)

5.0

4.0

~3.0 !z ILl U a: ILl 0..

2.0

H. U. ANDERSON AND M. C. PROUDIAN

o SrO.98 Ti03

t;. Sr0.99 Ti03

v Sr I .00 Ti03

D Srl.OI Ti03

<> Srl.03 Ti03

1.0'------1.----L...--..I...-----'---..I 1.5 2.0

%LiF

Weight Loss of Specimens Heated at 690°C for 250 Hours.

SINTERING OF LiF FLUXED SrTi03

5.0

4.0 CJ) CJ)

9 ~ ~ (!)

~ ~3.0 z w

ffi Il.

2.0 o SrO.98Ti~ 6 SrO.99 Ti03

V Srl.OO Ti03 D Srl.OI Ti03 <> Srl.03 Ti03

1.0'-----L----'---..I...----'----J

%LiF

Figure 11 Weight Loss of Specimens Heated at 910°C for 250 Hours.

content. The exact nature of the liquid phase and volatile components is not known but it is probably in the form of a Sr, Ti oxyfluoride.

291


REFERENCES

1. R. W. Rice, "Production of Transparent MgO at Moderate Temperatures and Pressures," 64th Annual Meeting of the American Ceramic Society, April 30, 1962, New York, NY (White Wares Division No. 5-W-62); for abstract see American Ceramic Society, Bulletin 41 (4), 271 (1962).

2. E. Carnall, Jr., "Densification of MgO in the Presence of a Liquid Phase," Mater. Res. Bull. 2 (12),1975-1986 (1967).

3. P. E. Hart, R. B. Atkin and J.-A. Pask, "Densification Mechanisms in Hot Pressing of Magnesia with a Fugative Liquid," J. Amer. Ceram. Soc. 53 (2) 83-86 (1970).

4. B. E. Walker, Jr., R. W. Rice, R. C. Pohanka and J. R. Spann, "Densification and Strength of BaTiO_1 with LiF and MgO Additives," Amer. Cer. Soc. Bull. 55 (3) 2T4-276, 284 (1976).

5. V. V. Rana, S. M. Copley and J. ~Whelan, "Sintering of Powder Compacts With A Volatile Liquid Phase (MgO-LiF), pp 434-443, in Ceramic Microstructures "76," edited by R. M. Fulrath and J. A. Pask, Westview Press, 1976.

6. R. B. Amin, H. U. Anderson, C. E. Hodgkins, U. S. Patent, 4,082,906, April 1978.

7. H. U. Anderson, K. Atterberry, R. Amin, C. Hodgkins, "Low Temperature Fired Ceramic Capacitors," - communications at the ACS Meeting, Cincinnati, 1979.

8. J. M. Haussonne, "Communication at The 83rd American Ceramic Society Meeting - "Sintering of Barium Titanate with Lithium Fluoride, and Dielectric Properties and Importance of Stoichiometric," May '81, Washington, D. C.

9. J. M. Haussonne, proceedings of the 11th International Conference Sciences of Ceramics, "Study of the Sintering of Barium Titanate with Lithium Fluoride, and Dielectric Characteristics of These Materials." June '81, Vol. 11, pp. 521-526.

10. G. Desgardin, Ph. Bajolet, B. Raveau, et J. M. Haussonne, "Barium Titanate with Lithium Fluoride: A New Perovskite," Proceedings of the "International Conference on New Trends in Passive Components," Paris, March '82, pp. 18-25.

11. J. M. Haussonne, P. Aigoin, G. Desgardin et B. Raveau, "Influence of Powders Mixing Prior to Burning on the Characteristics of the Further Obtained Ceramics," - proceedings of the "International Conference on New Trends in Passive Components," Paris, March '82, pp. 167-175.

12. A. Beauger, A. LaGrange, C. Houttemane, J. Ravez, "Dielectric Properties of Oxyfluoride Ferroelectric Ceramics - Application to Multilayer Ceramics Capacitors," - proceedings of the International Conference on new trends in passive components," Paris, March '82, pp. 10-17.

13. M. P. Pechini, U. S. Patent #3,330,699, "Method of Preparing Lead and Alakaline Earth Titanates and Niobates and Coatings Method Using the Same to Form aCapacitor." July 11, 1967.

INFLUENENCE OF Bi203 ON CADMIUM OXIDE SINTERING

INTRODUCTION

B. V. Mikijelj

University of Washington Department of Ceramic Engineering Seattle, Washington 98195

V. D. Mikijelj

Institute of Technical Sciences of SASA

Beograd, Yugoslavia

The usefulness of traditional models to establish the sintering mechanisms in complex systems typical of industrial practices is questionable since the systems usually consist of many particles which are nonuniform in size and shape. In such systems many mechanisms of mass transport can be active. Other complications such as grain growth and particle rearrangement which are even observed in studies involving uniform spherical particles l make interpretation of shrinkage during sintering even more difficult.

The combination CdO-Bi 203 is one such complex system where it is expected that many mechanisms contribute to the sintering. 2 In particular it is known that CdO does not melt under atmospheric pressure but sublimes in the range 700°C - 1000°C3 and Bi20 exhibits five crystal modifications 4,5,6 before it melts. The exac~ melting point of Bi2033is not well established and is reported as 8204 , 8287 and 840°C • The system is further complicated by the presence of two compunds in the phase diagram - 6CdO·Bi203 and 5CdO·3Bi203.9

293

294 B. V. MIKIJELJ AND V. D. MIKIJELJ


Analytical grade powders of cadmium oxide and bismuth oxide were dried at 200°C overnight and mixed in a porcelain mortar. Pellets of 10, 5, 2, 1, .5 and .1 Vol. % Bi203 and pure CdO weighing about .5g were prepared in a 10 mm diameter, double acting die at 100 Mpa. Two sets of CdO pellets were prepared using as-dried powder and powder crushed in a porcelain mortor. All pellets were measured and weighed.

A Stanton thermobalance operating at a heating rate of 5-6°c/min was used to perform thermogravimetric analysis (TGA) to 850°C in order to check the extent of CdO sublimation and deadsorption of water and gases.

All specimens were sintered at the same time in an electric tube furnace on a bed of highly sintered CdO in an alumina boat. The boat was positioned in the center of the cold furnace, near a Pt-Pt, 10% Rh thermocouple. The furnace was heated at 10%C/min to the socking temperature of 850°C and maintained for 0, 15, 30, 60, 120 or 240 minutes. The pellets were cooled at 40°C/min after isothermal sintering and the linear and volume shrinkage and densities measured.

Polished and etched surfaces were examined metallographically and fracture surfaces from samples sintered for 4 hours were studied with scanning electron microscopy. In addition, the samples sintered for 4 hours were examined by X-ray diffraction.


Mass changes during heating

As-prepared pellets containing Bi203 show a 4% loss in weight on heating to 400°C, Figure 1. The source of the weight loss was not determined since it occurred below the temperature where significant densification occurs; however, the two-stage process was only observed for pellets of Bi20/CdO prepared from ground and blended powders. The implication is that the weight loss is related to water pick-up during blending. Heating at 850°C for 1 hr did not produce further measurable weight loss, indicating that CdO sublimation noted in the literature was very small.

Other changes during heating (non-isothermal sintering)

Shrinkage of pure CdO begins under 500°C. If additions of Bi ° do not alter this temperature as is observed with Bi203 ad~i~ions to ZnO lO then non-isothermal shrinkage can be expected

CADMIUM OXIDE SINTERING

::3 c C1J u ... ~2

E "E

<J

10 mol percent Bi 2 0 3

o~ __ ~ __ ~ __ ~ __ ~ __ ~ __ ~~~ o 100 200 850

295

Fig. 1. Mass change of a sample with 10 mol % Bi203 in edO, during heating to 850 0e at a rate of 5-6°e/min.

to occur for at least 35 minutes during heating to the 850 0e isothermal sintering temperature. In addition, since Bi203 melts around 840 0e and the known Bi203-CdO compounds melt some 1000e lower, sintering during heating of all Bi203 containing samples must involve three stages:

I. Solid state sintering during heating and possibly during cooling.

II. Sintering in the presence of a liquid phase from its appearance up to 850 0e.

III. Sintering in the presence of a liquid phase under is otherthermal conditions at 850 0e for times of 0, 15, 30, 60, 120 or 240 minutes.

Shrinkages observed for all samples at the end of the heat-up cycle (t=O) were found to range from 15 to 20% for the linear change and 42 to 49% for the volume change. Subsequent isothermal sintering at 850°C did not produce significant additional shrinkage, Figure 2. Thus all of the shrinkage observed for edO samples presumably involves only stage I, while stages I and II occur in the Bi203 containing samples.

Sintering under isothermal conditions

Although densification appears to be complete at the end of the heat-up cycle (t=O) for samples containing 5 mole % Bi203 , samples with low Bi203 contents were observed to become less dense

296

7.6

7.4

""E 7.2 u

ci. 7,0

6.8 ~

6.6

B. V. MIKIJELJ AND V. D. MIKIJELJ

0---0 t = 0 min

.......... t: 60min.

234 5 6 7 8 9 10

Fig. Z. Density dependence of samples sintered for 0.0 and 60 min. at 850°C on BiZ03 content in CdO.

with isothermal sintering time, Figure 2. In addition, Figures 3 through 9 show that for low concentrations of BiZ03 the shrinkage is less than that observed for pure CdO whereas above about 1 mole % BiZ03 the shrinkage exceeds that for pure CdO. Thus small additions of BiZ03 seem to inhibit shrinkage during nonisothermal and isothermal sintering.

50

40 pure Cd 0

~ 0 X' height .. • x' diameter <.>

~ 30 .:. x; volume Q.

'" "-'" <l 20 --------

10 0 2 3 4

t ( hours)

Fig. 3. Dependence of relative linear and volume shrinkages on time of CdO sintering at 850°C.

50

40 0.1 mol percent Biz 0 3

~ 0 x- heiQh! .. :: x- diameter .. • Q. 30 Il. x- volume

>< "-><

<J 20 .J:r2.-~---<>--------

2 3 4

(hours)

Fig. 4. Dependence of relative linear and volume shrinkages of sintering time of 0.1 mol % BiZ03 in CdO at 850°C.

CADMIUM OXIDE SINTERING

50~--~-----,-----r----,

40

c .. ~

~30 '" "-'" <l

20

0.5 mol percent 6i 2 0 3

Ox: height • x: diameter

~ x: volume

--------

2 (hours)

4

c: .. :: OJ Q.

'" "-

<l

50

40

30

20 \ 'tr

10 0

I mol percent BiZ 03

o x- height

• x - diameter c. x - volume

297

---------

3 4

( hours)

Fig. 5. Dependence of relative Fig. 6. linear and volume

Dependence of relative linear and volume shrinkage.s on sintering time of 1.0 mol % Bi203 in CdO at 850°C.

- 40-C .. ~ .. Co

- 30 )(

".. <l

shrinkages on sintering time of 0.5 mol % Bi203 in CdO at 850°C.

2 mol percent 6iz 0 3

Ox: height

• x: diameter ~ x: volume

-

20 -o-~-"""fJ-----<r--------- ..... ~

I

2 (hours)

I

3 4

- 40 C .. ~ .. Q.

- 30 f-

'" ..... '" <l 20~ __ _

~

Ox: height

• x: diometer

~ x: volume

..(")-.

10 l...-__ ...L.-I ___ I....-_-.L. ___ ~

° 2 3 4 ( hours)

Fig. 7. Dependence of relative Fig. 8. linear and volume

Dependence of relative linear and volume shrinkages on sintering time of 5.0 mol % BiZ03 in CdO at 850°C.

shrinkages on sintering time of 2.0 mol % Bi203 in CdO at 850°C.

298

,. ..... ,. <J

B. V. MIKIJELJ AND V. D. MIKIJELJ

50~--~r---~-----'-----'

~

40 10 mol percent Biz OJ

ox: height

• x: diometer

~ x: volume

----...=uoi

10L---~1~--~1----~1----~ o 2 3 4

(hours)

Fig. 9. Dependence of relative linear and volume shrinkages on sintering time of 10.0 mol % Bi203 in CdO at 850°C.

The volume of liquid phase present at the beginning of isothermal sintering (t=O) was estimated from a knowledge of the densities of various phases known to be present. The results are shown in Table I.

Table I. Volume fractions of liquid phase at the beginning of isothermal sintering in CdO pellets containing different amounts of Bi203 .

Bi203 content

(mol %) 0.1 0.5 1.0 2.0 5.0 10.0

Volume fraction of liquid phase 0.5 1.1 2.1 4.1 10.0 17.3

(%)

The large amounts of liquid phase (74%) for samples with 2 mole % of Bi ° or greater would permit sintering by dissolution and precipita~ion with the possible production of additional phases. Indeed, X-ray evidence was obtained to indicate the presence of an unidentified phase in samples containing 10 mole % Bi203 .

The argument for an active dissolution/precipitation mechanism in samples with 2, 5 and 10 mole % Bi203is supported by the micro-

CADMIUM OXIDE SINTERING 299

structure shown in Figure lOb. Here the grains are seen to be large (4011m), shaped for optimum pac.king and covered with remnants of a liquid phase. In comparison, samples with .1, .5, and 1 mole % BiZ03 prepared under similar conditions, 850 QC for 4 hrs., show

Fig. 10. SEM micrographs of a-O.l mol % and b-lO mol % Bi20 samples sintered for four hours at 850 Q C (fracturea surfaces).

a structure with only small (511m), angular grains with interconnecting neck, and visible pores. Optical metallographic studies of the polished sections of the 2, 5 and 10 mole % Bi203 samples revealed that the grain growth behavior was nearly cubic, Figure 11, with the 5 mole % Bi201 sample showing the fastest growth. The change in slope observea at 3 hrs could be the result ofa depletion of the liquid phase.

CONCLUSION

The addition of Bi203 (.1-10 mole %) to CdO and the formation of a liquid phase has been shown to be ineffective in contributing to the densification of powder compacts at 850°C. The isothermal shrinkage was observed to display a minimum at 15 min. for all mixed samples except for 10 mole % Bi203 .

Metallographic, scanning electron microscpic and X-ray studies support the premise that densification in the high B203 samples proceeds by a dissolution and precipitation mechanism.

300 B. V. MIKIJELJ AND V. D. MIKIJELJ

12 /'/'

./ ./

/' ./

./

10

8 E ::l

'" Q '":' 6

"

4

4 t ( hours )

Fig. 11. Dependence of cubed mean particle size on sintering time at 850°C for 2, 5 and 10 mol % Bi203 in CdO (from optical micrographs).

ACKNOWLEDGMENTS

Authors are grateful to Professors M. M. Ristic and M. Susic, corresponding members of SASA from the University of Beograd who were mentors for Diploma work of the first author for which experimental results used in this paper were done, as well as to other Yugoslav colleagues who helped during experimental work. Also, we are grateful to Professor O. J. Whittemore for his valuable suggestions and help.

REFERENCES

1. J. A. Varela and O. J. Whittemore, J. Am. Ceram. Soc. 66, 1, 77-82 (1983).

2. M. Bi1jana, Influence of Bi203 on Sintering of CdO, Diploma thesis, University of Beograd, Beograd (1982).

3. G. Remi, Kurs Neorganicheskoy Khimii, vol. 2, Mir. Moskva 1974. 4. L. P. Fomchenkov et a1., Neorganicheskie Materiali, 10 (11)2020,

1974. 5. G. Remi, Kurs Neorganicheskoy Khimii, vol. 1, Mir, Moskva 1974. 6. Korotkaya Khimicheskaya Encik1opedia, Tom 1, Sovetskaya Encik1o

pedia 1961.

CADMIUM OXIDE SINTERING 301

7. H. S. Va1eev, V. B. Kvaskov, Neoganicheskie Materia1i 9, (14) 714, 1973.

8. Z. M. Jarzebski, Oxide Semiconductors. International Series of Monographs in the Science of the Solid State, vol. 4, Pergamon Press-Vydawnictwa Naukova-Techniczne, Warszawa 1973.

9. V. A. Kutvitski et a1., Dok. Akad. Nauk SSSR, Neorg. Mat. 11 (12) 1975.

10. W. G. Morris, J. Am. Ceram. Soc. 56, 7, p. 360-364, 1973. 11. V. N. Yermenkov et a1., Spekanie V-Prisustvii Zhydkoy Meta1-

icheskoy Fazi, Naukova Dumka, Kiev 1968. 12. Ya. E. Geguzin, Fizika Spekania, Izdate1'stvo "Nauka", Moskva

1967.

SINTERING OF COMBUSTION-SYNTHESIZED TITANIUM CARBIDE

ABSTRACT

B. Man1ey,1 J. B. Ho1t,2 and Z. A. Munir1

(1) Division of Materials Science and Engineering University of California Davis, CA 95616

(2) Materials Science Division Lawrence Livermore National Laboratory University of California Livermore, CA 94550

The sintering of combustion-synthesized titanium carbide was investigated relative to that of commercially available powders. Depending on the preparation parameters, the synthesized powders had variable shrinkages at the same sintering conditions. Moreover, the commercial powder experienced a higher densification than any of the powders prepared in this study. These observations are interpreted in terms of the influence of free carbon on the sintering process. Approximately calculated amounts of free carbon show an inverse relationship with the measured shrinkages. Exper imenta1 ver ification for this is provided by sintering data on carbon-doped commercial powders of titanium carbide.

The activation energies for sintering were determined as 390 ± 26 and 458 ± 13 kJ .mo1-1 for the commercial and combustion-synthesized powders, respectively.

INTRODUCTION

If the enthalpy of exothermic reaction is relatively large then, once initiated, the reaction will self-propagate and ceases only when the reactant mixture has been converted to the product. The method of producing compounds through this process is referred to as combustion synthesis or self-propagating high temperature synthesis. A large number of refractory ceramics have been

303

304 B. MANLEY ET AL.

prepared by this method and claims have been made of their superior properties relative to their conventionally-produced counterparts. 1-3 Since these compounds are formed under nonequilibrium conditions, it has been suggested that they are highly stressed and are more sinterable. Despite these assertions, there is no experimental verification of the enhanced sinterabi1ity of combustion-synthesized materials. This work was initiated to provide experimental information on the sinterability of combustion-synthesized titanium carbide relative to that of commercially available powders.

The sintering of titanium carbide, regardless of the method by which it is prepared, appears not to have been adequately investigated. Ordanyan et al. 4 studied the densification of combustion-synthesized titanium carbide and concluded that the relative density of the sintered samples depended on stoichiometry, i.e., on x in TiCx ' It was found that the activation energy for densification decreased from 468 to 293 kJ.mol- l as x decreased from 1.0 to 0.6. It should be noted that the upper limit value of x stated in the report of Ordanyan et al. 4 is inconsistent with the Ti-C phase diagram reported by Storms. 5 The phase TiCx exists onll up to x ~ 0.96. Moreover, the results of Ordanyan et al. show a functional dependence on x which is opposite to that reported by Sar ian6 , 7 for the dependence of the activation energy of carbon diffusion in TiCx ' Sarian's results show a change in the activation energy from 398 to 459 kJ.mol-l as x decreases from 0.97 to 0.67. These results are consistent with the earlier work of Eremeev and panov8 in which the activation energy for the diffusion of carbon in TiCO.47 was reported as 462 kJ.mo1- l • In contrast to the above, the activation energy for the diffusion of Ti in TiCx was found9 to be independent of x and has a value of 737 ±15 kJ.mol- l •

Other investigations on the sintering of titanium carbide have dealt with primarily grain growth and recrystallization. lO- 12 Kushtalova lO studied the sintering of loosely poured titanium carbide through grain size determinations and reported an activation energy for grain growth of 242 ± 6 kJ .mol-l • Apparently no attention was made to the stoichiometry of titanium carbide. In contrast, the work of Samsonov and Bozhkoll examined grain growth in relation to departure from stoichiometry and concluded that a higher degree of grain growth is attained with higher departure from stoichiometry. An interesting aspect of this work concerns the behavior of annealed specimens. Annealing of combustionsynthesized samples for one hour at 1173-1273 K prior to their sintering at 2273 K resulted in no grain growth. Similar effects were attained when the samples were heated slowly up to the sintering temperature. 11 Another investigation on the

SINTERING OF COMBUSTION-SYNTHESIZED TITANIUM CARBIDE 305

sintering and grain growth of titanium carbide was reported by Chermant, Coster, and Mordike. 12 From a comparison between their experimental results and the predictions of a sintering diagram which they constructed for titanium carbide, these authors concluded that the final stages of sintering are controlled by grain boundary diffusion. From grain growth data, they calculated an activation energy of 192 kJ.morl for samples prepared from sub-micron sized commercial (Starck) powders.

EXPERIMENTAL MATERIALS AND METHODS

Sintering samples were prepared from commercially available and combustion-synthesized titanium carbide powders. Commercial powders were obtained from the Starck Company of Germany. Seven sets of titanium carbide samples were prepared by combusting mixtures of graphite and titanium powders. The graphite powder was obtained from Union Carbide as spectroscopic grade with an average particle size of 10 ~m. The average particle size of the ti tanium powder (obtained from Alfa Products) was 22 ~ m. Carbon and titanium powders mixed in the desired CITi ratio were first blended in a shaker then combusted in a glovebox (GB) or furnace (F) in a loose or pellet form. Combustion was carried out under an argon atmosphere in the glovebox, and in vacuum (10-3 Pal in the furnace. To obtain nstoichiometricn titanium carbide, powders were mixed with 19 and 81 percent by weight carbon and titanium, respectively. This ratio was ohosen so as to be slightly below the maximum oarbon content of the TiCx single phase region. 5 Additionally, two sets of samples were mixed in proportions to give sub-stoichiometric ratios of C/Ti. Two other sets of samples were made by using titanium hydride instead of titanium as the starting material. This was done to minimize oxygen contamination since, presumably, the titanium resulting from the decomposition of the hydride should be oxygen-free.

When combustion was carried out in a glovebox, ignition of the reactants was achieved by means of a tungsten wire placed approximately 3 mm above the mixture. In the furnace, combustion is effected by raising the temperature of the furnace until ignition is achieved, typically at about 1870 ± 50 K. When TiH2 was used as a reactant instead of titanium powder, the mixture (TiH2 + C) was first heated to 873-923 K and held there until the hydride was completely decomposed, typioally about six hours. At the end of this treatment, the sample temperature was raised until ignition was achieved as described above. Details of the preparation method, the CITi ratios of the resulting phases, and the pycnometric densities of the prepared powders are listed in Table 1. Pycnometric densities were measured on powders which had been milled for 30 minutes in a tungsten

Mat

eria

l D

esig

nat

ion

Syn

1

Syn

2

Syn

3

Syn

4

Syn

5

Syn

6

Syn

7

Com

mer

cial

(S

tarc

k)

TA

BLE

1

Ch

ara

cte

rist

ics

of

Sy

nth

esiz

ed T

itan

ium

Car

bid

e P

owde

rs

Py

cno

met

ric

Den

sity

-3

(g

.cm

)

± 0

.00

5

4.6

4

4.7

9

4.8

8

4.8

0

4.9

1

4.6

9

4.7

6

4.9

1

CIT

i

(fin

al)

0.9

53

0.9

55

0.9

50

0.9

54

0.9

51

0.8

58

0.7

03

0.9

53

Pre

par

atio

n R

emar

ks

loo

se p

owde

r (G

B)

pell

et,

no

bak

e (G

B)

pell

et,

wit

h b

ake

(F)

pell

et,

no

bak

e (F

)

pell

et,

T

iH2

(F)

loo

se p

owde

r,

no

n-s

toic

hio

met

ric

pell

et,

T

iH2

, n

on

-sto

ich

iom

etri

c

w

o 0)

!II ~ » z r m -< m

-t » r


carbide vibratory ball mill. Milling for significantly lower times showed a dependence of the densities on the milling time.

Following combustion, the samples were broken up in a boron carbide mortar and pestle and then milled in the tungsten carbide ball mill for various times depending on the desired final specific surface area. Surface areas were measured by means of a gas adsorption (BET) method. When analyzed by x-ray methods, the products of combustion showed the presence of lines corresponding to the "TiC" phase and, in a few cases, relatively minor lines corresponding to graphite. A spectrochemical analysis of the impurities in the synthesized product is compared in Table 2 to similar ones for the starting carbon and titanium powders. The results presented in this table show that generally there is a decrease in the impurity level as a result of the combustion synthesis. The exceptions to this observation (Fe, Ni, Cr, and B) were introduced during the handling of the product (steel spatula and boron carbide mortar and pestle). A typical microstructure of a combustion-synthesized titanium carbide pellet is shown in Figure 1. As is evident from this figure, the resulting phase is highly porous ("'50% porosity) with relatively large grains.

Figure 1. Microstructure of combustion-synthesized titanium carbide.


TABLE 2

Emission Spectrochemical Analysis of Powders (ppm by wt.)

C Ti TiC

Al 3000-4000 1000-2000

Ca 3 2000 30

Zr 1000 300

Mg 100 ~3

Si 10 100 100

Ba < 30 < 30

Mn 20 20

Sr 10 <1

Fe 5 100

B <3 80

Cu <3 <3

Cr <1 6

Ni <1 10

Sintering experiments were made on pellets prepared by pressing powder samples in air in a double action steel die under a pressure of about 30 MPa using stearic acid as a die-wall lubricant. The resulting cylindrical pellets were typically 0.635 cm in diameter and 1.02 cm in length, and had densities which were 65-67 percent of theoretical. Sintering was carried out under a vacuum of 10-3 Pa in a resistance heating Brew furnace. The degree of sintering was determined from dimensional analysis of the pellets. The height and diameter of the pellets were measured with an accuracy of 2 x 10-3 em. Temperatures were measured with an optical pyrometer with a maximum uncertainty of 10 K. In a typical sintering experiment, the sample is first heated to 1273 K at a rate of 20 K.min-l and then to the


sintering temperature at a 30 K.min-1 rate. Sintering runs were made at temperatures ranging from 1433 to 1873 K over time intervals ranging from 60 to 1020 minutes.


Resu1 ts of the time-dependence of the vo1umetr ic shr inkages of samples made from the commercial powder and sintered at temperatures in the range 1471-1666 K are presented in Figure 2. The surface area of these powders was 13.6 m2.g-1 • Figure 3 shows similar results for samples prepared from synthesized powders (Syn 1) and sintered over the temperature range of 1539-1724 K. For these samples the starting powder had a specific surface area of 12.4 m2.g-l • A comparison of these two sets of results reveals that at any given time and temperature the commercial powders sinter to a higher density than the powders produced by combustion synthesis. As will be shown later, this observation is qualitatively true for all synthesized samples.

o

< > <I

0.20

0.10

1666K

1636K

1553K 1539K 1490K

0.03 1471K

0.02

o 100

Time (min)

m =0.33

o m=0.36

m = 0.41 m =0.44

1000

m=0.42 m = 0.34

Figure 2. Time-dependence of volumetric shrinkage of sintered commercial (Starck) titanium carbide powders.


In Figure 4 plots of In /).V!Vo (the volumetric shrinkage) vs the reciprocal of the absolute sintering temperature are shown for commercial and Syn 1 powders which had been sintered for 60 minutes. The nearly one order of magnitude difference in the volumetr ic shr inkage between these two powders cannot be attributed to the relatively small difference in surface area (13.6 vs 12.4 m2.g-l ). This was demonstrated by additional experiments on Syn 1 powders which had been milled to a surface area of 15 m2.g-l and sintered in the same temperature range. The results showed only a slight improvement in shrinkage over those shown in Figure 4 for the Syn 1 powders.

Activation energies were calculated from the slopes of the lines in Figure 4 and employed a time dependence constant obtained from Figures 2 and 3. The resulting values were 390 ± 26 and 458 ± 13 kJ.mol- l for the commercial and combustion synthesized titanium carbide powders, respectively. The lower densification of combustion-synthesized powders relative to the commercial powder is demonstrated in Table 3. The shrinkage data

0.20 0

< > 0.10 <l

0.03

1724K

1646K 1636K

1539K

100

Time (min)

1000

Figure 3. Time-dependence of volumetric shrinkage of sintered combustion-synthesized (Syn 1) powders.


are obtained after sintering for 60 minutes at 1813 K. Also listed in Table 3 are specific surface areas, pycnometric densities, and oxygen contents of the various powders. The latter information was obtained from neutron activation experiments.

In theory, it is possible to show that lower pycnometric densi ties result from titanium carbide powders containing free carbon. Experimental evidence for this expectation has been provided for the case of combustion-synthesized zirconium carbide powders, 12 i.e., lower pycnometric densities correlate with larger amounts of unbonded (free) carbon. Examination of the densities listed in Table 3 shows consistency of these results with the concept of free carbon. The lower density of Syn 1 powders is indicative of a higher free carbon content which resul ted from the incomplete combustion of the loosely assembled reactant powders. As stated earlier in this paper, the density of the reactant mixture influences the rate and extent of

o

< > <l

-=

1725 1613

-2.0

-3.0

SYN 1 So = 12.4 m2/g

1515 1429K

a = 458 ± 13 kJ/mol

Commercial So = 13.6 m2/g

o o

-4.0 L-..--~----L __ -L-_--l __ ...l..-_--L __ L----l 5.8 6.2 6.6 7.0

104 /T

Figure 4. Temperature-dependence of the volumetric shrinkage for the commercial and synthesized powders.

Mate

rial

Syn

1

Syn

2

Syn

3

Syn

4

Syn

5

Syn

6

Com

mer

cial

(S

tarc

k)

TA

BLE

3

Co

mp

arat

ive

Vo

lum

etri

c S

hri

nk

age

of

Tit

aniu

m C

arb

ide

Pow

ders

Sin

tere

d a

t 18

13 K

fo

r 60

M

inu

tes

f:J.V

/Vo

0.0

00

0.0

11

0.0

64

0.0

53

0.0

68

0.2

21

0.2

19

Py

cno

met

ric

Den

sity

-3

(g

.cm

)

4.6

4

4.7

9

4.8

8

4.8

0

4.9

1

4.6

9

4.9

1

S o

2 -1

(m

.g

)

3.7

5

3.7

2

3.8

1

3.8

5

3.9

1

3.2

9

4.0

2

Wt.%

O

xyge

n

1.0

0.8

8

1.2

0

0.6

6

1.9

6

0.4

5

w '" !II

~ » z .... m -<

m

-I

» r


combustion. Likewise, the presence of volatile impurities influences the combustion process. Syn 3 and Syn 4 powders were made under identical conditions except that Syn 3 reactants were baked out in vacuum for 12 hours at 1223 K prior to combustion. Thus the difference between the pycnometric densities of the resulting phases is attributed to differences in the free carbon content of these materials. We were not successful in determining experimentally the amount of free carbon in the samples. When polished samples were examined under a scanning electron microscope, only regions with high tungsten content could be discerned (see the lighter regions in Figure 5). These localized impurity regions were introduced during the milling operations. Attempt to analyze for carbon as a separate phase gave ambiguous results because of the uncertainty produced by the use of diamond paste as a polishing agent.

We calculated the percent free carbon content (i.e., percent of total carbon that is unreacted) from the measured C/Ti ratio, the pycnometric density of the powder, and the density of graphite. The results showed a trend which is consistent with the shrinkage data listed in Table 3. However, these calculations resulted in a negative value for the carbon content of the commercial powder, and thus suggested that other factors

~ ~ . -.. 1" I .

/

., /. .~

) V

r-E0 ~m-l ..f

Figure 5. SEM micrograph of synthesized TiCx . Lighter regions represent segregation of tungsten contaminants.


contribute to the amount of free carbon. The work of Nezhevenko et a1. 13 and Shkiro et a1. 14 on combustion-synthesized zirconium and titanium carbides showed a roughly one-to-one correlation between the weight percentages of free carbon and oxygen in the samples. Taking this into account, we calculated the amount of free carbon in our samples by adding to the value calculated from the pycnometric density an amount atomically equivalent to the oxygen content. The results of these approximate calculations are qualitatively consistent with the values obtained from the more exact method of calculation using the pycnometric density. Table 4 shows the calculated free carbon contents along with the shrinkage data for sintering at 1813 K for 60 minutes. To provide experimental verification for the implied conclusion that shrinkage has an inverse dependence on the amount of free carbon, a series of determinations was made using the commercial powders as a starting material. These investigations and their results are descr ibed in the following paragraph.

TABLE 4

Calculated Amounts of Free Carbon in Relation to Volumetric

Shrinkage of Samples Sintered at 1813 K for 60 Minutes

Material

SYN 1

SNY 2

SYN 3

SYN 4

SYN 5

Commercial

Calculated % Free Carbon

14-17

8-10

6-7

6-7

5-6

2

flV/Vo ± 0.003

0.000

0.011

0.064

0.053

0.068

0.219


Graphite powders in amounts calculated to give free carbon in percentage ranging from zero to 14.00 were mixed with commercial titanium carbide powders which had been milled to a specific surface area of 4 m2.g-1 • Pellets, pressed under identical conditions to those employed in the additive-free samples, were sintered at 1723 and 1843 K for 60 minutes. The resu1 ts of these sinter ing exper iments are shown in Figure 6 as shr inkage vs percent free carbon for samples sintered at these temperatures. It is clearly evident that an increase in the amount of free carbon results in a decrease in the amount of shrinkage. In both cases the addition of a relatively small amount of free carbon to an otherwise "pure" titanium carbide results in a relatively larger decrease in shrinkage.

34

TiC (commercial)

30

I:::, 1723K

26 o 1843K

~ 22 0 > --> <l

18

14

10 0

Free carbon (at % of total)

Figure 6. The effect of added free carbon on the sintering of commercial titanium carbide powders.


SUMMARY

Titanium carbide powders prepared by the combustion-synthesis method were less sinterable than commercially available powders. The sinterability of the synthesized materials was dependent on the synthesis process parameters and the differences in densification of these powders was interpreted in terms of the amount of free carbon present in each sample. Experimental verification for the influence of free carbon on the densification of commercial powders has been generated.

ACKNOWLEDGEMENTS

This work was supported by a grant from the Lawrence Livermore National Laboratory.

REFERENCES

1. A.G. Merzhanov, G.G. Karynk, and I.P. Borovinskaya, Sov. Powd. Met., 20, 709 (1981).

2. A.G. Merzhanov and I.P. Borovinskaya, Acad. Sci. USSR Chern. Phys., 204, 366 (1972).

3. O.R. Bergmann and J. Barrington, J. Amer. Cere Soc., 49, S02 (1966) •

4. S.S. Ordanyan, G.S. Tabatadze, and L.V. Kozlovskii, Sov. Powd. Met., IB, 45B (1979).

S. E.K. Storms, The Refractory Carbides, Academic Pr'~ss, New York, 1967.

6. S. Savian, J. Appl. Phys., 39, 330S (1968). 7. S. Savian, J. Appl. Phys., 39, S036 (196B). 8. V.S. Eremeev and A.S. Panov, Sov. Powd. Met., ~, 65 (1967). 9. S. Savian, J. Appl. Phys., 40, 3S1S (1969).

10. I.P. Kushtalova, Sov. Powd. Met., ~, 604 (1967). 11. G.V. Samsonov and S.A. Bozhko, Sov. Powd. Met., ~, S42

(1969). 12. J.L. Chermant, M. Coster, and B.L. Mordike, Sci. Sintering,

12,171 (1980). 13. L.B.1Nezhevenko, V.I. Groshev, B.D. Gurevich, and O.V. Bokov,

Refractory Carbides, G.V. Samsonov, ed., Consultants Bureau, New York, 1974, p. 89.

14. V.M. Shkiro, V.K. Prokudina, and I.P. Borovinskaya, Sov. Powd. Met., 21, 868 (1982).

ACTIVATED SINTERING OF CHROMIUM AND MANGANESE POWDERS WITH NICKEL

AND PALLADIUM ADDITIONS

R. Watanabe, K. Taguchi and Y. Masuda

Department of Metal Processing Faculty of Engineering Tohoku University, Sendai, Japan 980

INTRODUCTION

Cr and Mn are very difficult to sinter into dense compacts under normal sintering conditions presumably because of their ease of oxidation. In addition, the relatively high vapor pressures of these two metals, limits the use of high sintering temperatures. In this study, it was attempted to obtain dense compacts of Cr and Mn by utilizing activated sintering through the addition of Group VIII transition metals, which has been well established for the sintering of a number of refractory metals [1] - [15]. Ni and Pd were selected as the most promising activators [14] for the sintering enhancement of Cr and Mn powder compacts. The effect of the quantity of additive and of the particle size of the sample powders on the sintering densification has been investigated as a function of sintering temperature.


Electrolytic sponge Cr powder of 99.3% purity and electrolytic Mn powder with fragmented shape and of 99.4% of purity were used as sample materials. They are shown in Fig. l(a) and Fig. 2(a), respectively. The sample powders were ball-milled in helium and the particle sizes were controlled by varying ball-milling time. Figun=sl(b) and 2(b) show examples of the ball-milled Cr and Mn powders. Ni and Pd were impregnated into the sample powders with aqueous solutions of Ni- and Pd-nitrates. It is to be noted here that the Mn particles were chemically attacked during the salt impregnation treatment and an intensive refinement occurred as shown in Fig. 3. The impregnated powders were dried in air at 80-90°C

317

318

Fig. 1.

Fig. 2.

R. WATANABE ET AL.

Electrolytic Cr powders. (a) As-received, (b) Ball-milled. Specific surface areas are: (a) 0.47 m2/g and (b) 1.21 m2g.

Electrolytic Mn powders. (a) As-received, (b) Ball-milled. Specific surface area: (a) 0.23 m2/g, (b) 0.74 m2/g.

and then compacted in a floating die at a pressure of 200 MPa into a cylindrical form of 14 mm in diameter. The powder compacts were heated in hydrogen to 800°C for Cr and 500°C for Mn to eliminate the nitrate radicals and subsequently sintered 1 h at 900-1400°C for Cr and at 700-1200°C for Mn. Linear shrinkage and relative density values were measured on the sintered specimens and their microstructures were examined.

ACTIVATED SINTERING OF POWDERS WITH ADDITIONS 319

Fig. 3. Electrolytic Mn powders treated with (a) Ni-nitrate. aqueous solution and (b) Pd-nitrate aqueous solution. (a) As received, 1% Ni, 4.48 m2 jg, (b) Ball-milled, 1% Pd, 5.56 m2 jg.

Fig. 4. Microstructures of the sintered Cr with additions of Ni and Pd. The effect of Pd is shown as compared with that of Ni. Ni has little effect on the sintering acceleration of Cr.

320 R. WATANABE ET AL.

EXPERIMENTAL RESULTS

Figure 4 shows the typical microstructures of the Cr powder compacts sintered 1 h in hydrogen at 1200 and l300°C with Ni and Pd additions. As can be seen in these photographs, dense compacts are obtained by the addition of 1% Pd, while Ni has been found to have no effect on the sintering densification.

Fig. 5. Microstructures of sintered Mn powder compacts: (a) without additives, (b) with 1% Pd and (c) with 1% Ni. (Sintered 1 h in hydrogen at 1100°C).

Figure 5 shows the sintered structure of the Mn powder compacts without additives, with 1% Ni and with 1% Pd, sintered 1 h in hydrogen at 1100°C. In this case, both of Ni and Pd additions are seen to be effective for the sintering acceleration.

Figure 6 shows the relation between the relative density and sintering temperature for Cr powder compacts with and without Pd additions. Sintering acceleration started at about 950°C and was most pronounced at about l200°C. The suppression of the densification enhancement over l200°C is supposed to be due to grain growth in the final stage of sintering.

Figure 7 shows the effect of Ni and Pd additions on the sintering densification of Mn powder compacts. A similar enhancement effect of Cr sintering with addition of small quantities of Ni and Pd was found. The sintering enhancement is seen to be more pronounced in the case of the ball-milled powder having smaller particle size. Note that a densification parameter was used to normalize the density changes because the green density of each of the three sample powders, without additives, and with Ni and with Pd, was appreciably different presumably due to the appreciable refinement of powder particles by the salt-impregnation treatment.

ACTIVATED SINTERING OF POWDERS WITH ADDITIONS

l00Ir--------------------,

90

?;-

.~ 80 o .. . ~ ~ "ii a:

70

(Sintering in H2) ___ --0-- A

o

B

-0- Cr .1·I.N

-0- Cr

Sintering Temp.f'C

321

Fig. 6. Relation between relative density and sintering temp~rature for Cr powder compacts. (Ball-milled powder, 1.21 m /g).

1.0 1.0 (Sintering in H2) Mn, As-received (Sinterlng In H2)

er d:' d:' -o-Mn.l·,.Ni I -o-Mn.l·I.NI

.f 0.a --6--Mn. ,.,. Pd §' 0.8 --6-- M n • l"I. Pd

-<>-Mn ~ -o-Mn d! I I elf' c£' 0.6 ~ 0.6 .. : ~ Go ii ii E E :! I! 01, ~ 0.4 '" Q. c: c: .2

.~ .~ '" 0.2 0.2 u 'iii :;:: 'iii c:

Go c: C .. 0

0.0 m.p. of Mn 0.0 m.p. of Mn

-0.1 -0.1 600 800 1000 1200 11000 600 800 1000 1200 1400

Sintering Temp.I·C Sintering Temp./'C

Fig. 7. Relation between densification parameter and sintering temperature for Mn powder compacts.

322

18~----------~---------,

(Sinll'ring in Hz ) 16

Cr Powder Compact

14

"o! 12

~ ~ 10 c

~ ~ .. 6 c :.J

4

2

-<>- 1200·C 1 h -1100

~1050

1.2 1.6 2.0 21. 2.8

Pd Content/mass 'J,

R. WATANABE ET AL.

1.0,------,.--------,

I

: 0.8

d:' ::r :: 0.6 .. Q; E

~ n. 0.4

c: .Q ;,; v ~ 0.2 c: .. o

(Sintering in H2)

Mn-Pd --0- 1100'C, 1 h

-6-- looo'C,1 h

Mn.( Ball-milled poYICIer)

Mn-Ni --looo'C,1 h

°0L---L-~L-~~~--~--~~ 0.5 1.0 1.5 2.0 2.5 3 .0

Pd or Ni Content/mass".

Fig. 8. Effect of Ni and Pd additions on the sintering of Cr and Mn powder compacts, where the finest sample powders were used.

Figure 8 shows the effect of the amount of additive on the sintering enhancement for Cr and Mn powder compacts, where the finest sample powders were used. It can be seen in this diagram that an optimum quantity of the additives exists for the sintering enhancement as is often the case in the activated sintering of refractory metals. The optimum quantity of the additives for Cr sintering was about 1% and 1.5% for Mn sintering. The addition of activators of more than these values was found to be ineffective in further increasing the densification acceleration.

As has been shown in Fig. 7, the sintering enhancement has been found to be more pronounced for the smaller particle size. The particle size effect was examined by plotting the densification rate against the specific surface area of the sample powders. Figure 9 shows the relation between the linear shrinkage and the specific surface area of the Cr powder with and without Pd additions. The percentage shrinkage increased linearly with increase in the specific surface area of the sample powder. The particle size effect is seen to be more pronounced in the sintering with Pd addition.

A similar effect of particle refinement was also observed in the case of Mn sintering as shown in Fig. 10. However, it should be noted here that the activating effect in Mn-Ni system seems to be strongly depressed, that is, in spite of having much smaller particle size, the sintering enhancement in this case is not so pronounced as compared with that of Mn-Pd system.


Fig,

<a> 19 18 (105O"C, 1 h ,H2) 18 (12oo"C, 1 h ,H2 ) (b)

16 -0- Cr + 1 ./. Pd 16 -0- Cr + 1'/. Pel --Cr -- Cr 14 14

;;'! 12 . ;- 12

}1O a. ElO

.E c:

.L: 8 ~ 8 III III

Z 6 j 6 .E ~ ~

4 4

2 2

0 0 0 0.2 Q4 0.6 0.8 to t2 1.4 1.6 0 Q2 1.6

9.

Specific Surface Area/(nI/g) Specific Surface Area I(nffg)

Effect of the specific surface area of sample powder on the shrinkage of Cr powder compacts with and without Pd.

.- tOr;:::======:;---------------, ~ -x- 900·C I

~ -Lr- 1100·C ;::: O. d:! -0- 1200 ·C I a,UI

..: 0.6 (Mn) GI -GI E

~0.4 / c: o

~ _ 0.2 'iii

~

Specific Surface Area I( m2/g)

7 /

6.0

Fig. 10. Effect of the specific surface area of sample powder on the shrinkage of Mn powder compacts without additives, with Ni and with Pd.


DISCUSSION

The activating effect in the sintering of refractory metals with addition of some transition metals has long been ascribed to the enhancement of the grain boundary diffusion by the segregation of the activators at grain boundaries between particles of host metals. There has been some evidence for the segregation of activators at the grain boundaries of the refractory metals [6], [8], [15], and the resulting enhancement of the grain boundary diffusion [6], [16]. Such an enhancement effect has also been supported by electronic theory [7], [14]. Sintering models have been proposed on this concept and the isothermal shrinkage equations have been derived [1], [8], which have been supported by some experimental data [6], [17].

A number of criteria have been proposed for activated sinter ing, which have been concerned with mutual solubility, particle size, quantity of additives, segregation of additive elements at grain boundaries and diffusion enhancement and so forth [14], [17]. The most widely accepted and obvious criterion for activated sintering is the mutual-solubility requirement. The solubility of activators in refractory metals should be much less than that of the latter in additives [18]. Other criteria so far proposed are considered to be connected with the sintering mechanism itself and usually based on some assumptions. On the other hand, the solubility criterion is an obvious one which may easily be determined from the corresponding phase diagrams. In our case, this criterion is satisfied in Cr-Pd and Mn-Pd systems [19]. In these systems, the sintering enhancement has actually been realized and it can be explained by the theories so far proposed, which are based on the segregation of activators to grain boundaries of host metals and the resulting diffusion enhancement. On the contrary, in Cr-Ni and Mn-Ni systems, Ni readily dissolves in Cr and Mn at the sintering temperatures employed, therefore the solubility condition is not fulfilled. While no sintering enhancement was observed in the Cr-Ni system quite in accordance with the solubility criterion, a definite densification acceleration was observed in the Mn-Ni system as has been shown in Fig. 7. However, considering that the densification acceleration in Mn-Ni system has been unexpectedly small considering the fineness of the sample powder,the activating effect of Ni itself on the sintering of Mn powder is supposed to be small and the densification acceleration in this case should be mainly due to the appreciable refinement of the sample powder during salt-impregnation treatment. Since few data are available on the additive segregation and the resulting diffusion enhancement for the systems, Cr and Mn with Ni and Pd, we are not able to say more about the densification mechanisms including the optimization behaviors with respect to the additive quantity


Kaysser et al [20-22] have recently observed that during the sintering of Mo with Ni additions some rapidly migrating grain boundaries are formed in the inter-particle regions by recovery and recrystallization processes. These grain boundaries migrate leaving the solid solution behind and Ni dissolves into Mo as much as the solubility limit. A linear relationship holds between the fractional shrinkage and the Ni concentration of the Mo-Ni solid solution. From these observations, they have concluded that the recovery and recrystallization in the refractory metal is accelerated by the addition of activator and the mobility of the grain boundary increases due to the segregation of activator to the grain boundary. There has been some evidence that the rapidly migrating grain boundary serves as an enhanced diffusion path for the host metal in alloy systems [23,24]. From this fact, Kaysser et al have concluded that the rapidly migrating grain boundaries they observed during the activated sintering of Mo-Ni system also acted as an enhanced diffusion path for the pore elimination. This concept is quite different from that of the enhancement of diffusion in the stationary grain boundary. According to their opinion, the rapidly migrating grain boundary not only acts as an enhanced diffusion path for the shrinkage but also causes the dissolution in the activated sintering, hence the direct relationship is to be expected between the shrinkage and the Ni concentration in the Mo-Ni solid solution. Their experimental results have also indicated that the shrinkage and elimination behaviors in the activated sintering will be very sensitive to powder characteristics and heating conditions, as well as to sintering atmospheres. Such a concept would give some insight into the densification acceleration mechan-ism and the optimization behaviors of the activated sintering.

SUMMARY

The hydrogen sintering of electrolytic Cr and Mn powders with additions of Ni and Pd have been studied. The densification of Cr powder compacts during sintering was accelerated by the addition of a small quantity of Pd. On the contrary, Ni addition has revealed to have little effect on the sintering of Cr. Dense compacts of Cr were always obtained by hydrogen sintering with the addition of l% Pd below 1200°C. In the sintering of Mn powder, both Ni and Pd additions have been found to be effective for the sintering and a remarkable activating effect was observed in the temperature range between 1000-1100°C. In the Cr-Pd and Mn-Pd systems, Pd has been thought to segregate at grain boundaries, enhance the diffusion and cause the densification acceleration. On the other hand, in the Mn-Ni system, the appreciable refinement during salt-impregnation treatment has been thought to be the main reason for the densification acceleration.


ACKNOWLEDGEMENT

The authors are grateful to Toyo Soda Industries Ltd. Tokuyama, Japan for providing the sample powders.

REFERENCES

1. J. H. Brophy, L. A. Shepard and J. Wulff, "Powder Metallurgy", W. Leszynski (ed.). Interscience. New York. (1961), p. 113.

2. J. H. Brophy. J. W. Hayden and J. Wulff. Trans. AIME. 224 (1962), p. 797.

3. H. W. Hayden and J. H. Brophy, J. Less-Common Metals. ~ (1964), p. 214.

4. A. L. Prill, H. W. Hayden and J. H. Brophy, Trans. AIME, 230, (1964), p. 769.

5. J. Toth and N. A. Lockington, J. Less-Common Metals, 12 (1967), p. 353.

6. W. Schint1meister and K. Richiter, P1anseeberichte fur Pu1vermet, 18 (1970), p. 3.

7. G. W. Samsonov and W. I. Jackow1ev, Z. Meta11kunde, g (1971), p. 621.

8. G. H. Gessinger and H. F. Fischmeister, J. Less-Common Metals, 12 (1972), p. 129.

9. G. V. Samsonov and V. I. Yakow1ev, Soviet Powder Met. Metal Ceram., 14 (1975), p. 474.

10. R. M. German and Z. Munir, J. Less-Common Metals, ~ (1976), p. 333.

11. R. M. German and V. Ham, Intern. J. Powder Met. Powder Tech., 11 (1976), p. 115.

12. R. M. German and Z. Munir, J. Less-Common Metals, 12 (1977), p. 141.

13. R. M. German and Z. Munir, Powder Met., 20 (1977), p. 145. 14. R. M. German, "Sintering-New Developments," M. M. Ristic (ed.)

Elsevier Scientific, New York, (1978), p. 257. 15. R. M. German and Z. Munir, J. Less-Common Metals, 58 (1978),

p. 61. 16. G. H. Gessinger and Ch. Buxbaum, "Sintering and Catalysis",

G. C. Kuczynski (ed.), Plenum Press, New York (1976), p. 295. 17. R. M. German and C. A. Labombard, Intn. J. Powder Met. Powder

Tech., 18 (1982), p. 147. 18. G. C. Kuczynski, "Sintering-New Developments," M. M. Ristic

(ed.), Elsevier Scientific, New York, (1978), p. 245. 19. M. Hansen and K. Anderko, "Constitution of Binary Alloys,"

McGraw-Hill, New York (1958). 20. W. A. Kaysser and S. Pejovnik, Z. Meta11kunde, 11 (1980), p.649. 21. W. A. Kaysser and M. H. Amtenbrink and G. Petzow, Proc. 5th

Table Conf. on Sintering, Portoroz, (1981). 22. W. A. Kaysser and M. H. Amtenbrink and G. Petzow, Proc. Int.

Powder Met. Conf. in Florence. (1982). P. 17.


23. K. Smidoda, W. Gottschalk andH. Gleiter, Acta Met., 26 (1978), p. 1833.

24. M. Hillert and G. R. Purdy, Acta Met., 26 (1978), p. 333.

REACTIVE PHASE CALSINTERING OF DOLOMITE

ABSTRACT

G.L. Messing, A.R. Selcuker, and R.C. Bradt

Ceramic Science and Engineering Program Department of Materials Science and Engineering The Pennsylvania State University University Park, PA 16802

The densification by the reactive phase calsintering of a compact formed from an oxide precursor is presented. The essential features of the process are the development of a reactive, high surface area matrix upon calcination of the precursor and the presence of a reactive liquid phase during sintering. The densification process is described for Fe203 doped dolomite in terms of the elimination of intra-aggregate ana interaggregate porosities via liquid phase sintering. It is demonstrated that high densities (Z95%) and rapid sintering kinetics can be obtained with coarse (>lO~m) precursor powders.

INTRODUCTION

Production of fine-grain size, high density ceramic components by sintering usually requires the use of reactive ceramic powders. In this context reactivity refers to a high surface area and thus demands a fine grain size as the driving force for material transport and densification. Of the variety of methods for preparing highly reactive powders, many require calcination of a precursor (e.g., hydroxide, alkoxide, oxalate, carbonate, etc.) to obtain a suitable oxide powder. It is clear that the maximum reactivity of these powders is achieved at the lowest calcination temperatures and that calcination at higher temperatures results in a much lower surface area. The powder surface area can be diminished by either coarsening processes and/or aggregate formation through localized neck formation between individual particles. Consequently, the development of powder reactivity is not only a function of the synthesis process per se, but also can be affected by the subsequent calcination procedures.

329

330 G. L. MESSING ET AL.

Recognizing the aforementioned calcination temperature/surface area relation, researchers have developed various methods to utilize ceramic powders at their maximum reactivity. These approaches include reactive hot pressing (1,2 and pressure calsintering (3,4). In these two processes a preform is consolidated from the powder precursor and then heated in a die to effect decomposition as pressure is applied either before, or during the decomposition of the precursor.

Extensive investigations of reactive hot pressing have been carried out by Chaklader (1) and Chaklader and McKenzie (2) who have reported hot pressing various naturally occurring materials including gibbsite, magnesite, brucite, etc. Morgan and Scala (3) and Morgan (4) have demonstrated that a high degree of densification while maintaining a fine grain size can be achieved by "pressure calsintering" Al(OH)3' Mg(OH)2' Th(OH)4' Cr(OH)3 and MgCa(CO)2 (3-4). Matkin et al. (5) have reactively hot pressed Al(OH)3~ith similar success. Although these processes have merit, their general utility has been limited by the need for specialized equipment and because of problems associated with gas evolution from the decomposition reactions during pressing.

Recent research has demonstrated that it is not necessary to utilize external pressure to capitalize on the maximum reacti-vity of .a calcined powder, if a reac.tive liquid phase can be properly introduced to be present during sintering. In this process the appropriate additive to form the reactive liquid phase with the calcined powder product is mixed with the precursor prior to fabrication and heating. Consequently, there develops an interrelationship between the calcination procedure and the liquid phase during the sintering process. This paper describes the aforementioned process for the reactive liquid phase calsintering of an Fe203 doped dolomite (MgCa(C03)2). Microstructural changes are discussea relative to the calcinatlon and densification processes and the kinetics of densification are addressed with regard to liquid-phase sintering.

EXPERIMENTAL

A dolomite from California was selected for these studies because of its high purity (Table 1), large grain size (1.76~m), and relatively high bulk density of 2.84 glcc (p =2.86 g/cc), and thus, pore free structure. These attributes are adv~ntageous for control and analysis of the chemical and microstructural features that occur during the reactive liquid phase calsintering process. The dolomite stone was reduced to a powder by dry ball milling with high alumina media for a short period of time (~10 minutes). The milled powder was then separated into two size fractions: -100,+270 mesh (149-53~m) and -325,+400 mesh (44-37~m),for specifically examining the effect of precursor particle size. Because the grain size of the dolomite before the milling is 1.76mm, it is understood that the milled

REACTIVE PHASE CALSINTERING OF DOLOMITE 331

Table 1. Dolomite Chemistry

Chemical Composition (wt%)

MgO ZO.6

CaO 31. 7

FeZ03 O.lZ

SiOZ 0.50

AlZ03 0.07

Loss on ignition 47.01

particles are essentially single crystal in nature. A fine, median diameter of 3]1m, Fe 03 powder was mixed with the dolomite powder via a H20 suspension with a Z% addition of an acrylic wax emulsion binder for pressing. After mixing, the suspension was dried with intermittent stirring to prevent chemical segregation, then die pressed at ZlOMPa to produce specimens 4mm thick x lZmm diameter with green densities of ~75% of theoretical.

These specimens were then sintered at temperatures ranging from l200°C to l600°C in air for time periods to 4 hours. In this paper a sintering time of "zero" minutes refers to heating the specimen to the specific sintering temperature, followed by immediate cooling. The specimen heating schedule through 1000°C was ~ hour to 750°C, followed by an increase of 100°C per hour to 1000°C, with a 15 minute hold at 1000°C. The temperature was then rapidly increased (~15 minutes) to the sintering temperature. After sintering, the bulk densities of the sintered pellets were calculated from the weights and dimensions of the specimens.

To determine the surface area changes during calcination, dolomite powders were heated with the same schedule used for the sintering, but within a special system that permitted BET surface area measurements of the decomposition products without their exposure to ambient conditions. This is an important precaution because of the hydration susceptibility of the calcined material. Microstructural changes at later stages of densification were observed by scanning electron microscopy of selected samples.

CALCINATION

The surface areas of the dolomite during various stages of heating and decomposition are presented on a schematic of the heating


schedule in Figure 1. Although the carbonates begi2 decomposing between BOO-900oe, the surface area maximum of 29 m Igm occurs at 11000e as this is the point of complete decomposition for the given heating schedule. With additional heating to l2000e and a 12 minute hold at that temperature, the surface area decreased to 17 m Igm as a result of particle coarsening. The BET equivalent spherical diameter is ~O.lvm. It is evident that with a very rapid heating to the desired sintering temperatures, that the calcined product will tend to remain as a fine particle size powder and therefore reactive during sintering.

At this state of the calsintering process it is informative to estimate the porosity of the compact prior to further densification. The as-pressed density of the compact was 2.15 glcc or 75% of the theoretical density of the dolomite. Thus, there initially exists approximately 25% porosity between the grains. This type of porosity will be referred to as inter aggregate as it exists between the individual aggregates. Aggregate is used here to emphasize the structure of the dolomite grains after calcination. During the decomposition of the carbonate grains, there is an additional weight loss of about

1200

1100 1000

u 900 0

LLI 800 It: 700 ::::l ~ <t It: LLI a.. ~ LLI ~

Figure 1. Heating schedule for the calsintering process and the evolution of surface area of the dolomite at various stages of heating.


47%, with a resultant production of about 55% porosity within the aggregates (6). This decomposition generated porosity will be referred to as intra-aggregate porosity. After calcination the compact density is only about 1.1 glcc, just 33% of the theoretical density based on the lime-magnesia mixture (p = 3.35 g/cc).

o

SINTERING

The influence of adding 1 wt% Fe ° on the sintering characteristics of the dolomite is i11ustra~eJ in Figure 2. At sintering temperatures below 1200°C, there is little densification relative to the as-calcined density of 1.1 glcc for the decomposed dolomite. At higher sintering temperatures the Fe201-free dolomite increases in density, but only achieves 78% of the fheoretical value at l600°C. This density is approximately the predicted value for the material if only the intra-aggregate porosity is eliminated. In the absence of any liquid phase during the sintering, it is reasonable to conclude that the very fine intra-aggregate porosity should be eliminated prior to the much coarser interaggregate voids simply as a consequence of its finer structure. The 1 wt% Fe203 doped specimens, however, readily sinter to >90% at only 1400°C and achieve a density of 93% at 1600°C, indicating that densification is significantly enhanced by the addition of Fe203 . Examination of phase equilibria as well as the literature (7) reveals that CaO and Fe203 will react to form CaO e Fe20 and 2CaO e Fs203 which melt at l2l6°C and 1449°C, respectively and form3s1ightly lower melting eutectics at 1205°C and 1438°C, re-spectively.

100

90 ;! !...

~ 80

!:: (/)

70 z IU C

C IU a:

TIME • 2 Hrs IU t- -325, +400 mesh z c;; 0 INTRINSIC

40 A 1% Fe20 3

Figure 2. Influence of an iron oxide addition on the sintering behavior of dolomite.


The sintering kinetics for the 1 wt% Fe ° doped dolomite in Figure 3 clearly illustrate the importance ot ~emperature on densification. At 1200°C the rate of densification is typical of that for a solid state mechanism with an increase in density from only 31% to 42% of theoretical in four hours. For sintering temperatures at 1400°C and 1600°C the sintering kinetics ascribe to the characteristic form of liquid phase sintering (8). That is, there is a rapid initial densification stage followed by an intermediate stage with reduced densification kinetics and finally an asymptotic levelling of the densification at extended times.

The interpretation (9) of the rapid initial stage of densification as observed in Figure 3 is that of particle rearrangement aided by the formation of liquid between the particles. However, in the sintering of dolomite by this process two distinct types of pore structure must be reduced to achieve the high densities reported in Figure 3 for sintering at 1400°C and 1600°C. The important distinction between the two different pore structures is that the intraaggregate pores are very fine, crysta11ographica11y ordered and surrounded by submicron particles; whereas the interaggregate voids are much larger, ~1/5 the size of the initial aggregates, and irregular in shape. Therefore when the CaO and Fe203 react to produce liquid on the surface of the calcined aggregate, a large capillary pressure is developed, resulting in the intrusion of the liquid phase into the fine intra-aggregate porosity. The dihedral angles between the 2CaO'Fe203 liquid and CaO and MgO have been reported to be 10° and 15°, respectively (10), indicating that intrusion along CaO-CaO, MgO-MgO boundaries is energetically favorable. Direct evidence for

100

~ ~

>-l-ii) Z w -325, +400 mesh 0

60 0 12000 e 0 w ~ 14000 e Q:

0 1600 0 e w l- SO Z ;:;;

40

1.0 2.0 3.0 4.0 TIME (Hrs)

Figure 3. Effects of sintering temperature on the densification kinetics of 1% Fe203 doped dolomite.


intra-aggregate liquid intrusion is illustrated in Figure 4, with a photomicrograph of the matrix after sintering at 1600°C for 2 hours. The dark grains are MgO, the gray are CaO and the white is the iron oxide rich liquid phase which has intruded between the grains.

The densification depicted in Figure 3 is a combination of the kinetics of both intra-aggregate and interaggregate shrinkage. It is difficult to separate their relative contributions as the shrinkage of both types of voids must occur concurrently to achieve the density levels which are observed. For example, complete elimination of the intra-aggregate porosity corresponds to 70% of theoretical density or about 2.5 gm/cc, a level of densification which is achieved very rapidly at 1400°C and 1600°C. The higher levels of densification depicted in Figure 3 can only be achieved by elimination of the larger interaggregate voids and as such should be dependent on the original aggregate particle size. The remarkable increase of densification between 1400°C and 1600°C can probably be attributed to the greater solubility of the CaO in the iron oxide rich liquid at the higher temperature and the promotion of particle rearrangement and solution precipitation processes.

It is evident that capillarity results in the intrusion of the iron oxide containing liquid phase into the intra-aggregate porosity with rapid densification of those pores. However, the voids between

Figure 4. Photomicrograph showing sintered microstructure of the dolomite sample with 1% iron oxide addition fired at 1600°C for 2 hours.

336 G. l. MESSING ET Al.

the aggregates are also being eliminated. These two effects of the liquid phase were examined by sintering -100,+270 mesh and -325,+400 mesh aggregates at l400°C and l600°C. The difference in aggregate size changes the spacing of the large inter aggregate voids but does not affect the fine intra-aggregate pores. The results are summarized in Figure 5. Clearly, the two different aggregate sizes do not densify to the same degree at either sintering temperature. The finer powders not only densify more rapidly during the initial stages, but also reach greater end point densities. These differences cannot simply be accounted for by increased intrusion distance, because densification has essentially stopped for both size fractions after 4 hours, at which point the densities are significantly different. Furthermore, these densification results cannot be interpreted on the basis of surface area differences as both size powders have essentially the same surface area after calcination. Therefore, it is proposed that the finer aggregates must be much more influenced by aggregate rearrangement processes and the solution-precipitation can more completely reduce the size of the interaggregate voids.

The further investigation of the effect of aggregate size involved the sintering at l400°C of a nominal 10~m air classified dolomite with a 1% Fe203 addition. Structurally, the compact consists of approximately Z ~m interaggregate voids which are similar in size to the intra-aggregate porosity. That densities of 95% to 99.5% were achieved at l400°C (Figure 5) after ~ hour and 4 hours, respectively, with 10 ~m aggregates clearly illustrates the technical potential for reactive phase calsintering.

100

~ !!..

>-I-(ii

7 z w 0

0 w 1°4 Fe203 0:: w 0 1600oe, -325, +400 mesh l- • 1600oe, -100, +270 mesh z (J) 0 1400oe, -325, + 400 mesh

• 1400o e, -100, +270 mesh 6 1400o e, ..... IOfLm

3 "0" 1.0 2.0 3.0 4.0 TIME (Hrs)

Figure 5. The effect of particle size on the sintering kinetics at two different sintering temperatures.


MICROSTRUCTURE

Densification by the aforementioned process initially involves a structure that possesses only interaggregate voids; however, during calcination, intra-aggregate porosity is formed with presumably little or no changes in the interaggregate void structure. Just prior to liquid phase formation, the "open" structure consists of one of an assemblage of coarse voids and fine pores. With further heating to the liquid formation temperature, the intra-aggregate pore structure rapidly begins to densify by capillary intrusion of the liquid phase into the aggregate and the occurrence of solution precipitation processes. Initial reduction of the interaggregate voids occurs almost simultaneously because of the multiple particle nature of the interaggregate contacts. After the preceding has occurred, only isolated inter aggregate voids remain.

The later stages of densification are illustrated in the sequence in Figure 6. The microstructure consists of a continuous CaO matrix (light color) surrounding individual MgO grains with large interspersed interaggregate voids. Surprisingly, there is no direct evidence that a liquid phase existed in these lower magnification photos which is in sharp contrast to the highly reflecting pockets of 2CaO'Fe203 usually observed in dolomite structures formed by traditional processing. Furthermore, because of the generally more uniform distribution of the liquid phase during singering there are no obvious relics of the original interaggregate boundaries.

At 85% of theoretical density the vestiges of the inter aggregate voids are still quite angular in shape, but there is no obvious intraaggregate porosity. These observations support the earlier proposition that the intra-aggregate porosity is eliminated first. With increased sintering it is observed that a spheriodization of the interaggregate porosity occurs and its shrinkage proceeds.

Figure 6. Representative microstructures at three different sintered densities for a -100,+270 mesh powder (a) 85%, (b) 93%, (c) 96%.


SUMMARY

It has been demonstrated that the presence of a reactive liquid during the calcination of an oxide precursor results in rapid densification kinetics and the attainment of high densities. The unique aspect of the process is the use of relatively large aggregates to form the ceramic. Clearly, the reactive nature of the precursor at the point of calcination coupled with the presence of a liquid phase results in efficient utilization of the reactive product of calcination. Although the nature of the intra-aggregate porosity is fundamental to calsintering, it is the interaggregate porosity which determines the degree of densification. This is particularly obvious when comparing the densification of lOO~m aggregates and lO~m aggregates, in that the 100~m aggregates densify to 82% density after 4 hours at l600°C while the lO~m aggregates densify to 95% density after 30 minutes at l400°C and nearly 100% after 4 hours at l400°C. It is the use of large particles for forming and the considerable enhancement of reactivity that makes reactive phase calsintering a commercially attractive process.

ACKNOWLEDGEMENTS

The authors thank the U.S. Bureau of Mines for their financial support of this study and Dr. M.L. Van Dreser of Kaiser Aluminum and Chemicals for providing the dolomite. The constructive comments of Dr. B.R. Patterson are also appreciated.

REFERENCES

1. A.C.D. Chaklader, "Reactive Hot Pressing: A New Ceramic Process," Nature, 206 (4), 392-3 (1965).

2. A.C.D. Chaklader and L.G. McKenzie, "Reactive Hot Pressing of Clays and Alumina," J. Am. Ceram. Soc., ~ (9), 477-483 (1966).

3. P.E.D. Morgan and E. Scala, "The Formation of Fully Dense Oxides by Pressure Calsintering of Hydroxides," in Sintering and Related Phenomena, G.C. Kuczynski, H. Hooten, and C. Gibbon, eds., Gordon and Breach, New York, pp. 861-892 (1967).

4. P.E.D. Morgan, "Superplasticity in Ceramics," in Ultrafine Grain Ceramics, J.J. Burke, N.L. Reed and V. Weiss, eds., Syracuse University Press, Syracuse, N.Y., pp. 251-271 (1970).

5. D.1. Matkin, W. Munro, T.M. Valentine, "The Fabrication of a-Alumina by Reactive Hot-Pressing," J. Mat. Sci., 6, 974-980 (1971). -

6. D.J. McVittie, "Advances in Dolomite Technology," Refractories, 37 (1), 2-6 (1961).

REACTIVE PHASE CALSINTERING OF DOLOMITE

7. K.H. Obst and W. Munchberg, "Technische Sinterdolomite, Mineralbestand, Textur and Verwendbarkeit," Tonind-Ztg., 91 (7), 280-285 (1967).

339

8. W.J. Huppmann, "Sintering in the Presence of Liquid Phase," in Sintering and Catalysis - Vol. 10, G.C. Kuczynski ed. Plenum Press, New York, N.Y., pp. 359-378 (1975).

9. W.D. Kingery, "Densification During Sintering in the Presence of a Liquid Phase. I - Theory," J. Appl. Physics, 30 (3), 301-306 (1959).

10. D.S. Buist, B. Jackson, I.M. Stephenson, W.F. Ford and J. White, "The Kinetics of Grain Growth in Two Phase (Solid-Liquid) Systems," Trans. Brit. Ceram. Soc., 64, 173-209 (1965).

A CONTRIBUTION TO THE STUDY OF CONSOLIDATION OF PRECIPITATION

STRENGTHENED MATERIALS

D. C. Stefanovic, I. P. Arsentjeva and M. M. Ristic

Institute of Technical Sciences of the Serbian Academy of Sciences and Arts Belgrade 11000, YUGOSLAVIA

INTRODUCTION

From our previous investigations l - 4 , we have come to the conclusion that the consolidation of powder may have to be considered as a unique process. According to our results5 we can comprehend materials consolidation, i.e. sintering as a unique process in which the relative parameter of the system may be changed. These parameters, define the change in materials activity during the sintering and pressing processes5 and are presented schematically by the block diagram in Fig. 1.

Powder

N P

5 p

A P

Pe 11 e t NO 5intered sample

5. ,A. ,N. = f(P) I I I 50

5 ,A ,N = f(T,t) s s s

Fig. 1. A block diagram of the sintering process with the parameters which define the system during the particular stages of sintering.

In the block diagram S, A and N are the total surface energy of the system, the total surface area and the defect concentration respectively. While the indexes p, i and s refer to powder, a sample during pressing and a sample during sintering, respectively.

341

342 D. C. STEFANOVIC ET AL.

In this paper, the fundamental problems relating materials properties to the sintering process is considered for the case of the Ni-A1 203 system.

THE DEPENDENCE OF HARDNESS OF SINTERED MATERIALS ON DISPERSIVE POWDER PRESSING

The pressing process of dispersive powder can in fact be reduced to a more simple contact interaction of the dispersed material particles. According to our investigations, the pressing process can be divided into several stages. 2 Each of the stages is characterized by a particular change in the electronic structure of the particles in the pressed pellets. 5

The initial stage of the pressing process5 is characterized by s+d or s+d+f electron transfers. The relatively low green density of pellets in this initial stage causes a high effective pressure to be reached at contact points between particles. According to a previous analysis6 these pressures are sufficiently high to cause excitation of electrons in the subsurface region of the particles. 7 Due to s+d or s+d+f electron transfers, the surface layers of the metal particles will undergo structural changes which will result in alterations in their physical properties. In thin layers, in which pressures reach critical values to cause structural changes, pre-existing defects will be annihilated. This will result in an increase in the microhardness of the particle surface. The recovery of structure due to pressure has been proved experimentally.8 It was established that the surface layers in metals and compounds almost reach the structure of ideal crystals. The recovered surface structure will influence the sinking behavior.

Evidence that surface structural changes are important in sintering was obtained from experiments on the effect of pressure on the sintering behavior of the Ni-A1203 system. Fig. 2 shows the effect of pure Ni and Ni + 40% A1203 for three different size powders. It can be seen that the mechanical properties of the compacts are improved significantly by the presence of the A1203 when the applied pressure, for compaction, is sufficient to cause particle deformation. At pressures between 300 to 700 MPa, the hardness of the Ni-A1203 compacts is increased by more than a factor of three over that for the pure nickel metal. Within this pressure range, the porosity of the compacted pellets is about 40%.2

We established previously5,7 that the end of the first stage of the pressing process is characterized by ever increasing favorable packing of particles l.lnder conditions of a minimal friction

CONSOLIDATION OF PRECIPITATION STRENGTHENED MATERIALS

a 0

2 HB (kp/mm )

140

120

Ni

100

80

v:/ ~ 40

2 4 6

0 - d 1

~ - d 2

A - d A 3

0 2 4 6 8 P (10 8 Pa)

343

b

Fig. 2. The dependence of Brinell hardness on pressure for pressed and sintered powders of A) pure nickel and B) Ni + 40% Al203 , of different particle sizes (d).

force. When the most favorable particle packing is reached, particle redistribution ceases and deformation strain in the particles becomes apparent. Under the dynamical conditions of pres- 7 sure the porosity is reduced below a critical value of about 20% in some regions of the porous system. This occurs primarily in the regions where the particles are in contact.


From our experimental results on iron only small amounts of deformation are necessary to bring about the transition of localized electrons into higher energy states. This electron pressure causes atoms to diffuse with the result that densification will occur. Such a condition will predominate until a density of about 75% is reached at which time the following equation

1 - p - 0.675 - 0.75F = 0 0.9 + O.lF

(1)

will fulfill the condition of statistical homogeneity in the whole sample. Here P = Vp/V where Vp = pore volume and V is total pellet volume minus the porosity and

F = {l - (1 - 0) p}-l

where 0 is the pellet deformation. The excitation of electrons to higher energy states due to the applied pressure and the subsequent movement of atoms results in the generation of dislocations. The generation of dislocations becomes predominate when the relative density of the sample reaches about 75%. This appears to be independent of the type of materia17 and was proved experimentally by N. Andreeva et a1. 9

The pressures that correspond to the first stage of the pressing process are approximately equal to that to cause plastic flow in the material (i.e. 0 = 0.2). Thus the second stage of the processing process is characterized by plastic deformation of the particles and by a constant generation of dislocations. 10 The rate of generation of dislocation and their subsequent annihilation at particle surfaces will be determined by the particle size and shape. An irreversible process of dislocation generation is controlled by 1 the concentration of localized electrons bound to the dislocations. During the second or intermediate stage of the pressing process the contact between particles may keep on increasing due to plastic deformation of the particles brought about by the annihilation of dislocations at the contact surfaces. This results in an increased concentration of localized electrons in the surface regions of the particles. The increased electron localization is compensated for by a de10calization of plastic deformation within the particle volume. Such a compensation results in a reduced material activity during during the sintering process.

During sintering pre-existing dislocations in the compact are annihilated. Since the residual concentration of dislocations in the consolidated samples is proportional to the applied pressing pressure, the mechanical properties of the pure metal will degenerate with increased pressure. That this is indeed the case can be seen from Fig. 2 which shows that the hardness of pure nickel decreases from the initial pressing pressure of 400 MPa.

CONSOLIDATION OF PRECIPITATION STRENGTHENED MATERIALS 345

In contrast to the pure metals, the properties of a dispersive strengthened material will be influenced by somewhat different processes when the intermediate stage of pressing is reached. Dispersive particles tend to form at the ends of dislocations. This influences both the generation and annihilation of dislocations. Therefore the intermediate stage of pressing will be extended. Dispersive particles thus reduce the activity of the material during sintering. The high density of dislocations which remains in the vicinity of the particles after sintering results in an increase in the mechanical properties of the material as evidenced by the results shown in Fig. 2. There is little probability for dislocations to be annihilated during sintering because they are inhibited from motion by the nonmetallic particles. Therefore pressing pressures in the range 400-600 MPa results in an increase in mechanical properties with increased pressure.

Finally, it should be pointed out that at the end of the intermediate stage and at the beginning of the first stage of pressing, the growth of contacts between particles occurs which causes a reduction in the pressure between the contacts. This leads to a reduction in the material activity during the sintering process. 4 A recovered structure which contains no defects, will result in a higher hardness in the consolidated pure materials.

REFERENCES

1. D. C. Stefanovic and M. M. Ristic, A Contribution to Investigating the Consolidation Process Based on the Electronic Structure of Solids in "Sintering - New Developments," M. M. Ristic, ed., Elsevier Scientific Publ. Company, AmsterdamOxford-New York (1979).

2. D. C. Stefanovi6, S. Pejovic, V. Petrovic and M. M. Ristic~ Shrinkage Anisotropy Taking Place During Sirttering Considered from the Standpoint of Electronic Theory, in "Sintering Processes," G. C. Kuczynski, ed., Plenum Press, New York and London (1980).

3. D. C. Stefanovic, V. Petrovic and M. M. Ristic, Contribution to Electronic Theory of Consolidation Process, in "Modern Development in Powder Metallurgy," H. H. Hausner, ed., Amer. Powder Met. Inst., Princeton (1981).

4. D. Vikicevic and D. C. Stefanovic, The Investigation of Consolidation Process of the Dispersion Strengthened copper, Sci. of Sintering, 14:109 (1982).

5. M. M. Ristie, D. C. Stefanovie, M. Susie, L. F. Pryadko and I. P. Arsentjeva, The Principles of the Superhard Material Production by the Consolidation Method, presented at the International Seminar "Superhard Materials," Kiev (1981).


6. D. C. Stefanovic and M. M. Ristic, The Consolidation of Dis~ persive Powders During the Pressing Process, Powder Techn., 30:37 (1981).

7. D. C. Stefanovic and M. M. Ristic, The Effects of Pressing Process on Sintering Process and Final Compact Properties, presented at the 5th International Round Table Meeting on Sintering, Portoroz (1981).

8. G. V. Samsonov, V. I. Kovtun and G. A. Bovkun, Poroshkovaya Metallurgiya, 124:87 (1973) (in Russian).

9. N. V. Andreeva and all, Poroshkovaya Metallurgiya, 150:32 (1975). 10. Ya.I. Dehtyar, Electronic Structure of Defects in Metals, in

"Metally, Elektrony, Reshetka," Naukova dumka, Kiev (1975) (in Russian).

11. B. A. Hatt and J. A. Roberts, Acta Met., 8:575 (1960). 12. J. S. Paprocki and S. E. Hodge, The Compaction of Powder by

Isostatic Pressure, in "Mechanical Behavior of Materials under Pressure," H. D. Pugh, ed., EPCL, Amsterdam-Landon-New York (1970).

INDEX

Additives, 107 Adsorption, 137, 226, 230 Agglomerate, 273 Annealing, 271 Atmospheres, 121

hydrogen, 223 oxygen, 223

Atomic volume, 28, 40

B.E.T., 256 Boron, 109

Cadmium oxide, 160, 293 Calcination, 331 Calsintering, 329 Carbon, 109 Carbon monoxide, 126 Carbide, 109 Catalysts, 181, 224

bimetallic, 235 metal loading, 235 platinum metal, 223 supported metal, 199, 223 thick film, 20

Ceramics, U5 Characterization, 138 Coarsening, 3, 12, 129 Cobalt, 192 Consolidation, 341 Computer

code, 246 method, 38 program, 46 simulation, 35, 40

Connectivity, 49, 50 Copper, 107

Density, 41, 99 Densification, 27, 32, 50, 73, 92,

116, 250, 268, 281, 287 Diamond, 175 Diamond - Titanium, 171 Diffusion

boundary, 13, 63 flux, 29 grain boundary, 30, 32, 41,

92, 247, 262 surface, 35, 63, 93, 140,

154, 245, 248 volume, 32, 73, 119, 154, 245

Diffusivity, 13 Dihedral angle, 82 Dilatometry, 1, 4, 15, 18, 95,

256 Dislocation, 214, 258 Densification, 72, 103, 260

kinetics, 1 Dolomite, 329

Fourier coefficients, 185 Fracture

transgranular, 11 surface, 7, 65, 139, 270 free energy, 124

Geometric ratio, 51 Grain boundaries, 26, 36

artificial, 87 Grain growth, 53, 72, 92, 93, 99,

128, 129, 154 Grain size, 65, 71, 95, 99 Green compacts, 3 Green density, 6, 89, 90, 96, 159

347

348

Greskovich-Lay mechanism, 131

Halides, 109 Heating rate, 42, 245 Herring's scaling law, 45, 63 Hot pressing, 71 Hydrogen, 226, 234

Impurities, 122 Interfacial energy, 3 Intermeta11ic phase, 108 Iron, 103 Isodensity, 270

Lattice parameter, 174, 177

Mass transport, 260 Material transport, 35 Mercury porosimetry, 96, 137,

146 Metal oxide, 208 Microstructure, 339 Microstructure development, 145,

147 Microstructural evolution, 159 Mu1ticomponent systems, 123

Network channel, 49

Newton-Raphson method, 38 Nickel, 108

Ostwald ripening, 81, 86, 129, 150, 162, 163, 199

Oxygen pressure, 137 Oxygen treatment, 228

Particle coarsening, 122 Particle radius, 166 Particle size, 12, 65, 336 Particle size

distribution, 68, 16 ratio, 68

Phase transformation, 258 Phosphorus, 108 Pore

coarsening, 81 diameter, 97, 141 volume, 51, 96

Porosity, 13, 24, 96

Powder A1203 , 3, 92, 94, 245 Alcoa, 64 alumina, 253, 265 amorphous, 1 BaTi03 , 281 copper, 33 CdO, 159, 294 chromium, 318 MgO, 92, 94, 281 manganese, 317, 320 NaC1, 194

INDEX

monodispersed, 1, 18, 19 nickel, 317 palladium, 317 Sn02' 159 Sumitomo, 98 synthesis, 254 Ti02 , 2, 245 urania

Pressure, 172 Process

interface controlled, 72

Redispersion, 223, 227

Scaling law, 3, 44, 65, 73 Serial section, 50 Shape factor, 73 Shrinkage, 7, 44, 101, 140, 147,

244, 249, 256, 297, 310 Sintering, 254, 333

activated, 317 activation energy, 12, 14,

15, 17, 18 catalysts, 181 channel network, 56 constant heating rate, 15 diamond, 171 driving force, 71 enhanced, 103 enhancers, III final stage, 7, 49, 145, 152 force, 51, 58 initial stage, 7, 35, 116,

253 intermediate stage, 6, 7, 13,

14, 17, 91 iron, 106 isothermal, 5, 40, 295

INDEX

Sintering (continued) kinetics, 2, 12, 19 liquid phase, 103, 295 LiF, 281 map, 251 mechanisms, 39, 237 microstructure, 23 models, 1, 116 nickel, 189 non-isothermal, 294 powder, 63 reactive, 171 second stage, 50 strain, 272 temperature, 33, 43 third stage, 50, 126 time, 42 topological model, 49, 57 ultra-rapid, 245

Shock loaded, 267 Solid solutions, 123 Stereological, 33 Structure

evolution, 25 Sulfur, 108 Surface area measurement, 137,

255 Surface free energy, 13, 37, 43 Surface tension, 55

Tammann temperature, 214 Thermal treatment, 226 Thin film, 206 Tin, 108

oxide, 163 Titanium, 109 Titanium carbide, 172, 303 Transformation

topological, 53 Transmission Electron Microscopy,

227

Vacancy annihilation, 26, 27, 28 concentration, 31

Vacancies, 23, 30 Vapor transport, 115, 116, 122,

129, 145, 147, 160

Water vapor, 137 Wetting, 17

349

X-ray diffraction, 172, 181, 232, 255, 256, 281

X-ray spectra, 177

Zener limit, 90

materials science research: volume 16 sintering and heterogeneous catalysis

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