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SOME FUNDAMENTAL ASPECTS CONCERNING PROCESSING OF TI(C,N)-BASED CERMETS ZHENG QI A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOHPY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2004

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Page 1: SOME FUNDAMENTAL ASPECTS CONCERNING PROCESSING OF … · Sintering 20 4.1 Fundamentals of Gibbs Free Energy Functions 20 4.1.1 Partial Gibbs Energies of the solutes in a Solid Solution

SOME FUNDAMENTAL ASPECTS CONCERNING

PROCESSING OF TI(C,N)-BASED CERMETS

ZHENG QI

A THESIS SUBMITTED

FOR THE DEGREE OF DOCTOR OF PHILOSOHPY

DEPARTMENT OF MECHANICAL ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2004

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Acknowledgment

I would like to thank my supervisor, A./Prof. Lim Leong Chew, for his

guidance throughout this project. I would also like to thank the non-academic staff in

Materials Science Laboratory for their assistance. Finally, I would like to thank all

the members in my family for their help and encouragement.

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Table of Contents

Acknowledgment i

Table of Contents ii

Summary vii

List of Figures ix

List of Tables xii

Chapter 1 Introduction 1

Chapter 2 Literature Review 3

2.1 Processing of Cermets 3

2.2 Events Occurring during Liquid Phase Sintering of Cermets 5

2.2.1 Solid State Reactions during Heating 5

2.2.2 Densification via Particle Rearrangement

(1st Stage of Sintering) 5

2.2.3 Densification via Dissolution-Reprecipitation

(2nd Stage of Sintering) 6

2.2.4 Solid State Densification Processes

(3rd Stage of Sintering) 7

2.2.5 Solute Precipitation during Cooling 8

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2.3 Evolution of Core-Rim Structure in Cermets 8

2.3.1 Core-Rim Structure in Cermets 8

2.3.2 Mechanisms of Rim Growth 10

2.3.3 Kinetics of Particle (or Rim) Growth 11

(a) Particle (or Rim) Growth via Ostwald Ripening 11

(b) Particle (or Rim) Growth via Solute Precipitation

during Cooling 12

2.4 A Note on Wetting in Cermet Systems 13

Chapter 3 Statement of Present Work 17

3.1 Unsolved Issues 17

3.2 Objectives 18

3.3 Organization of Remaining Chapters 19

Chapter 4 Thermodynamics of Cermet Processing Prior to Liquid Phase

Sintering 20

4.1 Fundamentals of Gibbs Free Energy Functions 20

4.1.1 Partial Gibbs Energies of the solutes in a Solid Solution 20

4.1.2 Standard Free Energy of Formation of an Interstitial Phase 20

4.1.3 Gibbs Free Energy of Reactions Involving Gaseous Phases 21

4.2 Relevant Gibbs Energies in TiC-Mo2C-Ni Cermet Systems 23

4.2.1 Ni-Ti and Ni-Mo Solid Solutions 23

4.2.2 Ti(C,N), (Ti,Mo)C and (Ti, Mo)(C,N) Solid Solutions 25

4.3 Reactions in TiC-based Cermets 25

4.3.1 Oxidation and Dissolution Reactions 28

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4.3.2 Solute Moderation via Rim Formation 31

4.3.3 Reduction Reactions 33

(a) Reduction of TiO2 in TiC-Ni Systems 34

(b) Reduction of TiO2 in TiC-Mo2C-Ni Systems 34

(c) Effect of Free Carbon Addition 36

4.4 Extension to Ti(C,N)-based Cermet Systems 36

4.5 Discussion 37

4.5.1 Role of Mo2C in Cermet Processing 37

4.5.2 Effect of Process Variables 39

4.6 Summary 40

Chapter 5 Wettability and Spreading of Liquid Binder Phase

in Powder Compacts 42

5.1 Background 42

5.2 Theoretical Consideration 45

5.3 Application to Ti(C,N)-based Cermet Processing 51

5.3.1 Experimental Details 51

5.3.2 Results and Discussion 57

5.4 Conclusion 62

Chapter 6 Rim Growth in Cermets during Liquid Phase Sintering 64

6.1 Introduction 64

6.2 Conceptual Analysis of Rim Formation Mechanisms during

Liquid Phase Sintering of Cermets 64

6.2.1 Inner Rim Formation via Solid State Reactions 64

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6.2.2 Outer Rim Formation via Ostwald Ripening 65

6.2.3 Outer Rim Formation via Precipitation from

Solution during Cooling 67

6.3 Geometric Analysis of Core-Rim Structure 71

6.3.1 Geometric Consideration of Plane Sectioning 71

6.3.2 Construction of f Distribution Curves and

their Significance 74

6.3.3 Application to Rim Growth during

Liquid Phase Sintering 77

(a) Rim Growth via Ostwald Ripening during

Sintering 78

(b) Rim Growth via Solute Precipitation during

Cooling 80

6.4 Experimental f Distribution Curves 82

6.5 Discussion 86

6.6 Summary 89

Chapter 7 Conclusions 90

Chapter 8 Recommendations for Future Work 94

References 96

Appendix I Coating Mo2C on Ti(C,N) Particles 102

I.1 Introduction 102

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I.2 Conceptual Considerations 102

I.3 Estimation of Amount of Mo2C Coating 103

I.4 Experimental Verification 104

Appendix II Derivation of Equation (6.5) 109

Appendix III Derivation of Equation (6.6) 113

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Summary

Theoretical considerations of the various events occurring during cermet

processing are attempted in this work, including the events occurring during heating

of the powder compact, spreading of the liquid binder phase and aspects concerning

rim growth during the liquid phase sintering stage and on subsequent cooling.

Experiments were performed to attest the predictions.

The results show that Mo2C or pure Mo and free carbon play several important

roles in cermet processing. Via a series of dissolution, rim formation and reduction

reactions, solid state processes help keep the hard phase free of oxides and the system

of residual oxygen during heating so that complete wetting can be achieved during the

subsequent liquid phase sintering stage. Furthermore, the processes help moderate the

content of Ti in the Ni binder phase, thus preventing the formation of intermetallic

phases in the system.

The conditions for the spreading of the liquid binder phase in a powder

compact are evaluated theoretically. The present results show that spreading occurs

when the radius ratio of the liquid binder sphere to the solid hard ones is above a

critical value; the latter in turn is a function of the contact angle and the local packing

factor. Using the model, the contact angles were obtained experimentally, being about

65° and 10° for the Ti(C,N)-Ni and Ti(C,N)-Mo2C-Ni system, respectively.

An analysis on rim growth during liquid phase sintering of cermets was also

conducted. The result shows that the rim thickness is relatively independent of the

grain size when rim growth is dominated by Ostwald ripening during the liquid phase

sintering stage, whereas it increases with initial grain size when solute precipitation

during subsequent cooling is the controlling mechanism. With the above finding, a

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geometric analysis was described for the identification of dominant rim growth

mechanism via the plane-sectioning technique. Experiments with Ti(C,N) based

cermets show that rim growth is dominated by the solute precipitation during cooling

at low sintering temperatures (i.e. 1400-1480°C) and by Ostwald ripening at

sufficiently high sintering temperatures (i.e. C°≥ 1560 ). An activation energy of 34 ±

6 kJ/mol was obtained for the dissolution of the hard solid in Ti(C,N)-Mo2C-Ni

system.

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List of Figures

Chapter 2

Figure 2.1 A back-scattered electron (BSE) micrograph showing the core-rim structure in typical Ti(C,N)-Mo2C-Ni cermets. The cores of darker contrast are surrounded by the rim of grayish contrast. The bright matrix phase is the Ni binder. The scattered black patches and spots are the pores. 9

Figure 2.2 When the oxygen partial pressure was 10-16 atm, Ni lost its drop shape and the carbide grains rose to the melt. As a result, it was difficult to measure the contact angle accurately. This was not the case of the oxygen partial pressure at 10-14 atm. (After Ref. [10]) 16

Chapter 4

Figure 4.1 Various oxygen scavenging reactions in TiC-Ni-Mo2C cermets during heating to the liquid phase sintering temperature. 29

Figure 4.2 Various mixed carbide rim formation reactions after residual oxygen in the system has been depleted. 32

Figure 4.3 TiO2 reduction reactions with and without Mo2C addition in TiC-based cermets. 35

Chapter 5

Figure 5.1 Geometry of a sessile drop test. Point O indicates a three-phase contact point. 43

Figure 5.2 A liquid sphere embedded in a matrix of solid spheres. The dotted circle, the solid dark circle and smaller white circles represent the boundary of the compact, the binder sphere and hard phase spheres, respectively. 47

Figure 5.3 The liquid binder filling up the voids in between the solid spheres after the spreading. 48

Figure 5.4 Conditions for spreading as a function of the contact angle θ for powder compacts of different packing factors f. Note that above the curves, the liquid sphere is unstable and will spread in the powder compact. The reverse is true below the curves. 50

Figure 5.5 As-received powders: (a) Ti(C0.7,N0.3) powder (b) Mo2C powder, and (c) Ni powder. 53

Figure 5.6 Particle size distributions of (a) Ti(C0.7,N0.3), (b) Mo2C and (c) Ni powders after ball-milling. Results of two runs are shown in (b) and (c). 54

Figure 5.7 The dewaxing cycle used. 56 Figure 5.8 Heat flow as a function of temperature for (a) Ti(C0.7,N0.3)-Ni and

(b) Ti(C0.7,N0.3)-Mo2C-Ni powder mixtures. 56

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Figure 5.9 The sintering cycle used. 56 Figure 5.10 Typical micrographs showing (a) spreading and (b) non-spreading

states in the Ti(C0.7,N0.3)-Ni system studied. 58 Figure 5.11 Typical micrographs showing (a) spreading and (b) non-spreading

states in the Ti(C0.7,N0.3)-Mo2C-Ni system studied. 59 Figure 5.12 Experimental data pertaining to non-spreading cases expressed in

terms of the apparent ),( NCTiNi rr and local packing factor f for the Ti(C0.7,N0.3)-Ni system. Data with the largest ),( NCTiNi rr values for a given f can be taken as the ‘critical radius ratio’ for that f value. The best fit curve is that of equation (5.11) with °= 65θ . 60

Figure 5.13 Experimental data pertaining to non-spreading cases expressed in terms of the apparent ),( NCTiNi rr and local packing factor f for the Ti(C0.7,N0.3)-Mo2C-Ni system. Data with the largest ),( NCTiNi rr values for a given f can be taken as the ‘critical radius ratio’ for that f value. The best fit curve is that of equation (5.11) with °= 10θ . 61

Chapter 6

Figure 6.1 Rim thickness (nt

δ ) as a function of initial radius of grains (ot

R ) for various sintering conditions corresponding to different final mean grain radii ( ntR ). All

ntδ ,

otR and ntR are normalized with respected to the

initial mean particle size ( otR ). 68 Figure 6.2 (a) Schematic cross-section of a hard phase grain with a concentric

core-rim structure and (b) the plain view of the ith cross-section. 73 Figure 6.3 f distribution curves for different δo values with Ro =0.6 µm,

∆z = 0.005 µm and N = 120. 75 Figure 6.4 f distribution curves for different N values hence hard phase grains

sizes for the case when the rim growth is controlled by Ostwald ripening during the liquid phase sintering stage (∆z = 0.005 µm; δo = 0.15 µm). Similar results are obtained for other δo values. 79

Figure 6.5 f distribution curves for different N values hence hard phase grain sizes for the case when the rim growth is controlled by solute precipitation during the cooling stage (∆z = 0.005 µm; fo = 0.10). Similar results are obtained for other fo values. 81

Figure 6.6 f distribution curves for Ti(C,N) grains of different radius groups in compacts sintered at different temperatures (a) 1400°C, (b) 1440°C, (c) 1480°C, (d) 1520°C and (e) 1560°C. iR is the apparent hard phase grain radius as measured from the SEM micrograph. 85

Figure 6.7 Rim growth curve for Ti(C,N)-Mo2C-Ni system at low sintering temperatures (1400°C-1480°C). ir and iR are, respectively, the means of apparent core and grain radii of all Ti(C,N) grains determined from the SEM micrographs of the sintered samples. 88

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Appendices

Figure I.1 Time-temperature cycle used for the pyrolysis reaction process. 105 Figure I.2 Time-temperature cycle used for the two-stage reduction process. 105 Figure I.3 XRD pattern of Ti(C0.7,N0.3) powder after the pyrolysis reaction. 107 Figure I.4 XRD pattern of Ti(C0.7,N0.3) powder after the two-stage conversion

treatment. 107 Figure II.1 A schematic showing smaller shrinking grains of radius Ri, distributed

in the form of a spherical cage of radius L with the growing grain located at its center. The dotted grains are hypothetical grains which may not exist in practice but are shown to illustrate the pseudo-spherical symmetry nature of the problem. r is the radial distance from the centre of the embedded growing grain in the middle. 110

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List of Tables

Chapter 4

Table 4.1 Gibbs energies of solid solutions and pure substances for KTK 15731173 ≤≤ . 24

Table 4.2 L-parameters for Ti(C,N), (Ti,Mo)C and (Ti,Mo)(C,N) reported by various researchers. 26

Table 4.3 Possible oxidation reactions of TiC and Mo2C and related reactions in the presence of residual oxygen (taking

( ) ( ) ( ) atmPPP COCOO510

22

−≈≈≈ ). 27

Chapter 6

Table 6.1 Values of fp and fp/fo obtained from Figure 6.3 (∆z = 0.005 µm; Ro = 0.6 µm; N = 120). 76

Appendices

Table I.1 Example calculation of the amount of Mo2C coating produced by the two-stage conversion treatment. 108

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Chapter 1

Introduction

The word “cermets” is originated from a mixture of the two words, “ceramics”

and “metals”. In 1929, cermets made their commercial debut in Germany, which used

TiC as the hard phase and pure Ni as the binder. However, the performance of the

earlier cermets was disappointing because they were too brittle for machining. In

1956, Humenik and Parikh [1] reported that by using TiC particles as the hard phase

and solid solution of Ni-Mo as the binder, a cermet with excellent hardness and

reasonable toughness could be produced. In 1959, a TiC-Mo-Ni cermet suitable for

machining was announced in USA.

Compared with high-speed steels and cemented carbides, cermets are more

wear-resistant and find niche applications in high-speed finishing and milling

operations [2]. In cermet processing, the green compact is made up of a mixture of

powders, which generally are TiC/Ti(C,N), Mo/Mo2C and Ni. The added Mo/Mo2C

powder helps promote wetting between the liquid binder phase and TiC or Ti(C,N)

particles at liquid phase sintering temperatures. After liquid phase sintering, fine hard

ceramic grains are embedded in a tough metallic alloy binder phase. Also evident in

typical cermets is the core-rim structure (see, for example, Figure 2.1). The core is

thought to be the remnant of undissolved TiC or Ti(C,N) hard phase and the rim is

(Ti,Mo)C or (Ti,Mo)(C,N) solid solution, which grows epitaxially on the core during

sintering. Sometimes the rim structure could also be divided into inner and outer rims

according to the different element contents and forming mechanisms.

Although cermets are used extensively in metal cutting industry, research on

cermets has been largely carried out on a trial-and-error basis. For example, although

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experimental results showed that Mo/Mo2C helps promote wetting, the reason for

such and whether or not this is related to the rim formation remains not well

understood.

This thesis work aims at performing a systematic study on the various

fundamental aspects concerning processing of cermets, including the thermodynamics

of the various reactions occurring during heating of the compact, the spreading of the

liquid binder in the compact at the beginning of the sintering stage and the growth of

rims during the liquid phase sintering and subsequent cooling stage.

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Chapter 2

Literature Review

2.1 Processing of Cermets

Cermet cutting tools are manufactured in the form of small, replaceable

pieces, called inserts. To make turning, milling and drilling of metals more effective

and economical, there is a wide range of cermet inserts with different shapes and

grades. Some cermets are coated with hard and wear-resistant materials to improve

their metal cutting performance further.

The processing of cermets consists of the following steps: powder preparation,

powder mixing, ball-milling, compaction, dewaxing, liquid phase sintering and final

dressing. To obtain cermet inserts with desired mechanical properties, each

processing step should be properly controlled.

Today’s cermets consist of TiC, TiC-TiN or Ti(C,N) particles as the main hard

phase, with minor addition of other carbides, nitrides or carbonitrides of elements

from groups IVb (Zr, Hf), Vb (V, Nb, Ta) or VIb (Cr, Mo, W) of the Periodic Table

for enhanced hardness and/or fracture toughness. The binder phase is generally pure

Ni or Ni-Co alloy. It is important that the amount of the binder should be sufficient to

achieve full densification during the liquid phase sintering stage so as to produce

cermets of good machining characteristics. However, too high an amount of binder

would lower the hardness and wear resistance of the resultant cermets.

In addition to the hard phases and the metallic binder, Mo or Mo2C powder is

commonly added for wetting improvement purposes [1]. Lubricant, such as

carbowax, is also a crucial ingredient in cermet processing, although it does not

participate in the final microstructure of cermets [3,4]. The amount of lubricant

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should be appropriate to improve the compaction and handling characteristics of the

powder mixture. With too low lubricant content, the green compacts are fragile,

which tend to chip and/or break up easily during handling. With too high an amount

of lubricant, the compacts are too damp to hold their shape during handling.

After mixing and ball-milling, the powder mixture is compacted to the desired

shape. Then, the compacts are given a dewaxing process in which they undergo a

heating cycle to burn off the organic lubricant. After dewaxing, the compacts are

heated to sufficiently high temperatures to effect liquid phase sintering, during which

full density is generally attained [5,6]. After liquid phase sintering, the hard phase

grains form a rigid skeleton embedded in the continuous binder phase.

Sintering temperature plays an important role in cermet processing. A high

sintering temperature is preferred for improved wetting and fast densification [7,8].

This is because the solubility of the solutes, such as Mo and Ti, in the liquid binder

increases with temperature, which in turn aids in the wetting between the liquid binder

phase and solid hard phase grains. Besides, the liquid binder is less viscous and mass

transfer via diffusion is faster at higher sintering temperatures. However, too high a

sintering temperature results in a coarse microstructure of the cermets produced,

which is detrimental to the mechanical properties [9].

Sintering time also plays an equally important role. Too short sintering time

leads to incomplete sintering and densification, while too long sintering time

promotes grain and microstructural coarsening [9]. Ideally, the sintering time should

be sufficiently long to enable complete densification during the liquid phase sintering

stage with minimum grain coarsening.

A relatively high heating rate is generally preferred during cermet processing.

However, the temperature difference between the surface and interior part of the

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compact should not be too severe during both heating and cooling. Otherwise, the

high thermal stresses and associated circumferential shrinkage could produce defects

or even cracks in the sintered compact. The rate of heating and/or cooling should

therefore be controlled to minimise microstructural defects and to prevent crack

formation.

The control of sintering atmosphere is also crucial in cermet processing.

Residual oxygen has been reported to adversely affect the wetting of cermet systems

[10], which in turn produces cermets of inferior mechanical properties. We shall

discuss this in more details in Section 2.4.

2.2 Events Occurring during Liquid Phase Sintering of Cermets

2.2.1 Solid State Reactions during Heating

During heating to sufficiently high but below the liquid phase sintering

temperature, solid state sintering occurs. Also occurring is the dissolution of various

elements in cermets, such as Ti and Mo, etc., into the binder phase via solid state

processes.

Upon reaching the liquid phase sintering temperature, the binder melts. With

the availability of the liquid phase, the following processes take place simultaneously

to bring about the densification of the compact.

2.2.2 Densification via Grain Rearrangement (1st Stage of Sintering)

After the binder becomes liquid, the compact shrinks as the solid hard phase is

partially dissolved by the liquid binder. The wetting of the liquid binder onto the

surface of solid grains exerts a capillary force between solid grains. This causes the

grains to instantaneously rearrange and repack as the melt spreads and fills the pore

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space in between them. As a result, most pores and packing irregularities in the green

compact are eliminated and the center-to-center separation between the grains are

reduced, giving rise to significant densification [9].

Several requirements should be met to ensure substantial densification via

grain rearrangement [11,12]. Firstly, the quantity of the liquid binder phase should be

sufficient. Secondly, wetting should be complete to ensure good atomic bonding

between the resultant hard phase and the metallic binder phase. Thirdly, the surface

of grains should be smooth to reduce the friction between them. And, lastly, the green

compact should be fairly homogeneous in microstructure such that it is free from

macroscopic voids.

With more and more pores eliminated via grain rearrangement, the viscosity of

the compact increases accordingly. As a result, the rate of densification via grain

rearrangement decreases continuously with time [7].

2.2.3 Densification via Dissolution-Reprecipitation (2nd Stage of Sintering)

Although densification via grain rearrangement dominates at the initial stage

of liquid phase sintering, with increasing time at temperature, the grain rearrangement

process slows down and dissolution-reprecipitation becomes the dominant process to

bring about further densification of the compact [13].

In most liquid phase sintering systems, the quantity of liquid is insufficient to

fill all void space via grain rearrangement. Further densification via other means is

thus required to help eliminate the voids left over from the first stage of sintering.

This can be achieved via the dissolution-reprecipitation process, during which the

grains are dissolved preferentially at the contact points and reprecipitate out in shape

to accommodate each other better. As a result, the existing void space is reduced, the

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center-to-center separation of grains is decreased and the density of the compact is

increased [7].

A well-known phenomenon accompanying the dissolution-reprecipitation

process is the progressive growth of larger grains at the expense of smaller ones, more

commonly referred to as Ostwald ripening in literature. The reason is that the

solubility of a grain varies inversely to its size. Thus, smaller grains tend to dissolve

more readily and hence the liquid surrounding them is richer in solute concentration

than the liquid surrounding larger grains. This difference in solute concentration

gives rise to a driving force for mass transport of solutes from small grains to larger

ones via diffusion through the liquid binder phase. As a result, larger grains grow at

the expense of smaller ones and the mean grain size increases with sintering time,

even though the volume fraction of the hard phase may remain relatively constant

during most part of the liquid phase sintering stage.

2.2.4 Solid State Densification Processes (3rd Stage of Sintering)

Near the completion of the liquid phase sintering stage, the pores are largely

eliminated (unless in cases where the pores are stabilized by trapped gases). The solid

grains have also sintered sufficiently together to form a rigid skeleton. When such

occurs, the rate of densification via dissolution-reprecipitation process slows down

significantly. At this stage, both grain growth and further densification may continue

via solid-state diffusion processes. As a result, the grains may coarsen further leading

to a coarse microstructure. In addition, residual pores may coalesce and enlarge

causing compact swelling. Prolonged sintering at high temperatures should thus be

avoided in order to produce cermets of a fine microstructure and superior mechanical

properties [11,14].

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2.2.5 Solute Precipitation during Cooling

During cooling, the solubility of solutes in the binder decreases with

temperature. As a result, the solutes would precipitate out from the liquid binder

phase on cooling to room condition [15].

In practical cermet processing, the green compact contains a high volume

fraction of the hard phase even at the end of the liquid phase sintering stage. These

hard phases provide the ready sites for the solutes to precipitate out from the liquid

binder phase, which in turn contributes to rim growth in the cermet. This is more

commonly referred to as secondary nucleation in literature.

Under the condition of extremely high cooling rates, nucleation of the hard

phase may occur from within the liquid binder phase, referred to as primary

nucleation in literature. However, such a nucleation mode is less common in practical

cermet processing due to the abundance of the hard phase present in the system at the

end of the liquid phase sintering stage.

2.3 Evolution of Core-Rim Structure in Cermets

2.3.1 Core-Rim Structure in Cermets

A typical micrograph of a cermet is shown in Figure 2.1. It is evident that

after liquid phase sintering, a unique core-rim microstructure evolved in cermets. The

microstructure of TiC-based cermets were studied by Humenik and Parikh [16] and

Suzuki et al. [17] and in TiC-TiN and Ti(C,N)-based cermets by Nishigaki et al. [18]

and Fukuhara et al. [19]. Doi [2] conducted an extensive study on the rim formation

in TiC and TiC-TiN–based cermets and noted that too thick a rim surrounding a core

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Figure 2.1 A back-scattered electron (BSE) micrograph showing the core-rim structure in typical Ti(C,N)-Mo2C-Ni cermets. The core of darker contrast is surrounded by the rim of grayish contrast. The bright matrix phase is the Ni binder. The scattered black patches and spots are the pores.

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would make cermet inserts susceptible to chipping and breakage. Therefore, to

achieve good mechanical properties, an understanding of rim growth kinetics during

sintering of cermets is essential so as cermets of optimum rim thickness could be

reproducibly manufactured.

2.3.2 Mechanisms of Rim Growth

Nighigaki and Doi [20] studied TiC-TiN based cermets and reported that

Mo2C started to dissolve in solid Ni and then re-precipitated out on TiC particles to

form (Ti,Mo)C rim even at 1173K. At T > 1273K, TiN was transferred into the

(Ti,Mo)C lattice, resulting in formation of the (Ti,Mo)(C,N) rim on TiC particles.

Their results showed that (Ti,Mo)(C,N) rim could be formed on hard phase particles

via solid state processes prior to the liquid phase sintering stage.

Gee et al. [21] investigated Ti(C,N)-based cermets and found that the

composition of (Ti,Mo)(C,N) rim was inhomogeneous. They noted that the rim was

composed of an inner rim and an outer rim, with the inner rim rich in elements of high

atomic numbers, such as Mo. They proposed that the inner and outer rims were

formed at different stages of liquid phase sintering.

Rolander [22] studied the TiC-TiN cermet system by means of the atom-probe

field ion microscopy. They noted that a thin inner rim was observed on some Ti(C,N)

particles even at 1573K, i.e. before Ni became liquid. Such inner rims were often

incomplete and only observed at the contact points between the hard phase particles

and Ni binder particles. At the liquid phase sintering temperature, e.g. 1703K, a

thicker outer rim was formed on every Ti(C,N) grain. They thus proposed that the

inner rim was grown epitaxially onto hard phase particle surfaces via solid state

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processes during heating, while the outer rim was formed via the dissolution-

reprecipitation process during the sintering stage.

During the sintering stage, a well-known phenomenon accompanying the

dissolution-reprecipitation process is the progressive growth of larger grains at the

expense of smaller ones, more commonly referred to as Ostwald ripening in literature

[7]. Researchers [23,24] studied TiC-based cermets and found that Ostwald ripening

was controlled by the diffusion of solutes (such as Mo) through liquid Ni or Co.

Hellsing [25] studied WC-Co cemented carbides by means of TEM and

APFIM. He found that during cooling from the sintering temperature to room

conditions, the solute W dissolved earlier in the Co binder precipitated out onto WC

grains. As a result, zones depleted of W were formed in the Co binder close to the

WC grains. The solute precipitation process should also occur in cermets. However,

little work has been reported on this aspect as of to-date.

2.3.3 Kinetics of Grain (or Rim) Growth

(a) Grain (or Rim) Growth via Ostwald Ripening

As described in Section 2.2.3, during liquid phase sintering, Ostwald ripening

causes large grains to grow at the expense of smaller ones. Lifshitz and Slyozov and

Wagner had provided a detailed theoretical description of the Ostwald ripening

phenomenon (often referred to as the LSW theory in literature). According to the

LSW theory, the grain growth kinetics follows the expression below:

Ktddnn=− 0 (2.1)

where d and 0d are the arithmetic mean grain radii at time t and time zero. n is the

rate exponent and K is the rate constant.

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The rate of grain (or rim) growth via the Ostwald ripening process may be

dominated by either of the two processes: diffusion through the liquid phase (i.e.

diffusion controlled) or by mass transfer across the interface (i.e. interface reaction

controlled). The rate exponent (n) is 3 for diffusion controlled grain growth and 2 for

interface reaction controlled grain growth [26].

Several researchers have likened the Ostwald ripening process to that of

crystal growth from a dilute solution [27,28]. In the latter, the crystal growth process

may be controlled either by interface reactions via the lateral spreading of atomic

layers or by solute diffusion across the solution. The former leads to faceted crystals

while the latter to spherical shaped crystals.

Equation (2.1) was derived for spherical grains dispersed in a very high

volume fraction of liquid. However, during liquid phase sintering, the volume

fraction of liquid binder is low. For example, during practical cermet sintering, the

volume fraction of Ni or Ni-Co is less than 25%. Therefore, the grain growth rate is

affected by the low volume fraction of the liquid and contacts between solid grains

[23,29].

(b) Grain (or Rim) Growth via Solute Precipitation during Cooling

During cooling from the sintering temperature to the room temperature, the

solubility of solutes in the liquid binder phase decreases with temperature. In the

process, the solutes would precipitate out from the binder onto existing grains,

contributing to grain (or rim) growth in cermets.

The amount of the transformed phase during holding at a lower temperature

has been investigated by the researchers [30]. The volume fraction of the transformed

phase (VV) is found to obey the well-known Avrami equation below:

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( )bV ktV −−= exp1 (2.2)

where t is the time at temperature. k and b are temperature dependent parameters

related to the nucleation and growth mechanisms of the new phase. b =3 for spherical

grains randomly distributed in the transforming phase [31]. The function k generally

follows the Arrhenius equation

−=

RTEAk exp (2.3)

where E is the activation energy for grain growth via the solute precipitation process.

A is pre-exponent factor and R the gas constant.

Although Equations (2.2) and (2.3) are valid for grain (or rim) growth via

solute precipitation at a given (but lower) temperature, in cermet processing, solute

precipitation is expected to occur during continued cooling from the sintering

temperature to room condition. In this case, the thickness of the rim so formed will be

determined by the amount of solute dissolved earlier in the liquid binder phase and

hence the sintering temperature employed. Little work has been reported on this

aspect as of to-date.

2.4 A Note on Wetting in Cermet Systems

Liquid phase sintering is a necessary process for cermet manufacturing. It was

reported [2] that complete wetting between the liquid binder and the solid hard grains

plays a major role in the development of desired cermet microstructures, which in turn

determine the resultant properties. Gurland and Norton [32] studied the WC-Co

system and reported that there existed a complete wetting of liquid Co on WC grains

at the sintering temperature. As a result, a thin continuous Co film was formed

around each WC grain with controlled WC grain growth even after prolonged

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sintering. A similar conclusion was made by Kingery [5] who pointed out that

complete wetting of solid grains by the liquid phase is essential for full densification

via liquid phase sintering.

Humenik and Parikh [1] noted that the wetting of liquid Ni on TiC grains was

incomplete in the TiC-Ni system. They tried different binary alloys and found that by

using Ni-Mo as the binder alloy, the resultant cermets exhibited improved mechanical

properties. From the microstructure, they noticed that the extent of grain coalescence

was reduced. By comparing with the observation made on WC-Co cemented

carbides, they deduced that addition of Mo to Ni must have increased the wettability

of the TiC-based cermet system, which in turn produced cermets of improved

hardness and impact resistance.

Later on, Parikh and Humenik [16] used the sessile-drop test to measure the

contact angles of the liquid binders (Ni and Ni-Mo) on a flat solid substrate of TiC.

They found that the contact angles at 1450°C of pure liquid Ni on solid TiC substrate

were 30° and 17° in 10-5mbar vacuum and in H2 atmosphere, respectively, while that

for liquid Ni-Mo on solid TiC substrate was 0°. Their experimental finding confirmed

that the addition of Mo to Ni binder helped improve wettability in TiC-based cermets.

Tahtinen and Tikkanen [10] studied the effect of residual oxygen content on

the wetting of liquid Ni droplet on solid TiC substrate. They observed that at 1400°C,

the contact angles were 12° and 42° at atmandPO1216 1010

2

−−= , respectively,

indicating that the increase of residual oxygen content in the hydrogen atmosphere

deteriorated the wettability of the TiC-Ni system. A similar phenomenon was also

reported by Barsoum and Ownby [33], who studied the wetting characteristics of

liquid Si on solid SiC, AlN and Si3N4 at different oxygen partial pressures.

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Using the auger electron spectroscopy technique, Froumin et al. [34]

investigated the surface oxidation of pure TiC compacts (starting powder size: ~2 µm,

purity: 99.5%) after heating them to 1600°C in a vacuum of 10-21 Pa or less in oxygen

partial pressure and reported oxygen coverage on the surface of the compact. Their

results showed that surface oxidation of TiC particles occurs even in ultra high

vacuum environments.

Tahtinen and Tikkanen [10] reported that at atmPO1610

2

−= , Ni not only

dissolved Ti and C, but also penetrated TiC grain boundaries. As a result, the melt no

longer maintained a lenticular shape and the carbide grains were dislodged and mixed

intimately with the melt, as shown in Figure 2.2. They pointed out that under the said

condition, the contact angle was very low and it was difficult to measure the contact

angle accurately. Aksay et al. [35] also noted this phenomenon. They attributed it to

dissolution reactions at the interface and inter-diffusion between the droplet and

substrate.

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Figure 2.2 When the oxygen partial pressure was 10-16 atm, melted Ni no longer

maintained a lenticular shape and the carbide grains were dislodged and mixed

intimately with the melt. As a result, it was difficult to measure the contact angle

accurately. This was not the case of the oxygen partial pressure at 10-14 atm. (After

Ref. [10])

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Chapter 3

Statement of Present Work

3.1 Unresolved Issues

It is evident from the works reviewed in Chapter 2 that by adding Mo2C/Mo to

the powder compact, TiC or Ti(C,N)-based cermets suitable for machining can be

produced. Earlier researches have also established that a core-rim microstructure

exists in such sintered cermets. It has also been reported that the oxygen partial

pressure affects the wetting of the liquid Ni on the surface of the existing TiC grains.

It is possible that during heating to the liquid phase sintering temperature, the oxide

might have been formed on the surface of TiC particles. Furthermore, by adding

Mo2C/Mo into the TiC-Ni system, earlier researchers observed that the rim would be

formed on the TiC particles even prior to the liquid phase sintering stage. The

questions as to whether all these phenomena are interrelated and how the addition of

Mo2C/Mo may affect the various phenomena described above remain to be answered

as of to-date.

Another relevant aspect is the desired degree of wetting between the TiC and

Ti(C,N) hard phases and the liquid binder phase for the production of cermets suitable

for machining. As described in Section 2.4, complete wetting is a prerequisite in

cermet processing. One widely used technique in assessing wettability is the sessile-

drop test, which measures the contact angle of a liquid droplet on a flat solid

substrate. However, it has been noted that the sessile-drop test is not accurate for the

measurements of low contact angles. One reason for this is the reactions occurring

between the materials under study including dissolution and diffusion. This is

especially so for the TiC-Ni and Ti(C,N)-Ni cermet systems, for which dissolution of

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Ti and/or C into both solid and liquid Ni occurs readily at sufficiently high

temperatures. Another reason is that the TiC or Ti(C,N) substrates used are hot-

pressed powder compacts, which contain fine pores for trapping the liquid droplet,

thereby changing the meniscus geometry of the system. Furthermore, although the

contact angle measurement via the sessile-drop test provides good information on the

wetting characteristics between the liquid binder and the solid substrate, whether or

not it adequately represents the spreading of the liquid binder phase in a powder

compact remains to be answered.

As mentioned in Chapter 2, it is undesirable to obtain too thick a rim. To

control the rim thickness in cermet processing, one should understand not only the rim

formation and but also the rim growth mechanisms. Although Ostwald ripening

during the sintering stage contributes to rim growth, so does solute precipitation

during the cooling stage. Prior to any quantitative description of the rim growth

phenomenon in cermet processing, it is important to establish the conditions under

which each of the two mechanisms dominates.

3.2 Objectives

The objectives of the present work are as follows.

(1) To understand better how the various phenomena reported by

earlier researchers during cermet processing. The focus is placed

on the effect of Mo2C addition and its role in oxide reduction,

solid state dissolution of Ti and Mo in Ni and rim formation

during the heating stage of the powder compact and how they are

linked together.

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(2) To understand better the condition for spreading of the liquid

binding phase in a powder compact and apply this to cermet

processing, and

(3) To understand better the mechanisms of rim growth in cermet

processing, notably, to establish the conditions under which rim

growth is dominated by either Ostwald ripening or solute

precipitation during the liquid phase sintering stage.

3.3 Organization of Remaining Chapters

The remaining part of the thesis is organized as follows: Chapter 4 provides a

theoretical analysis of the thermodynamics of the various reactions occurring during

the heating stage to the liquid phase sintering temperature, with an emphasis on the

effect of Mo2C/Mo addition on the wetting and rim formation phenomena in TiC- and

Ti(C,N)-based cermet processing.

In Chapter 5, the condition for spreading of the liquid binder phase in a

powder compact is evaluated. Also described is an experiment with Ti(C,N)-based

cermet system which is carried out to verify the theoretical finding.

The rim growth phenomena during liquid phase sintering and subsequent

cooling are investigated in Chapter 6. A geometrical analysis for the determination of

the true rim thickness from specimen cross-sections was first described. The

technique is used to determine the mechanisms and kinetics of rim growth in

Ti(C,N)-based cermets sintered at various temperatures.

Chapter 7 summaries and concludes the main findings of the present work

while Chapter 8 gives recommendations for future work.

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Chapter 4

Thermodynamics of Cermet Processing Prior to

Liquid Phase Sintering

4.1 Fundamentals of Gibbs Free Energy Functions

4.1.1 Partial Gibbs Energies of the Solutes in a Solid Solution

In a solid solution, the partial molar Gibbs energy of solute i in solvent j is

given by

[ ]iii aRTGG j ln0 += (4.1)

where 0iG is the standard molar Gibbs energy of pure i (at 1 atm) and ia is the activity

of i in the solid solution.

4.1.2 Standard Free Energy of Formation of an Interstitial Phase

Interstitial phases consist of the hydrides, carbides, nitrides and borides of the

transition metals. The metal atoms usually form a complete close-packed crystal

structure while the non-metal atoms enter into the interstitial sites of the structure.

Hillert and Staffansson [36] developed a regular solution model that was

extensively used to calculate the molar Gibbs free energy of these phases. In this

model, the phase is treated as consisting of two sublattices: one of which is

completely occupied by metal elements and the other is filled by interstitial non-metal

elements.

In a nonmagnetic quaternary system, the molar Gibbs energy of the phase

(M1,M2)a(X1,X2)c, in which M1 and M2 represent the metal elements on one sublattice

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and X1 and X2 are the non-metal elements on another, is given by Ref. [36]

mEideal

mXMXMXMXMXMXMXMXMm GTSGyyGyyGyyGyyG +−+++=2222121221211111 :

0:

0:

0:

0

(4.2)

where iMy or

jXy denotes the site fraction of the element Mi or Xj on its respective

lattice, ji XMG :

0 is the standard Gibbs energy of the state of reference for the

compound MiXj. The molar entropy of mixing in Equation (4.2), idealmS , is given by

Ref. [36]

22112211lnlnlnln XXXXMMMM

idealm ycyycyyayyayRS +++=−

(4.3)

where the symbols a and c denotes the fraction of sites in each sublattice. The excess

molar Gibbs energy in Equation (4.2), mEG , is also given by Ref. [36]

212212211211221221121121 ,:,::,:, XXMXXMXXMXXMXMMXMMXMMXMMmE LyyyLyyyLyyyLyyyG +++=

(4.4)

where 121 :, XMML ,

221 :, XMML , 211 ,: XXML and

212 ,: XXML are interaction parameters, in which

the comma and colon separate the elements on the same sublattice and different

sublattices, respectively. The L parameters are zero for an ideal solid solution.

4.1.3 Gibbs Free Energy of Reactions Involving Gaseous Phases

Consider the following reaction involving gaseous phases in which a moles of

solid A and b moles of gas B react and produce c moles of solid C and d moles of gas

D as follows:

[ ] ( ) [ ] ( )DdCcBbAa +→+ (4.5)

where the square brackets denote solid phases and the round parentheses denote

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gaseous phases, respectively. The free energy of reaction, RG∆ per mole of A, is

given by

[ ] ( ) [ ] ( )BADCR GabGG

adG

acG −−+=∆ (4.6)

The molar free energy of a solid or liquid is independent of the pressure, i.e.

0GG ≡ , where G0 is the free energy of the substance at 1 atm. For gaseous phases,

the molar free energy at pressure P atm is given by pRTGG ln0 += .

The free energy of reaction, RG∆ per mole of A for reaction (4.5), is thus given by

[ ] ( ) ( )( ) [ ] ( ) ( )( )BBADDCR pRTGabGpRTG

adG

acG lnln 0000 +−−++=∆

[ ] ( ) [ ] ( ) ( ) ( )BDBADC pRTabpRT

adG

abGG

adG

ac lnln0000 −+−−+=

( )

( )ab

ad

B

DR

p

pRTG ln0 +∆= (4.7)

where ( )Dp and ( )Bp are the partial pressures of the gases D (product) and B

(reactant), respectively. 0RG∆ , the standard free energy of reaction, is defined as

[ ] ( ) [ ] ( )00000BADCR G

abGG

adG

acG −−+=∆ (4.8)

When the reaction is irreversible and spontaneous, 0<∆ RG . Thus, the ratio

of the partial pressure of the gaseous product to that of the gaseous reactant should

satisfy

( )

( )

∆−<

RTG

p

p R

B

D

ab

ad

0

exp (4.9)

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4.2 Relevant Gibbs Energies in TiC-Mo2C-Ni Cermet Systems

4.2.1 Ni-Ti and Ni-Mo Solid Solutions

Ni-Ti-Mo ternary solid solution is of interest to the present work. However,

the activities of Ti and Mo in Ni-Ti-Mo solid solution are not available in literature.

In view of this, the partial molar Gibbs energies of Ti and Mo in Ni-Ti and Ni-Mo

binary solid solutions, respectively, will be derived from available literature instead,

which also serve to illustrate better the individual effects of Ti and Mo in cermet

processing.

Using the solid electrolyte galvanic cell technique, Chattopadhyay and

Kleykamp [37] determined the relative partial Gibbs energies of Ti at various Ti mole

fractions in Ni-Ti solid solution between 1100K and 1300K, while Koyama et al. [38]

measured the activities of Mo at different Mo mole fractions in Ni-Mo system

between 1183K and 1423K. Based on their results, the partial molar Gibbs energy of

Ti at the solubility limit in Ni-Ti solid solution, [ ]NiTiG (in kJ/mol. Ti) and that of Mo at

10.6 mol.% in Ni-Mo solid solution, [ ]NiMoG (in kJ/mol. Mo), as a function of

temperature from 1173K to 1573K, are derived and given in Table 4.1 [Equations

(A1) and (A2)]. This temperature range corresponds to typical heating stage of

cermet powder compacts prior to the formation of the liquid binder phase. The xTi and

xMo values quoted in Equations (A1) and (A2) were selected by reference to the

experimental conditions of Humenik and Parikh [1].

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Table 4.1 Gibbs energies of solid solutions and pure substances for KTK 15731173 ≤≤ .

[ ] [ ] ( )TxTTGG TiTiTi Ni ⋅×+×=−⋅−⋅×+= −−− 54250 108.81024.29.1241093.01095.6 TimolkJ ./ (A1)

[ ] [ ] ( )106.068.120235.00 =+⋅−= MoMoMo xTGG Ni

MomolkJ ./ (A2)

( ) ( ) ( ) yyyyRTGyyGG TiNTiCNCTi yy−−++−+=

−1ln1ln1 0

][0

][)],([ 1

),(./ 1 yy NCTimolkJ − (A3)

( ) ( ) ( ) xxxxRTGxxGG MoCTiCCMoTi xx−−++−+=

−1ln1ln1 0

][0

][]),[( 1

CMoTimolkJ xx ),.(/ 1− (A4)

( ) ( ) ( )( )( ) ( ) ( ) ( ) ( ) )1ln1ln1ln1ln11

110

][

0][

0][

0][],),[( 11

zzzzxxxxRTGzx

zGxGzxxzGG

MoN

MoCTiNTiCNCMoTi zzxx

−−++−−++−−+

−+−+=−−

),)(,.(/ 11 zzxx NCMoTimolkJ −− (A5)

[ ] [ ] [ ]13000 7505.7103.8 −− ⋅−−⋅×−+= TTGGG CMoMoC

MoCmolkJ ./ (A6)

[ ] [ ] ( ) 2053.85098531.05.0 0002

−⋅++= TGGG NMoMoN

MoNmolkJ ./ (A7)

[ ]13

250

1079269.29045.59285435.0

ln0529087.01014017.12

⋅×−−⋅+

⋅−⋅×−=

TT

TTTG CMo

CMomolkJ 2./ (A8)

[ ] ( ) [ ] [ ] ( )TxTGxGxG TiTiTiNiTiTiNiTiTi xx

⋅×+×=−⋅×++−= −−−−

54300 108.81024.23.2310411

TiTi xx TiNimolkJ −1./ (A9)

Note: See Ref. [39] for the standard molar Gibbs energies of other pure substances.

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4.2.2 Ti(C,N), (Ti,Mo)C and (Ti, Mo)(C,N) Solid Solutions

In carbides, nitrides and carbonitrides of B1-type structure, the metal atoms

form a complete close-packed crystal structure while the non-metal atoms enter into

the interstitial sites of the structure. The Gibbs energies of such solid solutions can be

evaluated using the regular solution model of Hillert and Staffansson described in

Section 4.1.2.

Jung et al. [40], Shim et al. [41] and Rudy [42] evaluated the Gibbs energies

of Ti(C,N), (Ti,Mo)C and (Ti,Mo)(C,N) solid solutions, respectively. From their

results, it may be concluded that such solid solutions behave similarly to ideal solid

solutions in that the excess Gibbs energy term is either negligible or much smaller

than the entropy term, as shown in Table 4.2. In the present work, the ideal solid

solution model will be used to evaluate the Gibbs energies of Ti(Cy,N1-y), (Tix,Mo1-

x)C and (Tix,Mo1-x)(Cz,N1-z) solid solutions (the subscript represents the site fraction

of an element in its sublattice), as shown in Equations (A3) to (A5) in Table 4.1.

4.3 Reactions in TiC-Based Cermets

Residual oxygen is present even in a high-vacuum environment, which causes

TiC, Mo2C (or Mo) and Ni to oxidize into their stable or metastable oxides, such as

TiO, TiO2, MoO2, MoO3, CO, CO2 and NiO. Among the possible oxide products,

TiO2 is the most stable, followed by MoO3 and CO2 [39]. However, as far as

oxidation of TiC and Mo2C is concerned, the likely reactions are those producing the

most energy gains. As shown in Table 4.3, in this regard, TiO/TiO2 and CO (instead

of CO2) are the most probable oxidation products of TiC (see footnote below

concerning MoO2). Note also that any TiO formed will be further oxidized to TiO2

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Table 4.2 L-parameters for Ti(C,N), (Ti,Mo)C and (Ti,Mo)(C,N) reported by various researchers.

Jung et al. [40]* Shim et al. [41]** Rudy [42]*

NCTiL ,: nil≈ ⁄ nil≈

NCMoL ,: ⁄ ⁄ nil≈

CMoTiL :, ⁄ T⋅− 027218.0845.32 nil≈

NMoTiL :, ⁄ ⁄ nil≈

* Deduced from their findings that Ti(C,N) (in Ref. [40]) and (Ti,Mo)(C,N) (in Ref. [42]) behave similarly to ideal solid solution.

** The excess Gibbs energy (kJ/mol. (Ti,Mo)C) obtained from the expression given is much smaller than the entropy. This agrees with the finding of Ref. [41].

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Table 4.3 Possible oxidation reactions of TiC and Mo2C and related reactions in the presence of residual oxygen (taking

( ) ( ) ( ) atmPPP COCOO510

22

−≈≈≈ ).

G∆ (kJ/mol. O2)

1173K 1573K

[ ] ( ) [ ] ( )COTiOOTiC +→+ 2 -475 -480 (B1)

[ ] ( ) [ ] ( )COTiOOTiC 32

232

232 +→+ -480 -447 (B2)

[ ] ( ) [ ]22 22 TiOOTiO →+ -491 -382 (B3)

[ ] ( ) [ ] ( )221

221

221 COTiOOTiC +→+ -422 -371 (B4)

[ ] ( ) [ ] ( )232

32

232 COTiOOTiC +→+ -400 -367 (B5)

[ ] ( ) [ ] ( )COMoOOCMo 52

254

2252 +→+ -296 -232 (B6)

[ ] ( ) [ ] ( )231

232

2231 COMoOOCMo +→+ -288 -217 (B7)

[ ] ( ) [ ] ( )COMoOOCMo 72

374

2272 +→+ -226 -165 (B8)

[ ] ( ) [ ] ( )241

321

2241 COMoOOCMo +→+ -229 -162 (B9)

( ) ( ) ( )22 22 COOCO →+ -249 -142 (B10)

[ ] ( ) [ ]322 22 MoOOMoO →+ -50 2 (B11)

Note: See Ref. [39] for the standard molar Gibbs energies of pure substances.

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28

due to the high energy gain associated with such a reaction. Similarly, CO may be

further oxidised to CO2 [reaction (B10) in Table 4.3]. However, as the latter

oxidation reaction produces much smaller energy gain, it is less likely to prevail when

limited oxygen is present.

4.3.1 Oxidation and Dissolution Reactions

As discussed above, in the presence of residual oxygen, TiC will be oxidized

via the following reactions during heating to the liquid phase sintering temperature [1]:

[ ] ( ) [ ] ( )COTiOOTiC32

32

32

22 +→+ (R1)

Here square brackets and round parentheses denote that the reactants and products are

in solid and gaseous states, respectively. The free energy of reaction (R1) at

( ) ( )510

2

−≈≈ COO PP atm [2] is plotted in Figure 4.1 over the temperature range of

interest.

Parallel to the above oxidation reaction, in the presence of solid Ni, the

following oxygen-assisted dissolution and mixed carbide rim formation reactions also

occur during heating to the liquid phase sintering temperature, i.e.

[ ] ( ) [ ] [ ] ( )COTiOTiC NiNi 222 2 +→+ (R2)

[ ] ( ) [ ] [ ] ( )COMoOCMo NiNi 242 22 +→+ (R3)

[1] The oxidation of Mo2C is ignored here, because the MoO2 formed is unstable and will react with TiC and/or Mo2C further to give Mo dissolving in Ni binder. This holds even if residual oxygen is present in the system. [2] This corresponds to a moderate vacuum condition (with a total system pressure ≈ 10-4 atm) for cermet processing. Should the vacuum level be improved, the free energy of the oxidation reaction (R1) becomes less negative. This means that reaction (R1) is still feasible but with less energy gain over the temperature range of interest. On the other hand, the free energies of the various oxygen-assisted dissolution and rim formation reactions (R2) to (R5) are more negative, meaning that they are preferred with improved vacuum environment.

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29

-800

-600

-400

-200

1173 1273 1373 1473 1573

Temperature (K)

Free

Ene

rgy

of R

eact

ion

(kJ/

mol

. O) [ ] ( ) [ ] [ ] ( )COTiOOTiCR Ni

32

32

32:1 22 +→+

[ ] ( ) [ ] [ ] ( )COTiOTiCR NiNi 222:2 2 +→+

[ ] ( ) [ ] [ ] ( )COMoOCMoR NiNi 242:3 22 +→+

[ ] ( ) ( )COOCR 22:6 2 →+

[ ] [ ] ( ) [ ]

[ ] [ ] ( )COMoTi

OCMoTiCR

NiNi

Ni

254

58

52

58:5 22

++

→++

[ ] [ ] ( ) [ ] ( )[ ]( ) [ ] ( ) [ ] ( )COMoxTix

CMoTiOCMoTiCRNiNixx

Ni

21212

222:4 122

+++−+

→++ −

Figure 4.1 Various oxygen scavenging reactions in TiC-Ni-Mo2C cermets

during heating to the liquid phase sintering temperature.

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30

[ ] [ ] ( ) [ ]

( )[ ] ( ) [ ] ( ) [ ] ( )COMoxTixCMoTiOCMoTiC

NiNixx

Ni

21212,222

1

22

+++−+

→++

(R4)

Note that reactions (R2) and (R3) may combine to give:

[ ] [ ] ( ) [ ] [ ] [ ] ( )COMoTiOCMoTiC NiNiNi 254

58

52

58

22 ++→++ (R5)

The free energies of reactions (R2) to (R5) at ( ) ( )510

2

−≈≈ COO PP atm and

9.0=x as a function of temperature are plotted in Figure 4.1. At low temperatures,

Reactions (R1) to (R5) are equally feasible. However, the Mo dissolution reaction

(R3) and the mixed carbide rim formation reaction (R4) are energetically more

favorable at higher temperatures, i.e. KT 1500> .

Therefore, the TiC particles in the compact will be covered with patches of

oxides and (Ti,Mo)C rim, while the solid Ni binder is alloyed both with Ti and Mo.

Note that both the dissolution and mixed carbide rim formation reactions are also

oxygen-scavenging mechanisms should residual oxygen be present in the system.

Also shown in Figure 4.1 is the oxidation reaction of free carbon with carbon

monoxide as the product; i.e.

[ ] ( ) ( )COOC 22 2 →+ (R6)

This reaction is highly probable over the temperature range of interest. Free

carbon is thus a very effective means of oxygen-scavenging in cermet processing.

Another point to note is that all the oxygen-assisted dissolution and rim

formation reactions, i.e. (R2) to (R5), result in the nickel binder being enriched with

Ti (and Mo). This, however, is not so for the case of free carbon. We shall discuss

the implication of this later.

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31

4.3.2 Solute Moderation via Rim Formation

Let us examine the feasibility of the following rim formation reactions after

oxygen in the system has been depleted [3].

[ ] [ ] [ ]

[ ] ( )[ ] [ ]Nixx

Ni

Ni

MobabaxCMoTi

Tiba

axCMoba

bTiCba

a

+−

−+→

+−+

++

+

−1

2

(R7)

which reduces to (R7a) and (R7b) below for a=0, b=1 and a=1, b=1, respectively.

[ ] [ ] [ ] ( )[ ] ( ) [ ]Nixx

NiNi MoxCMoTiCMoxTi ++→+ − 1, 12 (R7a)

[ ] [ ] [ ] [ ] ( )[ ] [ ]Nixx

NiNi xMoCMoTiTixCMoTiC +→

−++ −12 ,

21

21

21 (R7b)

In the presence of free carbon, the various rim formation reactions are modified to:

[ ] ( ) [ ] ( ) [ ] ( )[ ]CMoTiCxCMoxxTi xxNi

−→+

+−

+ 12 ,2

12

1 (R7c)

[ ] ( ) [ ] [ ] ( )[ ]CMoTiCMoxxTi xxNiNi

−→+−+ 1,1 (R8)

[ ] [ ] [ ]CMoCMo Ni22 →+ (R9)

Figure 4.2 shows the free energies of the above reactions for 9.0=x . Similar

trends with comparable energy gains were obtained for these reactions for x varying

from 0.7 to 1.0. This figure shows that although their free energy gains are modest,

being less than 50 kJ/mol. (Tix,Mo1-x)C, (R7c), (R8) and (R9) are feasible even at low

temperature while (R7a) and (R7b) are feasible at sufficiently high temperatures (i.e.

KT 1350> ). More importantly, all these rim formation reactions deplete the nickel

[3] Note that the reactions, ( ) [ ] [ ] [ ] ( )[ ] ( ) [ ]Nixx

NiNi TixCMoTiTiCMox −+→+− − 1,1 1 (i.e., 1=a and 0=b in (R7)),

and its modified form with free carbon, i.e., ( ) [ ] [ ] ( )[ ] ( )[ ]CMoTiCxTiCxMox xxNi

−→−++− 1,11 , both have 0≈∆G . They are thus ignored in our discussion.

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32

-60

-30

0

30

60

1173 1273 1373 1473 1573

Temperature (K)

Free

Ene

rgy

of R

eact

ion

(kJ/

mol

. (Ti

x,M

o1-x

)C)

[ ] [ ] [ ] ( )[ ] ( ) [ ]Nixx

NiNi MoxCMoTixTiCMoaR ++→+ − 1,:7 12

[ ] [ ] [ ]

[ ] ( )[ ] [ ]Nixx

Ni

Ni

xMoCMoTi

TixCMoTiCbR

+→

−++

−1

2

,21

21

21:7

( ) [ ] [ ] ( ) [ ] [ ] ( )[ ]CMoTiCxxTiCMoxcR xxNiNi

−→+

++−

12 21

21:7

[ ] ( ) [ ] [ ] [ ] ( )[ ]CMoTiCMoxxTiR xxNiNiNi

−→+−+ 11:8

[ ] [ ] [ ] [ ]CMoCMoR NiNi22:9 →+

Figure 4.2 Various mixed carbide rim formation reactions after residual

oxygen in the system has been depleted.

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33

binder of Ti, regardless of if free carbon is present. Note also that these mixed

carbide rim formation reactions are possible only if Mo is present, be it in the form of

Mo2C or as a solute in the Ni binder.

Therefore, the rim is likely to form during the initial heating stage when

oxygen is available and continues to form even after the oxygen is depleted. Since the

energy gains for reactions (R7) to (R9) are comparable for a range of x values, the rim

formed via the solid state reactions is expected to have a range of composition. Note

that upon depletion of oxygen in the system and at sufficiently high temperatures, the

Ti content in the solid Ni binder is moderated via a host of rim formation reactions

involving Mo2C and/or free carbon.

4.3.3 Reduction Reactions

As discussed above, TiO2, mixed carbide rim, Ti[Ni], Mo[Ni] and CO are formed

during heating of the TiC-Ni-Mo2C powder compact. While gaseous CO will be

removed from the system, either by vacuuming or the flowing carrier gas, solid TiO2

and (Tix,Mo1-x)C will be formed on the surface of TiC particles. Although the rim

formed is not detrimental to subsequent wetting, the TiO2 surface layer, or patches of

TiO2, must be removed as otherwise it could adversely affect the wetting behavior

during subsequent liquid phase sintering. Even if the oxide could still be reduced

during the liquid phase sintering stage, the gaseous CO released would form bubbles

and would require a much longer time to sinter out of cermet, during which excessive

grain growth and rim thickening may occur leading to inferior properties of the

resultant cermet. In what follows, we shall examine if the TiO2 formed earlier will be

reduced after oxygen is depleted.

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34

(a) Reduction of TiO2 in TiC-Ni Systems

In the absence of Mo2C, the oxide formed on the TiC particles may be reduced

via the following reaction:

[ ] [ ] [ ] [ ] ( )COTiTiCTiO NiNi 2322 +→+ (R10a)

And, upon reaching the solubility limit, *Tix , we have

[ ] [ ] [ ] [ ] ( )COTiNix

xTiNix

TiCTiOTi

Tixx

TiTiTi

241

134192 3*

*

1*2 ** +

−−

++−

(R10b)

The free energies of reactions (R10a) and (R10b) at ( ) ( )510

2

−≈≈ COO PP atm

over the temperature range of interest are plotted in Figure 4.3. This figure shows

that, in the absence of Mo2C, TiO2 can be reduced so long as the Ni binder remains

unsaturated with Ti. At sufficiently high temperature, i.e. KT 1500> , TiO2 can also

be reduced even after Ni has become saturated with Ti but with concurrent

intermetallic formation.

(b) Reduction of TiO2 in TiC-Mo2C-Ni Systems

In the presence of Mo2C, the reduction reaction is modified to:

[ ] [ ] [ ] [ ] ( ) [ ] ( )[ ] ( )COCMoTiMoxTixCMoTiO xxNiNiNi 2232)12(4 122 +++→−++ − (R11)

Note that similar reduction reaction but with concurrent intermedtallic

formation is irrelevant here because reaction (R11) depletes the nickel binder of Ti,

making such a reaction kinetically not probable. The free energy of reaction (R11) at

( )510−≈COP atm over the range of temperature of interest is plotted in Figure 4.3. It

shows that, although (R10a) is favored at low temperatures, i.e. KT 1300< , reaction

(R11) is favored at higher temperatures. More importantly, reaction (R11) consumes

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35

-600

-300

0

300

600

1173 1273 1373 1473 1573

Temperature (K)

Free

Ene

rgy

of R

eact

ion

(kJ/

mol

. TiO

2)

[ ] [ ] [ ] [ ] ( )COTiTiCTiOaR NiNi 232:10 2 +→+

[ ] [ ] [ ][ ] [ ] ( )COTiNi

xx

TiNix

TiCTiObR

Ti

TiNi

xxTi

TiTi

241

13

4192:10

3*

*

1*2 **

+

−−

++−

[ ] [ ] [ ] [ ]

( ) [ ] ( )[ ] ( )COCMoTiMox

TixCMoTiOR

xxNi

NiNi

2232

)12(4:11

1

22

+++

→−++

[ ] [ ] [ ] [ ] ( )COTiCTiOaR NiNi 22:12 2 +→+

[ ] [ ] [ ] [ ] ( )COTiCCTiObR Ni 23:12 2 +→+

Figure 4.3 TiO2 reduction reactions with and without Mo2C addition in

TiC-based cermets.

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36

Ti in the nickel binder, thereby reducing the risk of intermetallic formation in the

cermet.

(c) Effect of Free Carbon Addition

Let us examine what will happen if free carbon alone is used. In this case,

reactions (R10a) and (R11) are modified to:

[ ] [ ] [ ] [ ] ( )COTiCTiO NiNi 222 +→+ (R12a)

and [ ] [ ] [ ] ( )COTiCCTiO 232 +→+ (R12b)

The free energies of reactions for (R12a) and (R12b) at ( ) ( )510

2

−≈≈ COO PP atm

are also plotted in Figure 4.3, which shows that both reduction reactions are feasible

over the temperature range of interest. Note that since the reaction

[ ] [ ] [ ]TiCCTi Ni →+ is also feasible over the temperature range of interest, free

carbon not only is effective in reducing TiO2 on the surface of TiC particles but also

in depleting the Ni binder of Ti, thus minimizing the risk of intermetallic formation in

the system.

4.4 Extension to Ti(C,N)-Based Cermet Systems

In Ti(C,N)-based cermets, in addition to the oxide film and Ni-Ti and Ni-Mo

solid solutions, the rim of (Ti,Mo)(C,N) is formed on the surface of Ti(C,N) particles.

While some basic reactions remain unaltered, other basic reactions, which involve

Ti(C,N) as a reactant (instead of TiC), are modified as follows:

( )[ ] ( ) [ ] ( )[ ] ( )CONCTizyyTiOONCTi

zyz

zzyy +

−−

+→+

−−

−− 1221 ,121

21,1

21 (R1a)

( )[ ] ( ) [ ] [ ] ( )[ ] ( )CONCTizyyTiONCTi

zyz

zzNiNi

yy 2,122,12 121 +

−−

+→+

−−

−− (R2a)

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37

( )[ ] ( ) [ ] [ ] ( )( )[ ] ( ) [ ]Niyyxx

NiNiyy TixNCMoTiMoxNCTi −+→−+ −−− 1,,1, 111 (R7c)

[ ] ( )[ ] [ ] [ ] ( )[ ] ( )CONCTizyyTiNCTi

zyzTiO zz

NiNiyy 2,123,12 112 +

−−

+→

−−

+ −− (R10c)

[ ] ( )[ ] [ ]

[ ] ( )[ ] ( )CONCTizyyTiNi

xx

TiNix

NCTizyzTiO

zzTi

Ti

xxTi

yy TiTi

2,1241

13

419,12

13

112

+

−−

+

−−

+

−−

+

−−

(R10d)

where y and z are the mole fractions of C in the non-metal sublattice before and after

the reactions, respectively. Note that the above equations are valid only for yz < .

Our calculations show that the results mentioned in TiC-based cermets also apply to

Ti(C,N)-based cermets.

4.5 Discussion

4.5.1 Role of Mo2C in Cermet Processing

It is evident from the present work that one key aspect in successful cermet

processing is to control the resultant reaction products containing Ti, which could be

an oxide, as Ti solutes in the Ni binder, or as a component in either the mixed carbide

rim or intermetallic rim.

Some amount of Ti in Ni is good as it would promote the wetting between the

liquid Ni binder and TiC grains. Similarly, good wetting is to be expected between

Ti-containing Ni binder and the mixed carbide rim. In the contrary, wetting between

the Ni binder and hard-phase particles will be impaired should TiO2 or intermetallic

rim be present in the system. The two latter cases would lead to weak interfaces in the

resultant cermet.

As shown in Section 4.3.1, during heating to the liquid phase sintering

temperature, the residual oxygen present will cause the starting TiC or Ti(C,N)

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38

powder to oxidize, forming a TiO2 surface layer. Also occurring at the same time are

the oxygen-assisted dissolution and rim formation reactions. All these processes

deplete the system of oxygen. The compact thus consists of TiC or Ti(C,N) particles

covered with patches of oxides and (Ti,Mo)C or (Ti,Mo)(C,N) rim. The mixed

carbide or carbonitride rim is not detrimental to the wetting during subsequent liquid

phase sintering, but the TiO2 surface layer must be reduced prior to the formation of

the liquid binder phase.

On further heating, the TiO2 formed earlier is unstable and will be reduced.

However, in the absence of Mo2C or pure Mo, as more and more Ti becomes

dissolved in the Ni binder accompanying the reduction reaction, the tendency for

intermetallic formation increases accordingly. The formation of intermetallic rims not

only leads to partial wetting of the liquid binder onto the solid hard phase particles but

also a weak resultant cermet.

In the presence of Mo2C, the availability of the reaction (R11) not only

reduces the TiO2 surface layer with much higher energy gain but also depletes the

system of residual oxygen via reactions (R3) to (R5). Furthermore, through the

formation of (Ti,Mo)C and/or (Ti,Mo)(C,N) rims, Mo2C (or Mo) helps regulate the

amounts of solute Ti (and Mo) in both solid and liquid Ni, therefore reducing the risk

of formation of brittle intermetallic phases in the system.

With TiO2 surface layer removed and the system free of Ni3Ti phases, the TiC

or Ti(C,N) particles would be readily wetted by the liquid binder upon being heated to

the liquid phase sintering temperature, yielding a dense and strong cermet.

Otherwise, the resultant cermet will be unsuitable for machining purposes. The

addition of free carbon produces a similar effect. However, with free carbon alone

(i.e. without Mo presence be it in the form of Mo2C, pure Mo or Ni-Mo alloy binder),

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39

the risk of intermetallic formation remains should free carbon be totally consumed.

On the other hand, any residual free carbon is expected to adversely affect the

properties of the resultant cermet. The concurrent addition of pure Mo or Ni-Mo

alloy thus plays an important role in tying up any residual free carbon via the

following reactions:

[ ] [ ] [ ]CMoCMo Ni22 →+ (R13a)

[ ] [ ] [ ]CMoCMo 22 →+ (R13b)

both reactions are feasible over the temperature range of interest with modest energy

gain of less than -50 kJ/mol Mo[Ni] or Mo. Note that the uses of pure Mo or Ni-Mo

alloy binder are equivalent, because the reaction [ ] [ ] [ ]NiNi MoMo → is feasible over

the temperature range of interest with modest energy gain, i.e. 30−≤∆G kJ/mol. Mo.

4.5.2 Effect of Process Variables

As reactions (R1) to (R12) are thermodynamically feasible during cermet

processing, a host of reaction products may be formed during the heating stage

depending on the prevailing kinetic conditions. The present work thus shows that

proper control of process variables is crucial to ensure effective cermet processing.

This can be achieved by the following means.

Firstly, the residual oxygen level or the partial oxygen level in the system must

be kept low. This is because, the presence of oxygen not only promotes the formation

of more TiO2 but also the decomposition of Mo2C and TiC, thereby leading to an

increased degree of Ti (and Mo) dissolution in solid Ni via reactions (R2) to (R5).

Secondly, an optimum heating cycle should be as follows. A high heating rate

to a temperature slightly below the liquid phase sintering temperature should be used

to avoid excessive dissolution of Ti and Mo in solid Ni. Then, the compact is held at

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40

temperature for a sufficient period to enable complete removal of TiO2 surface oxide

via reaction (R11) and to rid the system of any residual oxygen present via reactions

(R2) to (R5). Finally, the compact is heated up rapidly to the sintering temperature to

effect liquid phase sintering.

Even in a vacuum system, it is imperative that a sufficient amount of Mo2C be

present to keep the system free of oxides and/or residual oxygen until the formation of

the liquid binder phase. An excessive amount of Mo2C, however, should be avoided

as this may result in a thick (Ti,Mo)C or (Ti,Mo)(C,N) rim being formed, which is

detrimental to the properties of the resultant cermet [2]. One way to avoid such a

problem is to use supplementary amounts of free carbon in the starting powder.

In addition, the amount of Ni added should also be sufficient to dissolve the

Mo present without the formation of brittle intermetallic phase. Too much Ni,

however, should be avoided since it will lower the hardness of the resultant cermet

and its machining performance.

4.6 Summary

The present work shows that during the initial heating stage of the powder

compact, a host of reactions involving TiC and Mo2C and residual oxygen occur

simultaneously. TiC will be oxidised to TiO2 and Mo tends to dissolve in solid Ni or

form rims of (Ti,Mo)C or (Ti,Mo)(C,N). The compact thus consists of TiC or

Ti(C,N) particles covered with patches of TiO2 and (Ti,Mo)C or (Ti,Mo)(C,N)

reaction products. On heating to sufficiently high but below the liquid phase sintering

temperature, TiO2 becomes unstable and will be reduced. In the absence of Mo2C (or

pure Mo), the oxide reduction process will further enrich the Ni binder of Ti with

potential risk of intermetallic formation. The presence of Mo2C or pure Mo and free

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41

carbon not only helps rid the system of oxide and residual oxygen via a series of

mixed carbide formation reactions but also regulate the Ti content in the Ni binder

phase through the formation of (Ti,Mo)C or (Ti,Mo)(C,N) rim, thus minimizing the

risk of intermetallic formation. The use of supplementary amounts of free carbon is

highly efficient to this effect.

To obtain the maximum benefit of the above process, the optimum sintering

cycle should consist of a high heating rate to the temperature slightly below the liquid

phase sintering temperature to avoid excessive dissolution of TiC and Mo2C in solid

Ni. The compact is then held at temperature to enable the surface oxide to be

reduced. Then, the compact is heated up rapidly to the sintering temperature to effect

liquid phase sintering with minimum grain growth and rim formation.

Proper control of starting powder composition, process environment and

heating cycle are thus essential to produce TiC and Ti(C,N) based cermets of superior

microstructures and, hence, properties.

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42

Chapter 5

Wettability and Spreading of Liquid Binder Phase

in Powder Compacts

5.1 Background

Liquid phase sintering is a necessary processing step for cermet

manufacturing. During liquid phase sintering, the wetting between the liquid binder

and the solid hard grains plays a major role in microstructural evolution of cermets,

which in turn determines their resultant properties [1,32]. Complete wetting is

therefore a prerequisite in cermet processing.

The sessile drop experiment has been used extensively for the determination

of the contact angle of a liquid droplet on a flat solid substrate [1,43]. Figure 5.1

shows that at equilibrium, a drop of liquid rests on a flat and nondeformable solid

substrate. The contact angle, θ, indicates the degree of wetting of the liquid on the

solid substrate. The relationship between the contact angle and various interfacial

energies in the system can be expressed by the Young’s equation:

lv

slsv

γγγθ −

=cos (5.1)

where γsv, γsl and γlv are the interfacial energies (per unit area) between the

solid-vapor, solid-liquid and liquid-vapor phases, respectively.

Humenik and Parikh [1] conducted sessile-drop experiments in vacuum and

found that, at 1450°C, the contact angle between the molten Ni-10wt%Mo alloy and

solid TiC substrate was 0°, while that between the molten pure Ni and solid TiC

substrate was 30°. They therefore concluded that the addition of Mo to Ni improves

the wettability of the system.

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43

Figure 5.1 Geometry of a sessile drop test. Point O indicates a three-phase contact point.

Solid

Liquid Vapour

θ γsl γsv

γlv

O

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44

Tahtinen and Tikkanen [10] studied the effect of residual oxygen content on

the wetting of liquid Ni droplet on solid TiC substrate. They observed that at 1400°C,

the contact angles were 12° and 42° at atmandPO1216 1010

2

−−= , respectively. On

the other hand, they noted that at atmPO1610

2

−= , the melted Ni no longer maintained

a lenticular shape and the carbide grains were dislodged and mixed intimately with

the melt, as shown in Figure 2.2. Thus, it was difficult to measure the low contact

angle accurately in this case. . Aksay et al. [35] also noted this phenomenon. They

attributed it to dissolution reactions at the interface and inter-diffusion between the

bulks.

Another reason is that typical solid substrates were prepared by hot-pressing

TiC powder and hence not fully dense [44]. During the test, the capillary effect

causes the molten Ni to infiltrate into the pores in the TiC substrate and change the

meniscus geometry of the system, making the contact angle measurement inaccurate

[35].

In practical cermet processing, the powder compact is highly porous.

Although the contact angle measurement via the sessile-drop test provides good

information on the wetting characteristics between the liquid binder and the solid hard

phase substrate, whether or not it adequately describes the spreading characteristics of

the liquid binder phase in a powder compact remains to be answered.

In what follows, based on an energy approach, an alternative method is

proposed which relates the contact angle between the liquid binder phase and the solid

hard phase substrate to the spreading characteristics in a powder compact. An

experiment with Ti(C,N) based cermet is also carried out to check the validity of the

model.

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5.2 Theoretical Consideration

Consider a powder compact formed by a powder mixture of ceramic particles

and binder phase particles. Assuming that the process time is extremely short such

that no sintering occurs in between the solid hard-phases and that no diffusion occurs

between the solid hard phases and the liquid binder phase. Under the said

circumstance, the infinitesimal change in the free energy of the system upon the

formation of the liquid binder phase is given by

lvlvsvsvslsl dAdAdAdG γγγ ++= (5.2)

where G is the Gibbs free energy, γij is the interfacial energy between the solid-liquid

(sl subscript), solid-vapor (sv subscript) or liquid-vapor (lv subscript) phase. Aij is the

total area of the relevant interface. Spreading of the liquid phase occurs when

0<dG .

For simplicity, we may further assume that the liquid binder phase is in the

form of a spherical droplet before spreading and that the hard phases are rigid solid

spheres. Furthermore, it is assumed that particle rearrangement is negligible before

and after spreading.

Let us consider first the case of no spreading. In this case, the liquid sphere

would retain its original shape despite it being embedded in a matrix of solid spheres.

This is shown schematically in Figure 5.2. Since the liquid-solid interfacial area is

negligible, the free energy of the system can be expressed as

( ) svsllvl

svsvlvlv

rrRnr

AAG

γπππγπ

γγ

⋅⋅−⋅+⋅=

⋅+⋅=

23343

342

1

44 (5.3)

where rl and rs are the radii of the initial liquid sphere and the solid spheres,

respectively, R is the radius of the overall powder compact encompassing the initial

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46

liquid and solid spheres and n is the number of solid spheres per unit volume of the

compact less that occupied by the initial liquid sphere.

Now, let us consider the case when spreading of the liquid occurs. In this

case, the liquid binder infiltrates itself through the void space in between the solid

spheres by capillary force, as shown in Figure 5.3.

For simplicity without loss of generality, we assume that the volume of the

original liquid sphere is equal to the total volume of the void space in between the

solid spheres and that the overall volume of the compact remains unchanged before

and after the spreading. Since the solid-vapor interfacial area now becomes

negligible, the resultant free energy of the system is given by

( ) ( ) slsllvl

slsllvlv

rrRnrR

AAG

γπππγππ

γγ

⋅⋅−⋅+⋅+=

⋅+⋅=

23343

3422

**2

444 (5.4)

The number of solid spheres per unit volume, n, in Equations (5.3) and (5.4) can be

expressed as

334

srfnπ

= (5.5)

where f is the packing factor of solid spheres in the system. From the assumption, we

have

( ) ( ) 3343

343

341 ll rrRf πππ =−⋅− (5.6)

giving

lrffR ⋅

−−

=31

12 (5.7)

Note that the liquid sphere will spread completely when 012 <−=∆ GGG ;

otherwise it will retain its original spherical shape. Combining Equations (5.3), (5.4),

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Figure 5.2 A liquid sphere embedded in a matrix of solid spheres. The

dotted circle, the solid dark circle and smaller white circles

represent the boundary of the compact, the binder sphere and

hard phase spheres, respectively.

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48

Figure 5.3 The liquid binder filling up the voids in between the solid

spheres after the spreading.

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49

(5.5) and (5.7), we can express the spreading condition as:

( ) ( ) 01211

432

31

2 <

−⋅+⋅

−⋅−⋅⋅

⋅sv

sl

s

l

sv

lvsvl r

rf

fff

frγγ

γγγπ (5.8)

which reduces to

( ) ( )

lv

slsvs

l fff

rr

γγγ −

−⋅−

>

32

31

21

(5.9)

Since the interfacial energies are related via the Young’s equation,

( ) lvslsv γγγθ −=cos , where θ is the contact angle, the above inequality can be

expressed as

( ) ( )

θcos

21 32

31

fff

rr

s

l

−⋅−

> (5.10)

The critical radius ratio of the liquid sphere to the solid sphere for spreading is

thus

( ) ( )

θcos

21 32

31

fff

rr

cs

l

−⋅−

=

(5.11)

Equation (5.11) is plotted as a function of the contact angle for powder

compacts of different packing factors in Figure 5.4. Note that when ( )cslsl rrrr >

(i.e., above the curves), the liquid binder sphere is unstable; it will spread and fill up

the void space in between solid spheres. On the other hand, when ( )cslsl rrrr < (i.e.,

below the curves), the liquid binder sphere is stable and will retain its spherical shape;

i.e. no spreading occurs.

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50

cs

lr

r

θ , °

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50 60 70 80 90

Spreading

No Spreading

0.7

0.5

f = 0.4

0.6

0.8

Figure 5.4 Conditions for spreading as a function of the contact angle θ for powder compacts of different packing factors f. Note that above the curves, the liquid sphere is unstable and will spread in the powder compact. The reverse is true below the curves.

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51

It is interesting to note from Figure 5.4 that for at low θ values, i.e. °< 45θ ,

( )csl rr is relatively independent of θ and a weak function of the packing factor f in

the compact, its value increasing from 1 to 3 as f decreases from 0.80 to 0.40. On the

other hand, at high θ values, i.e. °> 45θ , ( )csl rr increases appreciably with

increasing θ but with decreasing f values, its value being 10> for °> 75θ .

Conventionally, complete wetting (i.e. °= 0θ ) has been thought as a

prerequisite for spreading in cermet processing [5]. The present work shows that

spreading of the liquid binder phase in a powder compact is more complicated than in

a sessile-drop test, in which a much larger drop of liquid phase is used. For instance,

Figure 5.4 shows that even with °= 0θ , spreading of the liquid binder phase will not

occur if the packing factor is low (say, 4.0<f ) and the liquid sphere radius is small

(say, 3<sl rr ). Therefore, in a powder compact, both the packing factor and the

radius ratio of the binder sphere to hard phase particles are equally important factors

for spreading. Note that the above conclusion is based on the assumption that there is

minimum particle rearrangement upon spreading of the liquid binder phase. As will

be shown below, this holds under the case when the amount of liquid binder phase

present in the powder compact is much less than sufficient to fill the void space

between the solid hard grains in the powder compact.

5.3 Application to Ti(C,N)-Based Cermet Processing

5.3.1 Experimental Details

The starting powders used were Ti(C0.7,N0.3) (H.C. Starck; grade D; particle

size 1-2 µm), Mo2C (H.C. Starck; grade B, 2-4 µm) and pure Ni (Alfa; 2.2-3 µm)

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52

powders. Micrographs of the as-received powders are given in Figure 5.5. It shows

that although there was much less agglomeration in the as-received Ti(C0.7,N0.3)

powder, the as-received Mo2C and Ni powders were in the form of lumped and

chained agglomerates, respectively.

Fifty (50) grams each of the starting powders were planetary ball-milled in a

WC-Co lined jar with WC-Co balls for 10 hours to break up the agglomerates. The

volume of the ball-milling jar used was 800 cm3 and the diameter of the milling ball

was 2 cm. The ball-to-powder weight ratio used was 5:1. The rotation speed used was

200 rpm. After every 15 minutes of ball milling, the machine was stopped for 15

minutes before resuming again, to avoid excessive heating of the powder. The size

distributions of respective powders after the ball-milling were measured by means of

the Coulter particle size analyzer. The results are shown in Figure 5.6. It is evident

that both the Ti(C0.7,N0.3) and Mo2C powder particles are effectively broken up by the

ball-milling process, being about 0.5 µm in mean particle size. On the other hand, the

Ni powder remained very much in agglomerated form with a mean particle size of

about 5 µm.

Two 50 g powder mixtures, Ti(C0.7,N0.3)-Ni and Ti(C0.7,N0.3)-Mo2C-Ni, with

the weight ratios of 99.2:0.8 and 89.5:9.8:0.7, respectively, were prepared. Note that

the amounts of Ni powder used were very much less than that needed to fill the total

void space in between the hard phase particles. This is to enable the spreading

phenomenon to be studied more evidently. The respective powder mixture was

blended at a rotation speed of 60 rpm for 24 h. Then, a mixture of polyethylene

glycol with 2-propanol alcohol was added as lubricant into the powder mixture. The

amount of polyethylene glycol and the volume of 2-propanol alcohol added were 5 g

and 5 ml, respectively, per 100 g of the powder mixture. After that, the mixture was

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53

a

c

b

Figure 5.5 As-received powders: (a) Ti(C0.7,N0.3) powder, (b) Mo2C powder and (c) Ni powder.

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54

(a) Ti(C0.7,N0.3),(ball-milled)

(b) Mo2C (ball-milled)

(c) Ni (ball-milled)

Figure 5.6 Particle size distributions of (a) Ti(C0.7,N0.3), (b) Mo2C and (c) Ni powders after ball-milling. Results of two runs are shown in (b) and (c).

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55

planetary ball-milled (in the same WC-Co jar lined with WC-Co balls with the same

ball-to-powder weight ratio) at a rotation speed of 200 rpm for 10 h. Similar to earlier

ball-milling, the machine was stopped for 15 minutes after every 15 minutes of ball-

milling before resuming again, to avoid excessive heating of the powder mixture.

After ball-milling, the mixture was uniaxially compacted in a steel die at a

pressure of 300 MPa into a cylindrical shape of 10 mm in diameter and about 8 mm in

thickness. The thickness of the compact varied slightly depending on the actual

amount of the powder mixture used. Then, the compact was de-waxed in an alumina

tube furnace, into which argon gas was flowed continuously to remove the burnt

products of the lubricant. The time-temperature cycle used for the de-waxing process

is shown in Figure 5.7.

After dewaxing, the compact was sintered in a Centorr high vacuum furnace

at 10-5 mbar or better. Prior to the sintering run, differential scanning calorimetry

(DSC) was carried out to determine the temperature at which the liquid binder phase

is first formed in the compact. The heating rate was set at 25°C/min and the

maximum temperature was set at 1400°C. The results are shown in Figure 5.8. It is

evident that the liquid binder phase is formed over the temperature range from

1346°C to 1360°C for the Ti(C0.7,N0.3)-Ni system (Fig. 5.8(a)) and from 1356°C to

1376°C for the Ti(C0.7,N0.3)-Mo2C-Ni system (Fig. 5.8(b)).

Based on the above information, the sintering temperature was fixed at

1380°C for both powder compacts used. The full sintering cycle used is shown in

Fig. 5.9. To minimize the solution-reprecipitation process and grain coalescence, a

relatively high heating rate of about 10°C/min to 1380°C was used. After holding at

1380°C for 3 minutes to effect liquid phase sintering, the sintered compacts were

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56

Figure 5.7 The dewaxing cycle used. Figure 5.9 The sintering cycle used.

Figure 5.8 Heat flow as a function of temperature for (a) Ti(C0.7,N0.3)-Ni and (b) Ti(C0.7,N0.3)-Mo2C-Ni powder mixtures.

0

100

200

300

400

0 50 100 150 200

Time (min)

Tem

pera

ture

(°C

)

5.5°C/min

350°C, 2 hour

Furnace Cool

0

300

600

900

1200

1500

0 50 100 150 200

Time (min)

Tem

pera

ture

(°C

)

13°C/min

11°C/min

1380°C, 3min

100°C/min

10°C/min

-5

-2.5

0

2.5

5

1280 1300 1320 1340 1360 1380

Temperature (°C)

Hea

t Flo

w (m

W)

(a) Ti(C0.7N0.3)-Ni

-5

-2.5

0

2.5

5

1280 1300 1320 1340 1360 1380

Temperature (°C)

Hea

t Flo

w (m

W)

(b) Ti(C0.7N0.3)-Mo2C-Ni

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57

cooled at a fast rate of 100°C/min to 700°C and then cooled to room condition at

10°C/min.

After sintering, the specimen was cross-sectioned with a diamond-

impregnated cutter and then cold-mounted. The surface of interest was ground with

silicon carbide papers and then polished with 6 µm diamond paste until it was

scratch-free when observed under an optical microscope. After which, the specimens

were examined under the scanning electron microscope (SEM) to study the spreading

of the liquid binder phase in the compacts during the sintering.

5.3.2 Results and Discussion

Figures 5.10 and 5.11 show, respectively, typical SEM micrographs of “no

spreading” and “spreading” in the Ti(C0.7,N0.3)-Ni and Ti(C0.7,N0.3)-Mo2C-Ni systems,

respectively. The equivalent radii of non-spreading liquid Ni binder spheres were

determined from the SEM micrographs. The mean radius of Ti(C,N) grains was taken

from the mean particle size given in Figure 5.6(a). The radius ratios of the non-

spreading liquid binder sphere to the mean radius of Ti(C,N) grains were determined

correspondingly. Also estimated from respective SEM micrographs were the local

packing factors of the hard phase grains. In this work, the area-packing factors were

measured and taken to be the volume-packing factors [52].

Plotted in Figure 5.12 are experimentally obtained data points for the

Ti(C0.7,N0.3)-Ni system pertaining to the non-spreading Ni, expressed in terms of their

),( NCTiNi rr values and the local packing factor. A similar plot but for the

Ti(C0.7,N0.3)-Mo2C-Ni system is given in Figure 5.13. Note that since the data points

in Figures 5.12 and 5.13 were obtained from the specimen cross-sections, they are the

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58

Figure 5.10 Typical micrographs showing (a) spreading and (b) non-spreading states in the Ti(C0.7,N0.3)-Ni system studied.

a

b

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59

a

b

Figure 5.11 Typical micrographs showing (a) spreading and (b) non-spreading states in the Ti(C0.7,N0.3)-Mo2C-Ni system studied.

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60

Figure 5.12 Experimental data pertaining to non-spreading cases expressed in terms of the apparent ),( NCTiNi rr and local packing factor f for the Ti(C0.7,N0.3)-Ni system. Data with the largest ),( NCTiNi rr values for a given f can be taken as the ‘critical radius ratio’ for that f value. The best fit curve is that of equation (5.11) with °= 65θ .

( )11.5.Eq with °= 65θ s

lr

r

f

0

2

4

6

8

10

0.40 0.50 0.60 0.70 0.80

Spreading

No Spreading

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61

Figure 5.13 Experimental data pertaining to non-spreading cases expressed in terms of the apparent ),( NCTiNi rr and local packing factor f for the Ti(C0.7,N0.3)-Mo2C-Ni system. Data with the largest ),( NCTiNi rr values for a given f can be taken as the ‘critical radius ratio’ for that f value. The best fit curve is that of equation (5.11) with °= 10θ .

( )11.5.Eq with °= 10θ

s

lr

r

f

0

2

4

6

8

10

0.40 0.50 0.60 0.70 0.80

Spreading

No Spreading

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62

‘apparent’ radius ratios (although a few of them may well be ‘true’ radius ratios).

Nevertheless, to a good approximation, we may take the largest ),( NCTiNi rr value for a

given packing factor as the ‘true’ critical radius ratio for spreading for that packing

factor.

Also plotted in Figures 5.12 and 5.13 is the best fit ( )csl rr curve using

Equation (5.11), which passes through the largest experimentally obtained ),( NCTiNi rr

data, or the ‘critical radius ratio’, of respective material systems. It is evident that the

experimental data for the Ti(C,N)-Ni system are best described by Equation (5.11)

with a contact angle of 65° (Figure 5.12), while that for the Ti(C,N)-Mo2C-Ni system

fit reasonably well with a contact angle of 10° (Figure 5.13).

The present work shows that spreading of liquid binder phase in powder

compacts of both Ti(C,N)-Ni and Ti(C,N)-Mo2C-Ni systems can be adequately

described by the model proposed in the present work with a contact angle of about

65° and 10°, respectively.

5.4 Conclusion

In the present work, a model is developed to study the spreading of the liquid

binder phase in the powder compact. For a given packing factor, there exists a critical

radius ratio of the liquid binder sphere to the hard phase particles above which the

liquid binder sphere will spread. For contact angle °< 45θ , the critical radius ratio is

relatively independent of θ but a weak function of the packing factor f. For °> 45θ ,

the critical radius ratio for spreading depends appreciably on both the θ and f values.

Experiments were carried out to verify the predictions of the model and to

obtain the contact angles between the liquid Ni binder and Ti(C,N) phases with and

without Mo2C addition. Our experimental data, when fitted to Equation (5.11), give

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63

contact angles of about 65° and 10° for the Ti(C,N)-Ni and Ti(C,N)-Mo2C-Ni

systems, respectively. The results show that the addition of Mo2C to Ti(C,N)-Ni

system improves the wetting and spreading of liquid Ni binder onto the Ti(C,N)

grains during the liquid phase sintering stage.

The present work shows that to achieve good spreading of the liquid binding

phase in cermet processing, other than improving the wetting characteristics by Mo2C

addition, a fine initial particle size of the hard phase, a high packing factor and a

relatively uniform green structure of the powder compact are equally important.

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64

Chapter 6

Rim Growth in Cermets during Liquid Phase Sintering

6.1 Introduction

As mentioned in Chapter 2, too thick a rim on Ti(C,N) particles would render

cermet insert susceptible to chipping and breakage. To control the rim thickness in a

cermet, one should understand the various rim formation and growth mechanisms

during cermet processing. In Chapter 4, the formation of rims via solid-state reactions

during heating to the liquid phase sintering temperature has been discussed. In this

Chapter, the rim formation mechanisms during the liquid phase sintering stage and on

cooling the sintered cermet to room conditions will be investigated and discussed.

6.2 Conceptual Analysis of Rim Formation Mechanisms during Liquid Phase

Sintering of Cermets

6.2.1 Inner Rim Formation via Solid State Reactions

Before the green compact reaches the sintering temperature, the rim could be

formed at sufficiently high temperatures via solid-state processes. The rim so formed

grows epitaxially onto the surface of the particle in the form of solid solution [20]. It

has been referred to as the inner rim. Besides, various elements in cermets, such as Ti

and Mo, are dissolved into the solid binder phase (see in Chapter 4). This solid state

dissolution process will continue until the binder is saturated with the elements,

although it is possible that saturation might not be reached due to the high heating rate

used in practical cermet processing.

Compared with the rim formed during the liquid phase sintering stage to be

discussed below, the amount of rim growth via solid-state processes is comparatively

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65

thin [22]. And, during the initial stage of liquid phase sintering when the process of

solid dissolution prevails, this inner rim may be partially or totally dissolved by the

liquid binder phase.

6.2.2 Outer Rim Formation via Ostwald Ripening

For spherical grains dispersed in a very high volume fraction of liquid,

Lifshitz and Slyozov and Wagner had provided a detailed theoretical description of an

Ostwald ripening process (often referred to as the LSW theory in the literature).

According to the LSW theory, the grain growth kinetics follows the expression below:

ntt tKRR on =−33

(6.1)

where otR and ntR are the mean grain radius at time to and that at time tn, respectively,

and K is the growth-rate constant, which is given by

kTDCK o

2

98 Ω

=γ (6.2)

where γ is the interfacial tension between the solid and the liquid, Ω the atomic

volume of the solid, D the diffusion coefficient of the solute in the liquid, Co the

solubility of the solid in the liquid above a flat solid-liquid interface, and k the

Boltzmann constant. Dividing the reaction time into n equal time intervals, i.e.

tntn ∆⋅= , Equation (6.1) can be rewritten as

on tnt RR λ= where 31

31

∆⋅+=

ot

n

R

tKnλ (6.3)

The growth of individual grains by the Ostwald ripening process has also been

discussed by Greenwood [45], which follows the relationship below:

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66

( )

−= 1

3

RRK

dtRd where

kTDCK o

2

6 Ω=

γ (6.4)

where R is the radius of the grain in question and K is the growth-rate constant

pertaining to the grain concerned.

However, during liquid phase sintering, earlier researchers [23,24,46,47] noted

that the mean grain growth rate is affected by the low volume fraction of liquid binder

phase β and resultant grain contiguity G, defined as the average fraction of surface

area shared by one grain of the solid with all neighboring grains. Equation (6.4) thus

becomes (see appendix II for details)

−⋅⋅⋅= 113

RR

fRRA

dtdR (6.5)

where ( ) ( )kT

DCGA osl22

1129 Ω

⋅−⋅−

⋅=γ

ββ and 1<f .

Equation (6.5) can be solved numerically (see appendix III for details), giving

on tnt RR ⋅⋅⋅⋅⋅⋅= λλλλ 321 (6.6)

where

31

1

1321

12

12

22

32

22

13 11111

+

−⋅⋅

⋅⋅⋅⋅⋅⋅⋅⋅

⋅⋅⋅⋅⋅⋅⋅

∆=

−−− o

o

o

o

ot

t

n

n

t

t

nnntn R

RfR

R

R

tAλ

λλλλλλλλλλ

λ

(6.6a)

and nλ is given by Equation (6.3). Thus, the rim thickness at time tn ( tn ∆⋅= ) of

respective grains of initial radius ot

R is given by

oonn tnnttt RRR 11321 −⋅⋅⋅⋅⋅⋅=−= − λλλλλδ (6.7)

Figure 6.1 gives the rim thickness nt

δ as a function of initial grain radius ot

R

for various sintering conditions corresponding to different final mean grain radii ntR

(all normalized with respect to the initial mean grain radius otR in this figure). It is

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67

evident that for a given sintering condition, corresponding to a fixed ntR / otR value,

the nt

δ / otR values remain relatively constant within the range of initial grain radius

(ot

R / otR ) highlighted by the shaded region in the figure. For example, when

1.1=on tt RR , 3.0≈ontt Rδ for 253 ≤≤ oo

tt RR and 00.125.0 −=f . Similar

observations are also made for other sintering conditions with the value of nt

δ / otR

increases with increasing ntR / otR . In other words, when rim growth via Ostwald

ripening prevails during liquid phase sintering, the grains will attain comparable rim

thickness so long as the initial grain radius lies within the shaded region in Figure 6.1;

that is, the rim thickness is independent of initial grain radius for such grains. This

grain radius range will be used as a guide in the analysis of our experimental data to

be described in Section 6.4.

6.2.3 Outer Rim Formation via Precipitation from Solution during Cooling

During subsequent cooling, the solubility of solutes in the liquid binder phase

decreases with temperature. As a result, the solutes will precipitate out and deposit

onto the existing grains. Such a precipitation process gives rise to a rim of which the

thickness is largely determined by the amount of solute dissolved earlier in the liquid

binder phase and hence the sintering temperature employed.

Practical cermet systems contain a high volume fraction of hard phases of

larger than 0.75 at room condition. The volume fraction of hard phases remains

comparatively high even at the end of the liquid phase sintering stage prior to cooling.

These hard phases provide ready sites for the growth of rims via solute precipitation

during cooling. Therefore, in the derivation of rim thickness at the end of the cooling,

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68

Figure 6.1 Rim thickness (nt

δ ) as a function of initial radius of grains (ot

R )

for various sintering conditions corresponding to different final mean grain

radii ( ntR ). All nt

δ , ot

R and ntR are normalized with respected to the initial

mean grain size ( otR ).

( )00.1=fforRR oott

0 15 30 45 60 75

( )75.0=fforRR oott

0 10 20 30 40 50

( )50.0=fforRR oott

0 5 10 15 20 25

( )25.0=fforRR oott

0

1

2

3

4

0 20 40 60 80 100

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0t

t

Rn

δ

1.9

2.0=0tt RR n

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69

we may assume that the number of the solid particles remains constant, because

nucleation of hard phases from within the liquid binder phase is insignificant.

Let fh/b be the equilibrium volume of hard phase dissolved by unit volume of

the liquid binder phase at the sintering temperature. Note that fh/b is a thermodynamic

property of the material system concerned and is given by

−⋅=

kTQAf obh exp/ (6.8)

where Ao is constant and Q the dissolution energy per atom of the hard phase in the

liquid binder phase. Note that fh/b does not vary from location to location in the

system.

Now let us consider a local region in a cermet system at the end of the

sintering run prior to cooling. Let fh and fb be the volume fractions of the hard phase

and the binder phase in the starting compact at room temperature. Upon reaching

equilibrium at the sintering temperature, the volume fraction of undissolved hard

phase is given by

bbhhundis ffff ×−= / (6.9)

For simplicity, let us assume that all the hard phase grains in this region have

the same initial radius ot

R (note that ot

R may vary from region to region in the

cermet). Mass conservation requires that

3

34

otpundis Rnf π×= (6.10)

where np is the number of the hard phase grains per unit volume in the local region of

the cermet. Assuming that the radius of the grains increases from ot

R (at sintering

temperature) to nt

R (at room temperature) as a result of rim growth via solute

precipitation during cooling, mass conservation requires that the volume fraction of

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70

the rim phase precipitated out of the liquid binder on cooling equals the equivalent

volume fraction of the dissolved hard phase at the sintering temperature minus those

retained in the solid binder on cooling to room conditions, i.e.

−×+×=× 33'

// 34

34

on ttpbbhbbh RRnffff ππ (6.11)

where '/ bhf is the equilibrium volume of hard phase dissolved in unit volume of the

solid binder phase at room condition. Note that in Equation (6.11), it is assumed that

the volume fraction of the binder phase in the system remains relatively unchanged

before and after liquid phase sintering. Since '// bhbh ff >> , Equation (6.11) can be

simplified to give

−×=× 33

/ 34

34

on ttpbbh RRnff ππ (6.12)

Dividing Equation (6.12) by (6.10) and invoking 1=+ bh ff and Equations

(6.8) and (6.9) give

=

kTQ

ff

ARR

b

bo

t

t

n

o exp1

13

(6.13)

or 3

1

exp1

1−

−=kTQ

ff

ARRb

bott on

(6.14)

where fb is the volume fraction of the binder phase in the starting powder compact.

Since non ttt RR δ+= where

ntδ is final rim thickness (upon cooling to room

temperature), Equation (6.14) gives

on tt Rαδ = where

−=−

1exp1

13

1

kTQ

ff

Ab

boα (6.15)

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71

Note that α is a constant for a given cermet system and sintering temperature.

Thus, the rim thickness attained by individual particles via solute precipitation during

cooling is proportional to its initial radius. This is in contrast to that formed via the

Ostwald ripening process described earlier in which the resultant rim thickness is

independent of the initial particle size.

Since all particles grow proportionally to their respective initial radii, i.e.

( )α+⋅= 10tt RR

n, it follows that ( )α+⋅= 10tt RR n at all sintering conditions.

Equations (6.13) to (6.15) are also valid for the mean particle size and rim thickness,

i.e.

=

kTQ

ff

ARR

b

bo

t

t

n

o exp1

13

(6.16)

and 3

1

exp1

1−

−=kTQ

ff

ARRb

bott on (6.17)

Note that QQ = when rim growth is dominated by solute precipitation during

cooling.

6.3 Geometric Analysis of Core-Rim Structure

6.3.1 Geometric Consideration of Plane Sectioning

After sintering, the samples are cross-sectioned, ground and polished and then

examined under the scanning electron microscope (SEM). It should be noted that the

core-rim structures observed from SEM micrographs represent random cross-sections

of individual hard phase grains. The observed rim thickness is thus the apparent rim

thickness. In what follows, a geometric analysis of the core-rim structures obtained

from random cross-sections of individual hard phase grains will be presented to relate

the apparent rim thickness to its true thickness.

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72

Considering that the hard phase grains are spherical in shape both before and

after sintering and that they have a concentric core-rim structure. Let Ro and ro be the

true radii of a particle and its core, respectively. The true rim thickness, δo, is thus

given by ooo rR −=δ .

Assuming that each hemisphere of the hard phase grain in question with the

core-rim structure is sectioned into N parallel disks of equal thickness, ∆z, as shown in

Figure 6.2(a), i.e. zRN o ∆= , Figure 6.2(b) shows the cross-section of the particle on

the ith section.

Let us consider the case when the cutting produces a cross-section near the

middle portion of the grain. In this case, each cross-section shows two concentric

circles (Figure 6.2(b)), the outer circle corresponding to that of the grain while the

inner circle to that of the core.

Let Ri be the apparent radius of the outer circle and ri be that of the inner circle

of the ith section. The area in between the two circles is the rim phase, of which the

apparent thickness δi and its ratio to the apparent radius of the particle fi are given by

(see Figure 6.2(a)):

( ) ( )iiiiiii CBCArR −=−=δ (6.18)

i

ii R

f δ= (6.19)

where ( ) ( ) ( )22 ziRCA oii ∆⋅−= and ( ) ( ) ( )22 ziRCB ooii ∆⋅−−= δ . Since the true

rim thickness, ooo fR ⋅=δ , Equations (6.18) and (6.19) become

( ) ( ) ( ) ( ) ( )22222 1 zifRziR oooi ∆⋅−−⋅−∆⋅−=δ (6.20)

( ) ( )22 ziRf

o

ii

∆⋅−=

δ (6.21)

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73

(a)i = NPlate ic

∆z

i = 0

Plate i

A0 B0 C0

Ai Bi Ci

Plate 0

Ac Cc

(b)

Ai Bi C i

Figure 6.2 (a) Schematic cross-section of a hard phase grain with a

concentric core-rim structure and (b) the plain view of the ith cross-section.

(After Ref. [48])

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74

It should be noted that below a critical apparent particle radius Rc, only the rim

structure is produced by the sectioning technique, i.e. 0=cr (Figure 6.2(a)). This

corresponds to the case when

( ) ( ) ( ) ( ) coooooccc ffRrRCAR δ=−⋅=−== 222 (6.22)

Note that 1=if for cii ≥ .

6.3.2 Construction of f Distribution Curves and their Significance

The above analysis enables one to construct the distribution curve of the

apparent ratio of rim thickness to the overall radius of the hard phase grain obtained

from the plane sectioning technique, hereafter referred to as the f distribution curve.

To do this, we may fix the thickness of each plate ∆z at 0.005 µm. For a given value

of true grain radius Ro, the value of N ( zRN o ∆= / ) was determined. And, for a given

true rim fraction fo, where ooo Rf δ= , δo being the true rim thickness, a set of data of

fi, where

iii Rf δ= , for i increasing from 0 to N was determined. The data of fi so obtained

were arranged into groups with an interval of 0.1 in fi and the number distribution

(with respect to N) pertaining to each f interval was determined accordingly. Note

that for 0=i , the true rim thickness δo is the minimum of all the δi values.

Figure 6.3 shows the f distribution curves for 120=N but with different fo

values, corresponding to Ro = 0.6 µm and δo = 0.05, 0.10, 0.15, 0.20, 0.25 and 0.30

µm, respectively. For each curve shown in Figure 6.3, the peak value fp and the value

of the ratio 0ff p were determined. These values are given in Table 6.1 for easy

reference.

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75

Figure 6.3 f distribution curves for different δo values with mRo µ6.0= , mz µ005.0=∆ and 120=N .

Ro= 0.6 µm

∆z= 0.005 µm

N = 120

δo/∆z=

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Apparent Rim Fraction, f

Num

ber F

ract

ion

10

20

30

4050

60

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76

Table 6.1 Values of fp and fp/fo obtained from Figure 6.3 ( mRo µ6.0= ; mz µ005.0=∆ ; 120=N ).

δ0 (µm) f0 (=δ0/R0) fp fp/f0

0.05 0.08 0.13 1.63

0.10 0.17 0.22 1.29

0.15 0.25 0.30 1.20

0.20 0.33 0.38 1.15

0.25 0.42 0.47 1.12

0.30 0.50 0.55 1.10

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77

Table 6.1 and Figure 6.3 show that for 25.0≥oo Rδ , opo fff 2.1≤< , that is,

fp is a good representative value for fo in practical conditions. Furthermore, for

25.0≥oo Rδ , more than 90% of all sectioned grains have off 2< . In other words,

for a given hard phase size, there exists an insignificant number (less than 10%) of

cross-sections with off 2> . This implies that in analyzing experimental data of

core-rim structures, one may focus on the values of fo and fp of each f distribution

curve (of a given apparent hard phase size group). This helps in the actual analysis of

experimental data because in real specimen sections, those made from the top part of

large hard phase grains may be erroneously taken as data pertaining to smaller grains.

Such data, however, will have high f values. One may thus avoid such complications

by restricting the attention to the fo and fp values of the f distribution curves for

respective apparent hard phase size groups in the analysis.

6.3.3 Application to Rim Growth during Liquid Phase Sintering

As discussed in Section 6.2, Ostwald ripening during liquid phase sintering

and solute precipitation during cooling are the two main mechanisms of rim growth

during cermet processing. More importantly, these two processes have different grain

size dependence of rim growth behavior. When Ostwald ripening dominates rim

growth, the rim thickness is relatively independent of the initial size of the hard phase

grains (i.e., at the start of Ostwald ripening during the hold at the sintering

temperature). On the other hand, when rim growth is controlled by solute

precipitation during cooling, its thickness increases with the initial hard phase grain

size (i.e., that at the end of the sintering stage prior to cooling to room condition). In

what follows, we shall apply our geometric analysis described above to these two

cases separately.

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78

(a) Rim Growth via Ostwald Ripening during Sintering

When rim growth is dominated by Ostwald ripening, the resultant rim

thickness remains relatively constant and is independent of initial hard phase grain

size (Section 6.2.2). Thus, we may fix the value of δo in this case. Taking 15.0=oδ

µm, the f distribution curves for different true hard phase grain size (Ro) groups are

plotted in Figure 6.4. In this plot, the thickness of the sectioned discs, ∆z, is taken as

0.005 µm, and the number N for each Ro size group was obtained accordingly using

zRN o ∆= . Five different N values, hence hard phase grain size Ro, were used,

namely, N = 120, 140, 160, 180 and 200, corresponding to Ro = 0.6, 0.7, 0.8, 0.9 and

1.0 µm, respectively. Note that Ro here is the hard phase grain size at the end of the

temperature hold of the sintering cycle, which equals nt

R in Section 6.2.2.

Figure 6.4 shows that with increasing initial hard phase grain size (Ro

increasing from 0.6 to 1.0 µm or N increasing from 120 to 200), the f distribution

curves shift bodily towards smaller f values and hence having smaller values of fo and

fp. This can be readily visualized from the relationship: ooo Rf δ= . Similar findings

were obtained for other δo values.

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79

Figure 6.4 f distribution curves for different N values hence hard phase grain sizes for the case when the rim growth is controlled by Ostwald ripening during the liquid phase sintering stage ( mz µ005.0=∆ ;

mo µδ 15.0= ). Similar results are obtained for different δo values.

∆z= 0.005 µm

δ0 = 0.15 µm

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Apparent Rim Fraction, f

Num

ber

Frac

tion

N=200 (Ro=1.0 µm)

160 (0.8 µm)

120 (0.6 µm)140 (0.7 µm)

180 (0.9 µm)

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80

(b) Rim Growth via Solute Precipitation during Cooling

In this case, the resultant (true) rim thickness δo increases linearly with the

initial hard phase grain size ro, i.e., ( )000 δααδ −⋅=⋅= Rro , where Ro is the final

hard phase grain size and α is the proportional constant given by Equation (6.15).

Therefore, we have

αα

δδδ

+=

+==

1oo

o

o

oo rR

f (6.23)

In this case, we may keep the value of fo constant in the analysis regardless of the true

final hard phase grain size Ro, which equalsnt

R in Equation (6.14).

Taking 1.0=of , the curves of f distribution for different Ro size groups are

plotted in Figure 6.5. In this figure, the values of ∆z, and Ro, hence N, used are the

same as in Figure 6.4.

As shown in Figure 6.5, when solute precipitation dominates the rim growth

process, the f distribution curves pertaining to different N values, and hence hard

phases of different final grain sizes Ro, overlap nicely into a single curve; that is, they

have identical fo and fp values. This is true provided that the N value is sufficiently

large. Similar findings were obtained for other fo values.

It should be pointed out that unlike the theoretical f distribution curves, actual

experimental f distribution curves obtained from different hard phase grain size

groups may not overlap exactly. Nevertheless, we may conclude that when rim

growth is controlled by solute precipitation during cooling, different hard phase grain

size groups have f distribution curves of comparable fo and fp values.

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81

Figure 6.5 f distribution curves for different N values hence hard phase grain sizes for the case when the rim growth is controlled by solute precipitation during the cooling stage ( mz µ005.0=∆ ;

10.0=of ). Similar results are obtained for different fo values.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Apparent Rim Fraction, f

Num

ber F

ract

ion

∆z=0.005 µm

fo = 0.10

N = 120~200

Ro= 0.6~1.0 µm

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82

6.4 Experimental f Distribution Curves [48]

The starting materials used were Ti(C0.5,N0.5) powder (H.C. Starck; particle

size ≈ 1.5 µm), Mo2C powder (H.C. Starck; particle size ≈ 1 to 4 µm), and Ni powder

(Alfa Johnson Matthey; particle size ≈ 1 µm). Firstly, they were mixed by planetary

ball-milling in proportions of 0.7:0.1:0.2 in weight. To provide adequate lubrication

during compaction, carbowax was added as the lubricant. The ball-milling jars used

were lined with WC-Co on the inner surface and the volume of each of them was 800

cm3. The milling balls used were also made of WC-Co and the diameter of each of

them was 2 cm. Before ball-milling, 50g powder mixture and 2.5g carbowax were

put into a jar with 5 milling balls inside. The rotating speed used was 200 rpm. The

total time for every run was set as 10 hours, with every 30 minutes of ball-milling

followed by a break of 30 minutes.

After ball-milling, the mixture was uniaxially compacted in a steel die at a

pressure of 100 MPa into a rectangular-bar shape of about 51 × 8 × 6 mm in

dimensions. Then, the compact was dewaxed in an alumina tube furnace, into which

argon gas was flowed continuously to remove the burnt products of the lubricant. The

time-temperature cycle included heating at the rate of 5.5 °C/min, holding at 350 °C

for 1 h, followed by furnace cooling.

After dewaxing, the compacts were sintered in a Centorr high vacuum furnace

at 2 × 10-4 mbar or better. With a heating rate of about 12 °C/min, the compacts were

heated to one of the desired sintering temperatures (1400°C, 1440°C, 1480°C, 1520°C

or 1560°C), held for 90 min, and then cooled to the room temperature at a rate of

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83

about 12 °C/min (see footnote [4] below). Then, they were cross-sectioned, ground

polished, and then examined under the SEM.

From the SEM micrographs, the apparent rim thickness δi and the apparent

hard phase grain radius Ri were measured and recorded. The corresponding apparent

ratio of rim thickness to hard phase grain radius, fi, was calculated, where iii Rf δ= .

An average of 250 hard phase grains were counted per sample (i.e. per sintering

temperature). The fi data obtained were compiled into three groups according to their

apparent grain radii, i.e. Ri = 0.4-0.6 µm, 0.6-0.8 µm, 0.8-1.0 µm.

Figure 6.6 gives the number distributions of the apparent rim thickness ratio

(fi) for three size groups of hard phase grains (i.e. Ri = 0.4-0.6 µm, 0.6-0.8 µm, 0.8-1.0

µm) for five sintering temperatures of 1400°C, 1440°C, 1480°C, 1520°C and 1560°C.

It is evident from Figure 6.6(a) to (c) that the f distribution curves for different

hard phase grain size groups for the samples sintered at 1400°C 1440°C and 1480°C

have comparable fo and fp. In contrast, for the sample sintered at 1560°C (Figure

6.6(e)), not only do the f distribution curves have a much broader peak but also the

values of fo and fp decrease with increasing hard phase grain radius, suggestive of a

change in the rim growth mechanism.

4 After the sintering stage, several cooling rates were tested to determine the effect of the cooling rate on the rim thickness. It was found that the rim thickness remained the same when the compacts were cooled at the rate of 12 °C/min or lower. Therefore, in this work, a cooling rate of 12 °C/min was used to ensure that it reached the equilibrium cooling condition during liquid phase sintering.

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0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Apparent Rim Fraction, f

Num

ber F

ract

ion

(a) 1400°C

Ri = 0.8~1.0 µm

Ri = 0.6~0.8 µm

Ri = 0.4~0.6 µm

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Apparent Rim Fraction, f

Num

ber F

ract

ion

(b) 1440°C

Ri = 0.8~1.0 µm

Ri = 0.6~0.8 µm

Ri = 0.4~0.6 µm

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Apparent Rim Fraction, f

Num

ber F

ract

ion

(c) 1480°C

Ri = 0.8~1.0 µm

Ri = 0.6~0.8 µm

Ri = 0.4~0.6 µm

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85

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Apparent Rim Fraction, f

Num

ber F

ract

ion

(d) 1520°C

Ri = 0.8~1.0 µm

Ri = 0.6~0.8 µm

Ri = 0.4~0.6 µm

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Apparent Rim Fraction, f

Num

ber F

ract

ion

(e) 1560°C

Ri = 0.8~1.0 µm

Ri = 0.6~0.8 µm

Ri = 0.4~0.6 µm

Figure 6.6 f distribution curves for Ti(C,N) grains of different radius groups in

compacts sintered at different temperatures (a) 1400°C, (b) 1440°C, (c) 1480°C,

(d) 1520°C and (e) 1560°C. iR is the apparent hard phase grain radius as

measured from the SEM micrograph.

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6.5 Discussion

One obvious difference between the experimental f distribution curves and

those predicted theoretically is that the former have a much broader peak and higher

values of 0ff p , i.e. 20 ≈ff p for experimental f distribution curves compared with

20.10 ≤ff p predicted theoretically. This is because, firstly, apparent hard phase

grain sizes instead of true grain sizes were used in the experimental plots and,

secondly, each experimental f distribution curve was constructed from hard phases of

a range of grain sizes. Despite the said difference, as described in Section 6.3.1, in

analyzing the experimental results, we may focus our attention on how each hard

phase grain size group may affect the values of fp and fo of the f distribution curve and

compare the observed trend with the theoretical predictions.

Figure 6.6 shows that at low sintering temperatures (1400-1480°C), different

hard phase grain size groups have comparable f distribution curves and fo and fp

values. This agrees with the theoretical prediction of rim growth dominated by solute

precipitation during cooling (section 6.3.3). One may thus conclude that, at low

sintering temperatures (1400-1480°C), rim growth is controlled by solute-

precipitation process during cooling from the sintering temperature.

Our experimental results also show that after sintering at high temperatures

(i.e. 1560°C), hard phases of different grain sizes have distinctive f distribution curves

with the values of fo and fp decreasing with increasing apparent hard phase grain size

Ri (Figure 6.6 (e)). This is consistent with rim growth being dominated by Ostwald

ripening during the liquid phase sintering stage (Section 6.3.3).

The above results can be readily understood. At low sintering temperatures,

Ostwald ripening is limited and rim growth is dominated by solute precipitation

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mechanism; and the latter being determined by the amount of solutes dissolved in the

liquid binder phase at the sintering temperature. With increasing sintering

temperature, Ostwald ripening becomes more and more influential and would

dominate the rim growth process at sufficiently high temperatures.

Since the rim growth behavior at low sintering temperatures (i.e. for

CT °≤ 1480 ) is controlled by solute precipitation during cooling, taking natural log

on both sides of Equation (6.16), we have

kTQB

R

ro −=

− 3

3

1ln (6.24)

where r and R are the mean true core and grain radii of Ti(C,N) grains in sintered

cermets and ( ) bboo ffAB −⋅= 1ln . Figure 6.7 shows the plot of ( ) 331ln ii Rr−

versus 1/T for CT °≤ 1520 , where ir and iR are, respectively, the mean apparent

core and hard phase grain radii measured from the SEM micrographs of the sintered

samples. Using a least squares technique, a straight line was obtained with a slope of

− 4,100K, giving an activation energy of 34 ± 6 kJ/mol for the dissolution Ti(C,N) in

liquid Ni.

It has been reckoned that too thick a rim often leads to inferior mechanical

properties of cermets. Excessive rim growth via Ostwald ripening should therefore be

avoided. The present work shows that one should work within the temperature

regime where rim growth via solute-precipitation prevails; namely, by keeping the

sintering temperature to not more than 1480°C. Another advantage of keeping the

sintering temperature low is the avoidance of the denitrification process, which

becomes significant when sintering of nitrogen-containing cermets is performed at

sufficiently high temperatures, say, ≥ 1500°C [49,50].

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− 3

i

3i1Ln

R

r

T1 (x -310 K-1)

-0.50

-0.45

-0.40

-0.35

-0.30

-0.25

-0.20

0.56 0.57 0.58 0.59 0.60 0.61

Ti(C0.7,N0.3)-Mo2C- Ni

Slope = -4,100 K

Figure 6.7 Rim growth curve for Ti(C,N)-Mo2C-Ni system at low sintering temperatures (1400°C-1480°C). ir and iR are, respectively, the mean apparent core and grain radii of all Ti(C,N) grains determined from the SEM micrographs of the sintered samples.

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6.6 Summary

a) Ostwald ripening during liquid phase sintering and solute precipitation during

cooling give rise to different grain size dependent rim growth behaviors. When

Ostwald ripening dominates rim growth, the final rim thickness is relatively

independent of the initial hard phase grain size. On the other hand, when rim

growth is controlled by solute precipitation during cooling, its thickness

increases with initial hard phase grain size.

b) Our geometric analysis shows that when rim growth is controlled by solute

precipitation during cooling, the distribution curves of the ratio of apparent rim

thickness to apparent hard phase grain radius, f, for different size groups of hard

phase grains, as revealed by the plane-sectioning technique, appear similar with

comparable fo and fp values. On the other hand, when rim growth is dominated

by Ostwald ripening during liquid phase sintering, different hard phase grain

size groups display distinctive f distribution curves, hence different fo and fp

values. With the aid of the result of the geometric analysis, the rim growth

mechanisms during sintering of Ti(C,N)-based cermets at different temperatures

were identified.

c) At low sintering temperatures (i.e. 1400-1480°C), rim growth in

Ti(C,N)-Mo2C-Ni cermets is dominated by solute precipitation during the

cooling stage, with an activation energy of 34 ± 6 kJ/mol. At sufficiently high

sintering temperatures (i.e., ≥1560°C), rim growth mechanism in

Ti(C,N)-Mo2C-Ni cermets is dominated by Ostwald ripening via the

dissolution-reprecipitation mechanism during the liquid phase sintering stage.

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Chapter 7

Conclusions

Based on the findings presented in the previous three chapters, the following

conclusions can be drawn concerning cermet processing:

(I) Concerning effects of Mo2C, pure Mo and free C addition in cermet

processing

1. During the initial heating stage of the powder compact, a host of reactions

involving TiC and Mo2C and residual oxygen occur simultaneously. TiC will

be oxidised to TiO2 and Mo tends to dissolve in solid Ni or form rims of

(Ti,Mo)C or (Ti,Mo)(C,N). The compact thus consists of TiC or Ti(C,N)

particles covered with patches of TiO2 and (Ti,Mo)C or (Ti,Mo)(C,N) reaction

products.

2. On heating to sufficiently high but below the liquid phase sintering

temperature, TiO2 becomes unstable and will be reduced. In the absence of

Mo2C (or pure Mo), the oxide reduction process will further enrich the Ni

binder of Ti with potential risk of intermetallic formation. The presence of

Mo2C or pure Mo and free carbon not only helps rid the system of oxide and

residual oxygen via a series of mixed carbide formation reactions but also

regulate the Ti content in the Ni binder phase through the formation of

(Ti,Mo)C or (Ti,Mo)(C,N) rim, thus minimizing the risk of intermetallic

formation. The use of supplementary amounts of free carbon is highly

efficient to this effect.

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(II) Concerning the conditions for the spreading of the liquid binder phase during

liquid phase sintering

3. A model has been developed which relates the spreading of the liquid binder

phase in a powder compact to the packing factor and radius ratio of the liquid

binder sphere to the hard phase particles in the compact. For a given packing

factor, there exists a critical radius ratio of the liquid sphere to the hard phase

particles above which spreading will occur.

4. The model shows that at low θ values, i.e. θ < 45°, (rl/rs)c is relatively

independent of θ and a weak function of the packing factor f in the compact.

On the other hand, at high θ values, i.e. θ > 45°, (rl/rs)c increases appreciably

with increasing θ but with decreasing f values, its value being > 10 for θ >

75°. In contrast with conventional belief, the present work shows that even

with θ = 0°, spreading of the liquid binder phase will not occur if the packing

factor is low (say, f <0.4) and the liquid sphere radius is small (say, rl/rs < 3).

5. Experiments were carried out to verify the predictions of the model and to

determine the contact angles between the liquid Ni binder and Ti(C,N) phases

with and without Mo2C addition. Our experimental results give the contact

angles of 65° and 10° for the Ti(C,N)-Ni and Ti(C,N)-Mo2C-Ni compact

systems, respectively.

6. The present work shows that for good spreading in cermet processing, other

than keeping the initial size of the hard phase small, a high packing factor and

packing uniformity in the green structure are equally important. The system

should also be self-cleaning to ensure good wetting between the solid hard

phase and the liquid binder phase. Addition of Mo2C or pure Mo to TiC or

Ti(C,N)-based cermets plays a key role in this respect.

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(III) Concerning rim growth during cermet processing

7. Ostwald ripening during liquid phase sintering and solute precipitation during

cooling give rise to different grain size dependent rim growth behaviors.

When Ostwald ripening dominates, the rim thickness is relatively independent

of the grain size. When solute precipitation prevails, the rim thickness

increases with grain size.

8. A geometric analysis technique has been developed which describes the

distribution curves of the ratio of apparent rim thickness to apparent grain

radius, f, for hard phase grains of different grain radius groups determined

from cross sections of sintered cermets, from which the true grain radius and

rim thickness can be obtained. The results show that when rim growth is

controlled by solute precipitation during cooling, the f distribution curves for

different grain radius groups appear similar with comparable minimum cut-off

(fo) and peak (fp) values. On the other hand, when rim growth is controlled by

Ostwald ripening during liquid phase sintering, different grain radius groups

display distinctive f distribution curves, hence different fo and fp values.

9. The geometric analysis was used to investigate the rim growth mechanisms

during liquid phase sintering of Ti(C,N)-based cermets at different

temperatures, through which the dominant rim growth mechanism under

respective sintering conditions was identified. The results show that at low

sintering temperatures (i.e. 1400-1480°C), rim growth in the Ti(C,N)-Mo2C-

Ni cermets is dominated by solute precipitation during the cooling stage, with

an activation energy of 34 ± 6 kJ/mol.. At sufficiently high sintering

temperature (i.e. 1560°C), rim growth in the Ti(C,N)-Mo2C-Ni cermets is

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dominated by Ostwald ripening mechanism during the liquid phase sintering

stage.

(IV) Concerning overall cermet processing

10. The optimum sintering cycle should consist of a high heating rate to the

temperature slightly below the liquid phase sintering temperature to avoid

excessive dissolution of TiC and Mo2C in solid Ni. The compact is then held

at temperature to enable the surface oxide to be reduced. Then, the compact is

heated up rapidly to the sintering temperature to effect liquid phase sintering

with minimum grain growth and rim formation.

11. Proper control of starting powder composition and process environment are

essential to produce TiC and Ti(C,N) based cermets of superior

microstructures and, hence, properties; that is, the starting material should

contain sufficient amount of Mo2C (or Mo) and Ni, and residual oxygen level

in the system should be kept sufficiently low.

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Chapter 8

Recommendations for Future Work

Following are two recommendations for future work which will be useful in

attesting the new concept and/or experimental techniques put forth in the present work

and in providing a better understanding of processing of cermets.

1. The model on spreading of liquid binder in a compact, developed in Chapter 5 in

the present work, is applicable to any powder compact in liquid phase sintering.

The model predicts that spreading will occurs when the radius ratio of the liquid

binder sphere to the hard phase grains is above a critical value; the latter in turn

is a function of the contact angle of the system and the local packing factor.

Using the model, the contact angles between the hard phase grain and the liquid

binder phase in the Ti(C,N)-Ni and Ti(C,N)-Mo2C-Ni compacts were obtained

experimentally in the present work. It is recommended that more experiments

should be conducted to further attest the model and to evaluate the contact

angles in other relevant compacts such as TiC-Ni and Mo2C-Ni compacts. The

results should be compared with those obtained from the sessile-drop test with

both fully dense and partially dense powder compacts, to check the validity of

the sessile-drop test measurements.

2. In Chapter 6, a simple geometric analysis was proposed for the identification of

rim growth mechanism from cross-sections of sintered cermets. A simple

experiment was also performed with Ti(C,N)-based cermets. Our results show

that rim growth is controlled by solute precipitation at low sintering

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temperatures and by Ostwald ripening high sintering temperatures.

Furthermore, the activation energy for the hard phase dissolution was obtained

from the analysis. However, our experimental data remain limited such that we

are unable to perform similar analysis for rim growth under conditions when

Ostwald ripening dominates. Thus, more experiments should be carried out to

ascertain the sintering conditions which promote rim growth via Ostwald

ripening, i.e. at sufficiently high sintering temperatures. It should, however, be

noted that under a given processing condition, rim growth generally occur via a

combination of Ostwald ripening and solute precipitation. Since conditions

favoring each of these two rim growth mechanisms are very different, i.e. one

occurs during the liquid phase sintering and the other during subsequent cooling,

it is of interest for one to separate and assess the contribution of each rim growth

mode in a quantitative manner in order to enable a better control over the rim

growth behavior in cermet processing. This will be a challenging project for

further research.

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Appendix I Coating Mo2C on Ti(C,N) Particles

I.1 Introduction

As discussed in Chapter 4, the presence of Mo2C helps reduce the oxide

formed on the surface of Ti(C,N) particles, which consequently improves the wetting

at liquid phase sintering temperature. An alternative way to help eliminate the oxide

may be to work with coated powder, such a Ti(C,N) powder coated with either Mo2C

and/or Ni. In this work, a new process for coating Mo2C onto Ti(C,N) particles is

described. The advantages of using Mo2C coated Ti(C,N) powder are evident, as not

only can the powder compact be sintered at lower temperatures but also help

minimise the amount of Mo2C added, thereby providing better control over the rim

thickness in sintered Ti(C,N)-Ni based cermets.

I.2 Conceptual Considerations

The various process steps involved in coating Mo2C on TiC or Ti(C,N)

powder are as follows:

Firstly, MoO3 powder is dissolved into aqueous ammonia to form ammonium

molybdate, (NH4)2MoO4.

( ) 424233 MoONHOHNHMoO →++ (I.1)

On being heated to 300-400°C, (NH4)2MoO4 decomposes and MoO3 is formed

by the following pyrolysis reaction:

( ) OHNHMoOMoONH 233424 ⋅+→ (I.2)

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A two-stage conversion process is then used to convert Mo3O to Mo2C. The

first stage is to reduce MoO3 to MoO2 at 600-700°C. The second stage is to convert

MoO2 to Mo2C at 1000-1100°C, which is carried out in the presence of an excess of

C.

Stage I: OHMoOHMoO 2223 +→+ (I.3)

Stage II: OHCMoCHMoO 2222 442 +→++ (I.4)

I.3 Estimation of Amount of Mo2C Coating

We assume that all the (NH4)2MoO4 coated on the surface of Ti(C,N) powder

was transformed into MoO3 after the pyrolysis reaction and that all the MoO3 coated

on the surface of Ti(C,N) powder was transformed into Mo2C after the two-stage

conversion treatment.

Let x be the actual mass of bare Ti(C,N) powder, y the mass of MoO3 coating

on them before the two-stage conversion treatment, and z the mass of the resultant

Mo2C coating on the Ti(C,N) powder after the treatment. Then, if a and b are the

mass of the coated Ti(C,N) powders before and after the two-stage conversion

treatment, respectively, we have

x + y = a (I.5)

x + z = b (I.6)

Since the number of moles of the final product Mo2C is always half that of the

intermediate product MoO3, it follows that:

y/143.94 = 2 ×(z/203.89) (I.7)

Thus, by measuring the mass of the Ti(C,N) powder before and after the 2-stage

conversion treatement, a and b, one can estimate the mass of Mo2C from Equations

(I.5) to (I.7).

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I.4 Experimental Verification

Powders of MoO3, molybdenum (VI) oxide (Fluka), Ti(C0.7,N0.3) (H.C. Starck;

grade D; particle size 1-2 µm) and Mo2C (H.C. Starck; grade B, 2-4 µm) and pure Ni

(Alfa; 2.2 -3 µm) were used in the present work. Unlike the earlier three powders that

were relatively agglomerate-free, the as-received pure Ni powder existed in the form

of lumped or chained agglomerates (see Chapter 4 for SEM micrographs).

The following procedures were used to obtain the Mo2C coated Ti(C0.7,N0.3)

powder. Firstly, 2 mol of Ti(C0.7,N0.3) powder were put into a mortar made of

porcelain. After 0.3 mol of MoO3 was dissolved into 180 ml aqueous ammonia in a

beaker, 50 ml of the resultant solution was poured into the mortar. Ti(C0.7,N0.3)

powder with the solution was stirred with a pestle to a slurry state and then left to dry

to form the molybdate salt coating on the particles. The above procedure was

repeated three times to ensure a homogeneous coating formed on all the Ti(C0.7,N0.3)

particles.

After three coating cycles, the dried coated Ti(C0.7,N0.3) powder was held in an

alumina “boat” and placed inside the tube furnace, into which argon gas was flowed.

The time-temperature cycle used for the pyrolysis reaction is shown in Figure I.1,

which converts the ammonium molybdate salt to MoO3. The two-stage conversion

treatment was carried out in an electrically heated tube furnace, into which hydrogen

gas was flowed continuously. In the present work, the C-rich atmosphere is generated

by an excessive layer of Ti(C0.7,N0.3) powder in which the sample is encapsulated.

The time-temperature cycle used for the two-stage conversion treatment is shown in

Figure I.2.

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105

Figure I.1 Time-temperature cycle used for the pyrolysis reaction process.

Figure I.2 Time-temperature cycle used for the two-stage reduction process.

0

100

200

300

400

0 1 2 3 4 5

Time (min)

Tem

pera

ture

(°C

)330°C/h

350°C, 2 hour

Furnace Cool

0

300

600

900

1200

1500

0 2 4 6 8 10

Time (hour)

Tem

pera

ture

(°C

)

320°C/h

650°C, 2h

1050°C, 2h

400°C/h

Furnace Cool

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Figure I.3 and I.4 show the XRD patterns of the powder after the pyrolysis and

two-stage conversion treatment, respectively. The presence of MoO3 peaks indicates

that MoO3 was formed on the surface of Ti(C0.7,N0.3) powder after the pyrolysis

reaction (Figure I.3). After the two-stage conversion treatment, Mo2C peaks appear

confirming that a coating of Mo2C was formed on the surface of Ti(C0.7,N0.3) powder

(Figure I.4).

An example calculation is shown in Table I.1. The results show that in the

above three-cycle coating process, there was 0.02 mol of Mo2C coated on the surface

of 1.08 mol of the Ti(C0.7,N0.3) powder.

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0

200

400

600

800

5 25 45 65

2θ , °

I, c

ps

Ti(C0.7,N0.3)

Mo2C

0

250

500

750

1000

5 25 45 65

2 θ , °

I, c

ps

Ti(C0.7,N0.3)

MoO3

Figure I.3 XRD pattern of Ti(C0.7,N0.3) powder after the pyrolysis reaction.

Figure I.4 XRD pattern of Ti(C0.7,N0.3) powder after the two-stage conversion treatment.

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108

Table I.1 Example calculation of the amount of Mo2C coating produced by the two-stage conversion treatment.

Step Equation

Weight of coated Ti(C0.7,N0.3) powder before the two-stage conversion treatment ( yx + ):

gyx 12.71=+ (AI.1)

Weight of coated Ti(C0.7,N0.3) powder after the two-stage conversion treatment ( zx + ):

gzx 39.69=+ (AI.2)

Mass balance gives 89.203

294.143

zy×= (AI.3)

Solving Equations (AI.1) to (AI.3) gives:

x = 65.19g (or 1.08 mol) for Ti(C,N)

y = 5.93g for MoO3

z = 4.20g (or 0.02 mol) for Mo2C

Therefore, we have 4.20 g (0.02 mol) of Mo2C coated on 65.19 g (1.08 mol) of Ti(C0.7,N0.3) powder after each 3-cycle coating treatment.

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Appendix II Derivation of Equation (6.5)

Figure II.1 shows the schematic graph of smaller grains with their centres

evenly spaced on the surface of a spherical cage of radius L with the larger growing

grain located at its centre. During liquid phase sintering the smaller grains at the

periphery will shrink while the larger grain in the centre will grow accordingly.

Let us first consider the case when the smaller shrinking grains are in contact

with one another, forming a nice spherical cage. Ignoring local perturbation in solute

concentration right adjacent to individual grains within the spherical cage, the

problem at hand assumes a spherical or pseudo-spherical symmetry. This is especially

so when we focus our attention on the surface region of the growing grain in the

centre of the cage. In this case, the rate of volume increase of the growing grain can

be expressed as:

( )Rrdr

dCRDdt

RddtdV

=

⋅Ω== 23

34

4ππ (II.1)

where Ω is the atomic volume of the solute, R the radius of the growing grain at time

t, D the diffusion coefficient of the solute in liquid, drdC the concentration gradient

of the solute at distance r away from the centre of the growing grain.

When the surrounding shrinking grains are not in contact with one another, the

available solute flux to feed the growing grain in the middle will be reduced

accordingly. To a good approximation, the available solute flux is proportional to the

overall solid angle sustained by the surrounding grains with respect to the centre of

the growing grain which, in turn, is given by the area fraction of the hard phase within

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110

Figure II.1 A schematic showing smaller shrinking grains of radius Ri, distributed in

the form of a spherical cage of radius L with the growing grain located at its center.

The dotted grains are hypothetical grains which may not exist in practice but are

shown to illustrate the pseudo-spherical symmetry nature of the problem. r is the

radial distance from the centre of the embedded growing grain in the middle.

L

r

R

Ri’

R1’

R2’

Rn-1’

Rn’

x

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111

the spherical cage shown in Figure II.1. Taking area fraction equal volume fraction

for a random system, the fraction of available flux is given by (1 - β), where β is the

volume fraction of the liquid binder phase in the system. Equation (II.1) thus

becomes

( )Rrdr

dCRDdt

RddtdV

=

⋅Ω−== 23

34

4)1( πβπ (II.2)

Let R be the average radius of all the hard phases in the system 'R the

average radius of the shrinking grains in the cage shown in Figure II.1. For simplicity,

we may take 'R = f R , where f < 1. Assuming linear solute gradient along the radial

direction, the solute concentrate gradient can be expressed as shown in Equation

(II.3), assuming linear behavior.

xCC

drdC RR

Rr

−=

=

'

.

(II.3)

where RC and 'RC are the solute concentrations at the surfaces of the growing grain

and that of an average sized shrinking grain, respectively. x , defined as ( )'RRL +−

in Figure II.1, is the average free path that a solute atom has to travel from the

shrinking grains to the growing grain, which is given by [29]

( ) ( )GRx

−⋅

−⋅⋅=

11

134

ββ (II.4)

where β is the volume fraction of the liquid, and G the grain contiguity defined as the

average fraction of surface area shared by one grain of the solid with all neighbouring

grains.

According to Lifshitz and Slyozov [51], the expressions for solution

concentrations at the surfaces of the grains of radius R and 'R , respectively, are given

by

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112

Ω+⋅=

RkTCC sl

oR121 γ (II.5)

and

Ω+⋅=

'121' RkT

CC sloR

γ (II.6)

where Co is the solute concentration in the saturated solution, γsl the interfacial tension

between the liquid and solid, NA the Avogadro number and k the Boltzmann constant.

Substituting Equations (II.3), (II.4), (II.5) and (II.6) into Equation (II.2), we

obtain

−⋅⋅⋅= 113

RR

fRRA

dtdR (II.7)

where ( )kT

DCGA osl22

1)1(29 Ω

⋅−⋅−

⋅=γ

ββ .

It should be emphasized that Equation (II.7) is valid only for hard phase grains

which are much lagers in size than the average such that the smaller hard phase grains

will continue to dissolve to feed its growth. For grains which are only slightly larger

than the average sized grains, it may grow with respect to the smaller ones but shrink

with respect to the larger ones, or it may grow during the initial stage of sintering but

shrink at the later stage when all the smaller grains are consumed in the Ostwald

ripening process, a moderation factor may be used in conjunction with Equation

(II.7). The actual form of the moderation factor, however, may be fairly complex as it

has to take into account the statistical nature of the grain size distribution in the

system.

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113

Appendix III Derivation of Equation (6.6)

As described in Appendix II, the growth of individual hard grains via Ostwald

ripening during liquid phase sintering follows the relationship:

−⋅⋅⋅= 113

RR

fRRA

dtdR (III.1)

where ( ) ( ) kTDCGA osl22 1129 Ω⋅−⋅−⋅= γββ and 1<f .

When expressed in incremental form, we have

−⋅⋅⋅≈

∆∆ 113

RR

fRRA

tR (III.2)

We may divide the time period t, into n equal intervals, i.e. tntn ∆⋅= . Then,

for 1=n , we have

−⋅⋅⋅≈

−11

1

331

o

o

o

oo

t

t

t

t

o

tt

RR

fRR

AttRR

(III.3)

where 1t

R and ot

R are the radii of the grains concerned at time t1 and to, respectively,

and otR is the mean radius of all the grains at to. Let ottt −=∆ 1 , we get

ott RR 11λ= where

31

31 111

+

−⋅⋅⋅

∆=

o

o

o

o

ot

t

t

t

t RR

fRR

RtAλ (III.4)

At time t2 ( t∆×= 2 ), we have the radius of individual grains as

31

3 111

1

1

1

1

1

12

+

−⋅⋅⋅

∆=

t

t

t

t

ttt R

RfR

RR

tARR (III.5)

Substituting ott RR ⋅= 11 λ (from Equation (6.3) in the main text) and Equation (III.4)

into Equation (III.5), we get

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114

12 2 tt RR λ= where 31

1

1

12

132 11111

+

−⋅⋅⋅⋅⋅⋅

∆=

o

o

o

o

ot

t

t

t

t RR

fRR

R

tAλλ

λλλ (III.6)

Invoking Equation (III.4), we obtain

ott RR ⋅⋅= 122λλ (III.7)

Similarly, the radius of individual grains at time tn is given by

on tnt RR ⋅⋅⋅⋅⋅⋅= λλλλ 321 (III.8)

where

31

1

1321

12

12

22

32

22

13 11111

+

−⋅⋅

⋅⋅⋅⋅⋅⋅⋅⋅

⋅⋅⋅⋅⋅⋅⋅

∆=

−−− o

o

o

o

ot

t

n

n

t

t

nnntn R

RfR

R

R

tAλ

λλλλλλλλλλ

λ

(III.9)

Thus, the rim thickness nt

δ at the end of the sintering stage is given by

oonn tnnttt RRR 11321 −⋅⋅⋅⋅⋅⋅=−= − λλλλλδ (III.10)