reactive interdiffusion: a method for making composition...

High Temp. Mater. Proc., Vol. 31 (2012), pp. 97–103 Copyright © 2012 De Gruyter. DOI 10.1515/htmp-2012-0015

Reactive Interdiffusion: A Method for Making CompositionGraded Metal-ceramic Composites

S. N. S. Reddy,1 K. T. Jacob2;� and G. Rajitha2

1 Microelectronics Division, IBM, East Fishkill Facility,Hopewell Junction, New York, USA

2 Department of Materials Engineering, Indian Institute ofScience, Bangalore, India

Abstract. Presented is a new method for making composi-tion graded metal-ceramic composites using reactive inter-diffusion between a metal and a complex ceramic. Compo-sition variation in both metal and ceramic phases with dis-tance along the direction of diffusion is achieved. The de-sign criteria for developing such composites are discussed.The system should exhibit extensive solid solubility in bothmetallic and ceramic phases, a defined gradation in the sta-bilities of the oxides, and mobility of electrons or holesin the oxide solid solution. The complex ceramic usedfor making the composite should be polycrystalline withsufficient porosity to accommodate the volume expansioncaused by alloy precipitation. An inert atmosphere to pre-vent oxidation and high processing temperature to facilitatediffusive transport are required. The process is illustratedusing the reaction couples Fe-NiTiO3, Fe-(Mg,Co)TiO3

and Fe-(Ni,Co)TiO3.

Keywords. Composition-graded composites, metal-ceramic composite, diffusion, interfaces, microstructure.

PACS®(2010). 66.30.Ny, 81.05.Mh, 82.30.-b, 82.33.Pt.

1 Introduction

Implementation of the concept of functionally gradedmaterials (FGM) has enabled designers to meet morestringent specifications and create novel structures foradvanced technologies since material properties can bechanged as a function of spatial coordinates [1, 2]. FGMsare superior to monolithic or homogeneous materials formany applications such as armor [3], thermal barrier coat-ings (TBC) [4], slurry erosion resistant surfaces [5], andthermo and pyro-electric devices [6–8]. FGMs are usually

* Corresponding author: K. T. Jacob, Department of MaterialsEngineering, Indian Institute of Science, Bangalore 560 012, India;E-mail: [email protected].

Received: July 12, 2011. Accepted: December 17, 2011.

prepared by the powder metallurgy technique [3, 6, 9].Cui and Zhao have prepared (PbTe)1�x-(SnTe)x basedFGMs using pressure-less sintering [7]. Plasma sprayinghas also been used for the preparation of metal-ceramiccomposite FGMs [1,10,11]. For use in the plasma sprayingtechnique, a mixture of metal and ceramic powders isusually ball-milled in argon atmosphere. This ball-milledmixture is then plasma sprayed on to a suitable substrateto get a uniform layer of coatings. By changing the metalto ceramic ratio in the feed material, layers of differentcompositions can be deposited. The composite coatingwill have a graded structure. Sabatello et al. [2] have fab-ricated graded TiC-based cermets by infiltration of porousceramic preform with molten metal. Using laser-baseddirect material deposition, Yarrapareddy et al. [5] havedeposited an FGM consisting of Ni and WC powders onAISI 4140 steel plate. The FGM had a high percentage ofdiscrete WC particles in a Ni matrix, with the percentageof WC varying in each layer of the deposit [5]. Put etal. [12] have processed WC-Co ceramic-metal FGMs byelectrophoretic deposition (EPD) by applying a voltage of800 V between two parallel flat stainless steel electrodesplaced in a polytetraflourethylene cell containing organicacetone/n-butylamine medium in which particles to bedeposited were suspended The composition of the depositwas varied by continuously pumping concentrated slurryinto the deposition cell. The surface of the deposition elec-trode was coated with graphite to facilitate the removal ofthe deposit after EPD and to avoid cracking of the depositduring drying. After drying, the green WC-Co bodies werecold isostatically pressed at 300 MPa and sintered in agraphite furnace at 1563 K in vacuum (�10 Pa) [12].

The purpose of this communication is to report anew method – reactive interdiffusion – for the fabricationof graded metal-ceramic composites, albeit over smallerlength scales. All the fabrication methods for composition-graded metal-ceramic composites produce materials inwhich the ratio of metal to ceramic can be varied in oneor more directions. No method is available in which thecomposition of each phase in the composite can be variedsimultaneously with distance. The main advantage of reac-tive interdiffusion is its ability to affect spatial variation incomposition of the constituent phases. The microstructurecan consist of either alloy particles embedded in ceramicmatrix or alloy deposits along grain boundaries of the ce-ramic matrix. The ceramic matrix may be a single crys-tal or poly-crystalline, single-phase or multi-phase. The

Authenticated | [email protected] author's copyDownload Date | 7/9/12 3:45 PM

98 S. N. S. Reddy, K. T. Jacob and G. Rajitha

method evolved from studies on internal displacement re-actions in ternary and higher order oxides which have beenpublished [13–16]. The results suggested a new method formaking composition-graded metal-ceramic composites. Inthis review a more general approach from an engineeringpoint of view is presented. The system requirements forengineering such graded metal-ceramic composites are dis-cussed and the process illustrated with examples. Thermo-dynamic and kinetic constraints on systems that can gener-ate graded composites are analyzed from a theoretical an-gle.

2 Design Criteria for Engineering a Composition-Graded Metal-ceramic Composite

The method is based on a displacement reaction betweena metal (M) and an oxide component (NOc/ of a complexceramic (NaXbOp/. The complex ceramic may be visual-ized as an inter-oxide compound formed from binary oxidesNOc and XOd , such that ac C bd D p. The metal and ce-ramic are initially mated at an interface, where the reactionoccurs. The process is carried out in an inert atmosphere.The reaction involves the reduction of the oxide componentNOc of the complex ceramic by metal M, which can be rep-resented either as

.M/ C ŒNOc � ! ŒMOc� C .N/; (1)

were the binary oxides in bracket are oxide components ofthe complex oxide, or as

aM C NaXbOp ! MaXbOp C aN: (2)

The reaction results in a microstructure consistingof an alloy (MxN1�x/ and an oxide solid solution(MyN1�y/aXbOp, where the composition of the alloy des-ignated by x and of the solid solution designated by y varyin the direction of diffusion. The fabrication of such a com-position graded metal-ceramic composite by reactive inter-diffusion requires that the ionic and metallic radii of M andN be close rM2cC � rN2cC and rM � rN, differing by lessthan �12%, in order that a single-phase oxide solid solu-tion and alloy are obtained at high temperature. Further, thecrystals structures of the two metals, and the two ternary ox-ide phases should be similar. Electron affinities of the puremetals and acidity or basicity of the oxides should be com-parable. The phase diagrams for the binary alloy system M-N and pseudo-binary oxide system MaXbO- NaXbO wouldthen show continuous solid solubility.

The production of such a composite also requires thatthe normalized standard Gibbs free energy of formationof the different binary oxides should be in the order�Gı

f.XOd /=d � �Gı

f.MOc/=c < �Gı

f.NOc/=c. The

Gibbs free energies of formation of oxides are assessed for

one oxygen atom in the oxide for comparison of relativestability. With the indicated order of oxide stabilities, thecomponent XOd of the complex oxide will not be reducedby metal M, but component NOc will be reduced to form analloy M-N.

Since the reaction involves oxidative dissolution of metalM as M2cC into the complex oxide at the metal=oxide inter-face and the reduction of N2cC to metal N inside the oxidematrix, electronic conduction in the oxide phase is requiredfor the reaction to proceed. If the transport number of elec-trons is close to unity, the reaction rate will be controlled bycation transport. The displacement reaction cannot proceedto any significant extent if the oxide phase is predominantlyan ionic conductor.

The process temperature should be sufficiently high topermit diffusion in both metal and oxide phases. Theduration of the process and the length scale of the com-posite formed are dependent on the process tempera-ture. Under the conditions specified above, the forma-tion of compositionally-graded metal-ceramic composite(MxN1�x/ C .MyN1�y/XOp can take place. The designcriteria are based on theoretical considerations, temperedby experimental observations.

3 Experimental Illustration

Reactive-interdiffusion process for the formation of themetal-ceramic composite can be illustrated using the systemFe-NiTiO3, where metallic iron (Fe) is brought into contactwith a ternary oxide NiTiO3 with ilmenite structure at hightemperature. In this case a displacement reaction occursbetween Fe and NiTiO3 at the interface because of the dif-ference in the Gibbs free energies of formation of NiTiO3

[17] and FeTiO3 [18]:

Fe C NiTiO3 ! Ni C FeTiO3: (3)

The product Ni forms an alloy with reactant Fe, and sim-ilarly FeTiO3 forms a solid solution with NiTiO3 becauseof the close similarity in the metallic and ionic radii of Feand Ni and identical crystal structures of the two metal andoxide phases. The phase diagram showing the direction oftie-lines connecting the alloy and the oxide solid solutionwith ilmenite structure has been determined recently [19].Diffusion of Fe from the reaction interface into the initiallycontinuous NiTiO3 phase causes precipitation of Ni as analloy phase. A product layer is formed between the initialreacting phases with the passage of time as shown in Fig-ure 1.

The reaction–diffusion system can be divided into threezones; metallic Fe, reaction-diffusion zone or product layerconsisting of Fe-Ni alloy and (Fe,Ni)TiO3 solid solution,and unreacted NiTiO3. At 1273 K, the length of the prod-uct layer is 560 �m after 129.6 ks. Reddy et al. [13] have


Composition Graded Metal-ceramic Composites 99

Figure 1. Cross-section through the reaction-diffusion cou-ple Fe-NiTiO3 along the diffusion direction showing theformation of metal-ceramic composite through the dis-placement reaction, Fe C NiTiO3 D “Ni” C “FeTiO3”, at1273 K after 129.6 ks. Bright phase is (Ni-Fe) alloy; greyphase is oxide solid solution with ilmenite structure; darkareas in NiTiO3 and product layer are pores.

studied the reaction between Fe and polycrystalline NiTiO3

and between Fe and single-crystalline NiTiO3 at 1273 K. Ineach case, reaction resulted essentially in the formation oftwo-phase microstructure containing � -(Fe–Ni) alloy and(Fe,Ni)TiO3 solid solution in the reaction-diffusion zone.At higher magnification, a few specs of TiO2 precipitatewere seen inside the ilmenite grains when polycrystallineNiTiO3 was reacted with Fe, suggesting very minor de-composition of the ilmenite phase. No TiO2 precipitateswere seen when single crystal NiTiO3 was reacted with Fe.Compositions of the alloy and ilmenite solid solution werefound to vary with distance along the direction of diffusion.The nature of distribution of the alloy phase in the two-phase microstructure depended on the initial microstructureof NiTiO3. In the case of polycrystalline NiTiO3, the al-loy was mainly precipitated at triple grain junctions or nearpores; the precipitates get connected along the grain bound-ary with time. When single-crystalline NiTiO3 was used,the alloy precipitated as elongated ribbons, arranged in lay-ers perpendicular to the diffusion direction.

There is significant volume expansion in the productlayer, caused by the precipitation of the alloy in the oxidesolid solution phase. In the case of single crystal NiTiO3,the volume expansion results in the formation of cracks. Inpolycrystalline NiTiO3, the volume expansion caused by al-loy precipitation is largely absorbed by the pores presentin the initial polycrystalline oxide microstructure. Hence,sintered complex oxide having sufficient porosity to absorbthe volume expansion is required as the starting material

to make composition-graded metal-ceramic composites forengineering applications.

The compositions of both the alloy and the oxide solidsolution vary continuously inside the reaction-diffusionzone. Reddy et al. [13] have determined the composition ofthe oxide and alloy phases accurately as a function of dis-tance in the product zone using electron microprobe analy-sis (EPMA) of samples cooled from 1273 K after heat treat-ment for �230 ks. The concentration of Fe in the alloyphase and FeTiO3 in the oxide phase decrease, while thoseof Ni and NiTiO3 increase in the direction of diffusion asshown in Figure 2. In the product oxide, the concentrationTi remains constant. The ilmenite structure can be visu-alized as the corundum structure with Ni=Fe and Ti ionsalternating in layers along the c-axis of the unit cell. SinceNi and Fe ions diffuse on the same cation sub-lattice, theirfluxes may be correlated.

The compositions of the two phases in the composite lieon the dotted inclined quadrilateral in the isothermal tetra-hedral representation of phase equilibria in the quaternarysystem Fe-Ni-Ti-O shown in Figure 3, where the forma-tion of higher oxides of Fe and their solid solutions are notshown for clarity. Tie-lines connect alloy compositions tocomposition of titanate solid solution. The two-phase re-gion can exist over a range of oxygen potentials. How-ever, since many other phases can form at higher and loweroxygen potentials in this quaternary system, it is importantto conduct the reactive interdiffusion processes under inertconditions.

The growth of the product layer with graded compositionfollows parabolic rate law; the length (l) in the direction ofdiffusion increases linearly with the square root of time (t).The rate constant (kp) defined by the relation, l2 D 2kp � t ,has been found to be kp D 1:3 � 10�12 m2 s�1 at 1273K. The growth rate was almost the same when using sin-gle and polycrystalline NiTiO3 as the starting material forthe reaction. This indicates that the kinetics is controlled bythe lattice diffusion of Fe and Ni, and that any contributionof diffusion along grain boundaries is negligible. The grainboundaries in polycrystalline oxide act as preferred nucle-ation sites for � -alloy precipitates, as is evident in Figure 1.To calculate the magnitude of the rate constant a priori, in-formation on transport properties (diffusion data for Ni andFe) in (Ni,Fe)TiO3 should be available.

One would not generally expect the direct solid-state dis-placement reaction (3) to proceed to equilibrium. How-ever, careful analysis [14] shows that the compositions ofthe alloy and oxide in the composition-graded compositeexhibit only minor deviations from local equilibrium. Thiscan be explained by the occurrence of secondary reactionswhich push the compositions of the two phases towardsequilibrium. If the displacement reaction (3) does not reachequilibrium, the activities of Ni in the alloy and FeTiO3 inthe oxide solid solution will be lower and those of Fe andNiTiO3 higher than those at equilibrium. Because the ac-



0.0 0.1 0.2 0.30

100

200

300

400

500

600

700

800D

istan

ce

m

XFe in Fe-Ni in alloy

(a)

0.0 0.1 0.2 0.3 0.4 0.5

0

200

400

600

800

1000

NiTiO3

Dist

ance

m

Ni / (Fe + Ni + Ti) Fe / (Fe + Ni + Ti) Ti / (Fe + Ni + Ti)

Cation fraction in the oxide phase

Fe

Reaction Zone

(b)

Figure 2. Composition of the (a) alloy and (b) oxide phasesin the product layer formed by the reaction of Fe withpolycrystalline NiTiO3 at 1273 K after 230.4 ks

tivity of NiTiO3 is higher and that of Ni lower than that atequilibrium, NiTiO3 can dissociate according to the reac-tion:

NiTiO3 ! Ni C TiO2 C O2: (4)

Similarly, since the activity of FeTiO3 is lower and that ofFe higher when the displacement reaction is displaced fromequilibrium, the formation of FeTiO3 can occur by the re-action:

Fe C TiO2 C O2 ! FeTiO3: (5)

Since the oxygen partial pressure corresponding to the dis-sociation reaction (4) would be higher than that correspond-ing to the formation reaction (5) when the displacement re-action (3) is displaced from equilibrium, the coupled reac-tions (4) and (5) move the compositions closer to equilib-

Figure 3. Isothermal section in the quaternary system Fe-Ni-Ti-O showing phase relations of the interest to reactiveinterdiffusion in the couple Fe: NiTiO3.

rium. When full equilibrium is achieved, the oxygen po-tentials corresponding to reactions (4) and (5) would be thesame. If the rates of reactions (4) and (5) are equal, therewill be no TiO2 precipitate in the microstructure of the com-posite. Since only a limited number of small precipitates ofTiO2 were seen under high magnification when polycrys-talline NiTiO3 was reacted with Fe, it indicates that reac-tions (4) and (5) are almost compensating each other andthe system is close to equilibrium. The absence of TiO2

precipitates when single crystal NiTiO3 was used is perhapsattributable to the higher energy required to nucleate TiO2

inside the single crystal. This understanding is useful fordesigning more complex microstructures of composition-graded metal-ceramic composites.

4 Complex Microstructures

Microstructures of composition-graded metal-ceramiccomposites more complex than that illustrated in the pre-vious section can be designed using reactive interdiffusion.Three examples are considered. First, one can conceive athree-phase metal ceramic composite consisting of an alloyC oxide solid solution C oxide of constant stoichiometry.Such a microstructure can be generated by reacting metal-lic iron with a two-phase sintered oxide pellet consistingof an intimate mixture of NiTiO3 and TiO2. Reactiveinterdiffusion will produce a three-phase microstructureconsisting of Fe-Ni alloy and (Fe,Ni)TiO3 solid solutionof variable composition and TiO2. The advantage of thismicrostructure is that the oxygen chemical potential is de-fined by three-phase equilibrium at all locations inside thecomposite at high temperatures. The three-phase region isshown by a volume element bounded by a quadrilateral andfour triangles in Figure 3. For a fixed composition of thealloy or titanate solid solution, the three-phase equilibrium



is depicted by a triangle joining the compositions of thetwo solid solution phases in equilibrium with that of TiO2.Since the alloy and oxide solid solution compositionsvary with distance, there will be a corresponding variationin the oxygen potential profile, from a low value at theFe/product layer interface to a higher value at the productlayer/NiTiO3CTiO2 interface. There will be an oxygenchemical potential gradient even in the absence of TiO2 asa separate phase, but then the values at any location canvary over a range and are not well defined.

A second example considered is a composition-gradedcomposite consisting of a binary alloy and a pseudo-ternary oxide solid solution. Such a microstructure canbe generated by reacting metallic Fe with a complex ox-ide solid solution (pseudo-binary) of fixed compositionhaving the ilmenite structure. Consider the couple Fe-(Mg0:5Co0:5/TiO3. Because the Gibbs energy of forma-tion of MgTiO3 is very much more negative than those ofCoTiO3 [20] and FeTiO3 [18], metallic Fe will not reduceMgTiO3 component of the ilmenite solid solution. MetallicFe will only displace Co in the ilmenite solid solution, re-sulting in a microstructure consisting of Fe-Co alloy and aternary oxide solid solution (Mg,Co,Fe)TiO3. No precipita-tion of TiO2 was seen in the ilmenite phase, suggesting thatthe alloy-oxide equilibrium is close to equilibrium. SinceMgTiO3 is not reduced by Fe, one would expect its compo-sition in the ilmenite phase to be unaffected by the displace-ment reaction, at least to a first approximation. Figure 4shows the composition profile in the ilmenite phase of thecomposition-graded metal-ceramic microstructure obtainedusing the couple Fe-(Mg0:5Co0:5/TiO3. It is the seen thatMg profile exhibits a maximum in the reaction-diffusionzone, while the profiles for Fe and Co are as expected. TheMg profile can be explained in terms of variation of activ-ity coefficients in the pseudo-ternary titanate solid solutionand cross-coefficients in the transport coefficient matrix. Adetailed description and analysis of transport processes inthis reaction-diffusion couple is published elsewhere [15].A similar pattern of composition profiles was also observedfor the couple Fe:(Mg,Ni)TiO3 [16]. The important findingis that composition profiles exhibiting maxima in the oxidesolid solution can be generated in the composition-gradedcomposite.

The third example is a composition-graded metal-ceramic composite in which the alloy and oxide phasesare ternary (or pseudo-ternary) solid solutions along withan oxide of fixed composition. The microstructure con-sists of three phases, compositions of two ternary solu-tions varying with distance in the direction of diffusion.Such a composite can be generated by using the couple Fe-(Ni,Co)TiO3. Here, both components of the initial titanatesolid solution can be reduced by Fe, so that a ternary alloy(Fe,Ni,Co) is formed along with a ternary titanate solid so-lution (Fe,Ni,Co)TiO3. The system is characterized by twodisplacement reactions, unlike in the two examples consid-

Figure 4. Composition profiles of the titanate solid solutionformed by reaction of Fe with (Co0:48Mg0:52/TiO3 after360 ks at 1273 K.

ered earlier. In addition to the displacement reaction (3),there is an additional displacement reaction,

Fe C CoTiO3 ! Co C FeTiO3; (6)

because the Gibbs free energy of formation of CoTiO3 [20]is less negative than that of FeTiO3 [18]. When the twodisplacement reactions are away from equilibrium, in addi-tion to the dissociation of NiTiO3 according to reaction (4),there is an additional titanate dissociation reaction involv-ing CoTiO3:

CoTiO3 ! Co C TiO2 C O2: (7)

The formation reaction (5) will use the TiO2 and oxygengenerated by the two dissociation reactions to form FeTiO3.However, the single formation reaction cannot compensatefor the two dissociation reactions, with the result that athree-phase microstructure will invariably result with sig-nificant amount of TiO2 precipitated inside the titanate solidsolution phase. It is important to note that unlike in the firstexample, TiO2 was not a component of the starting mate-rials used to form the composite; it is formed in situ byreaction. Further, the excess oxygen released by the twodissociation reactions will cause an oxygen flux towards themetal Fe (the low oxygen potential side) and cause the for-mation of oxygen-rich phases (FeO or FeO-rich solid so-lution) adjacent to the metal. The composition profile ofCo in the titanate solid solution exhibits a maximum alongthe direction of diffusion because of the higher activity co-efficient of CoTiO3 in the (Fe,Ni,Co)TiO3 solid solutionsformed by the displacement reaction compared to the ini-tial (Ni,Co)TiO3 solid solution, and possible interaction be-tween the diffusion of Fe, Co and Ni on the same sublatticeof the ilmenite structure.

The similarities and differences between the three ex-amples of composition-graded metal-ceramic compositeswith complex microstructures discussed above are sum-marized in Table 1. The principles outlined here can be



Example Starting Materials Reaction Product Characteristics Special Features

1 Metal C Complex Displacement Three-phase Compositions of alloy and oxide ss

(ternary) oxide C reaction between microstructure. (Binary vary with distance. At high

Binary oxide metal and ternary alloy C Pseudo-binary temperature, oxygen potential is

oxide complex oxide ss C defined at all locations inside the

Binary oxide) composite.

2 Metal C Complex Displacement Two-phase Compositions of alloy and oxide ss

oxide ss (pseudo- reaction between microstructure. (Binary vary with distance. Composition

binary) metal and one alloy C Pseudo-ternary profile of one component of the oxide

component of the complex oxide ss) ss exhibits maxima.

oxide ss.

3 Metal C Complex Displacement Three-phase Compositions of alloy and oxide ss

oxide ss (pseudo- reaction between microstructure. (Binary vary with distance. Composition

binary) metal and both alloy C Pseudo-binary profile of one component of the oxide

components of the complex oxide ss C ss exhibits maxima. At high

oxide ss. Binary oxide). The binary temperature, oxygen potential is

oxide is produced by defined at all locations inside the

reaction. composite.

Solid solution is abbreviated as ss

Table 1. Similarities and differences between three composition-graded metal-ceramic composites with complex mi-crostructures prepared by reactive interdiffusion.

readily extended to design a variety of microstructures ofcomposition-graded metal-ceramic composites with morecomponents and differing profiles of composition.

5 Summary

Reactive interdiffusion has been introduced as the effectivemethod for the preparation of composition-graded metal-ceramic composites in which the composition of each phasecan be varied simultaneously with distance. The methodis based on one or more displacement reactions betweenthe metal and a complex oxide. The conditions for reac-tive interdiffusion to generate a two phase microstructureconsisting of an alloy (M-N) and a ceramic solid solution(M,N)aXbOp are (i) extensive solid solubility in the metal-lic and ceramic phases, (ii) a defined gradation in the sta-bilities of the oxides, (iii) mobility of electrons or holes inthe oxide solid solution, (iv) sufficient porosity in the ini-tial complex oxide to absorb volume expansion caused byalloy precipitation, (v) inert atmosphere to prevent oxida-tion of the metal and reduction of the oxide, and (vi) highprocessing temperature to facilitate diffusive transport. Theprocess is illustrated using the reaction couple Fe-NiTiO3

system, which generates a product layer in which an Fe-Ni alloy coexists with (Fe,Ni)TiO3. Compositions of bothphases vary with distance. More complex three-phase mi-crostructures with composition profiles exhibiting maxima

can be designed by suitable choice of starting oxide compo-sitions.

Acknowledgments

This work was partially supported by the University GrantsCommission, India, through the award of Dr. D. S. KothariPostdoctoral Fellowship to G. Rajitha, and by the IndianNational Academy of Engineering through the award ofDistinguished Professorship to K. T. Jacob.

References

[1] Y.-S. Yin, J.-D. Zhang, J. Li and Y. Chen, Mechanical Prop-erties of Fe3Al=Al2O3 Composite Graded Coatings, Appl.Surf. Sci., 221 (2004), 384–391.

[2] S. Sabatello, N. Frage and M. P. Dariel, Graded TiC-basedCermets, Mater. Sci. Eng., A, 288 (2000), 12–18.

[3] Z. He, J. Ma and G. E. B. Tan, Fabrication and Character-istics of Alumina-iron Functionally Graded Materials, J. Al-loys Compd., 486 (2009), 815–818.

[4] G. W. Meetham, Coating Requirements in Gas Turbine En-gines, J. Vac. Sci. Technol., A, 3 (1985), 2509–2515.

[5] E. Yarrapareddy, S. Zekovic, S. Hamid and R. Kovacevic,The Development of Nickel–tungsten Carbide FunctionallyGraded Materials by a Laser-based Direct Metal Deposi-tion Process for Industrial Slurry Erosion Applications, Proc.IMechE Part B: J. Engineering Manufacture, 220 (2006),1923–1934.



[6] Y. Gelbstein, Z. Dashevsky and M. P. Dariel, Powder Metal-lurgical Processing of Functionally Graded p-Pb1�xSnxTeMaterials for Thermoelectric Applications, Physica B, 391(2007), 256–265.

[7] J. L. Cui and X. B. Zhao, The Design and Properties of Pseu-dobinary Alloys (PbTe)1�x-(SnTe)x with Gradient Compo-sition, Mater. Lett., 57 (2003), 2466–2471.

[8] R. W. Whatmore, Q. Zhang, C. P. Shaw, R. A. Dorey andJ. R. Alcock, Pyroelectric Ceramics and Thin Films for Ap-plications in Uncooled Infra-red Sensor Arrays, Phys. Scr.,T129 (2007), 6–11.

[9] J. Ma, Z. He and G. Tan, Fabrication and Characterizationof Ti-TiB2 Functionally Graded Material System, Metall.Mater. Trans. A, 33 (2002), 681–685.

[10] K. Khor, Y. Gu and Z. Dong, Plasma Spraying of Function-ally Graded Yttria Stabilized Zirconia/NiCoCrAlY CoatingSystem Using Composite Powders, J. Therm. Spray Tech-nol., 9 (2000), 245–249.

[11] X. Xinhua, Z. Jingchuan, Y. Zhongda and L. Zhonghong,Fabrication and Microstructure of ZrO2=NiCrCoAlYGraded Coating by Plasma Spraying, Surf. Coat. Technol.,88 (1996), 66–69.

[12] S. Put, J. Vleugels, G. Anné and O. Van der Biest, Function-ally Graded Ceramic and Ceramic-metal Composites Shapedby Electrophoretic Deposition, Colloids Surf., A, 222 (2003),223–232.

[13] S. N. S. Reddy, D. N. Leonard, L. B. Wiggins and K. T.Jacob, Internal Displacement Reactions in MulticomponentOxides: Part I. Line Compounds with Narrow HomogeneityRange, Metall. Mater. Trans. A, 36 (2005), 2685–2694.

[14] K. T. Jacob, G. Rajitha and S. N. S. Reddy, Reactive Interdif-fusion: Deviation From Local Equilibrium in the Fe-NiTiO3

Couple, Scr. Mater., 63 (2010), 204–206.[15] S. N. S. Reddy, B. R. Sundlof and K. T. Jacob, Diffu-

sion Path During Internal Displacement Reactions in Multi-component Oxides: Reaction Between Fe and (Co,Mg)TiO3

Solid Solution at 1273 K, Solid State Ionics, 182 (2011), 1–7.[16] S. N. S. Reddy, Internal Displacement Reactions in Multi-

component Oxides: Part III. Solid Solutions of Ternary Ox-ide Compounds, Metall. Mater. Trans. A, 36A (2005), 2993–3000.

[17] K. T. Jacob, V. S. Saji and S. N. S. Reddy, ThermodynamicEvidence for Order-disorder Transition in NiTiO3, J. Chem.Thermodyn., 39 (2007) 1539–1545.

[18] G. M. Kale and K. T. Jacob, Chemical Potential of Oxygenfor Iron-Rutile-Ilmenite and Iron-Ilmenite-Ulvospinel Equi-libria, Metall. Mater. Trans. B, 23B (1992) 57–64.

[19] K. T. Jacob, S. Raj and S. N. S. Reddy, Activities in theFeTiO3-NiTiO3 Solid Solution from Alloy-oxide Equilibriaat 1273 K, J. Phase Equilib. Diffus., 30 (2009), 127–135.

[20] K. T. Jacob and G. Rajitha, Role of Entropy in the Stability ofCobalt Titanates, J. Chem. Thermodyn., 42 (2010) 879–885.


reactive interdiffusion: a method for making composition...

Documents