Kinetic Pathways of Phase Transformations in Two-PhaseTi Alloys

TAE WOOK HEO, DONALD S. SHIH, and LONG-QING CHEN

Possible phase transformation kinetic pathways from the high temperature b phase to the lowtemperature (a+ b) two-phase Ti alloys were analyzed using the graphical thermodynamicmethod and the assumption that diffusionless and displacive transformations take place muchfaster than phase separation which requires long-range diffusion. It is shown that depending onthe composition of a b-stabilizing element, many transformation mechanisms are possible,involving competing continuous and discontinuous displacive/diffusional transformations. Wediscuss the proposed phase transformation sequences employing existing experimental micro-structures.

DOI: 10.1007/s11661-014-2269-2� The Minerals, Metals & Materials Society and ASM International 2014

I. INTRODUCTION

TITANIUM (Ti) alloys have been extensively utilizedin aerospace applications, biomedical devices, andchemical processing equipment owing to their excellentstrength to weight ratio and corrosion resistance.[1] PureTi has two allotropic forms, hexagonal-close packed(hcp) a and body-centered cubic (bcc) b, and it under-goes b to a allotropic transformation upon cooling.Most commercial Ti alloys in structural applicationsdisplay (a+ b) two-phase microstructures for highstrength.[2] Incorporating 3d transition metals such asV, Mn, Fe, and Mo as alloying components whichstabilize the b phase[3] makes it possible for both phasesto coexist. The mechanical properties of Ti alloys arevery sensitive to the spatial configurations of the twophases in the microstructure. Therefore, the predictionof microstructural evolution of the phases plays a keyrole in the optimization of the mechanical properties ofTi alloys.

Different thermo-mechanical processing routes pro-duce a wide spectrum of complex (a+ b) two-phasemicrostructures such as fully lamellar structure (orbasket-weave and Widmanstatten structures) and bimo-dal (duplex) structure containing lamellae with primarya phases displaying globular morphology.[2,4] Therehave been a number of experimental efforts to under-stand the phase transformations and microstructuralevolution of binary[3,5–12] or multicomponent[13–16] Tialloys. The phase transformations in Ti alloys are

associated with complicated competitions betweennucleation-and-growth and spinodal decomposition, orbetween continuous and discontinuous displacive trans-formations. It is a significant challenge to distinguish thedifferent mechanisms experimentally. For example, thespinodal decomposition process of an intermediate a¢ ora¢¢ phase with high solute content or b phase during thephase transformation is not easily detectable in exper-iments, since the decomposed solute-rich and solute-poor phases exhibit a very small difference in latticeparameters.Systematic theoretical analyses on phase transforma-

tion mechanisms have previously been employed tounderstand coupled kinetic processes. For example,Khachaturyan, Lindsey, and Morris theoretically inves-tigated the equilibrium between a disordered solidsolution and an L12 ordered phase as well as the phasetransformation paths from a quenched disordered phaseto the two-phase field in Al-Li alloys.[17] Soffa andLaughlin[18] applied a graphical thermodynamic methodto theoretically analyze concurrent clustering or order-ing processes. Fan and Chen discussed the possibility ofspinodal decomposition during the structural phasetransformation in a ZrO2-Y2O3 system,[19] and Niet al.[20] discussed the transformation sequences associ-ated with a cubic to tetragonal structural changeaccompanied by a decomposition process. There havealso been attempts to model the formation of (a+ b)two-phase microstructures of Ti alloys.[21,22] However,the systematic approach to analyzing the phase trans-formation mechanisms in Ti alloys has not been wellestablished despite a number of existing thermodynamicanalyses.[7,23]

The main objective of this paper is to analyze thepossible phase transformation mechanisms in (a+ b)two-phase Ti alloys using graphical thermodynamics.[18]

The phase transformation sequences that may undergoeither nucleation-and-growth or a continuous transfor-mation such as spinodal decomposition and continuousdisplacive transformation are analyzed following Refer-ences 19 and 20. Microstructural features associated

TAE WOOK HEO, formerly Postdoctoral Scholar with theDepartment of Materials Science and Engineering, The PennsylvaniaState University, University Park, PA 16802, is now PostdoctoralResearch Staff Member with the Condensed Matter and MaterialsDivision, Lawrence Livermore National Laboratory, Livermore, CA94550. Contact e-mail: heo1@llnl.gov, htw584@gmail.com DONALDS. SHIH, Technical Fellow, is with the Boeing Research & Technol-ogy, St. Louis, MO 63166. LONG-QING CHEN, DistinguishedProfessor, is with the Department of Materials Science and Engineer-ing, The Pennsylvania State University.

Manuscript submitted February 3, 2014.Article published online April 2, 2014

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with the possible kinetic pathways are demonstratedusing the existing experimental microstructures.

II. PHASE STABILITIES AND KINETICPATHWAYS

We consider a Ti-M binary alloy system for simplicitywhere M is a b (isomorphous) stabilizing element suchas V, Mo, or Nb. The incorporation of M decreases theb to a transition temperature, and the schematic phasediagram of a binary alloy system is shown in Figure 1.[1]

We confine our attention to compositions and temper-ature changes at which an alloy undergoes the phasetransformation from the high temperature b phase tothe low temperature (a+ b) dual phases as indicatedwith a blue solid arrow in Figure 1. Since a recentresearch reported that no transient ordering was foundin the system,[3] it is not addressed in our analysis.

We explore the possible kinetic mechanisms involvingthe formation of intermediate phases or the existence ofmetastable states by analyzing the thermodynamic phasestabilities. The phase transformations in Ti alloysinvolve both solute diffusion and displacive structuraltransformation from a bcc (b) structure during cooling.With regard to the displacive structural transformation,the product phase can be a¢ (hcp, low solute content) ora¢¢ (orthorhombic or distorted hexagonal, high solutecontent) phase depending on the solute content. Thecriterion to determine the occurrence of a¢ or a¢¢ phase interms of solute content, i.e., the a¢/a¢¢ boundary as afunction of solute composition, for some selected binaryTi alloy systems with transition metals was discussed inReference 1. We represent the state of an alloy usingcomposition (X) of solute contents and order parameter(g) for the structural identification, i.e., g = 0 representsbcc (b) structure, and g = 1 represents displacivelytransformed structures from the b phase, i.e., hcp (a ora¢) or orthorhombic (a¢¢) structure. The local specific freeenergy is expressed as a function of those two variables,f(X, g). The two phases have separate free energy curvesfa(X) and fb(X), and the free energy function f(X, g)becomes fa(X) or fb(X) depending on the structural stateof the system, i.e., the order parameter value. Theschematic diagram of the free energy curves is shown in

Figure 2. Since the intermediate a¢ phase or a¢¢ phasewith a high content of b-stabilizer can be decomposedinto solute-rich and solute-poor phases, i.e., there is amiscibility gap for the a phase,[1,24] we assume a double-well type energy curve for fa(X). However, the single-well type energy curve is used for fb(X) for simplicity. Asa matter of fact, there may exist a miscibility gap in the bphase as the presence of oxygen might open up amiscibility gap[8] although the b miscibility gap isbelieved to be at lower temperature.[7,15] In this case,the free energy function of the b phase should displaythe double-well type curve (see the dashed line inFigures 2 and 3) as suggested in Reference 23.The thermodynamic stability of a solid solution can

be determined by analyzing the topological properties ofthe free energy curves as a function of composition andorder parameter.[18] In particular, we can specify theinstability regimes by taking into consideration thesecond derivatives of the free energy with respect to gand X. We also assume that a displacive structuraltransformation, which only requires shear and atomicshuffles, takes place much faster than phase separationwhich requires long-range diffusion. The combination ofthermodynamic stability of a and b phases at a givencomposition and temperature coupled with the assump-tion with respect to the relative rate of structuraltransformations and phase separation would allow usto determine the kinetic pathways for a given Ti alloy.An undercooled b phase can transform to the a phase

at a fixed composition if it leads to a free energy

Fig. 1—Schematic phase diagram of a Ti-M system.[1]

Fig. 2—Schematic diagram of free energy curves of a and b phases.

Fig. 3—Energy pathways of the variation of the structural orderparameter in a f-g-X space.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 45A, JULY 2014—3439

reduction. The b phase can be either metastable orunstable depending on the content of b-stabilizer in thealloy, i.e., b phase becomes more stable as the alloycontains more b-stabilizer. It is supported by the factthat the b phase retention upon cooling occurs when thealloy includes high content of b-stabilizer as well as thephase diagram of a binary Ti alloy in Figure 1 where theb transus decreases as the b-stabilizer compositionincreases. The transformation may take place through

nucleation-and-growth at which @2f@g2

���g¼0

>0 (high solute

content, metastable) or spinodal (or continuous) mech-

anism with @2f@g2

���g¼0

<0 (low solute content, unstable).

Figure 3 illustrates the schematic possible energy path-ways in f-X-g space for the variations of g with fixedcompositions. The state U on the figure is unstable withrespect to the displacive structural transformation, andthus, the transformation occurs spontaneously andcontinuously without the need to overcome a nucleationbarrier. On the other hand, the state M is metastablewith respect to the displacive structural transformation,and it undergoes the transformation through the nucle-ation-and-growth mechanism due to an energy barrier.The whole composition range is then divided into tworegimes according to the transformation mechanism asillustrated in Figure 4(a).

The transformed a phase can subsequently undergophase separation due to a compositional metastability orinstability of a phase with respect to its decompositionthrough either nucleation-and-growth or spinodal mech-anism, respectively, depending on the curvature of the

local free energy, @2fa@X2. The composition range where the

a phase is unstable with respect to the decomposition is

specified by @2fa@X2 <0 (Figure 4(b)).[25] Phase separation

occurs through the nucleation-and-growth process out-side the instability regime.

With the combined structural instability of the b phaseand composition instability of the a phase, the wholecomposition range within the two-phase regime can bedivided into four different sub-regimes for the kineticpathways as shown in Figure 4(c). The hatched portion offree energy curve of b phase (fb) represents the unstablestate of b phase with respect to the structural transforma-tion. If a solid solution of composition within regime I in

Figure 4(c) is rapidly quenched, it undergoes bcc to hcpdisplacive structural transformation continuously withoutcomposition change (congruently), resulting in an inter-mediate a¢ phase. The a¢ phase within this compositionrange is metastable with respect to the decomposition. Thenext step is the nucleation-and-growth of b phase from thesupersaturated a¢ solid solution, leading to an equilibrium(a+b) two-phase mixture. The kinetic pathway I isillustrated in Figure 5(a) and expressed as the following:

Pathway I: β α ' α + β [1]

We use a solid arrow to represent the continuousreaction, e.g., continuous displacive transformation orspinodal decomposition, and a dashed arrow to denotethe nucleation-and-growth in the figures as well as theexpressions of kinetic pathways.An undercooled b phase with a composition within

regime II undergoes more complicated transformations.The b phase transforms continuously and congruently tothe supersaturated a¢ phase with the hcp structure or a¢¢phase with the distorted hexagonal or orthorhombicstructure depending on solute content. The a¢ or a¢¢ phasewithin this composition regime is, however, unstable withrespect to the decomposition. Therefore, the decompo-sition process occurs through the spinodal mechanismwhich produces solute-rich (a1) and solute-poor (a2)phases. Figure 6(a) shows the experimental evidence ofspinodal decomposition within the a¢¢ phase which leadsto the modulated structure consisting of solute-rich andsolute-poor phases.[24] The composition of the solute-poor a phase gradually reaches the equilibrium a phasecomposition keeping the hcp structure, whereas thesolute-rich a phase experiences the hcp (a1) to bcc (b)structural change when the composition exceeds thecritical composition where fa and fb intersect each other.Eventually, the composition of the b phase reaches theequilibrium composition of b phase. Therefore, thekinetic pathway can be summarized as the following:

Pathway II: b! ða0 or a00Þ ! a1 solute-richð Þþ a2 solute-poorð Þ ! aþ b;

½2�

The corresponding graphical representation is shownin Figure 5(b).

Fig. 4—(a) Phase instability of initial b phase, (b) phase instability of intermediate a¢ or a¢¢ phase, and (c) 4 different subdivisions of a compositionrange.

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The phase transformation sequence in regime III issimilar to those in regime II. The only difference is thefirst stage within which the initial quenched b phase isstructurally metastable with respect to the displacivestructural transformation, and thus, the transformationtakes place through a nucleation-and-growth mecha-nism. In fact, the structural transformation from a bphase with such a high content of b-stabilizing element

under even rapid quenching hardly happens.[24] How-ever, existing structural defects, e.g., grain boundariesand dislocations, would promote the nucleation ofmartensitic phase. The product phase would be morelikely a¢¢ phase with the high solute content rather thana¢ phase. The subsequent sequence is the same as that ofthe regime II, i.e., the kinetic sequences in pathway III(shown in Figure 5(c)) is

Fig. 5—Phase transformation pathway in (a) the regime I, (b) the regime II, (c) the regime III, and (d) the regime IV.

Fig. 6—Experimental micrographs of intermediate phases: (a) modulated structure within a martensite plate (orthorhombic a¢¢) of a Ti-Mo alloy(decomposition of a¢¢ phase),[24] (b) morphology of an x phase,[15] and (c) modulated structure within a b phase of a Ti-6Al-4V alloy (decompo-sition of b phase).[15]

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 45A, JULY 2014—3441

A b phase in the regime IV is metastable with respectto bcc to hcp (or orthorhombic) displacive transforma-tion upon cooling, and the free energy of b phase islower than that of a phase with a same composition. Infact, multiple pathways are possible depending on thepresence of the intermediate phases in this regime. Firstof all, the direct formation of stable a phase from bphase through the nucleation-and-growth process,which mostly happens heterogeneously, without theoccurrence of intermediate phases is expected. Theexisting structural defects can be favorable nucleationsites for a plates when the alloy is slowly cooled down orisothermally processed at the relatively high temperatureas in the previous case. The kinetic pathway within theregime IV can be expressed by

Pathway IV: β α + β [4]

and the pathway is represented in Figure 5(d) as arepresentative pathway in this regime. The pathwayexpressed in Eq. [4] is essentially inclusive. In thisregime, it is also possible that the formation of precur-sors such as b¢ or x phases can nucleate a plates fromthe metastable b phase depending on the heat treatmenthistory.[1,7,26,27] For example, x phases which are knownto exhibit the ellipsoidal or cuboidal shape[1] mayprecipitate when the alloy is quenched, since the directbcc to hcp displacive reaction is suppressed due to highb-stabilizer content[1,23,28] in this regime. Figure 6(b)shows an example of experimental observations of the xphase.[15] The x precipitates play a role as nucleationsites of a phase during the aging process at highertemperature.[10,12] In this case, the kinetic pathway inEq. [4] can be extended as β β + ω α + β .Another possible kinetic pathway in this regime is thatthe metastable b phase (with respect to the displacivetransformation) containing high b-stabilizer content candecompose to (b+ b¢) through either spinodal ornucleation-and-growth mechanisms, and the solute leanphase (b¢) displacively transforms to x phase by thenucleation-and-growth mechanism[15] which acts as anucleation site of the a phase. Figure 6(c) shows amodulate microstructure consisting of solute-rich andsolute-poor phases resulting from the decomposition ofthe b phase.[15] The kinetic pathway in Eq. [4] can be

extend as β β + β ' β + ω α + β in this case.

It should be noted that, upon sufficiently slowcooling from the b phase field to (a+ b) two-phasefield, the phase transformation starts from the temper-ature just below the transition temperature at which theb phase is metastable. Therefore, the phase transfor-mation takes place through the nucleation-and-growthmechanism similar to the kinetic pathway III (Eq. [3])or IV (Eq. [4]). The a phase particles are also expectedto heterogeneously nucleate at the existing structuraldefects.

III. EXPERIMENTAL MICROSTRUCTURESAND KINETIC PATHWAYS

We analyzed the possible kinetic pathways during thephase transformations only in a binary Ti-M system as anexample. However, the analyses are generally applicableto any multicomponent systems. Commercial Ti alloysusually contain both a-stabilizer and b-stabilizer, althoughwe considered alloys only containing b-stabilizers. Itshould be noted that the decrease of b-stabilizer compo-sition is equivalent to the increase of a-stabilizer compo-sition and vice versa. Moreover, the phase diagram of amulticomponent system can be reduced to a quasi-binaryphase diagram. For example, a quasi-vertical section of aphase diagram of a Ti-Al-V ternary system is very similarto that of the binary system shown in Figure 1 except theformation of other phases such as Ti3Al in the presence ofAl as an a-stabilizer.[4] In other words, the consideration ofonly one b-stabilizer compositionwould be able to capturethe main physical consequences of phase transformationsinvolving multiple alloying elements. The main scenariofor the possible kinetic pathways in multicomponentalloys would be very similar to those proposed in theabove section. Therefore, we demonstrate how ourproposed kinetic pathways in Section II can be employedto understand the underlying phase transformation mech-anisms leading to experimentally observed typical micro-structural features by employing some examples ofexisting experimental microstructures of general Ti alloysin the following section.

A. Basket-Weave Microstructure

A basket-weave microstructure is associated with thestructural instability of the b phase. The formation ofthis type of microstructure can be explained using thekinetic pathways I or II. The kinetic pathway I and II,upon rapid cooling, involve a continuous displacivetransformation due to the structural instability. Figure7(a) shows the corresponding experimental micrographof a microstructure resulting from the displacive trans-formation.[24] It is known that the features of thestructure depend on the composition of alloying ele-ments. As the composition of b-stabilizer increases, themartensite plate becomes thinner and more acicular.[1,24]

The subsequent phase transformation step is the forma-tion of the b phase through either nucleation-and-growth (pathway I) or spinodal decomposition (path-way II). For the case of pathway I, the nucleation of bphases can occur homogeneously at the a¢ plate interioror heterogeneously at the a¢/a¢ boundaries. As a matterof fact, the heterogeneous nucleation is a more probablemechanism of b phase formation. When the solutecomposition exceeds the critical point of the composi-tional instability, the supersaturated a¢ or a¢¢ phase isspinodally decomposed within the a¢ or a¢¢ phase

[3]Pathway III: β α" α1(solute-rich) + α2(solute-poor) α + β

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(pathway II). The solute-rich regimes become equilib-rium b phases, and the solute-poor regimes becomeequilibrium a phases. The final experimental micro-structure as a result of above pathways would displaythe basket-weave type, and the morphological featuresof the microstructure are shown in Figure 7(b).[29]

B. Grain Boundary Nucleated Microstructure

Upon slow cooling and/or with a high content ofb-stabilizer, the a phase nucleates preferentially at the bgrain boundaries to minimize the strain energy as well asinterfacial energy, which results in the continuous alayer along the grain boundaries[1] as mentioned above.Depending on the solute composition, the a phase cannucleate directly or through the intermediate phasessuch as x and b¢ phases, similar to the kinetic pathwayIV (or its extensions), or the intermediate a¢¢ phase canfirst nucleate, which is followed by a phase separation,similar to the kinetic pathway III. Further cooling leadsto additional nucleation of a phase (directly or throughthe intermediate phases such as x and b¢ phases) at theinterface between continuous a layer and b phase or

remaining b grain boundaries, and the nucleated a phasegrows into the b grain interior (through pathway III orIV also). Thus, it displays the colony-type microstruc-ture or fully lamellar structure containing relativelythicker grain boundary a lamellae. The a colonies neargrain boundaries are shown in Figure 8(a)[30] as anexample. The continuous a layers along b grain bound-aries are clearly shown in an experimental micrograph inFigure 8(b).[30]

C. Bimodal (Duplex) Microstructure

The proposed kinetic pathways can also be applied toexplain the microstructural evolution in bimodal micro-structures (Figure 9(a)[2]). During the cooling processfrom the temperature at which the alloy is homogenizedin the b phase field to the (a+ b) two-phase field, themicrostructural evolution would follow the proposedkinetic pathways depending on the solute composition.The only difference in processing conditions leading tothe bimodal microstructure from the above cases is therecrystallization temperature. In this case, since the alloyis recrystallized at the (a+ b) two-phase field, the

Fig. 7—Experimental micrographs of (a) a microstructure of a Ti-Mo alloy resulting from a displacive phase transformation[24] and (b) a fullybasket-weave microstructure of a Ti-6Al-4V alloy.[29]

Fig. 8—Experimental microstructures of Ti-6Al-4V under slow cooling at (a) 473 K/h (200 �C/h)[30] and (b) 323 K/h (50 �C/h).[30]

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 45A, JULY 2014—3443

equiaxed primary a phase incoherently forms at b grainboundaries or mainly at triple junctions. In manycases, the recrystallization temperature is close to the btransus. Therefore, the b phases, which will be trans-formed to primary a phases, are essentially metastable,i.e., the primary a phase formation would follow thekinetic pathway III or IV (or its extensions) dependingon the solute content. In addition, the phase transfor-mation sequences for the remaining b phase to alamellae upon cooling after the recrystallization processwould follow the proposed pathways corresponding tothe solute composition of the remaining phase. How-ever, it should be noted that, if the cooling rate issufficiently slow, the primary a phases continue togrow, leading to a fully equiaxed microstructure asshown in Figure 9(b)[31] rather than formation of alamellae.[1,2] The equiaxed microstructure can be alsofound when the recrystallization temperature is suffi-ciently low such that the equilibrium volume fractionof a phase is high.[1,2]

IV. SUMMARY

We analyzed and determined the possible kineticpathways during the phase transformations in (a+ b)two-phase Ti alloy. It was shown that the wholecomposition range of b-stabilizer within the two-phaseregime can be divided into four different sub-regimes.Each composition regime displays a different kineticpathway by competing continuous and discontinuoustransformation processes. We demonstrated that all themajor types of existing experimental microstructures canbe rationalized using the proposed pathways fordescribing the interplay between the structural transfor-mation and diffusional process in Ti alloys. A fullextension of thermodynamic analysis on the kineticmechanisms of phase transformations to multicompo-nent Ti alloys is underway.

ACKNOWLEDGMENTS

This work is funded by the Center for ComputationalMaterials Design (CCMD), a joint National ScienceFoundation (NSF) Industry/University CooperativeResearch Center at Penn State (IIP-1034965) and Geor-gia Tech (IIP-1034968).

REFERENCES1. G. Lutjering and J.C. Williams: Titanium, 2nd ed., Springer,

Berlin, 2007.2. G. Lutjering: Mater. Sci. Eng. A, 1998, vol. 243, pp. 32–45.3. I.B. Ramsteiner, A. Schops, F. Phillipp, M. Kelsch, H. Reichert,

and H. Dosch: Phys. Rev. B, 2006, vol. 73, p. 024204.4. H.M. Flower: Mater. Sci. Technol., 1990, vol. 6, pp. 1082–92.5. H.I. Aaronson, W.B. Triplett, and G.M. Andes: Trans. AIME,

1957, vol. 209, pp. 1227–35.6. M.J. Blackburn and J.C. Williams: Trans. Metall. Soc. AIME,

1968, vol. 242, pp. 2461–69.7. M.K.Koul and J.F. Breedis:ActaMetall., 1970, vol. 18, pp. 579–88.8. W. Fuming and H.M. Flower: Mater. Sci. Technol., 1989, vol. 5,

pp. 1172–77.9. D.L. Moffat and D.C. Larbalestier: Metall. Trans. A, 1988,

vol. 19A, pp. 1677–86.10. D.L. Moffat and D.C. Larbalestier: Metall. Trans. A, 1988,

vol. 19A, pp. 1687–94.11. E.S.K. Menon and R. Krishnan: J. Mater. Sci., 1983, vol. 18,

pp. 365–74.12. E.S.K. Menon and R. Krishnan: J. Mater. Sci., 1983, vol. 18,

pp. 375–82.13. M.A. Dyakova, E.A. Lvova, I.N. Kaganovich, Z.F. Zvereva, and

L.S. Meshchaninova: Russian Metall., 1977, pp. 122–26.14. C.G. Rhodes and J.C. Williams: Metall. Trans. A, 1975, vol. 6A,

pp. 2103–14.15. Z. Fan and A.P. Miodownik: J. Mater. Sci., 1994, vol. 29,

pp. 6403–12.16. S.M.C. van Bohemen, J. Sietsma, and S.v.d. Zwaag: Phys. Rev. B,

2006, vol. 74, pp. 134114.17. A.G. Khachaturyan, T.F. Lindsey, and J.W. Morris: Metall.

Trans. A, 1988, vol. 19A, pp. 249–58.18. W.A. Soffa and D.E. Laughlin: Acta Metall., 1989, vol. 37,

pp. 3019–28.19. D. Fan and L.-Q. Chen: J. Am. Ceram. Soc., 1995, vol. 78,

pp. 1680–86.

Fig. 9—Experimental micrographs of (a) bimodal (duplex) structure of IMI 834[2] and (b) a fully equiaxed structure of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si.[31]

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20. Y. Ni, Y.M. Jin, and A.G. Khachaturyan: Acta Mater., 2007,vol. 55, pp. 4903–14.

21. Y. Wang, N. Ma, Q. Chen, F. Zhang, S.-L. Chen, and Y.A.Chang: JOM, 2005, vol. 57, pp. 32–39.

22. Q. Chen, N. Ma, K. Wu, and Y. Wang: Scripta Mater., 2004,vol. 50, pp. 471–76.

23. R.B. Gullberg, R. Taggart, and D.H. Polonis: J. Mater. Sci., 1971,vol. 6, pp. 384–89.

24. R. Davis, H.M. Flower, and D.R.F. West: J. Mater. Sci., 1979,vol. 14, pp. 712–22.

25. J.W. Cahn: Acta Metall., 1961, vol. 9, pp. 795–801.

26. P.D. Frost, W.M. Parris, L.L. Hirsch, J.R. Doig, and C.M.Schwartz: Trans. ASM, 1954, vol. 46, pp. 231–56.

27. G. Aurelio, A.F. Guillermet, G.J. Cuello, and J. Campo: Metall.Mater. Trans. A, 2002, vol. 33A, pp. 1307–17.

28. F.R. Brotzen, E.L. Harmon, and A.R. Troiano: Trans. AIME,1955, vol. 203, pp. 413–19.

29. J.H. Zuo, Z.G. Wang, and E.H. Han: Mater. Sci. Eng., 2008,vol. 473, pp. 147–52.

30. N. Stanford and P.S. Bate: Acta Mater., 2004, vol. 52, pp. 5215–24.31. L.J. Huang, L. Geng, A.B. Li, G.S. Wang, and X.P. Cui: Mater.

Sci. Eng. A, 2008, vol. 489A, pp. 330–36.

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