Phase Transformation 1973

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PHASE TRANSFORMATIONS INMETALS AND ALLOYS 8546Glyn Meyrick and Gordon W. PowellDepartment f Metallurgical Engineering, The OhioState University, Columbus,OhioINTRODUCTIONUnderstanding a phase transformation involves an appreciation of the reasonsfor its occurrence and of the modeor modesby which it takes place. The formerwill not be explored herein beyond noting that a system can spontaneouslyundergo a change in phase (or phases) if by so doing its free energy is reduced.Provided a reduction in free energy ensues, the product of the transition need notbe that pertaining to the equilibrium state. A total change mayyield directly theequilibrium state or traverse a path composedof several tranformations involv-ing metastable phases. This, combinedwith the fact that a given change can beaccomplished by more than one kinetic mechanism generating modal competi-tion, endows the study of phase transformations and their consequences with thecomplexities that render it so intriguing. Phase transitions have received exten-sive investigation because of their inherent fascination and because they play aparticularly important role in property control for material applications.

As can be seen from someof the more recent surveys of the field (1-3) itcustomary to group together changes that exhibit common haracteristics in aneffort to classify phase transformations in a systematic manner. Criteria involvedin classification are predominantly of morphological character but also include,or imply, mechanistic processes. This process has led to the establishment ofaccepted group names: 1. continuous precipitation, 2. massive transformations,3. discontinuous precipitation, 4. martensitic transformations, 5. bainitic trans-formations, 6. order-disorder transformations, and 7. spinodal decomposition.Because of an initial restriction on the length of this review, order-disordertransformations and spinodal decomposition will not be considered here, butthey have been discussed by Wayman4) in a pievious volumeof this series.

Continuous precipitation is characterized by the formation of grain boundaryand intragranular particles of the newphase, which generally has a structure and

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328 MEYRICK POWELLcomposition different from that of the metastable matrix. The growth of the newphase is controlled by long range diffusion through the matrix, whose averagecomposition changes continuously as the reaction proceeds. The reaction at theinterface between the parent and product phases is presumed to be relativelyfast.

If the new phase forms by the massive mode, it has the same composition asthe parent phase and the reaction is accomplished by the rapid motion of a highenergy, incoherent boundary. Thus this solid state reaction does not involve longrange diffusion and the transfer of atoms from the parent to the product phaseis assumed to be effected by the uncoordinated, random jumps of individualatoms across the interphase boundary. Although Phillips (5) was apparently thefirst investigator to recognize this modeof transformation as a unique type ofsolid state reaction, the term massive was first applied by Greninger (6). It isappropriate term in the sense that it is descriptive of the relatively largemorphological units which in some cases form by this mode of transformation.

The discontinuous modeof transformation results in the formation of a two-phase mixture at an advancing, incoherent boundary. The atom transport andatom rearrangement required to produce the two-phase mixture are assumed totake place in the advancing boundary and also, if volumediffusion is significant,within a region immediately adjacent to the advancing boundary. The bulk ofthe metastable matrix remains essentially unchanged until traversed by theinterface. Generally, the compositions and crystal structures of the two phasesare different from that of the metastable matrix. The two phases are oftenarranged in the form of a lamellar aggregate.

The martensitic mode of transformation yields platelets of an oftentimestransitional phase by a displacive reaction which is diffusionless, producessurface relief effects, and is reversible in somealloy systems (7). In addition,definite crystallographic relationships exist between the product and parentphases, and the physical plane of the martensitic platelet is usually parallel to anirrational lattice plane (habit plane) of the metastable matrix. Since the formula-tion of th~ phenomenological theory of displacive reactions by Wechsler,Lieberman & Read (8) and Bowles & Mackenzie (9), much of the researchbeen concerned with the crystallographic and geometrical aspects (lattice rela-tionships, habit plane, shape deformation, and inhomogeneous deformationwithin the martensite) of martensitic transformations.

The bainitic modeof transformation is the subject of considerable controversyas demonstrated quite clearly by a recent debate on this reaction (10). Some olidstate reactions which occur in ferrous and nonferrous alloys and whose productshave distinctively different morphologies have been labeled bainitic. In the caseof hypoeutectoid steels, lower bainite has some of the characteristics (latticerelationships, surface relief, inhomogeneous ubstructure) of martensite, but theslow edgewise growth of the platelets of bainite is controlled by the rate ofdiffusion of carbon in the austenite matrix.Whereas a classification scheme based upon clearly distinguishable modes oftransformation has obvious merits, it can also be disadvantageous if adhered to


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PHASE TRANSFORMATIONS N METALS AND ALLOYS 329too rigidly. It is to be emphasized hat a phase transition can involve a structuralchange, a compositional change, or both. All of these can, in principle, beaccomplished by diffusion processes, while part can be achieved by displaeiveprocesses. Both processes could be operative in a given transformation and mightor might not be practically separable. Thus, although transformations exist that,by common greement, belong within a particular group, others exhibit charac-teristics of several groups. It is moreprofitable to regard this main classificationas establishing general guidelines rather than providing a series of separatecompartments into which all transformations can be unequivocally placed.

The objective of this review is primarily to summarize on the basis ofexperimental observations the current knowledge of the morphological andgrowth characteristics of the various modes of transformation. It does notconsider in any great detail mathematical models of these reactions. Each of thevarious modes of transformation will be considered under one of three broadgroups of solid state reactions: 1. diffusional transformations, 2. displacivetransformations, and 3. hybrid (mixed mode) transformations.DIFFUSIONAL TRANSFORMATIONSMassive TransformationsAs noted in the introduction, a massive transformation is accomplished by therapid motion of a high energy, incoherent boundary which converts the parentphase into a more stable phase of the same composition. Any nonmartensiticpolymorphic ransformation in a pure metal is obviously a degenerate or limitingcase of a massive transformation. Thus Owen& Gilbert (11) suggested that the"r-to-a transformation which occurs in pure iron at cooling rates less than5500C/sec is a massive reaction. These observations were made on bulkspecimens. Differences are to be expected for microscopic specimens; forexample, the a-to--/transformation in iron whiskers exhibits characteristics of amartensitic transformation and is well described by the phenomenological heory(12). Bibby & Parr (13), using iron containing less than 0.0017% C,concluded that the transformation at cooling rates less than 30,000C/sec ismassive. At higher cooling rates the "r-to-a transformation is martensitic. Typicalmassive microstructures obtained by cooling pure iron (0.001% C) at slow ratesare shown n Figure 1; in general the grain size decreases with an increase in thecooling rate. This modeof transformation does not 15roduce surface tilts (13-15),a fact consistent with the concept that the boundary between the transformedand untransformed region is displaced by the random, noncooperative move-ment of the atoms at the boundary; Transmission electron microscopy has shownthat the internal structure of the massiveferrite grains consists of a random rrayof dislocations and that neighboring massive grains are separated by high angleboundaries (14, 15) (Figure 2). The dislocations maybe the result of transforma-tion-lnduced stresses and quenching stresses.The motion of the austenite-ferrlte boundary in pure iron at undercoolings onthe order of 25-50C has been investigated by Eichen & Spretnak 06) and


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330 MEYRICK & POWELL

Figure I(b) 4000"C/sec.X 300.

Microstructureof high punty iron quenched at approximately a)800"C/sec and

F igure2 Random dislocations and high angle boundary in iron quenched at 3300" Usec.


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PHASE TRANSFORMATIONS N METALS AND ALLOYS 331Bharucha et al (17) by the use of thermionic emission microscopy. The geometryand motion of the austenite (light)-ferrite (dark) interface are shown n Figure3; the elapsed time between the two photographs is 15/16 sec. The a-v interfaceis highly irregular and faceted, and it moves in a definitely discontinuousmanner. That is, segments of the interface may remain stationary for a fractionof a second and then undergo sudden displacements. Discontinuous interfacemotion is not unique to the massive transformation in pure iron.

In the case of alloys, the massive transformation in the Cu-Ga ystem has beenstudied quite thoroughly; investigations of the massive transformation in Cu-Znalloys have also yielded some significant results. The discussion of the Cu-Gaand Cu-Zn alloys considers in order the following kinetic, morphological, andcrystallographic features: nucleation site, rate and mechanism of interfacemotion, lattice relationships between the massive phase and its parent, structureof the massive boundaries, and internal structure of the massive phase.The high temperature fl (bcc) phase in a Cu- 37 at.% Zn alloy can be retainedto room temperature by rapid quenching, but during the quench some of the flphase does transform to Widmanstatten alpha phase aw and also to massivealpha am" Both the aw and otm phases nucleate at the fl-fl grain boundaries. Theresults of rapid up-quenching experiments have shown that the aw-fl boundarieswhich may be semicoherent are not suitable sites for the formation of amphase(18). Furthermore, when his alloy is equilibrated at a temperature such as 840Cin the (a + /3) phase field and then quenched, the a,~ phase again nucleatespreferentially at fl-fl grain boundaries. Nucleation of a,~ was not observed at theaeq - fleq boundaries; such boundaries should be at least semicoherent and thuslack the mobility required for the massive transformation. Consequently, it maybe concluded that boundaries with disordered atom arrangements are favorablesites for the nucleation of a massive phase.

The growth rate of the massive phase am n the fl Cu-Zn alloys is approximat-ely 1 cm/sec (18, 19), which is orders of magnitudegreater than that associatedwith transformations controlled by long range volume diffusion. At such highgrowth rates, the massive phase must have the same composition as the parentphase. The microprobe scans of the ~,~ and/3 phases in a rapidly quenched Cu-38.5 at.% Zn alloy obtained by Massalski et al (20) are convincing demonstra-tions of this fact. The morphological development of the a,~ phase in a quenchedCu-37 at.% Zn alloy is shown in Figure 4. The am-fl surface enclosing anygiven morphological unit of a,~ contains many facets. Transmission electronmicrographs obtained by Hawbolt & Massalski (18) of the faceted a,,-/3interfaces show that interfaces contain steps or ledges, the smallest ~ 100/~ inheight (Figure 5). Ledges 6-30/~ in height have been observed on the faceted~,n-fl interfaces in /3 (bcc) Cu-Gaalloys (21). The existence of ledges onfaceted interfaces is consistent with the theory of growth proposed by Aaronson(22). According to this theory, growth perpendicular to the faceted interfaceoccurs by the lateral motion of the ledges across the interface which is assumedto have a misfit dislocation structure that renders it relatively immobile. Thehighly mobile ledges, on the other hand, are considered to have a disordered


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332 MEYRICK L POWELL

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Fi gure 3 Austenite (light)-to-ferrite(dark) transformation in high purity iron. Elapsedtime is 15/16 sec. Magnification is approximately X 100.

Figure 4 Morphology of the a phase in aCu-37.8 at.%Zn alloy.structure. Growth of the{ phase in /3 Cu-Ga alloys by the ledge mechanism hasbeen observed by K ittl & Massalski (21) using hot-stage microscopy.Thea (fcc) and /? (fcc) phases abutting one another across a faceted interfacein Cu-Zn alloys are oriented at random with respect to one another (18). Thefaceted interfaces do not correspond to any unique habit plane; attempts toobserve misfit dislocation arrays at these interfaces were unsuccessful. However,in the caseof the /? (bcc)+3, (hcp) reaction in /3 Cu-Ga alloys, crystallographycan play a role in the transformation. The J,,, grains often consist of two twin-related subgrains and at least one of the twin-related regions isbounded in part


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PHASE TRANSFORMATIONS N METALS AND ALLOYS 333by facets. The races of these facets are consistently parallel to the (0001) basalplane of the ~m phase and growth takes place by the rapid movement f ledgesalong facets (Figure 6). The volume change associated with the transformationinduces slip ahead of the advancing interface. If the parent and product phasesare related crystallographieally to one another according to Burgers latticerelationships (110)BII (0001)~m nd [11~]BII [1 l~0]~m, hen a (110} plane in the/3 matrix is parallel to the facets on the ~,n morphologicalunits. The {110}planeis a potential slip plane of the bcc lattice; in fact, slip in the/3 phase parallel tothe faceted sections of the fl-~,, interface has been observed. Slip in the /3matrix impedes the motion of the advancing interface and, according to Kittl &Massalski (21), provides a mechanism for the formation of ledges. Whenunimpeded sections of the interface contact a (110)~ plane on which sliptaking place, semicoherent /3-~m interfaces are formed and produce theinterface geometry shown in Figure 7. The precise mechanism by which thetwinned ~m units form is unknown. The lattice relationships between the twinsubgrain and the /3 matrix are undoubtedly established during the nucleationstage of the transformation.

The rapid growth rate of a massive phase and the ability on occasions of themassive phase to penetrate a grain boundary and grow into an adjoining grainare indicative of the random, incoherent structure of the boundary between themassive and parent phases. Somedirect experimental evidence supporting thisconclusion has been obtained by Perkins & Massalski (23) who studied the fl-to-~,n transformation in equilibrated (~ + ~) Cu-Ga-Gealloys. The massivetransformation occurred in the quenched alloys by motion of certain prior fl-~boundaries; the other /3-~ boundaries were inactive and remained stationary.Because small particles of untransformed fl phase were present in the quenchedalloys, it was established by transmission electron microscopy hat (a) no uniquecrystallographic relationships exist between he fl and ~ phases across either theactive (fl-~m) or the inactive (B-~) boundaries, but (b) the habit of the inactive(,8-~) boundaries corresponds to a low index plane such as the basal or prismplanes, whereas the habit of the active prior (/3-~) boundaries is in generalirrational. Thus if one thinks of the/3-~ boundaries in terms of regions of goodfit (coincidence boundary) connected by regions of bad fit, the irrational andactive/3-~ boundaries should have a higher density of the more mobile regionsof bad fit in comparisonwith the low index, inactive/3-~" boundaries.

The internal structure of the ~,n phase formedby the fl-to-~; m massive reactionin/3 Cu-Ga 24) and (fl + ~) Cu-Ga-Ge 23) alloys consists of an irthomogeneousdistribution of stacking faults and dislocations on the basal plane of the hcpstructure. The stacking faults maybe either growth faults or deformation faultsproduced by the transformation stresses. The massive phase produced by the/3-to-am transformation in a Cu- 37.8 at.% Zn alloy (18) also has n i n_homogeneousinternal structure composedof dislocations and possibly some stacking faults.Thus, with the exception of the stacking faults, the internal structure of the alloymassive phases amand ~m s not unlike that of its counterpart in pure iron.


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334 MEYR ICK ~r POWELL

F igure 5boundary. (a)M icrosteps, 100 8, in height, on am # boundary. (b)M acrosteps,on a,-P

Figure 6 L edge growth of the 8, phase in a Cu-22.8at.%G a alloy./ Ic _ _ c _

Figure 7 L edge growth of a twinned8, crystal accomodated by slip in the /3 matrix (afterK ittl & M assalski, 21).


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PHASE TRANSFORMATIONS N METALS AND ALLOYS 335Discontinuous PrecipitationDiscontinuous precipitation is the formation of a two-phase product from asingle metastable phase, the product phases normally being dispersed in the formof alternating, parallel lamellae. In the simplest case the metastable phase is asupersaturated terminal solid solution (ass) which transforms below the solvustemperature to equilibrium alpha, aeq, plus a second phase //, which has astructure and composition different from that of the O~eq with which it coexists.In the case of Fe-Zn alloys (25) discontinuous precipitation occurs at tempera-tures below approximately 0.93 of the absolute solvus temperature and, for anA1- 17 wt%Ag alloy (26), the reaction occurs below 0.87 of the absolute solvustemperature; at higher temperatures continuous precipitation occurs, but, over alimited temperature range, the two modes of transformation may compete withone another. The decomposition of Fe-C austenite to pearlite is a more complexdiscontinuous reaction because the parent and product phases all differ incomposition and structure. The massive transformation might be regarded as alimiting form of discontinuous precipitation in which only a lattice transforma-tion occurs, whereas the atom transport required for the precipitation of theother phase is prevented by the external constraints, e.g. cooling rate.

In 1953 Smith (27) set forth a theory of discontinuous precipitation which hasserved as the basis for many of the subsequent theoretical treatments of thisreaction. Smith stated that the cells, which nucleate at grain boundaries, growpreferentially into one of the grains which abut the grain boundary by themotion of a "disordered, incoherent" interface. The composition changesrequired to produce the lamellar product are brought about by lateral diffusionalong this interface. Futhermore, the disordered, incoherent interface boundingthe growing cell is actually continuous with the original grain boundary at whichnucleation of the cell occurred and which has bulged into the grain under theinfluence of the driving force for the transformation. Consequently, as pointedout by Smith, the predominant phase in the cellular product is continuous with(i.e. has the same orientation as) the grain away from which the growth frontmoving. It was anticipated that rational crystallographic relationships wouldexist between adjacent lamellae (a and B), thereby minimizing the proportionthe driving force consumed by the formation of new interfaces. Subsequentresearch on discontinuous transformations has not altered in any significant waySmiths description of this reaction.

The recent research on this mode of transformation has been concerned withthe nucleation stage of the transformation, the mechanism or the developmentof cooperative growth, the mechanism for changing the spacing betweenlamellae, and, of course, development of more rigorous mathematical models ofcell growth. This discussion of the discontinuous mode of transformationconsiders the following topics: nucleation of lamellae and the evolution ofcooperative growth, mechanisms or changing lamellae spacing, growth kinetics,and nonequilibrium transformation products.The cellular reaction in bicrystals of a Pb-7 at.% Sn alloy has been subject tothorough study by Tu & Turnbull (28-30). The bicrystals contained a [001]pb


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336 MEYRICK & POWELLsymmetric tilt boundary, the misorientation 0 about the [001]~,b ranging from7-37. The appearance of the tin-rich platelets at an early stage of thetransformation is shown in Figure 8 and the morphologyof well-developed cellsis shown in Figure 9. The crystallographic relationships between the tin-richlamellae and the solute-depleted lead are (010)sn [[ (11 l)pb and [001Isn 1[ [110]pb,the habit plane of the lamellae being (111}pb. The planes and directions involvedin these relationships are the most densely packed planes and directions of thetwo crystal structures. Note that the tilt boundary n Figure 8 is not straight, buthas becomebowedor deflected in the immediate vicinity of the tin-rich lamellaeat the boundary. Futhermore, the lamellae lie within the grain on the left. Thus,of the two broad faces which bound each platelet, one is a low energy interfaceand the other, which separates each platelet from the grain on the right, ispresumably a high energy, incoherent boundary because the platelets are notrelated in the crystallographic sense to this grain.

On the basis of these observations Tu and Turnbull have proposed that thedevelopment of a cell takes place in the manner shown schematically in Figure10. The arrows in Figure 10a indicate in each grain the (110) directions, whichalso are the traces of the (111) habit planes in the [001] bicrystals. Whenplatelet lying within the al grain forms at the grain boundary, the grainboundary must be deformed locally to satisfy the habit plane requirement of theplatelet (Figure 10b). Subsequently the high energy, incoherent/~-a 2 interface isreplaced by a lower energy fl-al interface due to displacement of the. grainboundary as shown in Figure 10c. Displacement of the grain boundary serves notonly to embed he platelet wholly in the o/I grain but also to movea segment ofthe grain boundary into an orientation favorable for the formation of a secondplatelet lying parallel to the first (Figure 10af). Thus he pattern of cooperativegrowth is established by a repetition of this process.

As noted earlier, Smiths (27) model of discontinuous precipitation requiresthat the lamellae within a cell be related crystallographically to the grain awayfrom which the cell is growing, and the mechanism depicted in Figure 10 isconsistent with this requirement. Tu & Turnbull (29) and Liu & Aaronson (31)have observed that cells do not form when the misorientation about the[001h,b axis of the bicrystals is smaller than 15. Here again, this observation isconsistent with Smiths model in that low angle tilt boundaries possess neitherthe structure nor the mobility to support cellular growth.

Although the mechanism llustrated in Figure 10 for cooperative growth isextremely attractive because of its relative simplicity, the operation of thismechanism in alloy systems other than Pb-Sn has not been reported in the literature. Some ecent research by Fournelle &Clark (32) on cellular precipita-tion in a Cu-9.5 at.% In alloy has yielded results which have led to theformulation of a generalized theory and criterion for the development ofcooperative growth. In this alloy the discontinuous reaction is preceded by theformation of well-developed grain boundary allotriomorphs of the 8 phase(CuaIn4) but develops subsequently from the allotriomorphs. The sequence


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PHASE TRA NSFORM AT IONS IN METALS AN D ALLOYS 337

Figure 8 Early stage of cellular growth Figure 9 Fully-developed cells in a Pb-in a bicrystal of a Pb-7 at.%Sn alloy. 7 at.%Sn alloy.

Figure 10 Developmentof cooperative growth by the Tu-Turnbull mechanism (after Tu& Turnbull,28).


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338 MEYRICK & POWELLevents producing cooperative growth is beautifully illustrated by the transmis-sion electron micrographs in Figure 11 and is illustrated schematically in Figure12. A grain boundary pinned at some points by allotriomorphs bows out betweenthe particles. As the grain boundary moves, it leaves behind solute-depleted ttphase, the solute having diffused along the bowedboundary to an allotriomorph.Consequently the allotriomorphs becomeextended parallel to the direction ofmotion of the grain boundary and the pattern of cooperative growth is therebyestablished. The initial driving force for grain boundary migration is derivedfrom such factors as the local curvature of the grain boundary and the relativeperfection of the abutting grains (strain-induced grain boundary migration).However, once the solute-depleted ~t forms behind the advancing interface, thedriving force for boundary migration is derived primarily from the difference ofthe chemical free energy between the supersaturated a phase and the solute-depleted a phase. The Fournelle-Clark mechanism for the development ofcooperative growth provides an explanation for the fact that continuous precip-itation occurs at temperatures above approximately 0.8-0.9 of the absolutesolvus temperature, whereas the cellular reaction is favored below this tempera-ture. In the higher temperature range the chemical free energy is simply not ofsufficient magnitude to bow out the boundary between the allotriomorphs.Although he austenite-to-pearlite transformation in steel has been the subjectof almost innumerable investigations, the mechanism(s) by which cooperativegrowth is established remains unknown. Hull & Mehl (33) proposed that thesidewise growth of a pearlite colony occurs by the successive nucleation of ferriteand cementite, the initial nucleus being a platelet of cementite. After theformation of the initial platelet of cementite, the platelets of ferrite nucleate inthe adjacent carbon-depleted austenite, etc. However, subsequent research(34-36) has demonstrated quite clearly that a pearlite colony can originate fromeither a ferrite (hypoeuteetoid steel) or cementite (hypereutectoid steel) nucleusand, furthermore, sidewise growth by successive nucleation of the lamellae hasnot been confirmed experimentally. The Fournelle-Clark mechanism (32) de-scribed above seems capable of being applied under some circumstances directlyto the pearlite reaction. Consider, for example, a ferrite allotriomorph (Figure13a) allowed to form isothermally in the (y + ct) phase field. As shownexperimentally by Hillert (37) and depicted schematically in Figure 13b, pearliteforms at the upper ~t-y boundary during a moderately fast quench from thetemperature at which the allotriomorph formed. In the initial stages of thequench; particles of cementite nucleate at the tt-y interface which may havemoved a small amount, thereby producing a local enrichment of the carboncontent within and/or in the immediate vicinity of the boundary. Continuedcooling produces the driving force necessary to bow out the a-y boundarybetween the cementite particles (Figure 13d). Subsequent growth of the cementiteparticles occurs as shown in Figure 12. In agreement with experiment, thepearlitic ferrite is continuous with the ferrite allotriomorph and thus has the samecrystallographic orientation. It is not clear, however, as to whether or not thecementite lamellae should have a specific crystallographic orientation.


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PHASE TRANSFORMATIONS IN METALS A ND ALLOYS 339

F igure 11

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Development of cellular growth fromallotriomorphs in a Cu- 9.5 at.% n alloy.% a'- L a I a'T w i n s8d e f

F igure 12Fournelle& Clark, 32).Development of cooperative growth by the Fournelle-Clark mechanism (after


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340 MEYRICK ~ POWELLAccording to Zeners theory (38) of the cellular reaction, the intedamellar

spacing S should vary inversely with the amount of undercooling, i.e. S a ATl .The results of some experimental studies (40, 41) have confirmed this relation-ship; however, in the case of Fe-Zn alloys Speich (25) found that the interlamel-lar spacing did not vary linearly with ATl , a result rationalized qualitatively bya modification of Cahns theory of cellular growth (39). A temperature changeduring the growth of a cell must be accompaniedby a change in the interlamellarspacing which can take place by one of the following mechanisms: branching,nucleation of new lamellae at the advancing cell boundary, or separation of thecell boundary from the tips of the lamellae. The first two mechanismsdecreasethe interlamellar spacing whereas the last increases the spacing.

Figure 14 is a schematic summary of the means whereby changes in thespacing between the cementite lamellae in pearlite have been observed to occur.In the case of pearlite the spacing is decreased by the branching mechanism(Figure 14a, b, c). Onecan regard the sequence of events illustrated in this figureas a variant of the Fournelle-Clark mechanism. When the temperature isdecreased, the ferrite-austenite boundary adjacent to the cementite lamellaebows out into the austenite, the carbon atoms subsequently collecting in andprecipitating on the displaced boundary. The driving force to bulge the boundaryinto the austenite adjacent to the cementite lamellae arises from the anticipatedlower carbon content of this austenite and hence a higher TO temperature. If the, temperature is suddenly raised during the growth of a pearlite colony, theinterlamellar spacing car~ be increased by replacive motion of the ferrite-austenite interface as shown n Figure 14d; this process also may involve partialdissolution of the eementite at the tip of the lamella. The interlamellar spacingmay be decreased by nucleation of new lamellae at the advancing interface, ascan be seen in Figure 11 for the Cu - 9.5 at.% In alloy. This mechanism lso hasbeen observed to operate in Pb-Sn alloys (29). In the case of pearlite, Sundquist(42) has stated "that interlamellar spacings observed experimentally are thosethe verge of instability with respect to the formation of a new lamella of Fe3 Cat the middle of a ferrite lamella-austenite interface."Data for the cellular growth rate ~ can often be fitted to an equation of theform

wherein AT s the undercooling and Q is the activation energy for diffusion. Thegrowth rate is low at high temperatures (small AT) because the interlamellarspacing is large and the driving force for the reaction is small, and is also low atlow temperatures because the diffusion rate is slow; thus the growth rate attainsa maximumalue at some intermediate temperature. On the basis of the simplemodels which yield an equation of this form, a value of n = 2 is associated withvolume-diffusion-controlled growth (38), whereas a value of n = 3 is appropriatefor interface-diffusion-controlled growth; consequently the corresponding activa-tion energies are those for volumeand grain boundary diffusion respectively. The


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PHASE TRANSFORMATIONS N METALS AND ALLOYS 341growth rate for the cellular reaction in the austenitic Fe-30Ni-6Ti alloy studiedby Speich (41)

G(mm/min) = 281 (982 - TC)2 exp(39 800~

Although this equation has the form associated with volume-diffusion-controlledgrowth, the activation energy of 39,800 cal/mol is considerably smaller than thatfor the diffusion of nickel in iron (67,500 cal/mol). Thus an unambiguousphysical interpretation of Equation 2 is not possible. If it is assumed hat thegrowth of pearlite occurs by diffusion of carbon along the pearlite-austeniteinterface and the effects of capillarity and imperfect carbon segregation are takeninto account, the cellular growth rate should be given by an equation of the sameform as Equation 1 with n ---- 3 (42). When ata for high purity Fe-C alloys arefitted to this equation the activation energy is computed o be 45,700 cal/mol,much arger than that expected for interface diffusion. Sundquist has attributedthe high activation energy to an impurity effect.

To derive a growth rate equation which in the final form does not containexplicitly the interlamellar spacing, it is necessary to employ a priori anextremum principle. For example, Zener assumed that the observed spacing isthat which maximizes the growth rate. Other criteria which have been used aremaximumate of entropy production (43) and maximumate of decrease in freeenergy (39). At the present time there is no evidence which suggests that onethese criteria is superior to the others.

The products of a cellular reaction may not have the compositions correspond-ing to the equilibrium state. Thus, in the case of the eutectoid reaction(/~ --> a + T) in a 94%Cu-6%Be alloy, the a phase is initially supersaturatedwith respect to beryllium, but with continued aging the supersaturation isrelieved by diffusion of the excess beryllium atoms to the T phase (44). A similarsituation has been found by Speich (25) in Fe-Zn alloys. The a phase of thecellular product is supersaturated with respect to zinc, the extent of the deviationfrom equilibrium increasing with decreasing reaction temperature and also withincreasing zinc content of the alloy (Figure 15). Here again, the supersaturationof the ct phase is relieved by diffusion of zinc to the T lamellae.

One of the phases in the lamellar product may be a metastable phase. This isapparently the case for the cellular reaction in an austenitic Fe-30Ni-6Ti alloy.At temperatures in the range of 700-900C, equilibrium requires a two-phasemixture of austenite plus (Fe, Ni)2Ti. However, the initial cellular productconsists of austenite plus Ni3 Ti lamellae (3.~ --~ 7B+ Ni3 Ti). The equilibriumstate is achieved subsequently by means of a second cellular reaction+Ni3Ti ~ "/c + (Fe, Ni)2Ti]. In some instances, however, the two reactions,Y,~ --> Ys + Ni3 Ti and )A -> )c + (Fe, Ni)2Ti, complete simultaneously with oneanother.Continuous PrecipitationThe discussion of this mode of transformation, characterized by long rangediffusion of solute atoms through the metastable matrix phase to the particles of


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342 MEYRICK ~ POWELL

INCOHERENT RIMOFFINE(z- X BOUNDARY PE~~-X GRAIN

BOUNDARY(a) (b) (c) (d)

Figure13 Formation f pearlite froma ferrite, allotriomorph.

Figure 14 Mechanisms y which the in-terlamellar spacing of pearlite maybechangedafter Hillert, 37).Figure 15 Nonequilibrium solvus linesfor the cellular reaction in Fe-Znalloys(after Speich,25).

the new phase, considers the following topics: morphology of the precipitate,mechanism nd kinetics of growth, and sequential precipitation.

At relatively low degrees of undercooling, nucleation of the new phase tendsto occur predominantly at grain boundaries and at dislocations within thevolume of each grain; at high degrees of supersaturation, on the other hand,precipitation tends to occur more generally throughout the structure because ofthe lower free energy barrier to nucleation. The structure of grain boundary can




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PHASE TRANSFORMATIONS N METALS AND ALLOYS 343have a significant effect on the morphological development of the precipitateparticles. For example, Toney & Aaronson (45) found that in (110) misorientedbicrystals of an Fe- 1.5 wt.% Si alloy allotriomorphs of austenite form when hemisorientation 19 is greater than 11, but when O


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344 MEYRICK a POWELLDislocations also are favored nucleation sites at low degrees of undercooling.

Thus at high aging temperatures Phillips (47) observed the growth of triangular-shaped platelets of Ni3 A1 along dislocations in the matrix of an Ni- 12.7 at.% A1alloy. The hypotenuse of the particles was coincident with the dislocation line;because of the size of aluminum toms it was anticipated that they should clusteralong the tensile side of the dislocation lines. In the case of the precipitation ofmetastable y-Ni3 Ti particles in a nickel-based alloy, the hexagonal y particlesnucleate at dissociated dislocations in the fcc matrix, the interaction between heparticle and the dislocation being primarily chemical rather than elastic in nature(48). Heterogeneous nucleation has been reviewed recently by Nicholson (49).

Mathematical analyses of the growth of allotriomorphs are based normally onan idealized particle shape (juxtaposed elliptical caps, oblate ellipsoid, etc) andan assumeddiffusion path (either volumeor interface diffusion or a combinationof both). For those models based on long range volume diffusion directly to thegrowing allotriomorph, the resulting kinetic equation(s) and the experimentalgrowth data can be combined to yield a value of the apparent diffusioncoefficient Dapp. If Dapp = Dv then this result essentially establishes the validityof the model. On he other hand, if Dapp >> Dv the growth rate is too high to beaccounted for by volume diffusion directly to the allotriomorph and consequent-ly the assumption regarding the diffusion path must be modified. Thus Aaron &Aaronson (50) found that at low homologous temperatures (0.54-0.69 ofabsolute solvus temperature) the allotriomorphs in an Al-4 wt%Cu alloy growat rates much oo high (Dapp/Dv ~ 500) to be accounted for by volume diffusiondirectly to the 0 particles; they proposed that growth occurs rather by a right-angle collector plate mechanism (Figure 17). Copper atoms move by volumediffusion to an a-a grain boundary where the atoms diffuse along the boundaryto the edge of the O allotriomorph; thickening of the allotriomorph requiresadditional diffusion of the copper atoms along the c~-O interface. The thickeningand lengthening of the particles were found experimentally to vary as t 1/3 andt I/4 respectively. The collector plate model predicts a t I/4 dependence forlengthening but a t 1/2 dependence for thickening; the slower than predicted rateof thickening was associated with the tendency of the O allotriomorphs todevelop facets. As the aging temperature increases the contribution of volumediffusion directly to the 0 particle increases and, at homologous emperaturesgreater than 0.91 of the absolute solvus temperature, growth is controlled solelyby volumediffusion directly to the precipitate as Dapp = Dv (51). AS pointed outby Goldman t al (51) no analysis of allotriomorphic growth that combines bothdirect volume diffusion and the contribution of the collector plate mechanismhas been made.The kinetics of thickening of ferrite allotriomorphs in a high purity Fe-0.11 wt% C alloy has been investigated by Kinsman & Aaronson (52) usingthermionic emission microscopy. The thickness varies parabolically with time(s = K tl/2). Goodagreement was found between the experimental rate constantK and the theoretical value predicted by a growth model based upon volumediffusion of carbon through the surrounding austenite. During the early stages of


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PHASE TRANSFORMATIONS N METALS AND ALLOYS 345

Il)V

DV

~ oe

Y

Figure 17 Collector plate mechanismorthe growthof an allotriomorph after Aa-ron &Aaronson,50).

~ ADVANCING GROUP GROUPS----~" RETREATING

/8 CRYSTAL i CRYSTAL

~ ~RT_~EIOT~~REACTION

REACTION(o) (b)

Figure 18 Thea + O to a + 0 transformation n a Cu-Alalloy (after Laird &Aaronson,54).growth the lengthening of ferrite allotriomorphs takes place at a constant rateand, here again, the kinetics of lengthening appears to be consistent with growthcontrol by volume diffusion of carbon through the austenite. The addition of asubstitutional alloying dement to an Fe-C alloy might slow down he thickeningkinetics of ferrite allotriomorphs due to a solute drag effect on the ferrite-austenite interface. Kinsman& Aaronson have suggested that this effect produc-es the bay in the time-temperature-transformations (TTT) diagram of an Fe-0.11% C-1.95% Mo alloy. The moving interface of a ferrite allotriomorph isassumed to be of the disordered type and therefore the growth rate is dependentupon such factors as interface and bulk compositions, diffusivities, etc. Thebroad faces of Widmanstatten ferrite may be dislocation interphase bouridarieswhosemobility normal to the plane of the boundary s highly restricted. If this


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346 MEYRICK ~ POWELLis actually the case, then the rate of thickening of Widmanstatten errite shouldbe less than that associated with carbon-diffusion-controlled motibn of adisordered ferrite-austenite interface. Measurements f the thickening of ferriteplatelets using thermionic emission microscopy confirm this conclusion. Inaddition the platelets were observed to thicken by the motion of superledgesalong the broad faces of the platelets in agreement with Aaronsons theory forthe development of the platelet morphology. However, the formation of Wid-manstatten ferrite has been shown to produce surface tilts (53), an effectassociated with a martensitic transformation. This fact alone makes our under-standing of the growth of Widmanstatten ferrite uncertain and calls for furtherresearch on this transformation.The reaction path by which a metastable phase attains the equilibrium statemay involve formation of transition precipitates which are eventually replacedby the equilibrium second phase. In an AI-4 wt.% Cu alloy the precipitationsequence is Guinier-Preston (GP) zones --> 0" --> 0 --> O (CuAI2); both 0 andare body centered tetragonal (bct). The mechanisms by which 8 is replaced by/9 in the temperature rangeof 325--430C have been investigated by Laird &Aaronson (54) using hot-stage transmission election microscopy. A nucleus of/9forms in a small proportion of the /9 plates and subsequent growth yields aplatelet of/9 with its broad faces either parallel to or at an angle to the broadfaces of the 8 plate (Figure 18). In this situation the /9 grows by the directtransformation of /9 to /9 (reaction 1 of Figure 18) and by growth into themetastable a matrix (reaction 2); the latter reaction may be accompaniedsimultaneous dissolution of noncontiguous as well as contiguous /9 plates(reaction 3). The majority of the O plates, however, do not contain a 8 nucleusand these particles simply undergo dissolution by countercurrent diffusion toneighboring but noncontiguous/9 particles. Dissolution of the/9 plates occurs bya ledge mechanism 55). The structure of the ledges is unusual in that the ledgecontains an edge dislocation whose Burgers vector, a (100), is normal to thebroad face of the plate; this structure differs from that of the growth ledge~ of/9plates. The decomposition of an Al-15 wt.% Ag alloy is another example ofsequential precipition. Spherical silver-rich GPzones which form initially beginto dissolve when heterogeneous nucleation of the transitional 3" phase occurs(56). The 3" phase in turn undergoes dissolution when particles of the stablephase form. Both the growth and dissolution of 3" and the growth of )t involveledge motion along the broad faces of the particles.MARTENSITIC TRANSFORMATIONSIntroductionDespite the effort devoted to the study of martensitic transformations, theirnature remains to be completely elucidated. No general theory is known intowhich all the accumulated data can be satisfactorily integrated and which iscapable of convincingly explaining aspects, such as the nucleation event, that stilldefy direct observation. The situation is further clouded by the existence ofmultiple terminologies and the lingering confusion as to what constitutes a


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PHASE TRANSFORMATIONS N METALS AND ALLOYS 347correct and sufficient definition of a martensitic transformation.The latter question has been the subject of much discussion (1, 57, 58).desirable definition would be one couched in terms of observable characteristicsthat wouldprovide a criterion for the unequivocal identification of a martensitictransformation. The crux of the problem is in the requirement that thecharacteristics be unambiguous nd, for complete satisfaction, capable of beingformulated into a concise definition sufficient in itself and needless of extensiveclarification.

Transformations that are accepted as martensitic can occur during quenching,as in many teels, but so also can the massive transformation. In somematerialsthe transformation takes place under isothermal conditions, the fraction trans-formed increasing with time as happens in interface-controlled diffusionaltransformations in some polymorphic changes (59). That the product ofmartensitic transformation is related to its parent through a habit plane anddefinite orientation relationships is again inconclusive, as the same can often betrue for precipitation from solid solution.

It has frequently been stated that the most definitive manifestation of amartensitic transformation is the topographical relief it produces on an initiallyfiat surface. For this to be true it is necessary that the relief be of a characterpeculiar to a martensitic transformation and distinguishable from that arisingfrom transformations that are clearly not martensitic. Surface relief caused bymartensitic transformations can be described phenomenologically as arisingfrom a macroscopically invariant plane strain. This observation is the basis ofcrystallographic theories of the transformation and has been implicit in defini-tions of martensite (58). Its importance has been reemphasized in a recentdiscussion (53) of surface relief effects in which a definition drawing morespecifically upon crystallographic theories was offered. As an illustration thesalient points of existing descriptions can be incorporated into a general thoughcumbersomestatement: a martensitic transformation is a structural changegenerated by atomic displacements and not achieved by diffusion, correspondingto a homogeneous eformation which may be different in small adjacent regions,and which gives rise to an invariant plane strain through which the parent andproduct are related by a substitutional lattice correspondence, an irrational habitplane, and a precise orientation relationship.

A martensitic transformation can produce a structural change without changein composition, which implies there is no necessity for long range diffusion.Furthermore, all first order phase changes that are agreed to occur without theneed for diffusion are called martensitic. It can be argued then that a martensitictransformation can be formally defined as a first order phase transition in whichthe newstructure grows without the necessity of atom interchange by diffusion.The complexity surrounding an operational definition for the martensitic reac-tion can be regarded as a consequence of the search for characteristics thatestablish the lack of control by diffusion. Attempts to tie the definition morestringently to the phenomenological theories seem unwarranted until suchtheories becomecompletely successful. Because there is no a priori reason for a


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348 MEYRICK & POWELLsystem to follow only a single path of transformation somehybridization is to beexpected, particularly under conditions where diffusion can occur reasonablyrapidly. Thus the creation of additional terms such as quasimartensite (5) doesnot serve to clarify the issue.

The discussion of the martensitic transformation considers the followingtopics: morphology of the product, original formulations of the phenomenolog-ical theory, comparison of the theory with experimental data, modifications ofthe theory, microstructure of martensitic crystals, and mechanism f the trans-formation.The Morphology of the Martensitic ProductThe crystals of the new phase display a variety of morphological characteristicsdependent upon the chemical nature of the parent and the crystallographicstructural change accomplished, which are consequences of the operative mech-anism of transformation and the influence of the elastic and mechanicalproperties of the matrix.Monocrystalline samples of some alloys of Au-Cd 60) and In-T1 (61) cancaused to transform so that the parent and product are separated by a singleinterface (the habit plane) which, upon migration, creates a single crystal of themartensitic phase, composedof a stack of twins visible by optical microscopy.More usually a number of martensitic crystals are formed within the parent andare influenced by the constraints of the matrix. In this respect there aretransformations which take place at the free surface of the specimen (62-64)which can be expected to differ in character from those representative of thebulk.In some simple cases the transformation yields parallel sided bands of newphase as in the fcc ~ hcp change in cobalt and cobalt-nickel alloys (65). Moreusually the martensitic crystal takes the form of a lenticular plate (Figure 19).Often such plates exhibit a structural discontinuity, called a midrib, on theequitorial plane. This morphology is one of the variants adopted by themartensitic products in iron-based alloys. The term plate martensite is adoptedfor this variant in keeping with a recent description of the morphology f ferrousmartensites (66). Martensitic plates generally form at angles to neighbors andso doing subdivide the matrix so that plates formed subsequently are reduced insize. Accordingly, growth is frequently inhibited by mutual impingement whichcan cause mechanical twinning (66) and microcracking (66, 67) as well as plasticdeformation.

Many workers have demonstrated the occurrence of plate martensite in anumber of concentrated binary alloys of iron and steels (68-72). On the otherhand, the product of the martensitic transformation in a variety of dilute ironalloys (73, 74) cannot be described as plate-like. Instead the microstructurecomposedof blocky units several microns in size (Figure 20) made up of fineparallel martensitic laths. Neighboring groups of laths can be twin-related orseparated by high or low angle boundaries. During formation the laths partitionthe matrix as does plate martensite but, unlike the latter, subsequent laths tend


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PHASE TRANSFORMATIONS IN METALS A ND ALLOYS 349

Figure I 9 Plate martensite in an F e- 13.9%M n alloy.X 1OOO.

P, Figure20 L ath martensite in an Fe-0.31% W alloy. X200.

to form in parallel orientations. This variant of the morphology has also beenchristened many names; the term lath martensite will be used herein.

The essential features of the morphologies described above have been wellestablished. With the exception of detailed shape change measurements yet to bediscussed there seems little more information that mightbegathered by optical


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350 MEYRICK & POWELLmicroscopy. Indeed the individual components of lath martensite and thesubstructure in plate martensites are generally too fine to be thus studiedprofitably.

The fact that the transforming region undergoes bbth a change in crystallo-graphic structure and in shape, with consequent modifications of the surfacetopology, while maintaining contiguity with the surrounding matrix, gives rise toseveral other important morphological aspects. The first of these is the shapechange itself. Its chz, racter is deduced from measurements made upon theexterior surface of the specimen and thus is subject to the doubts that can ariseconcerning the relationship of such observations to bulk phenomena. Apart fromcases where the depth of penetration of the martensitic crystal is small, as in thesurface martensites mentionedearlier, it is not clear that such doubts are valid.The fact that there can be very good agreement between the predictions oftwinning theory and surface topography (75) lends strong support to theargument hat indications from the surface can be descriptive of the bulk; so alsodoes the fact that the phenomenologieal crystallographic theory successfullydescribes some fully twinned martensitic products. The nature of the shapechange is deduced by use of interference microscopy and by measurements of itseffects upon prescribed lines upon the parent surface. Early results (76) whichdemonstrated that the topographic changes accompanying a martensitic transi-tion are consistent with those that would be produced phenomenologically by amacroscopically invariant plane strain, in which the invariant plane is the habitplane, have been substantiated subsequently in a number of systems. The habitplane is usually an irrational plane of the parent and is characteristic of thematerial concerned, as are the orientation relationships. These macroscopiccharacteristics form the basis of the crystallographic theories.Original Formulations of the Crystallographic TheoryThe basic crystallographic theory originated in the early 1950s (8, 9) and hasbeen frequently described in detail since (1, 72, 77). It pays no direct attentionto atomic mechanisms but has as its aim the construction of a transformationstrain which, when applied to the parent crystal, produces phenomenologicallythe results of the martensitic transition. The original theories are mathematicallyequivalent but differ in formulation.

The shape strain T can be written in matrix notation as T = RBP. Of these Bis the Bain strain which transforms a selected unit cell of the parent into one ofthe product. For example, in carbon steels the strain

~/ 00 03//

applied relative to orthonormal axes parallel to the [1]0], [110], and [001]directions in the fcc structure yields the bet structure. The bet unit cell of the


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PHASE TRANSFORMATIONS N METALS AND ALLOYS 351latter has its [100], [010], and [001] edges parallel to the system of axes and ofmagnitudes a~/.v/2, a~/~/2, and a~3, being derived from the bet cell of the feestructure outlined by the edges 1/2 a[l~0], 1/2 a[ll0], and a[001]. In thisexample all atoms are moved o their new positions by B; however, for structureswhich have primitive cells containing different numbersof atoms, only a fractionare correctly moved nd the remainder require additional shuffles (78, 79). Thechoice of B has to be made from an infinity of possibilities without clearguidance other than the intuitively plausible criterion of minimal principalstrains. Its application does not in general accomplish the lattice change and atthe same time leave a plane both unextended and unrotated. To conform to themacroscopic requirement of a homogeneous nvariant plane strain, additionalstrains are required. These must leave the lattice unchanged and comprise arotation R and a shear P chosen so that T has an invariant plane. P can refer toa strain accomplished by slip or twinning (which have equivalent mathematicaldescriptions) and, as written above, is applied to the matrix phase.

The evaluation of the strain T can be performed either graphically upon astereographic projection or through formal matrix algebra. Details of bothprocedures are presented in the referenced work. In essence the solution requires,first, the choice of a suitable correspondencebetween two cells of the structuresand the numerical expression of B from lattice parameter measurements. Second,a shear plane and direction are assumed and the magnitude of shear is found sothat BPyields a macroscopically unextended plane. Finally the matrix R whichensures that the unextended plane remains unrotated is obtained.Comparison of the Theory With Experimental DataThe most obvious output from the crystallographic theory is the identification ofthe habit plane (i.e. the invariant plane) and the orientation relationshipsdescribed by R. Significant failure to predict correctly these parameters consti-tutes grounds for rejection of the theory as formulated. On the other hand,success does not immediately indicate a completely satisfactory description asthis also requires internal consistency with the magnitude and direction of theshape strain and the martensitic substructure (80). In this respect the invariantplane strain T can.be written as T = I + mtlp whereI is the unit (3 3) matrix,m is the scalar magnitude of the strain, and d and p are unit vectors definingrespectively the displacement direction and the invariant plane normal.

Although the theory takes no formal cognizance of atomic mechanisms, themanner by which P is achieved can be expected to influence the mierostructureof the product. This can be appreciated physically by realizing that the strain RBapplied to a small region creates a product of the correct structure andorientation. With increase in its size the buildup of macroscopicdistortion in itsinterface is avoided by the operation of P. If the choice is twinning in themartensite, the latter can be expected to consist of a stack of twins. In this casetwo martensitic orientations exist equivalent to the operation of two crystallo-graphic variants of the Bain strain in volumes separated by a twinning plane




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352 MEYRICK & POWELLgenerated from a plane of symmetry n the parent (81). If P is by slip, one variantof B is to be expected, and twins ought to be absent, but the microstructure maycontain planar faults.

The precise determination of all the parameters relevant to testing the theoryis by no means a trivial operation and, in manycases, is beset with severedifficulties. Nevertheless the accumulated data, though sometimes incomplete,demonstrate the fit of theory to fact to range from excellent, through fair, toinadequate. Detailed reviews of the situation for transformations in pureelements and in alloys have been published (l, 72).

In general the theory affords an excellent description of cases where themacroscopic and microscopic characteristics are well defined and relativelysimple; but as these characteristics, particularly from the microstructural aspect,become irregular and increasingly complex the theory becomes progressivelyinadequate. Excellent agreement is found for the allotropic transformation incobalt (72) and for the more complexstructural changes in Au-Cd, In-T1 (77),-33%Ni, Fe- 22% Ni-0.8% C, and Fe-24.5% Pt (80). The first is simple in thatthe lattice change can be produced by a shear in a (1 l~) on every second (11plane of the fcc phase. The second two have small principal strains and asubstructure of evenly spaced twins visible at least away from the interface byoptical microscopy. On the other hand, the last three have large principal strainsand consist of regularly spaced twins of the correct type visible only by electronmicroscopy. The latter three alloys are interesting as they are examples of thecomparatively few ferrous alloys that show convincing agreement with thetheoretical predictions in an internally consistent manner. All three have habitplanes close to (3 l0 15)v which is predicted by the Bain correspondencementioned earlier and shear on a (1 l~)(11 l) system in the martensite. Experi-mentally this is an atypical habit plane when compared o the near (11 l)v habitin lath martensite of low-carbon steels and dilute binary alloys, the (259)v habitof plate martensite in high-carbon steels, and the {225)v habit commonor platemartensite in iron containing 0.8-1.4% C.

The variation of habit plane with composition change is further illustrated bythe progessive shift away from (3 10 15)v with decrease in Ni content of Fe-Nialloys (82). Whereas he existence of habits near (259)r and (225)r is presumablyassociated with the complex substructure of incompletely and irregularlytwinned plates, the significance of the association is at present unclear.Modifications of the Phenomenological TheoryCases of successful application of the theory have been held as a demonstrationof its essential soundness. Consequently, closer agreement with those ferrousmartensites which exhibit habits other than (3 10 15}v has been sought bymodifications of the basic formulation. A common rocedure (83) which leavesthe basic theory unchanged s to examine the results of alternative choices forthe plane and direction of the lattice invariant shear, but no combination hasproved completely satisfactory.


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PHASE TRANSFORMATIONS N METALS AND ALLOYS 353In one of the original formulations (9) somemodification was possible through

the use of an adjustable dilatational parameter ~ incorporated as a factor in theprincipal distortions of the Bain strain, which was varied from unity to improveagreement. This procedure amounts to relaxing the invariant plane conditionand permitting a slight isotropic dilatation in the interface. Althoughan arbitraryvariable is aesthetically displeasing, the possibility of a dilation cannot besummarily dismissed and its use has been frequent. Recent measurements (84)have shown hat the required dilatation for the (225}v habit plane in steels doesnot exist and in this case at least the dilatation parameter must be discarded.

In recent years there have been four main attempts to modify the theory. Allfour have in common hat the modification involves the introduction ofadditional lattice strains and is directed towards an attempt to resolve thedilemma posed by the {225}v habit. The first (85) considers a compositemartensite plate of twinned and untwinned regions and invokes, besides theusual R and B, an additional rotation and two shears, but has been shown (86)to be unsatisfactory. Of the others, one assumes an accomodation shear withinthe austenite ahead of the interface (86), while the other two replace the latticeinvariant shear P by two independent lattice invariant shears (87, 88). All threehave been discussed in detail recently (89) with the conclusion that themodifications improve the overall agreement but not to the state of satisfactionextant for the {3 10 15}~.Although the departure from a single simple lattice invariant strain appearsconsistent with the increased complexity of the martensitic substructure as thehabit moves rom {3 10 15}v, ne is left with the uncomfortable thought that anyshape change is describable given enough unrestricted combinations of shear;however, this loses the elegance of the original theory, increases the numberofinitial assumptions, and may well produce a result of dubious value.The Microstructure of Martensitic CrystalsElectron microscopydemonstrates that crystals formed martensitically are highlydefective and can contain twins, stacking faults, dislocations, and combinationsthereof. Some examples of relatively clear-cut cases in which the product iscompletely twinned and is thus composed of a stack of lamellar twins havealready been described. Transformations between close packed structures oftenresult in heavily faulted products. The product of the fcc to hcp allotropic changein cobalt is rich in stacking faults, as is consistent with the fact that the structuralchange can be obtained by shears of a/6 (11~) on every second parallel {111}plane. Indeed in situ electron microscopy (90) has shown that perfect disloca-tions can dissociate producing extended stacking faults during the phase change.By the same technique it has been demonstrated that arrays of extendeddislocations can be emitted from grain boundaries during the transformation(91). Similarly the a phase formed from the fcc/3 in lanthanum (92) is denselyfaulted. In this case the a is a modified hcp structure with a stacking sequenceABACABAC,which can be produced from the /3 by displacing two adjacentclose packed planes by a/6 (112) every fourth plane. Heavily faulted structures


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354 MEYRICK POWELLare also produced n alloys such as those of the extensively studied Cu-AI ystem(93, 94). Accordingo composition he fl phase can transform o ff or ill. Thesecan be regarded as arrays of stacking faults although the details are rathercomplex; lamellae of the stacking sequences ABCBCACAB,B, and ABChavebeen dentified (95).Ferrousalloys exhibit a wide ange of microstructuralcharacteristics describedin detail in tworecent reviews 96, 97). Thevariations are intriguing because hebasic structural changerequired is generally similar. Broadlyspeaking, platemartensites can be comprised ntirely of fine twins (80, 98) or consist of twinnedand untwinned egions (99-101), the latter containing dislocations, while lathmartensite is usually composed f bundles of elongated subgrains characterizedby complexdislocation structures (102-104), although twins have also beendetected (105). In all completely twinned martensitic crystals that are welldescribed by the crystallographic theory, the types of twins observed areconsistent with the lattice invariant shear invoked n the theory, fromwhich t isinferred that such twins are direct consequences f the mode f transformation.This is also a reasonable inference for the presenceof stacking faults in othermartensites. For steels the proper twin is of the {112}b ype which s observed nall twinned products. However 011)b twins are also found in incompletelytwinned bct martensite (100, 107) and the {l12)t ~ twins can themselves beinternally twinned(96, 108). In addition twins sometimes ppear (106) tobeen modified by slip processes. This has been used to explain the apparentdeviation of twins from he ideal .(112}b in Fe-Ni(109), but such deviationsalso arise fromexperimental rror (110). It can be seen that the complexitiesaresuch that a complete documentation of the microstructural features awaitsfurther painstaking tudies.Evenwith a complete description of the microstructural features a luthermajor problemarises concerning their origin. One issue here is: which arenecessary ingredients of the cransformationper se and whichare consequencesof the matrixconstraints? "[ he latter are said to correspondo a post-transforma-tion strain, although hey can presumably rise to some xtent concurrently. Inthis respect it has been argued(106) that {01 l}b twins are indirect productsthe transformation as they wouldbe derived froma nonmirrorplane via the Baincorrespondence.Twinnedwins are observed n foils prepared from the bulk andalso in those transformed n situ when he influences of the bulk are minimized(although other kinds are substituted) and have thus been claimed (108) toconsequences of the modeof transformation. The role of dislocations isproblematicalbecause any directly involved in promoting he structural changeought o be retained at the interface.The Mechanismof the TransformationAmajor area of martensitic transformations in which atisfactory understandingis lacking concerns the physical mechanisms y which the newphase nucleatesand grows. In all heterogeneous ransformations the growthof the newphase isprofoundly nfluenced by the nature of the interface that separates it from the


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PHASE TRANSFORMATIONS N METALS AND ALLOYS 355matrix. (In this context heterogeneous transformation implies that at any instantthe system can be divided into transformed and untransformed volumes.) This isespecially true of a martensitic transition in which the interface moveswithoutthe aid of diffusion and, as a result of its movement,creates the new phase. Itsorigin nature and behavior are thus central to understanding the mechanismsofthe transition. It is generally supposed hat the interface is glissile and is formedby a suitable array of dislocations or by the termination of a stack of twinlamellae. Indeed discussions of the various characteristics exhibited by ferrousalloys are based upon the effects of the pertinent vari.ables upon the competitiveprocesses of slip and twinning. As a general trend it can be stated that thedeparture from well-defined, completely twinned plates, to lath martensite isassociated with an increase in the Ms temperature and a reduction in alloyingcontent, which are of course interconnected, particularly with respect to austen-ite stabilizing elements. To the extent that these changes would be expected tofavor slip processes over twinning, the correlation is qualitatively reasonable.Oneof the early versions of the phenomenological theory (111) in~,olved theformal concept of surface dislocations, whereas the first specific model attempt-ing to describe the austenite-martensite interface in terms of an array of screwdislocations appeared earlier (112). Other models have been proposed subse-quently, including dislocation pole models (113) for the fcc to hop transition.More recently models of dislocation arrays and their interaction with soluteatoms have been considered (114). Although much progress has been maderecent years in resolving the physical details of a variety of boundaries andinterfaces (115) there exists very little factual knowledge, gained by directobservation, of the structure of martensitic interfaces, a lack that is particularlyacute for ferrous lath martensites.

The complexities of the problem are further compounded or transformationsconstrained within the matrix bulk as, for example, in ferrous plate martensites.Although the interface separates the new phase from the matrix, growth hasoccurred such that the equatorial dimensions of the lenticular platelet greatlyexceed its thickness. This raises the question of the processes leading to thegeneration of the interface and introduces the topic of nucleation phenomena.The status of nucleation ideas has been recently reviewed in detail (3). Classicalnucleation theory applied directly is inadequate and the existence of largeembryos capable of being rendered supercritical by quenching has not beendemonstrated. It appears that the formation of nuclei is heterogeneous and canbe autocatalitic, but, although imperfections such as stacking faults have beenassociated with the initiation process, the nature of the heterogeneous ites is notfully understood. In this context it is worth noting that these ideas considertacitly a static lattice. It is well known 116) that as the temperature is changed,softening of special elastic coefficients of a crystal can occur associated with theapproaching mechanical instability of the crystal structure, which results in highamplitudes of certain modesof lattice vibrations. These effects can be detectedby diffraction techniques before the onset of the macroscopically observabletransition [as, for example, n TiNi alloys (117)]. In the latter reference the effects


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356 MEYRICK & POWELLwere termed "premartensitic" although it seems reasonable to suppose that they,perhaps in conjunction with crystal defects, might lead directly to the onset ofthe transformation.HYBRID TRANSFORMATIONSThe transformations that have been described so far are mainly examples of"pure" transitions in that they can be separated convincingly according tomechanisms and resulting morphologies. There exist transformations whichcannot be completely satisfactorily placed in one or other of these categories butinstead incorporate characteristics pertaining to two or more of them. In thesecases the transformation is accomplished by a mixture of modes and the totaleffect is logically regarded as a hybrid transformation. In the following, thesalient features of two such examples will be presented. The first of these isferrous bainite, for which the discussion will consider in order its morphology,kinetics, a~ad mechanismsof growth. As a second example, the processes takingplace during the growth of ~ and -/precipitates in A1-Ag lloys will be outlined.BainiteThe name bainite was coined for the microstructural product that forms in steelswhen austenite is transformed under conditions that largely preclude theformation of martensite or pearlite. It consists of an aggregate of ferrite anddiscrete particles of iron carbide. As such, it is an accepted term and excludesother ferrite and alloy carbide aggregates that can arise in alloy steels (118).Because the actual processes that take place during the formation of bainite arenot those that are purely martensitic nor those that yield pearlite, it has becomecustomary to refer to them as comprising a bainitic transformation. In someways. this has been unfortunate, perhaps because such a terminology suggeststhat it represents a separable transformation possessing its ownunique charac-teristics. Indeed, in addition to those aspects of the topic that are themselves asyet unresolved, controversy exists over the definition of the bainitic transforma-tion. This has been the subject of two recent publications (119, 10) in which canbe found a rather comprehensive bibliography of relevant literature.The details of the morphology vary gradually with the temperature at whichthe reaction takes place making it difficult to identify any unique outstandingcharacteristics. In the upper range of temperature the product appears feather-like in the optical microscope and is composedof aggregates of parallel groupsof ferrite" laths, amongwhich, on the intercrystalline boundaries, lie cementiteplates oriented parallel to the local boundaries. Apart from the presence ofcarbides the microstructure on the scale viewed within the electron microscopeis quite similar to that of ferrous lath martensites. On he other hand, at lowertemperatures the ferrite plates adopt a more acicular aspect and carbidesoriented at about 60 to the main axis are found both within the crystals and incontact with the intercrystalline boundaries. The two extremes are called upperand lower bainite respectively. Whereas a sharp division between the two


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PHASE TRANSFORMATIONS N METALS AND ALLOYS 357variants does not appear to exist universally, it seems in general that the tworegimes lie on either side of approximately 350C. These observations refer tothe final products. Litde is knownof the precise sequence of events that leads tothe final microstructure, although in lower bainite metastable carbides other thancementite have been observed.The ferrite component f the microstructure produces relief effects on initiallyflat surfaces, thus indicating the presence of a macroscopic shape change whichmust therefore be explicable in terms of any mechanisn proposed for the modeof growth.

In plain carbon steels the conditions under which the product of thetransformation is pearlite or bainite merge together gradually; however, in alloysteels the processes can become eparable and when he obscuring effects of thepearlite morphologyare avoided there is found to exist a temperature, the Bstemperature, which marks the upper limit of the temperature range in whichbainite can form during isothermal holding. Above he Bs bainite will not form;however, it can form in increasing amounts at temperatures increasingly furtherbelow it. The Bs temperature is somewhatanalogous to the Ms temperature, ananalogy that is strengthened by the fact that bainite can be induced to formabove the Bs temperature by the application of stress, as can martensite abovethe Ms temperature. The growth rate of individual ferrite plates is slow and isanisotropic in that the thickening rates are exceeded by the rates of lengthening.

As is commonlyrue in solid state phase transformations the details of theatomic movements involved in the production of the new microstructure haveeluded direct observation. All that can be determined with some certainty areend consequences of the events, from which deductions concerning the modeoftransformation are perforce made. The more complex the consequences, thegreater the difficulties that beset attempts at interpretation.

The two primary consequences of the processes that form bainite are a matrixstructural change from fcc to bcc and the appearance of carbide particles. Twomain schools of thought exist concerning the manner by which these conse-quences are accomplished. Both accept the fact that the carbide particles indicatethat long range diffusion of carbon is undoubtedly involved, but diverge inopinion regarding the origin of the ferrite. On the one hand, the similarities inmicrostructure exhibited by bainitic ferrite and martensite, the occurrence ofsurface relief effects, and the fact that as the temperature is lowered the acceptedmartensitic transformation begins, have led to the opinion that the structuralchange might be accomplished by a martenstic transformation relating thesubstitutional atoms. In this hypothesis the substitutional atoms are converted tothe bcc structure by a diffusion!ess martensitic process. The slow growth rate isrationalized either by invoking a series of small rapid events interspersed byperiods of quiescence or by a continuous slow advance, with the overall ratebeing controlled by carbon diffusional processes,

The opposing view discounts any contribution to the growth of ferrite frommartensitic processes. Instead, lengthening of the individual ferrite units isdeemed to arise from the repeated nucleation of incoherent ledges in the




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358 MEYRICK POWELLinterface and the lateral migrationof these by substitutional diffusion. Again herate controlling process for thickening s thought o be diffusion of carbon n theaustenite.In these views the major clash arises in the mannerof ferrite formation,whereashe precipitation of the carbides is, in the main, subject to less seriousdifferences of opinion, althoughwhetheror not the precipitation takes place inthe ferrite as well as in the austenite is relevant to the former.Becausehe answeris not directly knownnferences are drawn rom indirect observations and arethus open to doubt. That cementite in upper bainite forms from austeniteappears to be generally accepted; however,opinions diverge on the question ofthe cementite and epsilon carbides in lower bainite. The morphologyof thecarbides within the ferrite plates and the similarities with temperedmartensitehave been aken to infer the initial formationof supersaturated ferrite followedby carbide precipitation therein. So far experimental bservationshave failed todemonstrate he existence of this supersaturation, but this c

Phase Transformation 1973

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