1973-Phase Transformation in Metals and Alloys

Copyright 1973. All rights reserved

PHASE TRANSFORMATIONS IN

METALS AND ALLOYS

Glyn Meyrick and Gordon W. Powell

Depart;nent of Metallurgical Engineering, The Ohio State University, Columbus, Ohio

INTRODUCTION

8546

Understanding a phase transformation involves an appreciation of the reasons for its occurrence and of the mode or modes by which it takes place. The former will not be explored herein beyond noting that a system can spontaneously undergo 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 not be that pertaining to the equilibrium state. A total change may yield directly the equilibrium state or traverse a path composed of several tranformations involving metastable phases. This, combined with the fact that a given change can be accomplished by more than one kinetic mechanism generating modal competition, endows the study of phase transformations and their consequences with the complexities that render it so intriguing. Phase transitions have received extensive investigation because of their inherent fascination and because they play a particularly important role in property control for material applications.

As can be seen from some of the more recent surveys of the field (1-3) it is customary to group together changes that exhibit common characteristics in an effort to classify phase transformations in a systematic manner. Criteria involved in classification are predominantly of morphological character but also include, or imply, mechanistic processes. This process has led to the establishment of accepted group names: 1. continuous precipitation, 2. massive transformations, 3. discontinuous precipitation, 4. martensitic transformations, 5. bainitic transformations, 6. order-disorder transformations, and 7. spinodal decomposition. Because of an initial restriction on the length of this review, order-disorder transformations and spinodal decomposition will not be considered here, but they have been discussed by Wayman (4) in a previous volume of this series.

Continuous precipitation is characterized by the formation of grain boundary and intragranular particles of the new phase, which generally has a structure and

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328 MEYRICK &: POWELL

composition different from that of the metastable matrix. The growth of the new phase is controlled by long range diffusion through the matrix, whose average composition changes continuously as the reaction proceeds. The reaction at the interface between the parent and product phases is presumed to be relatively fast.

If the new phase forms by the massive mode, it has the same composition as the parent phase and the reaction is accomplished by the rapid motion of a high energy, incoherent boundary. Thus this solid state reaction does not involve long range diffusion and the transfer of atoms from the parent to the product phase is assumed to be effected by the uncoordinated, random jumps of individual atoms across the interphase boundary. Although Phillips (5) was apparently the first investigator to recognize this mode of transformation as a unique type of solid state reaction, the term massive was first applied by Greninger (6). It is an appropriate term in the sense that it is descriptive of the relatively large morphological units which in some cases form by this mode of transformation.

The discontinuous mode of transformation results in the formation of a twophase mixture at an advancing, incoherent boundary. The atom transport and atom rearrangement required to produce the two-phase mixture are assumed to take place in the advancing boundary and also, if volume diffusion is significant, within a region immediately adjacent to the advancing boundary. The bulk of the metastable matrix remains essentially unchanged until traversed by the interface. Generally, the compositions and crystal structures of the two phases are different from that of the metastable matrix. The two phases are often arranged in the form of a lamellar aggregate.

The martensitic mode of transformation yields platelets of an oftentimes transitional phase by a displacive reaction which is diffusionless, produces surface relief effects, and is reversible in some alloy systems (7). In addition, definite crystallographic relationships exist between the product and parent phases, and the physical plane of the martensitic platelet is usually parallel to an irrational lattice plane (habit plane) of the metastable matrix. Since the formulation of the phenomenological theory of displacive reactions by Wechsler, Lieberman & Read (8) and Bowles & Mackenzie (9), much of the research has been concerned with the crystallographic and geometrical aspects (lattice relationships, habit plane, shape deformation, and inhomogeneous deformation

within the martensite) of martensitic transformations. The bainitic mode of transformation is the subject of considerable controversy

as demonstrated quite clearly by a recent debate on this reaction (10). Some solid state reactions which occur in ferrous and nonferrous alloys and whose products have distinctively different morphologies have been labeled bainitic. In the case of hypoeutectoid steels, lower bainite has some of the characteristics (lattice relationships, surface relief, inhomogeneous substructure) of martensite, but the slow edgewise growth of the platelets of bainite is controlled by the rate of diffusion of carbon in the austenite matrix.

Whereas a classification scheme based upon clearly distinguishable modes of transformation has obvious merits, it can also be disadvantageous if adhered to

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PHASE TRANSFORMATIONS IN METALS AND ALLOYS 329

too rigidly. It is to be emphasized that a phase transition can involve a structural change, a compositional change, or both. All of these can, in principle, be accomplished by diffusion processes, while part can be achieved by displacive processes. Both processes could be operative in a given transformation and might or might not be practically separable. Thus, although transformations exist that, by common agreement, belong within a particular group, others exhibit characteristics of several groups. It is more profitable to regard this main classification as establishing general guidelines rather than providing a series of separate compartments into which all transformations can be unequivocally placed.

The objective of this review is primarily to summarize on the basis of experimental observations the current knowledge of the morphological and growth characteristics of the various modes of transformation. It does not consider in any great detail mathematical models of these reactions. Each of the various modes of transformation will be considered under one of three broad groups of solid state reactions: l. diffusional transformations, 2. displacive transformations, and 3. hybrid (mixed mode) transformations.

DIFFUSIONAL TRANSFORMATIONS

Massive Transformations

As noted in the introduction, a massive transformation is accomplished by the rapid motion of a high energy, incoherent boundary which converts the parent phase into a more stable phase of the same composition. Any nonmartensitic polymorphic transformation in a pure metal is obviously a degenerate or limiting case of a massive transformation. Thus Owen & Gilbert (11) suggested that the y-to-a transformation which occurs in pure iron at cooling rates less than 5500°C/sec is a massive reaction. These observations were made on bulk specimens. Differences are to be expected for microscopic specimens; for example, the a-to-y transformation in iron whiskers exhibits characteristics of a martensitic transformation and is well described by the phenomenological theory (12). Bibby & Parr (13), using iron containing less than 0.0017% C, also concluded that the transformation at cooling rates less than 30,OOO°C/sec is massive. At higher cooling rates the y-to-a transformation is martensitic. Typical massive microstructures obtained by cooling pure iron (0.001% C) at slow rates are shown in Figure 1 ; in general the grain size decreases with an increase in the cooling rate. This mode of transformation does not produce surface tilts (13-15), a fact consistent with the concept that the boundary between the transformed and untransformed region is displaced by the random, noncooperative movement of the atoms at the boundary; Transmission electron microscopy has shown that the internal structure of the massive ferrite grains consists of a random array of dislocations and that neighboring massive grains are separated by high angle boundaries (14, 15) (Figure 2). The dislocations may be the result of transformation-induced stresses and quenching stresses.

The motion of the austenite-ferrite boundary in pure iron at undercoolings on the order of 25-50°C has been investigated by Eichen & Spretnak (16) and

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330 MEYRICK & POWELL

/

I' I ..

Figure 1 Microstructure of high purity iron quenched at approximately (a) 800°C/sec and (b) 4000°C/sec. X 300.

Figure 2 Random dislocations and high angle boundary in iron quenched at 3300°C/sec.

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Bharucha et al ( 17) by the use of thermionic emission microscopy. The geometry and motion of the austenite (light)-ferrite (dark) interface are shown in Figure 3; the elapsed time between the two photographs is 15/16 sec. The a-y interface is highly irregular and faceted, and it moves in a definitely discontinuous manner. That is, segments of the interface may remain stationary for a fraction of a second and then undergo sudden displacements. Discontinuous interface motion is not unique to the massive transformation in pure iron.

In the case of alloys, the massive transformation in the Cu-Ga system has been studied quite thoroughly; investigations of the massive transformation in Cu-Zn alloys have also yielded some significant results. The discussion of the Cu-Ga and Cu-Zn alloys considers in order the following kinetic, morphological, and crystallographic features: nucleation site, rate and mechanism of interface motion, lattice relationships between the massive phase and its parent, structure of the massive boundaries, and internal structure of the massive phase.

The high temperature /3 (bcc) phase in a Cu - 37 at.% Zn alloy can be retained to room temperature by rapid quenching, but during the quench some of the /3

phase does transform to Widmanstatten alpha phase aw and also to massive alpha am. Both the aw and am phases nucleate at the /3-/3 grain boundaries. The results of rapid up-quenching experiments have shown that the aw-/3 boundaries which may be semicoherent are not suitable sites for the formation of am phase ( 18). Furthermore, when this alloy is equilibrated at a temperature such as 840°C in the (a + f3) phase field and then quenched, the am phase again nucleates preferentially at f3-f3 grain boundaries. Nucleation of am was not observed at the aeq - f3eq boundaries; such boundaries should be at least semicoherent and thus lack the mobility required for the massive transformation. Consequently, it may be concluded that boundaries with disordered atom arrangements are favorable sites for the nucleation of a massive phase.

The growth rate of the massive phase am in the /3 Cu-Zn alloys is approximately 1 cm/sec (I8, 19), which is orders of magnitude greater than that associated with transformations controlled by long range volume diffusion. At such high growth rates, the massive phase must have the same composition as the parent phase. The microprobe scans of the am and f3 phases in a rapidly quenched Cu - 38.5 at.% Zn alloy obtained by Massalski et al (20) are convincing demonstrations of this fact. The morphological development of the am phase in a quenched Cu - 37 at. % Zn alloy is shown in Figure 4. The am -/3 surface enclosing any given morphological unit of am contains many facets. Transmission electron micrographs obtained by Hawbolt & Massalski ( I 8) of the faceted am-/3 interfaces show that interfaces contain steps or ledges, the smallest -100 A in height (Figure 5). Ledges 6-30 p. in height have been observed on the faceted rm-/3 interfaces in /3 (bcc) Cu-Ga alloys (21). The existence of ledges on the faceted interfaces is consistent with the theory of growth proposed by Aaronson (22). According to this theory, growth perpendicular to the faceted interface occurs by the lateral motion of the ledges across the interface which is assumed to have a misfit dislocation structure that renders it relatively immobile. The highly mobile ledges, on the other hand, are considered to have a disordered

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332 MEYRICK '" POWELL

Figure 3 Austenite (Iight)-to-ferrite (dark) transformation in high purity iron. Elapsed time is 15/16 sec. Magnification is approximately X 100.

Figure 4 Morphology of the am phase in a Cu-37.S at.% Zn alloy.

structure. Growth of the �m phase in {3 Cu-Ga alloys by the ledge mechanism has been observed by Kitt! & Massalski (21) using hot-stage microscopy.

The am (fcc) and f3 (fcc) phases abutting one another across a faceted interface in Cu-Zn alloys are oriented at random with respect to one another ( I8). The faceted interfaces do not correspond to any unique habit plane; attempts to observe misfit dislocation arrays at these interfaces were unsuccessful. However, in the case of the {3 (bcc) -+ �m (hcp) reaction in /3 Cu-Ga alloys, crystallography can play a role in the transformation. The �m grains often consist of two twinrelated subgrains and at least one of the twin-related regions is bounded in part

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by facets. The traces of these facets are consistently parallel to the (0001) basal plane of the Km phase and growth takes place by the rapid movement of ledges along facets (Figure 6). The volume change associated with the transformation induces slip ahead of the advancing interface. If the parent and product phases are related crystallographically to one another according to Burger's lattice relationships (1 10)p II (OOOI)Km and [ 111]p II [1120]Km, then a { 1 1O} plane in the 13 matrix is parallel to the facets on the rm morphological units. The { l lO} plane is a potential slip plane of the bcc lattice; in fact, slip in the 13 phase parallel to the faceted sections of the f3-Km interface has been observed. Slip in the 13 matrix impedes the motion of the advancing interface and, according to Kittl & Massalski (21), provides a mechanism for the formation of ledges. When unimpeded sections of the interface contact a {l lO}p plane on which slip is taking place, semicoherent f3-Km interfaces are formed and produce the interface geometry shown in Figure 7. The precise mechanism by which the twinned �m units form is unknown. The lattice relationships between the twin subgrain and the f3 matrix are undoubtedly established during the nucleation stage of the transformation.

The rapid growth rate of a massive phase and the ability on occasions of the massive phase to penetrate a grain boundary and grow into an adjoining grain are indicative of the random, incoherent structure of the boundary between the massive and parent phases. Some direct experimental evidence supporting this conclusion has been obtained by Perkins & Massalski (23) who studied the 13-to-Km transformation in equilibrated (f3 + n Cu-Ga-Ge alloys. The massive transformation occurred in the quenched alloys by motion of certain prior f3-� boundaries; the other f3-� boundaries were inactive and remained stationary. Because small particles of untransformed 13 phase were present in the quenched alloys, it was established by transmission electron microscopy that (a) no unique crystallographic relationships exist between the 13 and K phases across either the active (f3-Km) or the inactive (f3-K) boundaries, but (b) the habit of the inactive (f3-K) boundaries corresponds to a low index plane such as the basal or prism planes, whereas the habit of the active prior (f3-K) boundaries is in general irrational. Thus if one thinks of the f3-� boundaries in terms of regions of good fit (coincidence boundary) connected by regions of bad fit, the irrational and active f3-� boundaries should have a higher density of the more mobile regions of bad fit in comparison with the low index, inactive f3-� boundaries.

The internal structure of the �m phase formed by the f3-to-�m massive reaction in 13 Cu-Ga (24) and (f3 + n Cu-Ga-Ge (23) alloys consists of an inhomogeneous distribution of stacking faults and dislocations on the basal plane of the hcp structure. The stacking faults may be either growth faults or deformation faults produced by the transformation stresses. The massive phase produced by the 13-to-am transformation in a Cu - 37.8 at.% Zn alloy (18) also has an inhomogeneous internal structure composed of dislocations and possibly some stacking faults. Thus, with the exception of the stacking faults, the internal structure of the alloy massive phases am and �m is not unlike that of its counterpart in pure iron.

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{3

... ---- ...

Figure 5 (a) Microsteps, 100 A in height, on iY.m-i3 boundary. (b) Macrosteps, on iY.m-i3 boundary.

Figure 6 Ledge growth of the 8m phase in a eu-22.8 at.% Ga aHoy.

Figure 7 Ledge growth of a twinned 8m crystal accomodated by slip in the f3 matrix (after Kitt! & Massalski, 2 1).

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Discontinuous Precipitation

Discontinuous precipitation is the formation of a two-phase product from a single metastable phase, the product phases normally being dispersed in the form of alternating, parallel lamellae. In the simplest case the metastable phase is a supersaturated terminal solid solution (ass ) which transforms below the solvus temperature to equilibrium alpha, aeq, plus a second phase /3, which has a structure and composition different from that of the aeq with which it coexists. In the case of Fe-Zn alloys (25) discontinuous precipitation occurs at temperatures below approximately 0.93 of the absolute solvus temperature and, for an Al- 17 wt% Ag alloy (26), the reaction occurs below 0.87 of the absolute solvus temperature; at higher temperatures continuous precipitation occurs, but, over a limited temperature range, the two modes of transformation may compete with one another. The decomposition of Fe-C austenite to pearlite is a more complex discontinuous reaction because the parent and product phases all differ in composition and structure. The massive transformation might be regarded as a limiting form of discontinuous precipitation in which only a lattice transformation occurs, whereas the atom transport required for the precipitation of the other phase is prevented by the external constraints, e.g. cooling rate.

In 1953 Smith (27) set forth a theory of discontinuous precipitation which has served as the basis for many of the subsequent theoretical treatments of this reaction. Smith stated that the cells, which nucleate at grain boundaries, grow preferentially into one of the grains which abut the grain boundary by the motion of a "disordered, incoherent" interface. The composition changes required to produce the lamellar product are brought about by lateral diffusion along this interface. Futhermore, the disordered, incoherent interface bounding the growing cell is actually continuous with the original grain boundary at which nucleation of the cell occurred and which has bulged into the grain under the influence of the driving force for the transformation. Consequently, as pointed out 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 front is moving. It was anticipated that rational crystallographic relationships would exist between adjacent lamellae (a and /3), thereby minimizing the proportion of the driving force consumed by the formation of new interfaces. Subsequent research on discontinuous transformations has not altered in any significant way Smith's description of this reaction.

The recent research on this mode of transformation has been concerned with the nucleation stage of the transformation, the mechanism for the development of cooperative growth, the mechanism for changing the spacing between lamellae, and, of course, development of more rigorous mathematical models of cell growth. This discussion of the discontinuous mode of transformation considers the following topics: nucleation of lamellae and the evolution of cooperative growth, mechanisms for changing lamellae spacing, growth kinetics, and nonequilibrium transformation products.

The cellular reaction in bicrystals of a Pb - 7 at. % Sn alloy has been subject to thorough study by Tu & Turnbull (28-30). The bicrystals contained a [OOI)Pb

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symmetric tilt boundary, the misorientation (J about the [OOljPb ranging from 7-37°. The appearance of the tin-rich platelets at an early stage of the transformation is shown in Figure 8 and the morphology of well-developed cells is shown in Figure 9. The crystallographic relationships between the tin-rich lamellae and the solute-depleted lead are (OIO)sn II (II I)Pb and [OOJ]Sn II [l lOjPb' the habit plane of the lamellae being {l l l}Pb' The planes and directions involved in these relationships are the most densely packed planes and directions of the two crystal structures. Note that the tilt boundary in Figure 8 is not straight, but has become bowed or deflected in the immediate vicinity of the tin-rich lamellae at 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 interface and the other, which separates each platelet from the grain on the right, is presumably a high energy, incoherent boundary because the platelets are not related in the crystallographic sense to this grain.

On the basis of these observations Tu and Turnbull have proposed that the development of a cell takes place in the manner shown schematically in Figure 10. The arrows in Figure lOa indicate in each grain the ( 1 10) directions, which also are the traces of the {Il l} habit planes in the [OOlj bicrystals. When a fJ platelet lying within the LX. grain forms at the grain boundary, the grain boundary must be deformed locally to satisfy the habit plane requirement of the platelet (Figure lOb). Subsequently the high energy, incoherent fJ-a2 interface is replaced by a lower energy fJ-al interface due to displacement of the. grain boundary as shown in Figure lOco Displacement of the grain boundary serves not only to embed the platelet wholly in the al grain but also to move a segment of the grain boundary into an orientation favorable for the formation of a second platelet lying parallel to the first (Figure 1Od). Thus the pattern of cooperative growth is established by a repetition of this process.

As noted earlier, Smith's (27) model of discontinuous precipitation requires that the lamellae within a cell be related crystallographically to the grain away from which the cell is growing, and the mechanism depicted in Figure 10 is consistent with this requirement. Tu & Turnbull (29) and Liu & Aaronson (31) have observed that cells do not form when the misorientation e about the [OOljPb axis of the bicrystals is smaller than 15°. Here again, this observation is consistent with Smith's model in that low angle tilt boundaries possess neither the structure nor the mobility to support cellular growth.

Although the mechanism illustrated in Figure 10 for cooperative growth is extremely attractive because of its relative simplicity, the operation of this mechanism in alloy systems other than Pb-Sn has not been reported in the literature. Some recent research by Fournelle & Clark (32) on cellular precipitation in a eu -9.5 at.% In alloy has yielded results which have led to the formulation of a generalized theory and criterion for the development of cooperative growth. In this alloy the discontinuous reaction is preceded by the formation of well-developed grain boundary allotriomorphs of the � phase (Cu9In4) but develops subsequently from the allotriomorphs. The sequence of

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

t (0)

a, a2 f3 plo't!

(b)

Figure 9 Fully-developed cells in a Pb-7 at.% Sn alloy.

\

\ \

(c) (d)

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

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events producing cooperative growth is beautifully illustrated by the transmission electron micrographs in Figure I I and is illustrated schematically in Figure 12. A grain boundary pinned at some points by allotriomorphs bows out between the particles. As the grain boundary moves, it leaves behind solute-depleted a phase, the solute having diffused along the bowed boundary to an allotriomorph. Consequently the allotriomorphs become extended parallel to the direction of motion of the grain boundary and the pattern of cooperative growth is thereby established. The initial driving force for grain boundary migration is derived from such factors as the local curvature of the grain boundary and the relative perfection of the abutting grains (strain-induced grain boundary migration). However, once the solute-depleted a forms behind the advancing interface, the driving force for boundary migration is derived primarily from the difference of the chemical free energy between the supersaturated a phase and the solutedepleted a phase. The Fournelle-Clark mechanism for the development of cooperative growth provides an explanation for the fact that continuous precipitation occurs at temperatures above approximately 0.8-0.9 of the absolute solvus temperature, whereas the cellular reaction is favored below this temperature. In the higher temperature range the chemical free energy is simply not of sufficient magnitude to bow out the boundary between the allotriomorphs.

Although the austenite-to-pearlite transformation in steel has been the subject of almost innumerable investigations, the mechanism(s) by which cooperative growth is established remains unknown. Hull & Mehl (33) proposed that the sidewise growth of a pearlite colony occurs by the successive nucleation of ferrite and cementite, the initial nucleus being a platelet of cementite. After the formation of the initial platelet of cementite, the platelets of ferrite nucleate in the adjacent carbon-depleted austenite, etc. However, subsequent research (34-36) has demonstrated quite clearly that a pearlite colony can originate from either a ferrite (hypoeutectoid steel) or cementite (hypereutectoid steel) nucleus and, furthermore, sidewise growth by successive nucleation of the lamellae has not been confirmed experimentally. The Fournelle-Clark mechanism (32) described above seems capable of being applied under some circumstances directly to the pearlite reaction. Consider, for example, a ferrite aJlotriomorph (Figure 13a) allowed to form isothermally in the (y + a) phase field. As shown experimentally by Hillert (37) and depicted schematically in Figure 13b, pearlite forms at the upper a-y boundary during a moderately fast quench from the temperature at which the allotriomorph formed. In the initial stages of the quench; particles of cementite nucleate at the a-y interface which may have moved a small amount, thereby producing a local enrichment of the carbon content within and/or in the immediate vicinity of the boundary. Continued cooling produces the driving force necessary to bow out the a-y boundary between the cementite particles (Figure l3d). Subsequent growth of the cementite particles occurs as shown in Figure 12. In agreement with experiment, the pearlitic ferrite is continuous with the ferrite allotriomorph and thus has the same crystallographic orientation. It is not clear, however, as to whether or not the cementite lamellae should have a specific crystallographic orientation.

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Figure 11 Development of cellular growth from allotriomorphs in a Cu- 9.5 at.% In alloy.

Q b d

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

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According to Zener's theory (38) of the cellular reaction, the interlamellar spacing S should vary inversely with the amount of undercooling, i.e. Sa tl.T-1• The results of some experimental studies (40, 41) have confirmed this relationship; however, in the case of Fe-Zn alloys Speich (25) found that the interlamellar spacing did not vary linearly with L\T-l, a result rationalized qualitatively by a modification of Cahn's theory of cellular growth (39). A temperature change during the growth of a cell must be accompanied by a change in the interlamellar spacing which can take place by one of the following mechanisms: branching, nucleation of new lamellae at the advancing cell boundary, or separation of the cell boundary from the tips of the lamellae. The first two mechanisms decrease the interlamellar spacing whereas the last increases the spacing.

Figure 14 is a schematic summary of the means whereby changes in the spacing 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). One can regard the sequence of events illustrated in this figure as a variant of the Fournelle-Clark mechan.ism. When the temperature is decreased, the ferrite-austenite boundary adjacent to the cementite lamellae bows out into the austenite, the carbon atoms subsequently collecting in and precipitating on the displaced boundary. The driving force to bulge the boundary into the austenite adjacent to the cementite lamellae arises from the anticipated lower carbon content of this austenite and hence a higher To temperature. If the

, temperature is suddenly raised during the growth of a pearlite colony, the interlamellar spacing can be increased by replacive motion of the ferriteaustenite interface as shown in Figure 14d; this process also may involve partial dissolution of the cementite at the tip of the lamella. The interlamellar spacing may be decreased by nucleation of new lamellae at the advancing interface, as can be seen in Figure I I for the Cu - 9.5 at.% In alloy. This mechanism also has been observed to operate in Pb-Sn alloys (29). In the case of pearlite, Sundquist (42) has stated "that interlamellar spacings observed experimentally are those on the verge of instability with respect to the formation of a new lamella of Fe3 C at the middle of a ferrite lamella-austenite interface."

Data for the cellular growth rate (; can often be fitted to an equation of the form

l .

wherein L\ T is the undercooling and Q is the activation energy for diffusion. The growth rate is low at high temperatures (small L\T) because the interlamellar spacing is large and the driving force for the reaction is small, and is also low at low temperatures because the diffusion rate is slow; thus the growth rate attains a maximum value at some intermediate temperature. On the basis of the simple models which yield an equation of this form, a value of n = 2 is associated with volume-diffusion-controlled growth (38), whereas a value of n = 3 is appropriate for interface-diffusion-controlled growth; consequently the corresponding activation energies are those for volume and grain boundary diffusion respectively. The

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growth rate for the cellular reaction in the austenitic Fe-30Ni-6Ti alloy studied by Speich (41) is

G(mm/min) = 281 (982 - T°C)2 exp( -3�;00) 2.

Although this equation has the form associated with volume-diffusion-controlled growth, the activation energy of 39,800 cal/mol is considerably smaller than that for the diffusion of nickel in iron (67, 500 cal/mol). Thus an unambiguous physical interpretation of Equation 2 is not possible. If it is assumed that the growth of pearlite occurs by diffusion of carbon along the pearlite-austenite interface and the effects of capillarity and imperfect carbon segregation are taken into account, the cellular growth rate should be given by an equation of the same form as Equation 1 with n = 3 (42). When data for high purity Fe-C alloys are fitted to this equation the activation energy is computed to be 45, 700 cal/mol, much larger than that expected for interface diffusion. Sundquist has attributed the high activation energy to an impurity effect.

To derive a growth rate equation which in the final form does not contain explicitly the interlamellar spacing, it is necessary to employ a priori an extremum principle. For example, Zener assumed that the observed spacing is that which maximizes the growth rate. Other criteria which have been used are maximum rate of entropy production (43) and maximum rate of decrease in free energy (39). At the present time there is no evidence which suggests that one of these criteria is superior to the others.

The products of a cellular reaction may not have the compositions corresponding to the equilibrium state. Thus, in the case of the eutectoid reaction ({3 � IX + T) in a 94% Cu - 6% Be alloy, the IX phase is initially supersaturated with respect to beryllium, but with continued aging the supersaturation is relieved by diffusion of the excess beryllium atoms to the T phase (44). A similar situation has been found by Speich (25) in Fe-Zn alloys. The a: phase of the cellular product is supersaturated with respect to zinc, the extent of the deviation from equilibrium increasing with decreasing reaction temperature and also with increasing zinc content of the alloy (Figure 15). Here again, the supersaturation of the a 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 is apparently the case for the cellular reaCtion in an austenitic Fe-30Ni-6Ti alloy. At temperatures in the range of 700-900°C, equilibrium requires a two-phase mixture of austenite plus (Fe, Nih Ti. However, the initial cellular product consists of austenite plus Ni3 Ti lamellae (YA � Y8 + Ni3 Ti). The equilibrium state is achieved subsequently by means of a second cellular reaction [Y8 +Ni3Ti � Yc + (Fe, NihTi]. In some instances, however, the two reactions, YA � Y8 + Ni3 Ti and YA � Yc + (Fe, Nih Ti, complete simultaneously with one another.

Continuous Precipitation

The discussion of this mode of transformation, characterized by long range diffusion of solute atoms through the metastable matrix phase to the particles of

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INCOHERENT a·y BOUNDARY

� :/

RIM OF FINE r ,Fe3C

� PEd ��

y-y GRAIN BOUNDARY

(0 ) (b) (e) (d)

Figure 13 Formation of pearlite from a ferrite· allotriomorph.

y

;/I\� �b.C.d'-

:.w-� ·'-d,1

��I Figure 14 Mechanisms by which the interlamellar spacing of pearlite may be changed (after Hiller!, 37).

900

800

� II! 700

i '" 600 .... ....

500

400

r \1 ,'\ II

o EQUlUIflIUM SOLVUS � Xl. -0.097

"J' ()Xz.-0.152 ,, ; $ Xz.-0.235 • Xz.-0.305

a

•

,1 f> pi-I I , I

11 tt

" '� � � +

a .r

ATOMIC PERCENT ZINC

Figure 15 Nonequilibrium solvus lines for the cellular reaction in Fe-Zn alloys (after Speich, 25).

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

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

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have a significant effect on the morphological development of the precipitate particles. For example, Toney & Aaronson (45) found that in (110) misoriented bicrystals of an Fe - I.S wt.% Si alloy allotriomorphs of austenite form when the misorientation (3 is greater than 110, but when (3 < 110 idiomorphs are the predominant morphology with occasional stubby primary sideplates and allotriomophs being observed. In the case of grain boundary precipitation in an Ag-5.6 wt.% AI alloy (46), primary sideplates form at boundaries between grains misoriented by less than 170, allotriomorphs again being the predominant morphology at high angle boundaries (Figure 16). The ability of high angle boundaries to support the growth of allotriomorphs must be associated with the enhanced diffusivity at such boundaries. Why low angle boundaries should provide suitable sites for the growth of sideplates is not clear, but one factor may be the ability of these boundaries to act as sources of dislocations which may be required to form a semicoherent matrix-product interface.

(/) w X500 a. <t X250 (lOrnin.) r (/) X250 (4mlnJ (16 minJ w � I � 0:: fa R=5°

� a::: � -a. lL. I 0 R=20°

I. I W Secondary RJ600 (!) Prlrnary Z Sideplates Sideplates,

Allotrlomorphs -I � Sawteeth !-Mainly Allotrlornorphs

10 20 30 40 50 60

Figure 16 Variation of precipitate morphology with grain misorientation R. X, Y, and Z are the minimum rotations (degrees) required to bring the lattices of the abutting grains into coincidence (after Hawbolt & Brown, 46).

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Dislocations also are favored nucleation sites at low degrees of undercooling. Thus at high aging temperatures Phillips (47) observed the growth of triangularshaped platelets of Ni3 A I along dislocations in the matrix of an Ni -12.7 at. % AI alloy. The hypotenuse of the particles was coincident with the dislocation line; because of the size of aluminum atoms it was anticipated that they should cluster along the tensile side of the dislocation lines. In the case of the precipitation of metastable y' -Ni3 Ti particles in a nicke l-based alloy, the hexagonal y' particles nucleate at dissociated dislocations in the fcc matrix, the interaction between the particle 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 on an idealized particle shape Guxtaposed elliptical caps, oblate ellipsoid, etc) and an assumed diffusion path (either volume or interface diffusion or a combination of both). For those models based on long range volume diffusion directly to the growing allotriomorph, the resulting kinetic equation(s) and the experimental growth data can be combined to yield a value of the apparent diffusion coefficient Dapp. If Dapp = Dv then this result essentially establishes the validity of the model. On the other hand, if Dapp » Dv the growth rate is too high to be accounted for by volume diffusion directly to the allotriomorph and consequently the assumption regarding the diffusion path must be modified. Thus Aaron & Aaronson (50) found that at low homologous temperatures (0.54--0.69 of the absolute solvus temperature) the allotriomorphs in an AI -4 wt% Cu alloy grow at rates much too high (Dapp/Dv � 500) to be accounted for by volume diffusion directly to the () particles; they proposed that growth occurs rather by a rightangle collector plate mechanism (Figure 17). Copper atoms move by volume diffusion to an a-a grain boundary where the atoms diffuse along the boundary to the edge of the () allotriomorph; thickening of the allotriomorph requires additional diffusion of the copper atoms along the a-O interface. The thickening and lengthening of the particles were found experimentally to vary as (1/3 and (1/4 respectively. The collector plate model predicts a (1/4 dependence for lengthening but a (1/2 dependence for thickening; the slower than predicted rate of thickening was associated with the tendency of the (J allotriomorphs to develop facets. As the aging temperature increases the contribution of volume diffusion directly to the 8 particle increases and, at homologous temperatures greater than 0.91 of the absolute solvus temperature, growth is controlled solely by volume diffusion directly to the precipitate as Dapp = Dv (51). As pointed out by Goldman et al (5 1 ) no analysis of allotriomorphic growth that combines both direct volume diffusion and the contribution of the collector plate mechanism has 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) using thermionic emission microscopy. The thickness varies parabolically with time (s = K (1/2). Good agreement was found between the experimental rate constant K and the theoretical value predicted by a growth model based upon volume diffusion of carbon through the surrounding austenite. During the early stages of

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Y

- ADVANCING 9 GROUP I ---_ RETREATING 9' 8 CRYSTAL

" -"'2

8' ,/ RurTION 8'

3

(0)

Figure 17 Collector plate mechanism for the growth of an allotriomorph (after Aaron & Aaronson, 50).

GROUPS n 1m 8 CRYSTAL

"£ACTIOII

- - .......

--�o -:�ACT��-3-- 8'

( b)

Figure 18 The a + 9' to a + 9 transformation in a Cu-AI alloy (after Laird & Aaronson,

54).

growth the lengthening of ferrite allotriomorphs takes place at a constant rate and, here again, the kinetics of lengthening appears to be consistent with growth control by volume diffusion of carbon through the austenite. The addition of a substitutional alloying element to an Fe-C alloy might slow down the thickening kinetics of ferrite allotriomorphs due to a solute drag effect on the ferriteaustenite interface. Kinsman & Aaronson have suggested that this effect produces the bay in the time-temperature-transformations (TIT) diagram of an Fe-0 .11 % C - 1.95% Mo alloy. The moving interface of a ferrite allotriomorph is assumed to be of the disordered type and therefore the growth rate is dependent upon such factors as interface and bulk compositions, diffusivities, etc. The broad faces of Widmanstatten ferrite may be dislocation interphase boundaries whose mobility normal to the plane of the boundary is highly restricted. If this

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is actually the case, then the rate of thickening of Widmanstatten ferrite should be less than that associated with carbon-diffusion-controlled motion of a disordered ferrite-austenite interface. Measurements of the thickening of ferrite platelets using thermionic emission microscopy confirm this conclusion. In addition the platelets were observed to thicken by the motion of superledges along the broad faces of the platelets in agreement with Aaronson's theory for the development of the platelet morphology. However, the formation of Widmans tat ten ferrite has been shown to produce surface tilts (53), an effect associated with a martensitic transformation. This fact alone makes our understanding of the growth of Widmanstatten ferrite uncertain and calls for further research on this transformation.

The reaction path by which a metastable phase attains the equilibrium state may involve formation of transition precipitates which are eventually replaced

. by the equilibrium second phase. In an AI-4 wt.% eu alloy the precipitation sequence is Guinier-Preston (GP) zones - 8" - 8' - 8 (CuAI2); both 8' and 8 are body centered tetragonal (bet). The mechanisms by which 8' is replaced by 8 in the temperature range of 325-430°C have been investigated by Laird & Aaronson (54) using hot-stage transmission election microscopy. A nucleus of 8 forms in a small proportion of the 8' plates and subsequent growth yields a platelet of 8 with its broad faces either parallel to or at an angle to the broad faces of the 8' plate (Figure 18). In this situation the 8 grows by the direct transformation of 8' to 8 (reaction 1 of Figure 18) and by growth into the metastable IX matrix (reaction 2); the latter reaction may be accompanied by simultaneous dissolution of noncontiguous as well as contiguous 8' plates (reaction 3). The majority of the 8' plates, however, do not contain a 8 nucleus and these particles simply undergo dissolution by countercurrent diffusion to neighboring but noncontiguous 8 particles. Dissolution of the 8' plates occurs by a ledge mechanism (55). The structure of the ledges is unusual in that the ledge contains an edge dislocation whose Burgers vector, a (100), is normal to the broad face of the plate; this structure differs from that of the growth ledges of 8' plates. The decomposition of an AI-15 wt.% Ag alloy is another example of sequential precipition. Spherical silver-rich GP zones which form initially begin to dissolve when heterogeneous nucleation of the transitional 'I' phase occurs (56). They' phase in turn undergoes dissolution when particles of the stabley phase form. Both the growth and dissolution of 'I' and the growth of 'I involve ledge motion along the broad faces of the particles.

MARTENSITIC TRANSFORMATIONS

Introduction

Despite the effort devoted to the study of martensitic transformations, their nature remains to be completely elucidated. No general theory is known into which all the accumulated data can be satisfactorily integrated and which is capable of convincingly explaining aspects, such as the nucleation event, that still defy direct observation. The situation is further clouded by the existence of multiple terminologies and the lingering confusion as to what constitutes a

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PHASE TRANSFORMA TlONS IN METALS AND ALLOYS 347

correct and sufficient definition of a martensitic transformation. The latter question has been the subject of much discussion (I, 57, 58). A

desirable definition would be one couched in terms of observable characteristics that would provide a criterion for the unequivocal identification of a martensitic transformation. The crux of the problem is in the requirement that the characteristics be unambiguous and, for complete satisfaction, capable of being formulated into a concise definition sufficient in itself and needless of extensive clarification.

Transformations that are accepted as martensitic can occur during quenching, as in many steels, but so also can the massive transformation. In some materials the transformation takes place under isothermal conditions, the fraction transformed increasing with time as happens in interface-controlled diffusional transformations in some polymorphic changes (59). That the product of a martensitic transformation is related to its parent through a habit plane and definite orientation relationships is again inconclusive, as the same can often be true for precipitation from solid solution.

It has frequently been stated that the most definitive manifestation of a martensitic transformation is the topographical relief it produces on an initially flat surface. For this to be true it is necessary that the relief be of a character peculiar to a martensitic transformation and distinguishable from that arising from transformations that are clearly not martensitic. Surface relief caused by martensitic transformations can be described phenomenologically as arising from a macroscopically invariant plane strain. This observation is the basis of crystallographic theories of the transformation and has been implicit in definitions of martensite (58). Its importance has been reemphasized in a recent discussion (53) of surface relief effects in which a definition drawing more specifically upon crystallographic theories was offered. As an illustration the salient points of existing descriptions can be incorporated into a general though cumbersome statement: a martensitic transformation is a structural change generated by atomic displacements and not achieved by diffusion, corresponding to a homogeneous deformation which may be different in small adjacent regions, and which gives rise to an invariant plane strain through which the parent and product are related by a substitutional lattice correspondence, an irrational habit plane, and a precise orientation relationship.

A martensitic transformation can produce a structural change without change in composition, which implies there is no necessity for long range diffusion. Furthermore, all first order phase changes that are agreed to occur without the need for diffusion are called martensitic. It can be argued then that a martensitic transformation can be formally defined as a first order phase transition in which the new structure grows without the necessity of atom interchange by diffusion. The complexity surrounding an operational definition for the martensitic reaction can be regarded as a consequence of the search for characteristics that establish the lack of control by diffusion. Attempts to tie the definition more stringently to the phenomenological theories seem unwarranted until such theories become completely successful. Because there is no a priori reason for a

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system to follow only a single path of transformation some hybridization is to be expected, particularly under conditions where diffusion can occur reasonably rapidly. Thus the creation of additional terms such as quasimartensite (5) does not serve to clarify the issue.

The discussion of the martensitic transformation considers the following topics: morphology of the product, original formulations of the phenomenological theory, comparison of the theory with experimental data, modifications of the theory, microstructure of martensitic crystals, and mechanism of the transformation.

The Morphology of the Martensitic Product

The crystals of the new phase display a variety of morphological characteristics dependent upon the chemical nature of the parent and the crystallographic structural change accomplished, which are consequences of the operative mechanism of transformation and the influence of the elastic and mechanical properties of the matrix.

Monocrystalline samples of some alloys of Au-Cd (60) and In-TI (61) can be caused to transform so that the parent and product are separated by a single interface (the habit plane) which, upon migration, creates a single crystal of the martensitic phase, composed of a stack of twins visible by optical microscopy. More usually a number of martensitic crystals are formed within the parent and are influenced by the constraints of the matrix. In this respect there are transformations which take place at the free surface of the specimen (62-64) which can be expected to differ in character from those representative of the bulk.

In some simple cases the transformation yields parallel sided bands of new phase as in the fcc � hcp change in cobalt and cobalt-nickel alloys (65). More usually the martensitic crystal takes the form of a lenticular plate (Figure 19). Often such plates exhibit a structural discontinuity, called a midrib, on the equitorial plane. This morphology is one of the variants adopted by the martensitic products in iron-based alloys. The term plate martensite is adopted for this variant in keeping with a recent description of the morphology of ferrous martensites (66). Martensitic plates generally form at angles to neighbors and in so doing subdivide the matrix so that plates formed subsequently are reduced in size. Accordingly, growth is frequently inhibited by mutual impingement which can cause mechanical twinning (66) and microcracking (66, 67) as well as plastic deformation.

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

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Figure 19 Plate martensite in an Fe - 13.9% Mn alloy. X 1000.

Figure 20 Lath martensite in an Fe - O.31% W alloy. X 200.

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

The essential features of the morphologies described above have been wen established. With the exception of detailed shape change measurements yet to be discussed there seems little more information that might be gathered by optical

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micro sco py . Indeed the ind iv id ua l components o f la th martensi te and the substr uc ture in pla te mar ten si te s are genera lly too fine to be thus studie d profi ta bly .

The fac t tha t t he transformin g region under goes both a c hange in cry stallographic structure and in shape, with consequent modifications of the surface topology, while maintaining contiguity with the surrounding matrix, gives rise to several other important morphological aspects. The first of these is the shape change itself. Its ch&racter is deduced from measurements made upon the exterior surface of the specimen and thus is subject to the doubts that can arise concern in g the relationship of such observations to bulk phenomena. Apart from ca se s where the de pth o f pene tra tion o f the marten si tic cry sta l i s small, a s in the sur face mar ten si te s men tione d ear lier, it i s no t c lear tha t suc h doubts are va li d. The fac t tha t there can be very goo d a gree men t be tween the predic tions of twinn ing theory an d sur face to po graphy (75) len ds strong support to the argumen t tha t indications from the surface can be descriptive o f the bulk; so a lso does the fact that the phenomenological crystallographic theory successfully describes some fully twinned martensitic products. The nature of the shape c hange i s de duce d by use of interference microscopy and by measurements of its effects upon prescribed lines upon the parent surface. Early results (76) which de mon stra ted tha t the topographic changes accompanying a martensitic transition are consi sten t wi th tho se tha t wo uld be pro duce d pheno menolo gically by a macroscopically invariant plane strain, in which the invariant plane is the habit plane, have been substantiated subsequently in a number of systems. The habit plane i s usua lly an irra tiona l plane o f the parent and is characteristic of the material concerned, as are the orientation relationships. These macroscopic characteristics form the basis of the crystallographic theories.

Original Formulations of the Crystallographic Theory

The ba sic cry sta llo gra phic theory origi na te d in the ear ly 1950s (8, 9) an d has been fre quen tly de scr i bed in de ta i l since (I, 72 , 77) . It pay s no d irec t a tten tion to atomic mechanisms but has as its aim the construction of a transformation strain which, when applied to the parent crystal, produces phenomenologically the results of the martensitic transition. The original theories are mathematically equivalent but differ in formulation.

The shape strain T can be written in matrix notation as T = RBP. Of these B is the Bain strain which transforms a selected unit cell of the parent into one of the product. For example, in carbon steels the strain ., �11 0 0 )

f'. = 0 11 0 o 0 113

applied relative to orthonormal axes parallel to the [ ITO], [ 1 10], and [001] directions in the fcc structure yields the bct structure. The bet unit cell of the

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PHASE TRANSFORMATIONS IN METALS AND ALLOYS 3 51

latter has its [ 100] , [ 0 10] , and [001] edges parallel to the system of axes and of magnitudes aT/h/2, aT/!y/2, and aT/3 ' being derived from the bct cell of the fcc structure outlined by the edges 112 a[ l 10], 112 a[I 1O], and a[OOI]. In this example all atoms are moved to their new positions by B; however, for structures which have primitive cells containing different numbers of atoms, only a fraction are correctly moved and the remainder require additional shuffles ( 78, 79). The choice of B has to be made from an infinity of possibilities without clear guidance other than the intuitively plausible criterion of minimal principal strains. Its application does not in general accomplish the lattice change and at the same time leave a plane both unextended and unrotated. To conform to the macroscopic requirement of a homogeneous invariant plane strain, additional strains are required. These must leave the lattice unchanged and comprise a rotation R and a shear P chosen so that T has an invariant plane. P can refer to a strain accomplished by slip or twinning (which have equivalent mathematical descriptions) and, as written above, is applied to the matrix phase.

The evaluation of the strain T can be performed either graphically upon a stereographic projection or through formal matrix algebra. Details of both procedures are presented in the referenced work. In essence the solution requires, first, the choice of a suitable correspondence between two cells of the structures and the numerical expression of B from lattice parameter measurements. Second, a shear plane and direction are assumed and the magnitude of shear is found so that BP yields a macroscopically unextended plane. Finally the matrix R which ensures that the unextended plane remains unrotated is obtained.

Comparison of the Theory With Experimental Data

The most obvious output from the crystallographic theory is the identification of the habit plane (i.e. the invariant plane) and the orientation relationships described by R. Significant failure to predict correctly these parameters constitutes grounds for rejection of the theory as formulated. On the other hand, success does not immediately indicate a completely satisfactory description as this also requires internal consistency with the magnitude and direction of the shape strain and the martensitic substructure ( 80) . In this respect the invariant plane strain T can.be written as T = I + mdp' where I is the unit (3 X 3) matrix, m is the scalar magnitude of the strain, and d and p' are unit vectors defining respectively the displacement direction and the invariant plane normal.

Although the theory takes no formal cognizance of atomic mechanisms, the manner by which P is achieved can be expected to influence the microstructure of the product. This can be appreciated physically by realizing that the strain RB applied to a small region creates a product of the correct structure and orientation. With increase in its size the buildup of macroscopic distortion in its interface is avoided by the operation of P. If the choice is twinning in the martensite, the latter can be expected to consist of a stack of twins. In this case two martensitic orientations exist equivalent to the operation of two crystallographic variants of the Bain strain in volumes separated by a twinning plane

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generated from a plane of symmetry in the parent (8 1). If P is by slip, one variant of B is to be expected, and twins ought to be absent, but the microstructure may contain planar faults.

The precise determination of all the parameters relevant to testing the theory is by no means a trivial operation and, in many cases, is beset with severe difficulties. Nevertheless the accumulated data, though sometimes incomplete, demonstrate the fit of theory to fact to range from excellent, through fair, to inadequate. Detailed reviews of the situation for transformations in pure elements and in alloys have been published ( 1 , 72).

In general the theory affords an excellent description of cases where the macroscopic and microscopic characteristics are well defined and relatively simple; but as these characteristics, particularly from the microstructural aspect, become irregular and increasingly complex the theory becomes progressively inadequate. Excellent agreement is found for the allotropic transformation in cobalt (72) and for the more complex structural changes in Au-Cd, In-TI (77), Fe - 33% Ni, Fe - 22% Ni - 0.8% C, and Fe -24.5% Pt (80). The first is simple in that the lattice change can be produced by a shear in a (1 12) on every second { I l l} plane of the fcc phase. The second two have small principal strains and a substructure of evenly spaced twins visible at least away from the interface by optical microscopy. On the other hand, the last three have large principal strains and consist of regularly spaced twins of the correct type visible only by electron microscopy. The latter three alloys are interesting as they are examples of the comparatively few ferrous alloys that show convincing agreement with the theoretical predictions in an internally consistent manner. All three have habit planes close to {3 JO 15}y which is_ predicted by the Bain correspondence mentioned earlier and shear on a {112}<1 l 1) system in the martensite. Experimentally this is an atypical habit plane when compared to the near {I I l}y habit in lath martensite of low-carbon steels and dilute binary alloys, the {259}y habit of plate martensite in high-carbon steels, and the {225}y habit common for plate martensite in iron containing 0.8-1 .4% C.

The variation of habit plane with composition change is further illustrated by the progessive shift away from {3 JO l 5}y with decrease in Ni content of Fe-Ni alloys (82). Whereas the existence of habits near {259}y and {225}y is presumably associated with the complex substructure of incompletely and irregularly twinned plates, the significance of the association is at present unclear.

Modifications of the Phenomenological Theory

Cases of successful application of the theory have been held as a demonstration of its essential soundness. Consequently, closer agreement with those ferrous marten sites which exhibit habits other than {3 JO 15}y has been sought by modifications of the basic formulation. A common procedure (83) which leaves the basic theory unchanged is to examine the results of alternative choices for the plane and direction of the lattice invariant shear, but no combination has proved completely satisfactory.

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In one of the original formulations (9) some modification was possible through the use of an adjustable dilatational parameter I) incorporated as a factor in the principal distortions of the Bain strain, which was varied from unity to improve agreement. This procedure amounts to relaxing the invariant plane condition and permitting a slight isotropic dilatation in the interface. Although an arbitrary variable is aesthetically displeasing, the possibility of a dilation cannot be summarily dismissed and its use has been frequent. Recent measurements (84) have shown that the required dilatation for the {225}y habit plane in steels does not 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. All four have in common that the modification involves the introduction of additional lattice strains and is directed towards an attempt to resolve the dilemma posed by the {225}y habit. The first (85) considers a composite martensite plate of twinned and untwinned regions and invokes, besides the usual 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 within the austenite ahead of the interface (86), while the other two replace the lattice invariant shear P by two independent lattice invariant shears (87, 88). All three have been discussed in detail recently (89) with the conclusion that the modifications improve the overall agreement but not to the state of satisfaction extant for the {3 10 15}y .

Although the departure from a single simple lattice invariant strain appears consistent with the increased complexity of the martensitic substructure as the habit moves f.rom {3 10 15}y , one is left with the uncomfortable thought that any shape change is describable given enough unrestricted combinations of shear; however, this loses the elegance of the original theory, increases the number of initial assumptions, and may well produce a result of dubious value.

The Microstructure of Martensitic Crystals

Electron microscopy demonstrates that crystals formed martensitically are highly defective and can contain twins, stacking faults, dislocations, and combinations thereof. Some examples of relatively clear-cut cases in which the product is completely twinned and is thus composed of a stack of lamellar twins have already been described. Transformations between close packed structures often result in heavily faulted products. The product of the fcc to hcp allotropic change in cobalt is rich in stacking faults, as is consistent with the fact that the structural change can be obtained by shears of a/6 < I l2) on every second parallel { I l l} plane. Indeed in situ electron microscopy (90) has shown that perfect dislocations can dissociate producing extended stacking faults during the phase change. By the same technique it has been demonstrated that arrays of extended dislocations can be emitted from grain boundaries during the transformation (91). Similarly the a phase formed from the fcc f3 in lanthanum (92) is densely faulted. In this case the a is a modified hcp structure with a stacking sequence A BA CABA C, which can be produced from the f3 by displacing two adjacent close packed planes by a/6 (112) every fourth plane. Heavily faulted structures

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are also produced in alloys such as those of the extensively studied e u-AI system (93, 94). According to composition the {3 phase can transform to {3' or Pi . These can b e regarded as arrays of stacking faults although the details are rather complex; lamellae of the stacking sequences A BCBCA CAB, A B, and A BC have b een identified (95).

Ferrous alloys exhib it a wide range of microstructural characteristics describ ed in detail in two recent reviews (96, 97). The variations are intriguing b ecause the b asic structural change required is generally similar. B roadly speaking, plate martensites can b e comprised entirely of fi ne twins (80 , 98) or consist of twinned and untwinned regions (99-101), the latter containing dislocations, while lath martensite is usually composed of b undles of elongated sub grains characterized b y complex dislocation structures (102-104), although twins have also b een detected (105). In all completely twi nned martensitic cry stals that are well describ ed b y the crystallographic theory, the types of twins ob served are consistent with the lattice invariant shear invok ed in the theory, from which it is inferred that such twins are direct consequences of the mode of transformation. This is also a reasonab le inference for the presence of stack ing faults in other martensites. For steels the prop er twin is of the {112h type which is ob served in all twinned products. H owever {O l l)b twins are also found in incompletely twinned b ct martensi te ( 100, 107) and th e { 1 1 2 }b twi ns can th emsel ves b e internally twinned (96, 108). I n addition twins sometimes appear (10 6) to have b een modifi ed b y slip processes. This has b een used to explain the apparent deviation of twins from the ideal (112)b in Fe-Ni (10 9), b ut such deviations can also arise from experimental error (I 10). It can b e seen that the complexities are such that a complete documentation of the microstructural features awaits further painstak ing studies.

E ven with a complete descri ption of the microstructural features a futher maj or prob lem arises concern ing their origin. One issue here is: which are nece ssary ing redient s o f the transformation per se and which are consequences of the matrix constraints? l he latter are said to correspond to a post- transformation strain, although they can presumab ly arise to some extent concurrently. In this respect it has b een argued (106) that {O l l}b twins are indirect products of the transformation as they would b e derived from a nonmirror plane via the B ain correspondence. Twinned twins are ob ser ved in foils prepared from the b ulk and also in those transformed in situ when the infl uences of the b ulk are minimized (although other k inds are sub stituted) and have thus b een claimed (108) to b e consequences of the mode of transformation. The role of dislocations is prob lematical b ecause any directly involved in promoting the structural change ought to b e retained at the interface.

The Mechanism of the Transformation

A maj or area of martensitic transformati ons in which satisfactory understa nding is lacking concern s the physical mechanisms b y which the new phase nucleates and grows. In all heterogeneous transformations the growth of the new phase is profoundly infl uenced b y the nature of the interface that separates it from the

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matrix. (In this context heterogeneous transformation implies that at any instant the system can be divided into transformed and untransformed volumes.) This is especially true of a martensitic transition in which the interface moves without the aid of diffusion and, as a result of its movement, creates the new phase. Its origin nature and behavior are thus central to understanding the mechanisms of the transition. It is generally supposed that the interface is glissile and is formed by a suitable array of dislocations or by the termination of a stack of twin lamellae. Indeed discussions of the various characteristics exhibited by ferrous alloys are based upon the effects of the pertinent varil,lbles upon the competitive processes of slip and twinning. As a general trend it can be stated that the departure from well-defined, completely twinned plates. to lath martensite is associated with an increase in the Ms temperature and a reduction in alloying content, which are of course interconnected, particularly with respect to austenite stabilizing elements. To the extent that these changes would be expected to favor slip processes over twinning, the correlation is qualitatively reasonable.

One of the early versions of the phenomenological theory ( I l l) involved the formal concept of surface dislocations, whereas the first specific model attempting to describe the austenite-martensite interface in terms of an array of screw dislocations appeared earlier ( 1 1 2). Other models have been proposed subsequently, including dislocation pole models ( l 13) for the fcc to hcp transition. More recently models of dislocation arrays and their interaction with solute atoms have been considered ( 1 14). Although much progress has been made in recent years in resolving the physical details of a variety of boundaries and interfaces (1 15) there exists very little factual knowledge, gained by direct observation, of the structure of martensitic interfaces, a lack that is particularly acute for ferrous lath martensites.

The complexities of the problem are further compounded for transformations constrained within the matrix bulk as, for example, in ferrous plate martensites. Although the interface separates the new phase from the matrix, growth has occurred such that the equatorial dimensions of the lenticular platelet greatly exceed its thickness. This raises the question of the processes leading to the generation of the interface and introduces the topic of nucleation phenomena. The status of nucleation ideas has been recently reviewed in detail (3). Classical nucleation theory applied directly is inadequate and the existence of large embryos capable of being rendered supercritical by quenching has not been demonstrated. It appears that the formation of nuclei is heterogeneous and can be autocatalitic, but, although imperfections such as stacking faults have been associated with the initiation process, the nature of the heterogeneous sites is not fully understood. In this context it is worth noting that these ideas consider tacitly a static lattice. It is well known ( 1 1 6) that as the temperature is changed, softening of special elastic coefficients of a crystal can occur associated with the approaching mechanical instability of the crystal structure, which results in high amplitudes of certain modes of lattice vibrations. These effects can be detected by diffraction techniques before the onset of the macroscopically observable transition [as, for example, in TiNi alloys (I 17)]. In the latter reference the effects

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were termed "premartensitic" although it seems reasonable to suppose that they, perhaps in conjunction with crystal defects, might lead directly to the onset of the transformation.

HYBRID TRANSFORMATIONS

The transformations that have been described so far are mainly examples of "pure" transitions in that they can be separated convincingly according to mechanisms and resulting morphologies. There exist transformations which cannot be completely satisfactorily placed in one or other of these categories but instead incorporate characteristics pertaining to two or more of them. In these cases the transformation is accomplished by a mixture of modes and the total effect is logically regarded as a hybrid transformation. In the following, the salient features of two such examples will be presented. The first of these is ferrous bainite, for which the discussion will consider in order its morphology, kinetics, and mechanisms of growth. As a second example, the processes taking place during the growth of y' and y precipitates in Al-Ag alloys will be outlined.

Bainite

The name bainite was coined for the microstructural product that forms in steels when austenite is transformed under conditions that largely preclude the formation of martensite or pearlite. It consists of an aggregate of ferrite and discrete particles of iron carbide. As such, it is an accepted term and excludes other ferrite and alloy carbide aggregates that can arise in alloy steels (i 18). Because the actual processes that take place during the formation of bainite are not those that are purely martensitic nor those that yield pearlite, it has become customary to refer to them as comprising a bainitic transformation. In some ways, this has been unfortunate, perhaps because such a terminology suggests that it represents a separable transformation possessing its own unique characteristics. Indeed, in addition to those aspects of the topic that are themselves as yet unresolved, controversy exists over the definition of the bainitic transformation. This has been the subject of two recent publications ( i 19, 10) in which can be found a rather comprehensive bibliography of relevant literature.

The details of the morphology vary gradually with the temperature at which the reaction takes place making it difficult to identify any unique outstanding characteristics. In the upper range of temperature the product appears featherlike in the optical microscope and is composed of aggregates of parallel groups of ferrite laths, among which, on the intercrystalline boundaries, lie cementite plates oriented parallel to the local boundaries. Apart from the presence of carbides the microstructure on the scale viewed within the electron microscope is quite similar to that of ferrous lath martensites. On the other hand, at lower temperatures the ferrite plates adopt a more acicular aspect and carbides oriented at about 60° to the main axis are found both within the crystals and in contact with the intercrystalline boundaries. The two extremes are called upper and lower bainite respectively. Whereas a sharp division between the two

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variants does not appear to exist universally, it seems in general that the two regimes lie on either side of approximately 350°C. These observations refer to the final products. Little is known of the precise sequence of events that leads to the final microstructure, although in lower bainite metastable carbides other than cementite have been observed.

The ferrite component of the microstructure produces relief effects on initially flat surfaces, thus indicating the presence of a macroscopic shape change which must therefore be explicable in terms of any mechanisn proposed for the mode of growth.

In plain carbon steels the conditions under which the product of the transformation is pearlite or bainite merge together gradually; however, in alloy steels the processes can become separable and when the obscuring effects of the pearlite morphology are avoided there is found to exist a temperature, the Bs temperature, which marks the upper limit of the temperature range in which

bainite can form during isothermal holding. Above the Bs bainite will not form; however, it can form in increasing amounts at temperatures increasingly further below it. The Bs temperature is somewhat analogous to the Ms temperature, an

analogy that is strengthened by the fact that bainite can be induced to form above the Bs temperature by the application of stress, as can martensite above the Ms temperature. The growth rate of individual ferrite plates is slow and is anisotropic in that the thickening rates are exceeded by the rates of lengthening.

As is commonly true in solid state phase transformations the details of the

atomic movements involved in the production of the new microstructure have eluded direct observation. All that can be determined with some certainty are end consequences of the events, from which deductions concerning the mode of transformation are perforce made. The more complex the consequences, the greater the difficulties that beset attempts at interpretation.

The two primary consequences of the processes that form bainite are a matrix structural change from fcc to bcc and the appearance of carbide particles. Two main schools of thought exist concerning the manner by which these consequences are accomplished. Both accept the fact that the carbide particles indicate that long range diffusion of carbon is undoubtedly involved, but diverge in opinion regarding the origin of the ferrite. On the one hand, the similarities in microstructure exhibited by bainitic ferrite and martensite, the occurrence of

surface relief effects, and the fact that as the temperature is lowered the accepted martensitic transformation begins, have led to the opinion that the structural change might be accomplished by a martenstic transformation relating the substitutional atoms. In this hypothesis the substitutional atoms are converted to the bcc structure by a diffusionless martensitic process. The slow growth rate is

rationalized either by invoking a series of small rapid events interspersed by periods of quiescence or by a continuous slow advance, with the overall rate being controlled by carbon diffusional processes.

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

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358 MEYRICK &; POWELL

interface and the lateral migration of these by substitutional diffusion. Again the rate controlling process for thickening is thought to be diffusion of carbon in the austenite.

In these views the major clash arises in the manner of ferrite formation, whereas the precipitation of the carbides is, in the main, subject to less serious differences of opinion, although whether or not the precipitation takes place in the ferrite as well as in the austenite is relevant to the former. Because the answer is not directly known inferences are drawn from indirect observations and are thus open to doubt. That cementite in upper bainite forms from austenite appears to be generally accepted; however, opinions diverge on the question of the cementite and epsilon carbides in lower bainite. The morphology of the carbides within the ferrite plates and the similarities with tempered martensite have been taken to infer the initial formation of supersaturated ferrite followed by carbide precipitation therein. So far experimental observations have failed to demonstrate the existence of this supersaturation, but this cannot be unhesitatingly taken as proof of its absence. The alternative view is that the carbides are more or less always formed initially at the ferrite-austenite interface. It would seem that this is an important point as such carbides might well be engulfed by an interface migrating by a diffusional mechanism, but provide barriers to a glissile interface.

Probably the greatest single contribution to the adoption of the martensitic viewpoint is the surface relief associated with the bainitic ferrite. In this regard, also, the situation is confused and little if anything can be unequivocally concluded. As discussed before, part of the confusion arises from the need to prove that the surface relief necessitates a martensitic contribution. The opposite view requires substantiation by a convincing means of producing relief of the type observed other than through a martensitic mode. Applications of the phenomenological crystallographic theory of martensite fail to provide a consistent description; however, this is true for all except the well-behaved of the ferrous martensites and consequently the application of a theory that is known to be largely inadequate for ferrous materials is hardly to be expected to provide a reliable means of deciding for or against a martensitic contribution ,to bainitic ferrite.

Because the precise mode of growth of bainitic ferrite has not been established with certainty, further details of the process will not be considered here. Whatever the mechanism by which by which the ferrite is produced, the overall transformation is composed of at least two separate modes. It involves the simultaneous production of two phases; one, the carbide, is formed by continuous precipitation from one or both of the matrix phases, and the second, the bcc ferrite, is produced by an allotropic transformation.

The Formation of "I' and y in A l-Ag A lloys

In the section dealing with continuous precipitation reactions the Al-Ag system was mentioned as an example of a system in which sequential precipitation reactions are observed, namely GP zones, metastable hcp 1', and the stable hcp

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y phase. In all three the new phase is enriched with silver as compared with the matrix; consequently, substitutional long range diffusion is obviously a necessary ingredient in the processes. In addition, for the y' and y phases a structural transition of fcc to hcp occurs. In this case the details of the process have been studied by careful investigations using hot-stage transmission electron microscopy which has revealed that whereas the overall rate of the processes is diffusion controlled, the structural change is largely made through displacive rather than constructive mechanisms.

Nuclei of the y' phase form heterogeneously (56) at dislocations which, at the onset of the transformation, dissociate into pairs of glissile partial dislocations �onnected by ribbons of stacking faults. With additional ageing the partial dislocations are able to separate further because, as is a reasonable supposition, silver atoms migrate to the fault providing a reduction in energy. Growth in the direction normal to the close packed plane is accomplished by the formation of more glissile partials every second {I l l} plane and their subsequent migration in that plane. The reverse sequence occurs during dissolution when the temperature is raised. The total growth process involves three steps, the nucleation of partial dislocations, the diffusion of Ag to them, and their migration in the habit plane. The rate of dislocation migration is controlled by the substitutional diffusion; but in this case the thickening rate of the platelet occurred more slowly than permitted by diffusion, from which it was concluded that the nucleation of the dislocations was the rate controlling process.

The characteristics of the formation of the stable y phase in AI-Ag alloys have been examined in several recent investigations (120, 12 1). It forms as approximately hexagonally shaped plates whose broad faces, parallel to the {I I I} planes of the matrix, contain dislocations. These sometimes become arranged into stable networks which results in a marked reluctance for the plate to thicken; otherwise thickening is accomplished by the generation and migration of arrays of interface dislocations. Dislocations are formed during the lengthening of the platelet which apparently also involves the operation of a migrating ledge mechanism. Indeed, superledges of the order of 100 A in magnitude were observed to propagate around the circumference of some platelets.

In bulk samples the emergence of y plates at the free surface is associated with surface relief which, at least initially, is consistent with a plane strain. During prolonged annealing the surface tilts decrease somewhat in magnitude as processes take place that tend to relieve the strain energy.

It is evident from the foregoing that both the y' and y phases are produced by hybrid transformations in the sense used in this article. At least part of the structural change is accomplished by a displacive process, namely the glide of partial dislocations. Such a process, if it took place in the complete absence of diffusion, would clearly be martensitic. This is not so in this case where the rates at which the dislocations glide and at which the concurrent compositional changes are effected are dependent upon the diffusion of silver and aluminum atoms. The total transformation is not, however, attained by diffusional reconstructive processes. In detail, then, the events can be considered hybrid, although

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the overall process is one of continuous precipitation, in the sense that discrete particles nucleate heterogeneously within the matrix and grow more or less continuously in a manner controlled by diffusion, influenced by special interface characteristics.

ACKNOWLEDGMENTS

One of us (G. M.) is grateful for the support of the U. S. Army Research Office (Durham). In addition, the authors wish to thank the following for permissfun to use figures from their published works: G. Krauss and A. R. Marder; R. A. Fournelle and J. B . Clark; T. B. Massalski, J. E. Kittl, and E. B . Hawbott; G. H. Goodenow and R. F. Hehemann; J. W. Spretnak, E. Eichen, and J. F. Morral; and K. N. Tu and D. Turnbull.

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CONTENTS

EXPERIMENTAL AND THEORETICAL METHODS

Theoretical Approaches to the Determination of Phase Diagrams, Larry

Kaufman and Harvey Nesor

PROPERTIES, PHENOMENA

The Fracture Crack as an Imperfection in a Nearly Perfect Solid, Robb M.

Thomson 31

Critical Phenomena in Solids, M. E. Lines 53

Mass Transport in Solids, N. L. Peterson and W. K. Chen 75

Electrical Properties: Charge Injection Phenomena, Peter Mark and Myron

Allen 111

SPECIAL MATERIALS

Layer Compounds, A. D. Yoffe 147

High Temperature Compounds, Hans Nowotny and Stephan Windisch 171

Carbon and Graphite Science, Douglas W. McKee 195

Cement Paste and Concrete, Torben C. Hansen, Fariborz Radjy and Erik J.

Sellevold 233

Recent Advances in Liquid Crystals, Georges Durand and J. D. Litster 269

STRUCTURE

Some Aspects of Structural Disorder in Solids, Simon C. Moss 293

PREPARATION, PROCESSING, AND STRUCTURAL CHANGES

Chemical Vapor Deposition of Electronic Materials, James J. Tietjen 317

Phase Transformations in Metals and Alloys, Glyn Meyrick and Gordon W.

Powell 327

Synthesis of Materials From Powders by Sintering, A. L. Stuijts 363

Crystallization, A. A. Chernov 397

REPRINT INFORMATION 455

INDEXES

Author Index

Subject Index

Cumulative Index of Contributing Authors, Volumes 1-3

Cumulative Index of Chapter Titles, Volumes 1-3

457

471

481

482

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Documents

1973-Phase Transformation in Metals and Alloys