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The influence of lattice softening of the parent phase on the martensitic] transformation in FeNi and FePt alloys
Materials Science and Engineering, A127 (1990) 197-204
197
The Influence of Lattice Softening of the Parent Phase on the Martensitic Transformation in Fe-Ni and Fe-Pt Alloys WALTER S. OWEN*
Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (U.S.A.) (Received October 24, 1988)
Abstract
1. Introduction
Studies of the interactions between the magnetic transition and the first-order displacive martensitic transformation in Fe-Ni and ordered and disordered Fe-Pt alloys are reviewed in an effort to find answers to two questions. Is lattice softening a necessary pre-condition for transformation ? How does pre-transformation softening, when it occurs, affect the nucleation and growth of a martensitic plate ? The clear demonstration that the low temperature transformation which produces martensite with the well-known acicular morphology occurs only in the ferromagnetic fc.c. phase suggests that softening of the parent phase is necessary. However, the fact that a transformation to lath martensite occurs, at temperatures above room temperature, in dilute alloys in which the parent phase is paramagnetic, casts doubt on the validity of this generalization. There are a number of indications that the lattice softening which accompanies the magnetic transition influences the kinetics of the displacive transformation but the exact mechanisms by which nucleation is affected is still unclear. Single-crystal measurements of the soft modes in disordered Fe-Pt clearly show that they are not coupled directly to the transformation lattice strains and, consequently, it is unlikely that there is a direct connection between the soft mode lattice displacements and the displacements which produce the Bain strain. It is probable, however, that there are important indirect effects of softening on nucleation in these alloys. The influence of softening on growth, on the contrary, is clearer. Pre-transformation lattice softening is a necessary but not sufficient condition for thermoelastic reversible growth and shape memory properties.
The martensitic transformation in alloys of iron has been studied over a longer period of time and more intensively than first-order displacive transformations in all other alloy systems combined and yet many fundamental questions about it remain unresolved. Important among them is the question of whether or not lattice softening of the parent f.c.c. 7 phase is necessary before the transformation can occur. The most widely held opinion amongst metallurgists today is that it is not. However, pre-transformation elastic softening is quite marked in a number of important alloys and, thus, it is necessary to decide the influence that this has on the subsequent transformation. This matter has been studied in some detail for Fe-Ni and Fe-Pt alloys and here we offer a critical assessment of this work. It must be emphasized, however, that the magnetic phenomena which figure prominently in this discussion occur only in a limited number of alloy systems and, consequently, conclusions about their behavior are not necessarily applicable to other ferrous alloys. The alloys to be discussed are ferromagnetic over a range of temperatures. Thus, since changes in magnetization and associated properties of the parent phase accurately reflect lattice changes, pre-transformation phenomenon can be monitored conveniently. Furthermore, the Curie temperature of the Fe-Pt alloys can be changed without changing the composition by a simple heat treatment which changes the order in the f.c.c. 7 phase. The first part of the paper and Figs. 1 and 2 are taken from the work of NiUes [1] who used these experimental techniques to good effect. It is unfortunate that, in the intervening years, this work has not received the attention which it deserves. In all alloys of iron, the martensitic transforma-
*Present address: 1 Marine Terrace, Gwynedd, N. Wales LL49 9BL, U.K. 0921-5093/90/$3.50
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at least, the transformation in Fe-Ni and Fe-Pt alloys may be considered representative of "strongly first-order" displacive transformations.
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Fig. 1, Variation in M, and O c with solute concentration in disordered Fe-Ni and Fe-Pt alloys,
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tion, when it occurs, produces a lattice shape change which is large compared with the shear produced in the "weakly first-order" copper-base fl phase alloys, for example. Thus, in this respect
The ~ phases of Fe-Ni and disordered Fe-Pt are f.c.c. (A2) and the ordered Fe3Pt phase has a cubic Cu3Au (LI:) structure. These ~ phases undergo a magnetic transition at a temperature which increases with increasing nickel or platinum concentration and, in the Fe-Pt alloys, with increasing order. The variations in the Curie temperature O c with solute concentration are shown for both systems in the disordered state in Fig. 1. The shift of Oc to higher temperatures on ordering Fe-Pt alloys with compositions between 14 and 40 at.% Pt is shown in Fig. 2. The magnetic transition cannot be followed to low temperatures in the more dilute alloys because the y - a phase transformation intervenes. The variations in M s (the temperature at which the transformation of austenite to martensite starts during cooling) with nickel and platinum concentrations in the binary alloys are also shown in Fig. 1. It is clear that both alloy systems can be divided into dilute alloys which are paramagnetic and more concentrated alloys which are ferromagnetic before they transform. Both the Fe-Ni and the Fe-Pt series of alloys transform to a b.c.c, a phase but the morphology of the growing plates of a phase and the microstructure of the transformation product differ markedly depending on whether the parent phase was paramagnetic or ferromagnetic at M s. a phase formed from paramagnetic ~ phase has a habit plane in the vicinity of {111}~ and a substructure described by electron microscopists as lath martensite, which contains a high density of dislocations. The laths are, in fact, thin plates arranged in blocks which, in fully transformed specimens, fill space, a phase formed from the ferromagnetic ~ phase, on the contrary, consists of plates which are twinned and the habit planes are irrational, often near the center of the stereographic triangle. Such alloys in a narrow range between about Fe-29at.%Ni and Fe-32at.%Ni have an acicular microstructure in which separated plates are arranged in zigzag patterns embedded in a matrix of untransformed parent phase. Transformation is always incomplete even at the lowest temperatures attainable experimentally. Similar microstructures are found in
199
disordered Fe-Pt alloys but when formed from a partially or fully ordered parent phase the plates are arranged in blocks of approximately parallel plates with alternating shears. The transformation in ordered alloys goes to completion at some temperature below M~. Thus in Fe-Pt alloys the microstructure of the transformed alloy is a function of the degree of long-range order in the parent phase. Probably, short-range order is also significant but its effect is not well documented. (It might be thought by some that the different microstructures have been contrasted too sharply. Over a narrow range of composition separating the paramagnetic and ferromagnetic parent phases, a rich variety of structures can be found and these have been studied in great detail, but undue attention to these fine points tends to obscure the essential features and they will not be discussed further.) That changes in the transformation and its product are intimately connected with changes in the magnetic state of the parent phase is dramatically illustrated by the shift in the microstructural transition on ordering Fe-Pt alloys [1]. For the disordered alloys, the composition at which the M~ and ®c lines intersect is near Fe-26at.%Pt but for the ordered alloys the curves intersect at Fe-2 lat.%Pt (Fig. 2). This coincides exactly with the change in the concentration of platinum at which the microstructures change.
3. The parent phase The Fe-Ni alloys which are ferromagnetic and f.c.c, at room temperature (containing from 29 to about 45 at.% Ni) show pronounced magnetovolume and magnetostriction effects and are usually referred to as Invar alloys. They have a very small coefficient of thermal expansion, a large pressure dependence of magnetization, a positive temperature dependence of the elastic shear constants and, in some cases, of C44 as well, and an unusually large variation in Poisson's ratio and the elastic anisotropy ratio increase with decreasing temperature. The maximum Invar effect in Fe-Ni alloys, as revealed by any of these properties, occurs in the alloy with 35 at.% Ni. Because the decrease in M~ with increasing nickel content is very steep (Fig. 1), only alloys in a narrow range of nickel contents, 29-32 at.%, transform from a ferromagnetic ), phase. These are at the low end of the Invar range and, consequently, the effects related to the magnetostric-
tion phenomenon are not so pronounced as in an Fe-35at.%Ni alloy. Furthermore, the temperature interval between O c and M~ is small and thus temperature-dependent effects, such as the softening of C', produce little change before M Sis reached. Nevertheless, some decrease in C' as a falling temperature approaches M, has been reported in an alloy containing 30 at.% Ni [6]. It is not surprising, however, that there are no claims of substantiated elastic softening or of ordering based on Fe3Ni in these small ranges of compositions and temperatures. In sharp contrast, the y phase of alloys with composition near Fe3Pt have pronounced Invar properties in the temperature range immediately a b o v e M S. Acoustic phonon softening has been studied in detail by inelastic neutron scattering [13], and by X-ray and electron diffraction [14]. Tweed-like structures have been observed by transmission electron microscopy. Elastic softening has been measured in single-crystal and polycrystalline specimens [15]. The magnifudes of Invar effects are a function of the degree of order, being larger the more disordered the crystal. All three elastic constants CL ( = l(Cl~ + C 1 2 + 2 C 4 4 ) ) , C ( = C 4 4 ) and C' (=l(Cl,--C~2)) soften appreciably on cooling disordered or partially ordered alloys with compositions near to Fe3Pt through the Curie temperature [15, 16] (Figs. 3, 4 and 5 respectively). The temperature coefficients d CL/d T and d C'/d T of the shear constants are positive at all temperatures below ®c but
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Fig. 3. Temperature dependence of the elastic constant C as a function of the long-range order S in Fe3Pt (applied field, 0.8 T). The Curie temperatures O¢ as determined by the heat capacity measurements are indicate.d by the arrows.
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in magnetism. Increasing the degree of order increases the Curie temperature and decreases the slope of the curves at low temperatures. The curves intersect in each of the plots so that in the plot of C vs. T the relative magnitudes of C are reversed at the lowest temperatures. CL passes through a minimum which is deeper the smaller the value of the order parameter S. The variation in C' with order S and temperature T is complex because it reflects the behavior of both C and C L. It is clear from Fig. 2 that an ordered alloy with near-stoichiometric composition, Fe3Pt , experiences pronounced lattice softening before transforming, whereas in the disordered condition it is ferromagnetic over only a small temperature interval and, although softening of the shear constants occurs more rapidly than in the ordered alloy, little softening results before M s is reached. Thus, in this respect, disordered Fe3Pt is similar to Fe-30at.%Ni. ("Disordered Fe3Pt" means only that S = 0 but there is, undoubtedly, some shortrange order in the alloy.)
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Fig. 5. Temperature dependence of the elastic constant C L as a function of the degree S of order in Fe3Pt (applied field, 0.8 T). The Curie temperatures Oc as determined by the heat capacity measurements are indicated by the arrows.
d C/d T changes sign, producing a minimum in the curve. The changes in the slopes of the CL vs. T and C' vs. T plots do not coincide exactly with the Curie temperatures measured calorimetrically or by electrical resistivity and the discrepancy is still larger in the case of the constant CL but there can be little doubt that the change in the elastic properties of the lattice is induced by the change
The shear component of the total transformation shape change in Fe-30at.%Ni and Fe3Pt is large, about 2 x 10-1, and nearly an order of magnitude larger than in the weakly first-order fl phase alloys. There is also a striking difference in the thermodynamic driving force required for nucleation of a martensitic transformation in the two types of alloy. In the copper-base fl phase alloys the required driving force is estimated to be about 40 J tool -t, whereas in the magnetic y phase alloys it is between 100 and 1350 J mo1-1 [17]. The smallest values are for those Fe-Pt alloys which soften the most at M s. Thus an alloy of stoichiometric composition, Fe3Pt, in the ordered state, which softens considerably before the temperature falls to Ms, requires only a small driving force, about 100 J mol -], whereas in the same alloy when disordered the softening is small and the driving force is, as a result, large, being close to 1000 J mol-]. Incidentally, the fl phase alloys, which require a smaller driving force than even completely ordered Fe3Pt, soften to smaller values of the elastic constants at M s. The anisotropy of the elastic softening in a single crystal of Fe3Pt of near-stoichiometric composition has been studied in detail by acoustic measurements [15, 18] made as a function of the temperature (from 200 °C to Ms) and long-
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ordered specimen (S= 0.6), on the contrary, for which the ferromagnetic temperature range is larger, all the effective shear constants, including the soft mode, decrease with decreasing temperature (Fig. 7). However, in neither state of order does the soft mode reach or even come close to zero at M s.
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range order (between S = 0 and S = 0.6). The disordered crystal (S = 0) is ferromagnetic in the 7 phase over only a small temperature interval, whereas the more ordered alloy (S=0.6) softens considerably before transforming (Fig. 2). In both conditions there exists a pronounced soft mode as revealed by the polar plots of the effective shear constants (velocity envelopes) (Figs. 6 and 7). This is the same soft mode as is found in the fl-phase alloys: a T 2 mode in (001) and ( i l 0 ) planes reflecting the softness of C' = ~ ( 1 C 1 1 - C l 2 ) and a small resistance to (110)[i10] shear, as noted by Zener [19]. A second "special" soft mode was found in NiA1 by Nagasawa and Ueda [20] and confirmed in the /3 phase alloy Au-47.5at.%Cd [18]. No second soft mode was found in Fe3Pt. None of the effective shear constants for the disordered Fe3Pt crystal (S=0) changes significantly over a 180 °C temperature range immediately above M s (Fig. 6) because Oc is close to the transformation temperature. In the partially
5. Growth and thermoelastic effects
We know of no measurements of the kinetics of the movement of a single interface in a single crystal of a ferromagnetic f.c.c, phase. Work with polycrystalline specimens, in which many plates grow simultaneously, suggests that interfaces in Fe-30at.% Ni move rapidly but, in disordered Fe3Pt, growth of individual plates and of groups of plates is slow and can easily be observed by optical microscopy. Growth of martensite plates in Fe-30at.%Ni is not reversible on cycling, thermally or mechanically, through Ms and there are no significant thermoelastic effects. (There have been reports of very imperfect shape memory effects but these are not significant in the present context.) In Fe3Pt, in all but the most disordered alloys (S>0.2), growth is reversible. The hysteresis energy increases with decreasing order and, therefore, with decreasing pre-transformation lattice softening [16, 21]. The microstructure of the product of martensitic transformation in Fe-Pt alloys is also strongly influenced by the degree of order and, consequently, by the extent of lattice softening in the 7 phase at M~. When S is less than about 0.2 in a near-stoichiometric alloy, transformation occurs rapidly to produce an acicular microstructure similar to that in Fe-30at.%Ni. In more ordered specimens, thin-plate martensite is formed thermoelastically [22]. The first plates to appear grow rapidly in a radial direction until stopped by a grain boundary, another plate or some other barrier. Subsequently, they thicken only to an aspect ratio c/r of about 0.01 before adjacent new plates nucleate close to the broad faces and grow nearly parallel to the first plate. In this way, assemblies of plates with alternating shear directions develop to produce a distinctive microstructure. Umemoto and Wayman [22] have described the morphology and crystallography in detail. Martensitic growth of the a phase in Fe-Pt alloys with S>0.2 is thermoelastic and reversible, a phenomenon which is clearly related to
202 anisotropic softening of the elastic constants. Ling and Owen [23] have discussed thermoelastic growth in quantitative terms using a model which is an adaptation of Eshelby's treatment of the elastic strain field of an elastic inclusion in an elastic matrix. They proposed that an important criterion for reversibility is that all accommodation strain in the parent phase must be reversible. This means, in effect, that it either must be elastic or must occur by planar slip, twinning, or secondary martensitic transformation. The accommodation slip in specimens of Fe3Pt which are nearly completely ordered is, in fact, planar, as it is in all ordered crystals, but in more disordered specimens, with values of the order parameter S between 0.2 and about 0.8, it is not, and yet growth is thermoelastic [21]. This is clear evidence that elastic softening of the parent phase is sufficient alone to ensure thermoelastic reversible growth. Using measured values of the elastic constants and flow stresses and relying on the observed critical aspect ratio for the development of the self-accommodating arrangement of plates [22], the model [21] correctly predicts the change from reversible to irreversible growth when S falls below 0.2. The elastic strain field which envelops a plate growing in an elastically softened parent phase has an important influence on the autocatalytic nucleation of neighboring plates. In FeaPt with S> 0.2, secondary plates nucleate and grow, and groups of self-accommodating plates start to form before the first plate has thickened to an aspect ratio at which irreversible plastic accommodation strains are produced. This does not happen in more disordered specimens (S<0.2). The ferromagnetism of the ), phase has two important influences on the cooperative nucleation of adjacent plates: the elastic shear constants are reduced with the result that larger localized lattice distortions can be sustained before the yield stress is exceeded locally; the yield stress itself is increased markedly at low temperatures by interaction between moving dislocations and magnetic domains, a phenomenon known as Invar strengthening. Partially and fully ordered FeaPt (S>0.2) transforms completely on cooling to a sufficiently low temperature but when disordered it does not. In the ordered alloy, the groups of thin plates are found to be made up of four crystallographic variants of martensite. The crystallographic relationships between the variants and the coherency
of the interfaces beween them are two of the fundamental reasons why these alloys exhibit shape memory effects [22].
6. Inferences from the studies of Fe-Ni and Fe-Pt alloys
It seems, at first sight, that the studies of Fe-Ni and Fe-Pt alloys provide a clear answer to the question asked at the beginning. In concentrated alloys, lattice softening associated with a magnetic transition occurs before the displacive transformation, markedly affecting its kinetics and the microstructure of the product. In dilute alloys, however, the 7 phase is not ferromagnetic and the transformation is not preceded by softening or, as far as is known, by any other change in the parent phase. Thus it seems that lattice softening is not a prerequisite for a first-order displacive transformation. However, this conclusion depends on the assumption that the transformation is purely displacive. There can be little doubt that this is so in the case of the alloys in which the parent phase is ferromagnetic since all the Ms temperatures are below room temperature, but the assumption is questionable when applied to the dilute alloys which are not ferromagnetic before they transform because their transformation temperatures are above room temperature and therefore shortrange replacive effects could well be involved. This was pointed out more than 30 years ago [24], invoking much discussion at the time but, as the commonly used name "lath martensite" implies, more recently the point has been ignored. If, then, it is conceded that only the more concentrated alloys transform in a purely displacive fashion, the next question is as follows: what effect does the pre-transformation lattice softening have on the transformation in these alloys? The importance of the small changes in the lattice properties of the parent phase of Fe-30at.%Ni and disordered FeaPt is difficult to assess because the magnetic change becomes zero, i.e. O c and M s coincide, at a temperature near 0 °C. This is sufficiently high for short-range replacive processes to be possible, perhaps raising questions about the significance of the observations. However, no change in the microstructure is found on changing the nickel content of the Fe-Ni alloys over the narrow range (29--32 at.%) within which a pre-transformation martensitic
203 change occurs, although M s drops several hundred degrees Celsius. Nor does the microstructure change on changing the order parameter of Fe3Pt between S = 0 and S=0.2. Furthermore, the transformation kinetics and the microstructures are closely similar to those found in many other alloys of iron in which no premartensitic transformation effects have been detected. All these observations point to the conclusion that the small magnetic changes which occur before transformation in Fe-Ni and disordered FesPt do not affect the transformation significantly. In the partially and fully ordered Fe-Pt alloys, however, the magnetic change and associated lattice softening preceding transformation are large and their effects are marked. In this case, there is little possibility of thermally activated replacive processes occurring but the chemical ordering per se may affect the transformation. The results outlined earlier clearly indicate that pre-transformation lattice softening influences the nucleation kinetics, reducing the thermodynamic driving force at M~ and the hysterersis on cycling and also affects the growth process. In the f.c.c.-to-b.c.c, transformation the transformation lattice strain, the Bain strain, is achieved by a double shear, each component being of the type {111}(112) known as the Bogers-Burgers shears. The relevant elastic constant is I( C~~- C12 + C44), which is 1 5° away from the soft mode ½(C11- Cl2) illustrated in Figs. 6 and 7. Thus the transformation shears and the soft mode in disordered and ordered Fe3Pt are not coupled directly and it must be concluded that the displacements producing the Bain strain are determined by crystallographic constraints and not by the anisotropy of the lattice softening. In other words, the magnetic phonon displacements which produce the soft mode do not develop directly into the large displacements required by the transformation. It was observed also that the effective elastic constant corresponding to the soft mode has a significant positive value at M~, thus refuting the suggestion made by Zener in 1955 [19] and the assumption implicit in much of the discussion at this workshop. Nevertheless, it is equally clear that the nucleation kinetics are affected by the lattice softening, probably because the lattice properties in the vicinity of a nucleating defect are modified by the soft mode. Such ideas remain pure speculation,
however, until an acceptable model of the nucleation event is developed. This problem was discussed in detail by Clapp [25]. The effects of increasing the pre-transformation lattice softening in the Fe-Pt alloys on growth and the resulting microstructure are clear and unambiguous. Growth becomes thermoelastic and reversible. The microstructure changes from a partially transformed acicular structure to a fully transformed structure of blocks of selfaccommodating plates. The latter exhibits shape memory properties but the former does not. As discussed earlier, these growth characteristics are developed even though the degree of ordering is insufficient to produce planar slip. Thus, they can be exclusively attributed to the increased magnetization and its attendant lattice softening. The change in growth, at least in part, is due to a change from plastic to elastic accommodation strain and its affect on the autocatalytic nucleation of new plates. Additional changes, as mentioned earlier, are involved in shape memory effects. Thus, it appears that pre-transformation lattice softening is a necessary but not a sufficient condition for thermoelastic reversible growth and shape memory properties. The extensive literature on these phenomena in other alloy systems indicates that this conclusion is universally valid. In general, the mechanisms involved in growth processes are better understood than is the mechanism of nucleation but one aspect of growth is not well understood: the kinetics of motion of a single transformation interface driven by an applied stress or a change in temperature. This requires the development of a model of the interface and of the strain interactions between it and the elastically softened parent phase into which it is moving. Recent work has demonstrated the major influence of pre-transformation softening (the tweed structure) on the kinetics of motion of the fl1-7~ interface in a single crystal of Cu-AI-Ni [26]. Such studies address an important fundamental problem and clearly warrant further attention in the future.
Acknowledgments Much of the work discussed here was supported by the National Science Foundation under Grants GK 23985, DMR74-22719 and DMR8312697.
204
References 1 J.L. Nilles, Ph.D. Thesis, Comell University, 1969. 2 L. Kaufman and M. Cohen, Trans. AIME, 206 (1956) 1393. 3 A. Gilbert and W. S. Owen, Acta Metall., 10 (1962) 45. 4 R.G. Yeo, Trans. A1ME, 224(1962) 1222. 5 E W. Jones and W. I. Pumphrey, J. Iron Steel Inst., London, 163(1949) 121. 6 J. Crangle and G. C. Hallam, Proc. R. Soc. London, Ser. A, 272(1963) 119. 7 G. F. Bolling, A. Arrot and R. H. Richman, Phys. Status Solidi, 26 (1968) 743. 8 E. Klockman and E. J. Donahoe, J. Franklin Inst., 264 (1957) 59. 9 E. Efsic and C. M. Wayman, Trans. AIME, 239 (1967) 873. 10 A. E. Berkowitz, F. J. Donahoe, A. D. Franklin and R. P. Steijn, Acta Metall., 5 (1957) 1. l 1 T. Nakajima, J. Phys. Soc. Japan, 19(1964) 520. 12 R. M. Bozorth, Ferromagnetism, Van Nostrand, New York, 1961.
13 K. Tajima, Y. Endoh and Y. Ishikawa, Phys. Rev. Lett., 37 (1976) 519. 14 M. Foos, C. Frantz and M. Gantois, Scr. Metall., 12 (1978) 795. 15 H.C. Ling and W. S. Owen, Acta Metall., 31 (1983) 1343. 16 S. Kajiwara and W. S. Owen, Metall. Trans., 5 (1974) 2047. 17 H. C. Ling and W. S. Owen, Scr. Metall., 16 (1982) 819. 18 H. C. Ling and W. S. Owen, Scr. Metall., 15 (1981 ) 1115. 19 C. Zener, Trans. AIME, 203 ( 1955) 619. 20 A. Nagasawa and Y. Ueda, J. Phys. Soc. Jpn., 45 (1978) 1249. 21 D.P. Dunne and C. M. Wayman, Metall. Trans., 4 (1973) 137. 22 M. Umemoto and C. M. Wayman, Acta Metall., 26 (1978) 1529. 23 H. C. Ling and W. S. Owen, Acta Metall., 29(1981) 1721. 24 W. S. Owen, E. A. Wilson and T. Bell, in V. Zackay (ed.), High Strength Materials, Wiley, New York, 1965, p. 167. 25 P. Clapp, Mater. Sci. Eng., A127(1990). 26 M. Grujicic, G. B. Olson and W. S. Owen, Metall. Trans. A, 16(1985) 1713, 1723, 1735.
197
The Influence of Lattice Softening of the Parent Phase on the Martensitic Transformation in Fe-Ni and Fe-Pt Alloys WALTER S. OWEN*
Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (U.S.A.) (Received October 24, 1988)
Abstract
1. Introduction
Studies of the interactions between the magnetic transition and the first-order displacive martensitic transformation in Fe-Ni and ordered and disordered Fe-Pt alloys are reviewed in an effort to find answers to two questions. Is lattice softening a necessary pre-condition for transformation ? How does pre-transformation softening, when it occurs, affect the nucleation and growth of a martensitic plate ? The clear demonstration that the low temperature transformation which produces martensite with the well-known acicular morphology occurs only in the ferromagnetic fc.c. phase suggests that softening of the parent phase is necessary. However, the fact that a transformation to lath martensite occurs, at temperatures above room temperature, in dilute alloys in which the parent phase is paramagnetic, casts doubt on the validity of this generalization. There are a number of indications that the lattice softening which accompanies the magnetic transition influences the kinetics of the displacive transformation but the exact mechanisms by which nucleation is affected is still unclear. Single-crystal measurements of the soft modes in disordered Fe-Pt clearly show that they are not coupled directly to the transformation lattice strains and, consequently, it is unlikely that there is a direct connection between the soft mode lattice displacements and the displacements which produce the Bain strain. It is probable, however, that there are important indirect effects of softening on nucleation in these alloys. The influence of softening on growth, on the contrary, is clearer. Pre-transformation lattice softening is a necessary but not sufficient condition for thermoelastic reversible growth and shape memory properties.
The martensitic transformation in alloys of iron has been studied over a longer period of time and more intensively than first-order displacive transformations in all other alloy systems combined and yet many fundamental questions about it remain unresolved. Important among them is the question of whether or not lattice softening of the parent f.c.c. 7 phase is necessary before the transformation can occur. The most widely held opinion amongst metallurgists today is that it is not. However, pre-transformation elastic softening is quite marked in a number of important alloys and, thus, it is necessary to decide the influence that this has on the subsequent transformation. This matter has been studied in some detail for Fe-Ni and Fe-Pt alloys and here we offer a critical assessment of this work. It must be emphasized, however, that the magnetic phenomena which figure prominently in this discussion occur only in a limited number of alloy systems and, consequently, conclusions about their behavior are not necessarily applicable to other ferrous alloys. The alloys to be discussed are ferromagnetic over a range of temperatures. Thus, since changes in magnetization and associated properties of the parent phase accurately reflect lattice changes, pre-transformation phenomenon can be monitored conveniently. Furthermore, the Curie temperature of the Fe-Pt alloys can be changed without changing the composition by a simple heat treatment which changes the order in the f.c.c. 7 phase. The first part of the paper and Figs. 1 and 2 are taken from the work of NiUes [1] who used these experimental techniques to good effect. It is unfortunate that, in the intervening years, this work has not received the attention which it deserves. In all alloys of iron, the martensitic transforma-
*Present address: 1 Marine Terrace, Gwynedd, N. Wales LL49 9BL, U.K. 0921-5093/90/$3.50
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at least, the transformation in Fe-Ni and Fe-Pt alloys may be considered representative of "strongly first-order" displacive transformations.
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tion, when it occurs, produces a lattice shape change which is large compared with the shear produced in the "weakly first-order" copper-base fl phase alloys, for example. Thus, in this respect
The ~ phases of Fe-Ni and disordered Fe-Pt are f.c.c. (A2) and the ordered Fe3Pt phase has a cubic Cu3Au (LI:) structure. These ~ phases undergo a magnetic transition at a temperature which increases with increasing nickel or platinum concentration and, in the Fe-Pt alloys, with increasing order. The variations in the Curie temperature O c with solute concentration are shown for both systems in the disordered state in Fig. 1. The shift of Oc to higher temperatures on ordering Fe-Pt alloys with compositions between 14 and 40 at.% Pt is shown in Fig. 2. The magnetic transition cannot be followed to low temperatures in the more dilute alloys because the y - a phase transformation intervenes. The variations in M s (the temperature at which the transformation of austenite to martensite starts during cooling) with nickel and platinum concentrations in the binary alloys are also shown in Fig. 1. It is clear that both alloy systems can be divided into dilute alloys which are paramagnetic and more concentrated alloys which are ferromagnetic before they transform. Both the Fe-Ni and the Fe-Pt series of alloys transform to a b.c.c, a phase but the morphology of the growing plates of a phase and the microstructure of the transformation product differ markedly depending on whether the parent phase was paramagnetic or ferromagnetic at M s. a phase formed from paramagnetic ~ phase has a habit plane in the vicinity of {111}~ and a substructure described by electron microscopists as lath martensite, which contains a high density of dislocations. The laths are, in fact, thin plates arranged in blocks which, in fully transformed specimens, fill space, a phase formed from the ferromagnetic ~ phase, on the contrary, consists of plates which are twinned and the habit planes are irrational, often near the center of the stereographic triangle. Such alloys in a narrow range between about Fe-29at.%Ni and Fe-32at.%Ni have an acicular microstructure in which separated plates are arranged in zigzag patterns embedded in a matrix of untransformed parent phase. Transformation is always incomplete even at the lowest temperatures attainable experimentally. Similar microstructures are found in
199
disordered Fe-Pt alloys but when formed from a partially or fully ordered parent phase the plates are arranged in blocks of approximately parallel plates with alternating shears. The transformation in ordered alloys goes to completion at some temperature below M~. Thus in Fe-Pt alloys the microstructure of the transformed alloy is a function of the degree of long-range order in the parent phase. Probably, short-range order is also significant but its effect is not well documented. (It might be thought by some that the different microstructures have been contrasted too sharply. Over a narrow range of composition separating the paramagnetic and ferromagnetic parent phases, a rich variety of structures can be found and these have been studied in great detail, but undue attention to these fine points tends to obscure the essential features and they will not be discussed further.) That changes in the transformation and its product are intimately connected with changes in the magnetic state of the parent phase is dramatically illustrated by the shift in the microstructural transition on ordering Fe-Pt alloys [1]. For the disordered alloys, the composition at which the M~ and ®c lines intersect is near Fe-26at.%Pt but for the ordered alloys the curves intersect at Fe-2 lat.%Pt (Fig. 2). This coincides exactly with the change in the concentration of platinum at which the microstructures change.
3. The parent phase The Fe-Ni alloys which are ferromagnetic and f.c.c, at room temperature (containing from 29 to about 45 at.% Ni) show pronounced magnetovolume and magnetostriction effects and are usually referred to as Invar alloys. They have a very small coefficient of thermal expansion, a large pressure dependence of magnetization, a positive temperature dependence of the elastic shear constants and, in some cases, of C44 as well, and an unusually large variation in Poisson's ratio and the elastic anisotropy ratio increase with decreasing temperature. The maximum Invar effect in Fe-Ni alloys, as revealed by any of these properties, occurs in the alloy with 35 at.% Ni. Because the decrease in M~ with increasing nickel content is very steep (Fig. 1), only alloys in a narrow range of nickel contents, 29-32 at.%, transform from a ferromagnetic ), phase. These are at the low end of the Invar range and, consequently, the effects related to the magnetostric-
tion phenomenon are not so pronounced as in an Fe-35at.%Ni alloy. Furthermore, the temperature interval between O c and M~ is small and thus temperature-dependent effects, such as the softening of C', produce little change before M Sis reached. Nevertheless, some decrease in C' as a falling temperature approaches M, has been reported in an alloy containing 30 at.% Ni [6]. It is not surprising, however, that there are no claims of substantiated elastic softening or of ordering based on Fe3Ni in these small ranges of compositions and temperatures. In sharp contrast, the y phase of alloys with composition near Fe3Pt have pronounced Invar properties in the temperature range immediately a b o v e M S. Acoustic phonon softening has been studied in detail by inelastic neutron scattering [13], and by X-ray and electron diffraction [14]. Tweed-like structures have been observed by transmission electron microscopy. Elastic softening has been measured in single-crystal and polycrystalline specimens [15]. The magnifudes of Invar effects are a function of the degree of order, being larger the more disordered the crystal. All three elastic constants CL ( = l(Cl~ + C 1 2 + 2 C 4 4 ) ) , C ( = C 4 4 ) and C' (=l(Cl,--C~2)) soften appreciably on cooling disordered or partially ordered alloys with compositions near to Fe3Pt through the Curie temperature [15, 16] (Figs. 3, 4 and 5 respectively). The temperature coefficients d CL/d T and d C'/d T of the shear constants are positive at all temperatures below ®c but
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in magnetism. Increasing the degree of order increases the Curie temperature and decreases the slope of the curves at low temperatures. The curves intersect in each of the plots so that in the plot of C vs. T the relative magnitudes of C are reversed at the lowest temperatures. CL passes through a minimum which is deeper the smaller the value of the order parameter S. The variation in C' with order S and temperature T is complex because it reflects the behavior of both C and C L. It is clear from Fig. 2 that an ordered alloy with near-stoichiometric composition, Fe3Pt , experiences pronounced lattice softening before transforming, whereas in the disordered condition it is ferromagnetic over only a small temperature interval and, although softening of the shear constants occurs more rapidly than in the ordered alloy, little softening results before M s is reached. Thus, in this respect, disordered Fe3Pt is similar to Fe-30at.%Ni. ("Disordered Fe3Pt" means only that S = 0 but there is, undoubtedly, some shortrange order in the alloy.)
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Fig. 5. Temperature dependence of the elastic constant C L as a function of the degree S of order in Fe3Pt (applied field, 0.8 T). The Curie temperatures Oc as determined by the heat capacity measurements are indicated by the arrows.
d C/d T changes sign, producing a minimum in the curve. The changes in the slopes of the CL vs. T and C' vs. T plots do not coincide exactly with the Curie temperatures measured calorimetrically or by electrical resistivity and the discrepancy is still larger in the case of the constant CL but there can be little doubt that the change in the elastic properties of the lattice is induced by the change
The shear component of the total transformation shape change in Fe-30at.%Ni and Fe3Pt is large, about 2 x 10-1, and nearly an order of magnitude larger than in the weakly first-order fl phase alloys. There is also a striking difference in the thermodynamic driving force required for nucleation of a martensitic transformation in the two types of alloy. In the copper-base fl phase alloys the required driving force is estimated to be about 40 J tool -t, whereas in the magnetic y phase alloys it is between 100 and 1350 J mo1-1 [17]. The smallest values are for those Fe-Pt alloys which soften the most at M s. Thus an alloy of stoichiometric composition, Fe3Pt, in the ordered state, which softens considerably before the temperature falls to Ms, requires only a small driving force, about 100 J mol -], whereas in the same alloy when disordered the softening is small and the driving force is, as a result, large, being close to 1000 J mol-]. Incidentally, the fl phase alloys, which require a smaller driving force than even completely ordered Fe3Pt, soften to smaller values of the elastic constants at M s. The anisotropy of the elastic softening in a single crystal of Fe3Pt of near-stoichiometric composition has been studied in detail by acoustic measurements [15, 18] made as a function of the temperature (from 200 °C to Ms) and long-
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range order (between S = 0 and S = 0.6). The disordered crystal (S = 0) is ferromagnetic in the 7 phase over only a small temperature interval, whereas the more ordered alloy (S=0.6) softens considerably before transforming (Fig. 2). In both conditions there exists a pronounced soft mode as revealed by the polar plots of the effective shear constants (velocity envelopes) (Figs. 6 and 7). This is the same soft mode as is found in the fl-phase alloys: a T 2 mode in (001) and ( i l 0 ) planes reflecting the softness of C' = ~ ( 1 C 1 1 - C l 2 ) and a small resistance to (110)[i10] shear, as noted by Zener [19]. A second "special" soft mode was found in NiA1 by Nagasawa and Ueda [20] and confirmed in the /3 phase alloy Au-47.5at.%Cd [18]. No second soft mode was found in Fe3Pt. None of the effective shear constants for the disordered Fe3Pt crystal (S=0) changes significantly over a 180 °C temperature range immediately above M s (Fig. 6) because Oc is close to the transformation temperature. In the partially
5. Growth and thermoelastic effects
We know of no measurements of the kinetics of the movement of a single interface in a single crystal of a ferromagnetic f.c.c, phase. Work with polycrystalline specimens, in which many plates grow simultaneously, suggests that interfaces in Fe-30at.% Ni move rapidly but, in disordered Fe3Pt, growth of individual plates and of groups of plates is slow and can easily be observed by optical microscopy. Growth of martensite plates in Fe-30at.%Ni is not reversible on cycling, thermally or mechanically, through Ms and there are no significant thermoelastic effects. (There have been reports of very imperfect shape memory effects but these are not significant in the present context.) In Fe3Pt, in all but the most disordered alloys (S>0.2), growth is reversible. The hysteresis energy increases with decreasing order and, therefore, with decreasing pre-transformation lattice softening [16, 21]. The microstructure of the product of martensitic transformation in Fe-Pt alloys is also strongly influenced by the degree of order and, consequently, by the extent of lattice softening in the 7 phase at M~. When S is less than about 0.2 in a near-stoichiometric alloy, transformation occurs rapidly to produce an acicular microstructure similar to that in Fe-30at.%Ni. In more ordered specimens, thin-plate martensite is formed thermoelastically [22]. The first plates to appear grow rapidly in a radial direction until stopped by a grain boundary, another plate or some other barrier. Subsequently, they thicken only to an aspect ratio c/r of about 0.01 before adjacent new plates nucleate close to the broad faces and grow nearly parallel to the first plate. In this way, assemblies of plates with alternating shear directions develop to produce a distinctive microstructure. Umemoto and Wayman [22] have described the morphology and crystallography in detail. Martensitic growth of the a phase in Fe-Pt alloys with S>0.2 is thermoelastic and reversible, a phenomenon which is clearly related to
202 anisotropic softening of the elastic constants. Ling and Owen [23] have discussed thermoelastic growth in quantitative terms using a model which is an adaptation of Eshelby's treatment of the elastic strain field of an elastic inclusion in an elastic matrix. They proposed that an important criterion for reversibility is that all accommodation strain in the parent phase must be reversible. This means, in effect, that it either must be elastic or must occur by planar slip, twinning, or secondary martensitic transformation. The accommodation slip in specimens of Fe3Pt which are nearly completely ordered is, in fact, planar, as it is in all ordered crystals, but in more disordered specimens, with values of the order parameter S between 0.2 and about 0.8, it is not, and yet growth is thermoelastic [21]. This is clear evidence that elastic softening of the parent phase is sufficient alone to ensure thermoelastic reversible growth. Using measured values of the elastic constants and flow stresses and relying on the observed critical aspect ratio for the development of the self-accommodating arrangement of plates [22], the model [21] correctly predicts the change from reversible to irreversible growth when S falls below 0.2. The elastic strain field which envelops a plate growing in an elastically softened parent phase has an important influence on the autocatalytic nucleation of neighboring plates. In FeaPt with S> 0.2, secondary plates nucleate and grow, and groups of self-accommodating plates start to form before the first plate has thickened to an aspect ratio at which irreversible plastic accommodation strains are produced. This does not happen in more disordered specimens (S<0.2). The ferromagnetism of the ), phase has two important influences on the cooperative nucleation of adjacent plates: the elastic shear constants are reduced with the result that larger localized lattice distortions can be sustained before the yield stress is exceeded locally; the yield stress itself is increased markedly at low temperatures by interaction between moving dislocations and magnetic domains, a phenomenon known as Invar strengthening. Partially and fully ordered FeaPt (S>0.2) transforms completely on cooling to a sufficiently low temperature but when disordered it does not. In the ordered alloy, the groups of thin plates are found to be made up of four crystallographic variants of martensite. The crystallographic relationships between the variants and the coherency
of the interfaces beween them are two of the fundamental reasons why these alloys exhibit shape memory effects [22].
6. Inferences from the studies of Fe-Ni and Fe-Pt alloys
It seems, at first sight, that the studies of Fe-Ni and Fe-Pt alloys provide a clear answer to the question asked at the beginning. In concentrated alloys, lattice softening associated with a magnetic transition occurs before the displacive transformation, markedly affecting its kinetics and the microstructure of the product. In dilute alloys, however, the 7 phase is not ferromagnetic and the transformation is not preceded by softening or, as far as is known, by any other change in the parent phase. Thus it seems that lattice softening is not a prerequisite for a first-order displacive transformation. However, this conclusion depends on the assumption that the transformation is purely displacive. There can be little doubt that this is so in the case of the alloys in which the parent phase is ferromagnetic since all the Ms temperatures are below room temperature, but the assumption is questionable when applied to the dilute alloys which are not ferromagnetic before they transform because their transformation temperatures are above room temperature and therefore shortrange replacive effects could well be involved. This was pointed out more than 30 years ago [24], invoking much discussion at the time but, as the commonly used name "lath martensite" implies, more recently the point has been ignored. If, then, it is conceded that only the more concentrated alloys transform in a purely displacive fashion, the next question is as follows: what effect does the pre-transformation lattice softening have on the transformation in these alloys? The importance of the small changes in the lattice properties of the parent phase of Fe-30at.%Ni and disordered FeaPt is difficult to assess because the magnetic change becomes zero, i.e. O c and M s coincide, at a temperature near 0 °C. This is sufficiently high for short-range replacive processes to be possible, perhaps raising questions about the significance of the observations. However, no change in the microstructure is found on changing the nickel content of the Fe-Ni alloys over the narrow range (29--32 at.%) within which a pre-transformation martensitic
203 change occurs, although M s drops several hundred degrees Celsius. Nor does the microstructure change on changing the order parameter of Fe3Pt between S = 0 and S=0.2. Furthermore, the transformation kinetics and the microstructures are closely similar to those found in many other alloys of iron in which no premartensitic transformation effects have been detected. All these observations point to the conclusion that the small magnetic changes which occur before transformation in Fe-Ni and disordered FesPt do not affect the transformation significantly. In the partially and fully ordered Fe-Pt alloys, however, the magnetic change and associated lattice softening preceding transformation are large and their effects are marked. In this case, there is little possibility of thermally activated replacive processes occurring but the chemical ordering per se may affect the transformation. The results outlined earlier clearly indicate that pre-transformation lattice softening influences the nucleation kinetics, reducing the thermodynamic driving force at M~ and the hysterersis on cycling and also affects the growth process. In the f.c.c.-to-b.c.c, transformation the transformation lattice strain, the Bain strain, is achieved by a double shear, each component being of the type {111}(112) known as the Bogers-Burgers shears. The relevant elastic constant is I( C~~- C12 + C44), which is 1 5° away from the soft mode ½(C11- Cl2) illustrated in Figs. 6 and 7. Thus the transformation shears and the soft mode in disordered and ordered Fe3Pt are not coupled directly and it must be concluded that the displacements producing the Bain strain are determined by crystallographic constraints and not by the anisotropy of the lattice softening. In other words, the magnetic phonon displacements which produce the soft mode do not develop directly into the large displacements required by the transformation. It was observed also that the effective elastic constant corresponding to the soft mode has a significant positive value at M~, thus refuting the suggestion made by Zener in 1955 [19] and the assumption implicit in much of the discussion at this workshop. Nevertheless, it is equally clear that the nucleation kinetics are affected by the lattice softening, probably because the lattice properties in the vicinity of a nucleating defect are modified by the soft mode. Such ideas remain pure speculation,
however, until an acceptable model of the nucleation event is developed. This problem was discussed in detail by Clapp [25]. The effects of increasing the pre-transformation lattice softening in the Fe-Pt alloys on growth and the resulting microstructure are clear and unambiguous. Growth becomes thermoelastic and reversible. The microstructure changes from a partially transformed acicular structure to a fully transformed structure of blocks of selfaccommodating plates. The latter exhibits shape memory properties but the former does not. As discussed earlier, these growth characteristics are developed even though the degree of ordering is insufficient to produce planar slip. Thus, they can be exclusively attributed to the increased magnetization and its attendant lattice softening. The change in growth, at least in part, is due to a change from plastic to elastic accommodation strain and its affect on the autocatalytic nucleation of new plates. Additional changes, as mentioned earlier, are involved in shape memory effects. Thus, it appears that pre-transformation lattice softening is a necessary but not a sufficient condition for thermoelastic reversible growth and shape memory properties. The extensive literature on these phenomena in other alloy systems indicates that this conclusion is universally valid. In general, the mechanisms involved in growth processes are better understood than is the mechanism of nucleation but one aspect of growth is not well understood: the kinetics of motion of a single transformation interface driven by an applied stress or a change in temperature. This requires the development of a model of the interface and of the strain interactions between it and the elastically softened parent phase into which it is moving. Recent work has demonstrated the major influence of pre-transformation softening (the tweed structure) on the kinetics of motion of the fl1-7~ interface in a single crystal of Cu-AI-Ni [26]. Such studies address an important fundamental problem and clearly warrant further attention in the future.
Acknowledgments Much of the work discussed here was supported by the National Science Foundation under Grants GK 23985, DMR74-22719 and DMR8312697.
204
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13 K. Tajima, Y. Endoh and Y. Ishikawa, Phys. Rev. Lett., 37 (1976) 519. 14 M. Foos, C. Frantz and M. Gantois, Scr. Metall., 12 (1978) 795. 15 H.C. Ling and W. S. Owen, Acta Metall., 31 (1983) 1343. 16 S. Kajiwara and W. S. Owen, Metall. Trans., 5 (1974) 2047. 17 H. C. Ling and W. S. Owen, Scr. Metall., 16 (1982) 819. 18 H. C. Ling and W. S. Owen, Scr. Metall., 15 (1981 ) 1115. 19 C. Zener, Trans. AIME, 203 ( 1955) 619. 20 A. Nagasawa and Y. Ueda, J. Phys. Soc. Jpn., 45 (1978) 1249. 21 D.P. Dunne and C. M. Wayman, Metall. Trans., 4 (1973) 137. 22 M. Umemoto and C. M. Wayman, Acta Metall., 26 (1978) 1529. 23 H. C. Ling and W. S. Owen, Acta Metall., 29(1981) 1721. 24 W. S. Owen, E. A. Wilson and T. Bell, in V. Zackay (ed.), High Strength Materials, Wiley, New York, 1965, p. 167. 25 P. Clapp, Mater. Sci. Eng., A127(1990). 26 M. Grujicic, G. B. Olson and W. S. Owen, Metall. Trans. A, 16(1985) 1713, 1723, 1735.