Atomic mechanisms of diffusional nucleation and growth and comparisons with their counterparts in shear transformations

An integrated overview is presented of a viewpoint on the present understanding of nucleation and growth mechanisms in both diffusional and shear (martensitic) transformations. Special emphasis is placed on the roles played by the anisotropy of interphase boundary structure and energy and also upon elastic shear strain energy in both types of transformation. Even though diffusional nucleation is based on random statistical fluctuations, use of the time reversal principle shows that interfacial energy anisotropy leads to accurately reproducible orientation relationships and hence to partially or fully coherent boundaries, even when nucleation at a grain boundary requires an irrational orientation relationship to obtain. Since the fully coherent boundary areas separating most linear misfit compensating defects are wholly immobile during diffusional growth because of the improbability of moving substitutional atoms even temporarily into interstitial sites under conditions normally encountered, partially and fully coherent interphase boundaries should be immovable without the intervention of growth ledges. These ledges, however, must be heavily kinked and usually irregular in both spacing and path if they, too, are not to be similarly trapped. On the other hand, the large shear strain energy usually associated with martensite requires that its formation be initiated through a process which avoids the activation barrier associated with nucleation, perhaps by the Olson-Cohen matrix dislocation rearrangement mechanism. During growth, certain ledges on martensite plates serve as transformation dislocations and perform the crystal structure change (Bain strain). However, the terraces between these ledges in martensite (unlike those present during diffusional growth) are also mobile during non-fcc/hcp transformations; glissile dislocations on these terraces perform the lattice invariant deformation. Growth ledges operative during both diffusional and shear growth probably migrate by means of kink mechanisms. However, diffusional kinks appear to be nonconservative and sessile (and therefore resist immediate transmission of elastic shear strain energy), whereas those associated with martensitic growth must be conservative and glissile (and fully transmit such strain energy). The broad faces of both diffusionally and martensitically formed plates contain an invariant line, as emphasized by Dahmen and Weatherly. However, in the diffusional case, minimization of growth ledge formation kinetics seems to be the main role thereby played, whereas in martensitic growth, the main purpose of such an interface is to minimize elastic shear strain energy. The latter minimization requires that martensite forms as plates (or perhaps as laths) enclosed by a pair of invariant line-containing interfaces. During diffusional transformations, on the other hand, other interfaces at which growth ledge formation kinetics are not too much faster than those at the invariant line interface can also comprise a significant portion of the interfacial area, thereby leading to the formation of other, quite different morphologies, such as intragranular idiomorphs and grain boundary allotriomorphs. Critical problems remaining unsolved in diffusional transformations include calculation of critical nucleus shapes when the crystal structures of the two phases are significantly different, highly accurate calculation of the energies of the interphase boundaries thus formed, and direct observation of atomic scale kinks on the risers of growth ledges by means of a yet-to-be-invented three-dimensional (3-D) atomic-resolution form of transmission electron microscopy. Experimental identification and characterization of transformation dislocations and experimental testing of “nucleation” mechanisms are now of special importance in fundamental studies of martensitic transformations.     

Mechanism of Al2CuLi (T 1) nucleation and growth

Conventional strain contrast transmission electron microscopy (CTEM) and high-resolution transmission electron microscopy (HRTEM) were performed to establish the nucleation and growth mechanism of Al₂CuLi (T₁) precipitates in an Al-Li-Cu alloy. It is shown that the growth mechanism ofT ₁ precipitate plates occurs by the diffusional glide of growth ledges composed of b = 1/6〈112〉 partial dislocations on 111 matrix planes and that the growth ledges migrate by the ledge-kink mechanism, as previously suggested by Cassadaet al. 1 for this system.T ₁ plate nucleation is modeled as the dissociation of a perfect b = 1/2〈110〉 matrix dislocation in the vicinity of a dislocation jog. The coordinated dissociation of the dislocation line segments on each side of the sessile jog provides the displacement necessary for the formation of a new hexagonal plate or plate ledge. Strain contrast analysis of the Burgers vector of plate edges and the edges of growth ledges indicates the stacking of partial dislocations is of mixed displacement. Formerly Graduate Student, Department of Materials Science, University of Virginia,     

On the role of interphase-boundary structure in plate growth by diffusional mechanisms

The structures of planar phase interfaces and of interfacial defects responsible for their diffusional migration are discussed in terms of extensions of the O-lattice concept, in which the intersection of the two structures is treated analytically. Two cases are considered and illustrated with well-characterized experimental examples: one in which two-dimensional structural matching leads to O-planes, and a second in which linear matching yields an array of O-lines. It is suggested that growth ledges moving normal to the O-lines will often require lateral kink formation and motion for their propagation. The misfit associated with transformation ledges is modeled in terms of real (screened) dislocations, which may coexist with virtual (unscreened) dislocations representing a residual component of misfit. A macroscopic shear can result from the cumulative action of transformation ledges with shear components parallel to the habit plane. This article is based0 on a presentation made at the Pacific Rim Conference on the “Roles of Shear and Diffusion in the Formation of Plate-Shaped Transformation Products,” held December 18-22, 1992, in Kona, Hawaii, under the auspices of ASM INTERNATIONAL’S Phase Transformations Committee.     

Interphase boundary structures associated with diffusional phase transformations in Ti-base alloys

Interphase boundary structures generated during diffusional transformations in Ti-base alloys, especially the proeutectoid α and eutectoid reactions in a β-phase matrix, are reviewed. Partially coherent boundaries are shown to be present whether the orientation relationship between precipitate and matrix phases is rational or irrational. Usually, these structures include both misfit dislocations and growth ledges. However, grain boundary α allotriomorphs (GBA’s) do not appear to develop misfit dislocations at partially coherent boundaries. Evidently, these dislocations can be replaced by ledges which provide a strain vector in the plane of the interphase boundary. The bainite reaction in Ti-X alloys produces a mixture of eutectoid α and eutectoid intermetallic compound. Both eutectoid phases are partially coherent with theβ matrix, and both grow by means of the ledge mechanism, though unlike pearlite the ledge systems of the two phases are structurally independent. Even after deformation and recrystallization, the boundaries between the eutectoid phases and theβ matrix, as well as between these phases, are partially coherent. Titanium and zirconium hydrides have partially coherent interphase boundaries with respect to theirβ matrix. The recent observation of ledgewise growth of γ TiH within situ high-resolution transmission electron microscopy (HRTEM) suggests that, repeated suggestions to the contrary, these hydrides do not grow by means of shear transport of Ti atoms at rates paced by hydrogen diffusion. This paper is based on a presentation made in the symposium “Interfaces and Surfaces of Titanium Materials” presented at the 1988 TMS/AIME fall meeting in Chicago, IL, September 25–29, 1988, under the auspices of the TMS Titanium Committee.     

Atomic structure of interphase boundary enclosing bcc precipitate formed in fcc matrix in a Ni-Cr alloy

The atomic structure of the interphase boundaries enclosing body-centered cubic (bcc) lath-shape precipitates formed in the face-centered cubic (fcc) matrix of a Ni-45 mass pct Cr alloy was examined by means of conventional and high-resolution transmission electron microscopy (HRTEM). Growth ledges were observed on the broad faces of the laths. The growth ledge terrace (with the macroscopic habit plane ) contains a regular array of structural ledges whose terrace is formed by the (111)_fcc//(110)_bcc planes. A structural ledge has an effective Burgers vector corresponding to an transformation dislocation in the fcc → bcc transformation. The side facet (and presumably the growth ledge riser) of the bcc lath contains two distinct types of lattice dislocation accommodating transformation strains. One type is glissile dislocations, which exist on every six layers of parallel close-packed planes. These perfectly accommodate the shear strain caused by the stacking sequence change from fcc to bcc. The second set is sessile misfit dislocations (∼10 nm apart) whose Burgers vector isa/3[111]_fcc =a/2[110]_bcc. These perfectly accommodate the dilatational strain along the direction normal to the parallel close-packed planes. These results demonstrate that the interphase boundaries enclosing the laths are all semicoherent. Nucleation and migration of growth ledges, which are controlled by diffusion of substitutional solute atoms, result in the virtual displacement of transformation dislocations accompanying the climb of sessile misfit dislocations and the glide of glissile dislocations simultaneously. Such a growth mode assures the retention of atomic site correspondence across the growing interface. formerly Graduate Student, Kyoto University, Kyoto 606-01, Japan This article is based upon a presentation made at the Pacific Rim Conference on the “Roles of Shear and Diffusion in the Formation of Plate-Shaped Transformation Products,” held December 18–22, 1992, in Kona, Hawaii, under the auspices of ASM INTERNATIONAL’S Phase Transformations Committee.     

Intrinsic ledges at interphase boundaries and the crystallography of precipitate plates

The structure of intrinsic ledges at interphase boundaries has been interpreted with extended O-lattice/DSC-lattice approaches. The distribution of structural ledges can be predicted if the spacing difference between parallel matrix and product planes is treated as a measure of the relaxed coincidence condition. A small rotation away from the low-index planar parallelism introduces a series of interfacial dislocations that cancels the spacing difference, resulting in a lattice invariant line. Misfit-compensating ledges at bcc: hcp interfaces are produced as a ledged interface intersects additional O-points that are recognized with the incorporation of previously omitted bcc atom positions into the O-lattice construction. Energetic consideration suggests that structural interfacial energy may decrease when a flat interface becomes ledged with misfit-compensating ledges. Burgers vectors associated with structural ledges and misfit-compensating ledges are displacement shift complete (DSC) lattice vectors. Precipitate and martensite crystallography may both include a lattice invariant line, but they are involved in different interphase boundary characteristics. Assumptions and implications in precipitate and martensite crystallography are discussed in the framework of the O-lattice theory and phenomenological theory of martensite crystallography. This article is based on a presentation made at the Pacific Rim Conference on the “Roles of Shear and Diffusion in the Formation of Plate-Shaped Transformation Products,” held December 18-22, 1992, in Kona, Hawaii, under the auspices of ASM INTERNATIONAL’S Phase Transformations Committee.     

Some observations of grain boundary ledges and ledges as dislocation sources in metals and alloys

Direct observations of grain boundary ledges have been made in annealed Ni, Al, Cu, Mo, Ta, Ir, 304 Stainless Steel and Inconel 600 by transmission electron microscopy. Grain boundary ledges have been observed to be sources of dislocations during and after plastic deformation, and to resemble the appearance of dislocation pileups in the transmission electron microscope. Ledge density (number per unit length of grain boundary) has been observed to increase with an increase in grain boundary misorientation in Ni and 304 Stainless Steel, and the distribution of misorientations was observed to be continuous over the range 0 deg <θ< 90 deg at an annealing temperature of 1060°C. The mean grain boundary misorientation in 304 Stainless Steel was also observed to decrease with a decrease in the recovery temperature following cold reduction and to vary from 10 to 45 deg in the temperature range of 660 to 1060°C. An essential point of this investigation is that Li’s theoretical treatment of the flow-stress, grain-size relation based on the existence of grain boundary ledges and their action as sources of dislocations under stress is shown to be correct.     

The role of structural ledges as misfit- compensating defects: fcc-bcc interphase boundaries

An energetic justification is given for structural ledges as interfacial misfit compensating defects, based on elastic considerations. We detail the NW-x configuration in which the orientation is imposed by close matching along the (21 l)fcc and (110)bcc directions and (111) fcc and (110) bcc planes, respectively. Special prominence is given to the terrace between structural ledges, where it is shown that an elastic relaxation obtains at specific terrace lengths based on atomic matching. It is this relaxation that makes a stepped interface more stable than a planar one at all meaningful values of misfit. This article is based on a presentation made at the Pacific Rim Conference on the “Roles of Shear and Diffusion in the Formation of Plate-Shaped Transformation Products,” held December 18-22, 1992, in Kona, Hawaii, under the auspices of ASM INTERNATIONAL’S Phase Transformations Committee.     

Ledges and dislocations in phase transformations

The coupling of dislocations and ledges in phase transformations is considered in terms of the symmetry of phases meeting at an interface. Growth and structural ledges and a variety of dislocation arrays are treated. Symmetry and the absence of long-range strain fields alone are shown to produce few restrictions on possible interface structures. This article is based on a presentation made at the Pacific Rim Conference on the “Roles of Shear and Diffusion in the Formation of Plate-Shaped Transformation Products,” held December 18-22, 1992, in Kona, Hawaii, under the auspices of ASM INTERNATIONAL’S Phase Transformations Committee.     

Electron microscopy of transformation dislocations at interphase boundaries

The concept of structural units (SU’s) developed in order to describe the atomic structures of twin boundary facets is also used for interphase boundary (IB) facets quasi-parallel to small near-coincident planar cells of the two adjacent lattices. These facets, which have their own SU’s, are separated by transformation dislocations (TD’s), the cores of which are often related to ledges having heights equal to several interplanar spacings. It is shown that the Somigliana dislocation (SD) concept is a good tool for the computation of elastic displacement fields of these TD’s in anisotropic elasticity. Applications are presented concerning the following IB’s observed in high-resolution transmission electron microscopy (HRTEM): Si/TiSi₂, Si/CoSi₂, and Ni₃Al/Ni₃Nb. The identification of the atomic rows around some TD’s at Si/CoSi₂ and Ni₃Al/Ni₃Nb has been obtained by careful comparisons of experimental and calculated images. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Comparison of interfacial structure-related mechanisms in diffusional and martensitic transformations

Some central problems in understanding the similarities of and the differences between ledgewise martensitic and ledgewise diffusional growth are examined. Martensitic growth can be described in terms of a lattic correspondence and a plane undistorted by the shear transformation. Diffusional growth can be similarly described in some cases but not in others. On the basis of the Sutton-Balluffi definitions of glissile and sessile boundaries, only misfit dislocations (on terraces or risers) or orthogonal sets of disconnections provide a truly sessile interface. When closely spaced structural ledges (now termed “structural disconnections”) are present during diffusional growth, they must have been glissile in the formation of a local equilibrium structure during the initial stages of growth. Once they are in local equilibrium and evenly spaced, however, they can only move synchronously because of their local strain interaction. Under these circumstances, extrinsic sources of growth ledges are required to move such interfaces in a diffusional manner. During martensitic growth, however, disconnections in the form of transformation dislocations can move freely in a synchronous manner. Also, on this basis, the apparent (undistorted) habit plane is generally useful in deducing the transformation mechanism during martensite formation, but is only occasionally so during diffusional growth, where only the terrace plane is generally useful. This article is based on a presentation in the symposium “Interfacial Dislocations: Symposium in Honor of J.H. van der Merwe on the 50th Anniversary of His Discovery,” as part of the 2000 TMS Fall Meeting, October 11–12, 2000, in St. Louis, Missouri, sponsored under the auspices of ASM International, Materials Science Critical Technology Sector, Structures.     

Interfacial ledge structures in Ni3 Al-Ni3Cb eutectic composites

The interfacial structure of Ni₃Al-Ni₃Cb directionally solidified eutectic composites has been investigated by transmission electron microscopy. These interfaces contain at least three distinguishable arrays of features. Two of the arrays, misfit dislocations, have been discussed previously by Nakagawa and Weatherly. The third set, ledges which can fulfill both structural and kinetic growth functions, may interact with the dislocation arrays through strain-energy mechanisms. The interaction is manifested both as a local alteration of the line vector of the dislocation in certain circumstances, and as a change in the response of the dislocation image to ±g electron-microscope image-contrast experiments. A simple model of the strain field of a ledge based on that of an edge dislocation is formulated to rationalize the behavior of a misfit dislocation lying in close proximity to a ledge. The interaction of ledges and dislocation segments is expected to have significance in physical processes of practical interest such as production of matrix slip dislocations, misfit dislocation rearrangement, boundary sliding, and coarsening, and these processes are discussed in some detail.     

Thickening of grain-boundary α allotriomorphs in a Ti-Cr alloy by multiple sets of ledges

A computer model is developed to simulate the growth of grain-boundary allotriomorphs having more than one set of growth ledges at their interfaces. The growth is controlled by the volume diffusion of solute to or from the riser of a ledge. The time dependence of the growth rate of two orthogonal sets of ledges is found to be somewhat different from that of a single set of ledges. However, the operation of multiple sets of ledges is unlikely to alter significantly the growth kinetics of grain-boundary allotriomorphs from those predicted from the disordered growth theory, except at small ledge spacings or at short reaction times. Faster growth kinetics of proeutectoid α allotriomorphs than those of either planar or ellipsoidal disordered boundaries which have been reported in a Ti-6.6 at. pet Cr alloy are not likely to be accounted for with the heights and spacings of double sets of ledges actually observed on the interfaces of allotriomorphs. Hence, the grain-and interphase-boundary diffusion-assisted growth of precipitates, (rejector plate mechanism, RPM) appears to be operative during the growth of a allotriomorphs, as previously proposed on the basis of growth-rate measurements. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

General existence of ledges on α1 plates in Cu-Zn-Al alloys

A transmission electron microscopy (TEM) study was made of the interphase boundary structure between the matrix and α₁ plates formed at 250 °C, 300 °C, and 350 °C in three Cu-Zn-Al alloys. The experiments showed that the α₁ plates formed at each temperature studied in all of the alloys are initially free of stacking faults. This observation, confirming the results of previous investigations, shows that these plates cannot have formed by a shear mechanism. Ledges were shown to exist on the broad faces and/or at the growth edges of the α₁ plates. Indirect evidence implies that the ledges are mobile and that they can migrate along different directions on the broad faces.     

Atomic mechanisms of precipitate plate growth in the AlAg system—II. High-resolution transmission electron microscopy

High-resolution electron microscopy was used to study the interfacial structure of γ′ precipitates in an Al-15 wt% Ag alloy aged at 350°C. The results of these studies show that:

• 1.(1) all ledges are multiples of two {111} planes high, supporting the theory and conventional transmission electron microscopy observations that plate thickening occurs by passage of Shockley partial dislocations on alternate {111} planes
• 2.(2) most ledges are more than just two planes high, indicating a strong tendency toward diffusional and/or elastic interactions
• 3.(3) the terraces between ledges are atomically flat and ledges are uniformly stepped-down from the centers to the edges of isolated precipitates as predicted by the general theory of precipitate morphology
• 4.(4) the {111} planes are continuous across the edges of ledges, indicating that they are largely coherent and not disordered as treated in most kinetic analyses, and
• 5.(5) the edges of precipitate plates appear to be composed of similar two-plane ledges arranged vertically above one another and hence, may grow by the same mechanism of atomic attachment as ledges on the broad faces.

Examination of γ′ plates during early stages of growth indicates that their aspect ratio may deviate from the equilibrium value almost immediately, probably due to the ledge mechanism of growth. Lastly, an atomic model of a γ′ precipitate was used to test the high-resolution images obtained, and illustrate possible atomic growth mechanisms of the ledges.     

Dislocation structure in a single-crystal nickel-base superalloy during low cycle fatigue

An investigation of dislocation structure in a single crystal nickel-base superalloy during low cycle fatigue (LCF) at 760 °C has been conducted. Dislocation bands are found to be produced first in the matrix in some defined directions. With an increase in cycle numbers, there is an increase in dislocation density in the bands and a decrease in the spacing between the bands, leading to the formation of the dislocation walls or cells. Sometimes, three-dimensional (3-D) networks are formed also by the interaction between two sets of parallel dislocations. The Burgers vectors of the dislocations in the network are 1/2 〈110〉. Clustering of dislocations eventually occurs at γ′/γ interfaces because of the obstruction of the γ′-particles to moving dislocations. Most of the dislocations observed in the γ′-phases are in the form of superdislocations. Dislocation shearing through theγ′-phase was found occasionally. Reprecipitation of γ′-phase induced by strain was also observed in the present study.     

Structural ledges in interphase boundaries

This article addresses the properties of stepped misfitting interfaces and their energetic preference to planar misfitting interfaces. It highlights: (a) the purely geometrical or rigidlike, (b) the rigid (unrelaxed) energetic, and (c) the relaxed energetic properties of stepped interfaces. In (a), we address (1) the accommodation of misfit by the step or ledge mode through the cancellation of the mismatch, that builds up along a terrace, by the forwardpattern advance effected by a step,i.e., the relative displacement of atomic patterns on either side of the interface as observed in crossing a structural ledge along the interface, (2) the sideways (shear) pattern advance which seems to be energetically undesirable, (3) the need for tilt-type misfit dislocations to accommodate the misfit normal to the interface, and (4) the fact that at {III}_fcc(face-centered cubic)/{110}_{bcc(body-centered cubic) interfaces with rhombic symmetries, the misfits, as well as the pattern advances, are interrelated through the ratior = b/a of nearest-neighbor distances in the crystals. In (b), we exploit the rigid model approach that (1) yields ideality criteria for minimum energy and provides energetic justification for the step mode of misfit accommodation, (2) confirms that the average terrace widthl[inx} defined by this mode also meets the condition for positive energy gain, and (3) defines the upper and lower energy bounds to provide a perspective of the system energetics. In (c), the foregoing considerations are refined by a transition to the harmonic (elastic) model to yield (1) the dependence of the mean energy per atom of a stepped interface on interfacial misfit and pattern advance, as well as the dependence of the mean energy per atom of a planar interface on misfit, (2) expressions for the stresses related to the atomic interaction between opposing terraces, (3) atomic displacements that might be probed by modern analytical techniques, and (4) resolved shear stresses and normal stresses that may facilitate the formation of glide dislocations in the presence of applied stresses. The boundary in a two-dimensional space—spanned by misfit and pattern advance—between regions where stepped interfaces are more stable than planar ones has been determined, suggesting that a critical misfit exists above which only planar interfaces are stable. Whereas the resolved shear stress related to the formation of structural ledges may facilitate the formation of dislocations in the presence of a subcritical applied stress, the corresponding displacements (bending) of atomic planes are probably observable only with strain contrast electron microscopy techniques. Formerly with the Physics Department, University of Pretoria. Formerly Visiting Scientist, Physics Department, University of Pretoria, Pretoria, South Africa. This paper is based on a presentation made in the symposium “The Role of Ledges in Phase Transformations” presented as part of the 1989 Fall Meeting of TMS-MSD, October 1–5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL.     

Crystallographic and mechanistic aspects of growth by shear and by diffusional processes

Growth by shear and by diffusional processes, both taking place predominantly by means of ledge mechanisms, are reviewed for the purpose of distinguishing critically between them at the atomic, microscopic, and macroscopic levels. At the atomic level, diffusional growth is described as individual, poorly coordinated, thermally activated jumps occurring in the manner of biased random walk, whereas growth by shear is taken to be tightly coordinated “glide” of atoms to sites in the product phase which are “predestined” to within the radius of a shuffle. Obedience to the invariant plane strain (IPS) surface relief effect and the transformation crystallography prescribed by the phenomenological theory of martensite is shown to be an unsatisfactory means of distinguishing between these two fundamentally different atomic growth mechanisms. In substitutional alloys, continuous differences in compositionand in long-range order (LRO) from the earliest stages of growth onward are concluded to be the most useful phenomenological approach to achieving differentiation. At a more fundamental level, however, the details of interphase boundary structure are the primary determinant of the operative mechanism (when the driving force for growth is sufficient to permit either to occur). In the presence of a stacking sequence change across the boundary, terraces of ledges are immobile irrespective of their structural details during diffusional growth. Kinks on the risers of superledges are probably the primary sites for diffusional transfer of atoms across interphase boundaries. In martensitic transformations, on the other hand, terraces containing edge dislocations in glide orientation or pure screw dislocations are mobile and accomplish the lattice invariant deformation (LID), though probably only after being overrun by a transformation dislocation. Risers associated with transformation dislocations are also mobile and cause the crystal structure change during growth by shear. The successes achieved by the invariant line (IL) component of the phenomenological theory of martensite in predicting precipitate needle growth directions and precipitate plate habit planes (Dahmen and co-workers) are here ascribed to the rate of ledge formation usually being a minimum at an interface containing an IL, primarily because nuclei formed sympathetically at this boundary orientation are likely to have the highest edge energies. Since martensite plate broad faces also contain the IL, the ability of the phenomenological theory to predict the habit plane and the orientation relationships of both precipitate and martensite plates is no longer surprising. The IPS relief effect at a free surface can be generated by precipitate plates when growth ledges are generated predominantly on only one broad face and only one of several crystallographically equivalent Burgers vectors of growth ledges is operative. Both pReferences probably result from larger reductions in transformation strain energy for the particular geometry with which a given plate intercepts the free surface. Precipitate morphology often differs significantly from that of martensite even if precipitates are plate-shaped and can readily differ very greatly. Whereas martensite morphology is determined by the need to minimize shear strain energy, that of precipitates derives from the more flexible base of the interphase boundary orientation-dependence of the reciprocal of the average intergrowth ledge spacing, as modified by both the orientation-dependence of interkink spacing on growth ledge risers and the spacing/ height ratio dependence of diffusion field overlap upon growth kinetics. This paper is based on a presentation made in the symposium “Interface Science and Engineering” presented during the 1988 World Materials Congress and the TMS Fall Meeting, Chicago, IL, September 26–29, 1988, under the auspices of the ASM-MSD Surfaces and Interfaces Committee and the TMS Electronic Device Materials Committee.     

Kinetics of solution hardening

The flow stress of solution hardened single crystals and polycrystals is analyzed with respect to its dependence on temperature and strain rate. An evaluation of literature data, especially at low temperatures and low concentrations in fcc alloys, reveals that the interaction between dislocations and discrete, atomic-sized obstacles (or fixed clusters of them) cannot be responsible for solution hardening. A “trough” model is favored in which the effect of the solutes is postulated to be equivalent to a continuous locking of the dislocations along their entire length, during every waiting period. The macroscopic features of this model are similar to Suzuki’s chemical-hardening model. It can also explain the strong interaction of solution hardening and strain hardening at elevated temperatures, as well as basic features of dynamic strain-aging, in particular its strain dependence. This paper is based on a presentation made at the symposium “50th Anniversary of the Introduction of Dislocations” held at the fall meeting of the TMS-AIME in Detroit, Michigan in October 1984 under the TMS-AIME Mechanical Metallurgy and Physical Metallurgy Committees.     

Crystallographic theories,interface structures,and transformation mechanisms

The structure and properties of an idealized planar interface that traverses a single crystal of the parent phase are first discussed. A (macroscopic) coherent interface is defined in terms of a relatively coarse-grained Larché-Cahn network related to the observed shape deformation. Reconstructive and displacive transformations are distinguished, and a new category of “ diffusional-displacive” transformations is introduced. The crystallographic theory of martensite requires that the habit plane interface is atom conserving (or “glissile”), but nonconservative (”epitaxial”) interfaces may form in some diffusional-displacive transformations. A modified Eshelby procedure is used to discuss the strain energy of particles of a new phase forming, by any mechanism, inside a constraining matrix. It is shown that the effective Burgers vector of a step (or ledge) in a fully or partly coherent interface is dependent on the parameters of the shape deformation and increases with the ledge height. Multiple height ledges (”superledges”) should only be observed if their fields have been effectively neutralized, either by averaging over displacement directions that are spatially distinct but crystallographically equivalent or by combining with lattice dislocations through processes essentially equivalent to emissary slip or climb. In the latter case, the shape discontinuity is effectively transferred from the interface into the matrix or to a surface. The use of invariant line theories and the concepts of growth, structural, and misfit ledges are also examined. This article is based on a presentation made at the Pacific Rim Conference on the “Roles of Shear and Diffusion in the Formation of Plate-Shaped Transformation Products,” held December 18-22, 1992, in Kona, Hawaii, under the auspices of ASM INTERNATIONAL’S Phase Transformations Committee.