Ledges and dislocations in phase transformations
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I.
INTRODUCTION
S T E M M I N G from the work of Gibbs, tlj Kossel, 121 Stranski, t31 and Burton et al. t4] on the role of ledges in crystal growth from the vapor, ledge models have been developed for a variety of diffusional and diffusionless phase transformations in crystalline solids. The concept of structural ledges, introduced to minimize the interfacial free energy, has also appeared, tSJ In many cases, interfacial dislocations are associated with the ledges and an extensive literature has evolved in the description of the ledge/dislocation interactions as reviewed and discussed in References 6 through 12. These concepts are related to the prediction of the habit plane and orientation relationship of two adjoining phases. The general guidelines to such theories are that the mechanism of transformation should be simple (ledges, dislocations, shuffles) and that the habit planes should have low interfacial free energy. In turn, low interfacial free energy has been associated with favorable lattice matching at the interface. The theories broadly fall into three categories. The first, based on the phenomenological theory t~3,~41of martensite formation, is the invariant line theory. 05'16'171 The second is the theory of structural ledges, t5'~8,~91which minimizes the atom mismatch in the sense of broken bonds at the interface. The third derives from the concepts of the O-lattice model tz~ and of the coincidence site lattice and displacement shift complete models. [6'8,91 A recent symmetry theory developed by Pond t221 and based on the union of the crystal symmetry of the two crystals, i.e., the dichromatic complex, provides a general description of defects, faults, and habit planes that, in some cases, reduces to the above lattice models. A succinct comparison of these theories, except for the latter, is provided by Smith and Shiflet t23j and by Howe and Smith, I24] a treatment that is the starting point for the present work. Here, we focus on the equilibrium dislocation structure for interfaces, including those containing ledges. In some cases, this leads to the expectation of deviations from a simple habit plane and orientation relationship. We first review salient features of grain boundary theory and then turn to dislocation/ J.P. HIRTH, Professor, is with the Department of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920. 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. METALLURGICAL AND MATERIALS TRANSACTIONS A
ledge structures for several classes of interfaces, consider ledge bunching, and show that second-order coherency effects can exist. We follow many earlier workers and treat interfaces that are, on the average, planar and with unidirectional ledge/dislocation structures. The latter restriction is removed in some instances
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