The role of structural ledges as misfit- compensating defects: fcc-bcc interphase boundaries
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I.
INTRODUCTION
THIS article will review, extend, and elucidate our previous work on fcc:bcc interfaces containing linear defects that accommodate misfit. IJ-6j Emphasis in our analysis will be placed on consideration of the relative energy savings by inclusion of structural ledges t71 as a misfit-compensating defect. However, rather than duplicate extensive mathematics that has already been published for the fcc:bcc interface in our previous efforts, we will discuss certain aspects of the theory, to make clear the advantages of such an approach toward understanding the energetics of interfacial structures. A large portion of this article will be concerned with the terraces between structural ledges. We will consider a rigid lattice calculation as well as allow the interface to relax elastically. As the interfacial atomic planes of the most studied interfaces have rhombohedral symmetry this will be dealt with here; rectangular meshes have been addressed in earlier papers Lt-4J and differ only in the symmetry of the interaction potential. A. The {l l l}fcc-{l lO}bcc Interface The {lll}fcc closed packed surface interacting with the {ll0}bcc surface at azimuthal orientation of current interest is shown in Figure 1, which is a "map" of the relative energetics of the primary fcc:bcc orientation relationships.~Sl In this figure, the azimuthal rotations vary from 0 = 0 to 18 deg, with the rotation relative to the Nishiyama-Wasserman (NW) orientation placed at 0 deg; r is the ratio of nearest neighbor atoms, b/a, see (Figure 2(a)). Although a larger angular range would illustrate other energy minima, this is sufficient to highlight the two most commonly observed fcc:bcc orientation relationships. The deep minima corresponding to NW [9,101 and Kurdjumov-Sachs (KS) t~lJ (r = ra = 1.09, 0 = G.J. SHIFLET, William G. Reynolds Professor, is with the Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903. J.H. VAN DER MERWE, Professor, is with the Department of Physics, University of South Africa, Pretoria 0001, Republic of South Africa. 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
5.26 deg) orientation relationships are indicated. The NW is further divided into NW-x (r = rx = 0.94, 0 = 0) and NW-y (r = ry = 1.15, 0 = 0), where atomic matching is in the x or y direction, respectively. A plot of the overlapping rhombuses is shown in Figure 2(a). Here, the various parameters used to construct Figure 1 are shown geometrically. By varying r and 0, the geometric patterns associated with the NW and KS relationships can be mapped out (Figures 2(b) through (d)). This can be understood by comparing Figure 1 with the atomic sketches in Figures 2(b) and (c) for the NW-x and -y, respectively, and Figure 2(d) for
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