The motion of multiple height ledges and disconnections in phase transformations
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I.
INTRODUCTION
INTERFACIAL defects are known to exhibit step- or ledgelike character, dislocation character, or both.[1,2,3] The combined defect has been defined as a disconnection,[4] consistent with a general treatment of the crystallographic theory of connectivity at interfaces.[5] A scheme for formally defining the Burgers vector and ledge height has been presented[6] in terms of the description of the interface by means of the dichromatic complex of interpenetrating crystal lattices.[7,8] Interfacial defects have been classified on the basis of this description.[9] In essence, if one imagines the two crystals adjoining an interface containing a disconnection to be separated, the disconnection will be eliminated, splitting into two defects, free-surface ledges, one on each crystal. The overlap in positions of the ledge tops of the two ledges relates to the height of the ledge component of the disconnection and the differences in position of the ledge tops to the Burgers vector of the dislocation component.[6] A simple example following Reference 6 is shown in Figure 1. Free surface ledges on crystals m and l are represented in terms of a sense vector j and a surface normal n by translation vectors t(m) and t(l), indicating the translation of the surface from the bottom to the top of the ledge. If j or n were reversed in sign, then the signs of t(m) and t(l) would also be reversed. When the free surfaces are brought together as shown, part of the ledges overlap but a gap remains. The vertical overlap of the ledges is the interfacial ledge height h. When the gap is closed, the vertical separation of the gap becomes the normal component bn of the Burgers vector of the resulting dislocation as depicted. With respect to the classification of interfacial dislocation types,[3,9–13] the dislocations can include translational- and transformation-type character and may or may not require climb if the disconnection were to translate along a terrace on the interface. The elastic interaction energy among disJ.P. HIRTH and R.G. HOAGLAND, Professors, are with the School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99614-2920. R.J. KURTZ, Scientist, is with Battelle Pacific Northwest National Laboratories, Richland, WA 99352. This article is based on a presentation made in the symposium ‘‘Kinetically Determined Particle Shapes and the Dynamics of Solid:Solid Interfaces,’’ presented at the October 1996 Fall meeting of TMS/ASM in Cincinnati, Ohio, under the auspices of the ASM Phase Transformations Committee. METALLURGICAL AND MATERIALS TRANSACTIONS A
connections with dislocation components can either tend to prevent, via long-range repulsion, coalescence into multiple atom layer height ledges or to promote creation of multiple height ledges by short-range attraction.[14] In the case of diffusional growth, the elastic interaction modifies the dependence of ledge velocity on step spacing and, thereby, can either promote or deter the formation of multiple height ledges, depending on the spe
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