Interface dislocations and ledges in oxidation and diffusional phase transformations
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I.
INTRODUCTION
THE notion of crystal growth by a ledge mechanism for growth of a crystal from a fluid was anticipated by Gibbs, Ill who presented a qualitative discussion of growth by two-dimensional nucleation. Geometrical details of crystal growth from the vapor by a ledge mechanism were presented by Kossel t21 and Stranski [3] in what has come to be known as the "terrace-ledge-kink" or ~T-L-K" model (Figure I). Reversible work considerations show that kinks are both the sites of atomistic growth and dissolution and, usually, sites of local equilibrium of adsorbed or vapor species with the solid. Together with Frank's postulate t4] of growth spirals associated with screw dislocations at a free surface, this model provided the basis for a detailed kinetic analysis of crystal growth t~] that was later extended to dissolution, t61 A key feature of these analyses is that structural interface control of the processes occurs when the kink spacing or ledge spacing exceeds the respective mean free paths of adsorbed atoms (molecules) on ledges or on terraces. As revealed, for example, by atomistic computer simulations{71 or calculations, is1 the rigid block picture of Figure 1 is too formal, and there are local relaxations of atoms in terraces, ledges, and kink sites such that the local atomic spacings differ from bulk values. The deviations are generally by a small fraction of an atomic spacing. If one imagines welding another crystal with similar surface structure to that in Figure 1, one sees that the same qualitative picture of growth applies to solid-solid crystalline transformations. The vapor ledges can become ledges and/or dislocations at the interface; the surface kinks become kinks in steps or jogs in dislocations; and the terraces become regions of coherent or partially coherent interface. A model for such growth was suggested by Aaronson, t9] and growth ledges were observed on precipitates in A1-Ag alloys. 0~ There have since been many observations of ledge growth during solid-state precipitation, although recent work t'1,12] has demonstrated the importance of macroledges with epitaxial or semicoherent risers as well as monatomic height ledges. J.P. HIRTH, Professor, is with the Materials and Mechanical Engineering Department, Washington State University, Pullman, WA 99164-2920. 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. METALLURGICAL TRANSACTIONS A
Here, we first discuss the dislocation and ledge structure of interphase interfaces and then apply the concepts to the interface kinetics during oxidation of a metal. Some of the concepts are then extended to solid-state diffusional phase transformations.
H.
DISLOCATIONS AND STEPS
The physical structure of dislocations and ledges at interfaces is now clear. However, as discussed extensively by
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