On the role of elastic interactions in the nucleation and growth of ledges
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I.
INTRODUCTION
IN this contribution, we consider the influence of elastic interactions among growth steps on otherwise planar faces of precipitates. At the outset, it is noted that elastic terms are generally much smaller than the chemical terms in the overall free energy balance, and that, consequently, these elastic interactions may often be masked. Exceptions occur in processes which occur close to equilibrium, like nucleation and coarsening, and we will demonstrate that in these and similar cases, the elastic terms are capable of determining a number of important aspects of the reaction. Considering the interactions of straight parallel steps, two types of misfit are defined: one perpendicular and one parallel to the habit plane. The elastic fields of these two misfits are each modeled using an array of "fictitious" dislocations (each of which is used as a "Green's function" to model the elastic misfit). It is shown that like steps of the same parallel misfit attract and will tend to coalesce, while steps of like sign of perpendicular misfit repel. Although growth ledges have been observed in a large number of solid-solid precipitation systems, those found on the broad faces of 0' plates in A1-Cu alloys (where the misfit is perpendicular to the habit plane) have received perhaps-the greatest level of scrutiny, and we begin with a review of some of their properties. The energetics of nucleation of pillboxes on the faces of 0' plates is considered, and the magnitudes of the elastic energies are compared with those of the chemical and surface terms.
L.M. BROWN is with the Department of Physics, University of Cambridge, Cambridge, United Kingdom. J.R. DRYDEN is with the Department of Materials Engineering, University of Western Ontario, London, ON, Canada, V. PEROVIC is with Ontario Hydro Research Laboratory, Toronto, ON, Canada. G.R. PURDY is with the Department of Materials Science and Engineering, McMaster University, Hamilton, ON, Canada. 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 Transformation Committee of the Materials Science Division, ASM INTERNATIONAL. METALLURGICAL TRANSACTIONS A
The height and location of the pillboxes are set upon nucleation; their interaction may persist during growth. This possibility will be discussed next, with special attention paid to the elastic coupling between a growth ledge and a precipitate edge. An analysis to find the elastic interaction force between steps where the misfit is parallel to the habit plane is then presented. The dynamics of coalescence in t h e formation of superledges is developed and the stability of the faceted interface explored. II. PROPERTIES OF GROWTH LEDGES ON 0' PRECIPITATES IN AI-Cu The broad faces of the platelike 0' precipitates formed in dilute A1-Cu alloys are often found to be fully coherent; the misfit in the plane of the interface is very small, with
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