A comparison between three simple crystallographic principles of precipitate morphology
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I.
INTRODUCTION
THE morphology of precipitates in a solid matrix is of fundamental importance in materials science. Underlying most investigations of microstructures and their development is the assumption that the shape, orientation relationship, and interface structure of a product forming in a parent phase are interlinked. However, the nature of this link is not well understood, and morphological prediction is of limited success. It is generally implied that the link lies in the mechanism of strain accommodation, either during nucleation or in the process of coherency loss or growth, t~'2] Yet, for most cases, there is still no clear and simple relationship between the crystallographically observable features of a solid inclusion and its mechanism of formation. A notable exception is the phenomenological theory of martensitic transformations (e.g., Reference 3), which has been remarkably successful in many of its predictions. However, its application is limited to inclusions that are dominated by a single planar, glissile interface, and to cases where diffusion is negligible, so that an atomic correspondence is maintained during transformation. Most inclusions do not fulfill these conditions, since diffusion prohibits an atom-by-atom correspondence, and interfaces are neither constrained to be glissile nor to be planar. In fact, inclusions are found in a great variety of shapes and orientations, depending on crystal structure and transformation conditions. Since no atomic (as opposed to lattice) correspondence can be maintained during bainitic or diffusional transformations, one might expect random shapes and orientations, determined only by the parameters governing diffusion. Instead, most diffusional transformation products adhere to well-defined orientation relationships and exhibit a narrow range of shapes. In fact, a large U. DAHMEN, Senior Scientist and Director, is with the National Center for Electron Microscopy, Lawrence Berkeley Laboratory, Berkeley, CA 94720. 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
number of common precipitation systems form plateshaped inclusions similar to those of martensitic transformation products t41 which offer themselves readily to application of the concepts of martensite crystallography, regardless of their formation mechanism. Such attempts have often met with some degree of success, t5'61 showing that a lattice correspondence can be maintained during precipitation reactions. Other evidence for a lattice correspondence in a diffusional transformation was shown by Ryder and Pitsch, t71 who observed a limited range of orientation relationships during precipitation in a Co-Fe alloy. More recently, detailed studies have shown that many precipitation systems exhibit a single preferred ori
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