Structures in irrational singular interfaces
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I. INTRODUCTION
A large number of crystalline interfaces formed from precipitation transformations exhibit a strong tendency for faceting. According to a recent review, most observed facets are parallel to low index planes of both phases, especially when a ceramic phase is involved.[1] These facets are usually considered reasonable, since they are in accord with expected facets of a crystal surface.[2] However, a large number of experimental observations (mostly from metallic materials) have also revealed reproducible facets or broad interfaces (habit planes) that are not parallel to any low index plane in either one or both crystalline phases.[3–10] This type of interfaces is often referred to as irrational interfaces because their indexes cannot be expressed exactly by small integers on the basis of either crystal phase. They are often strictly flat over a considerably large dimension (e.g., 100 nm) and possess a unique orientation, though it is recognized that they must consist of steps on the atomic scale. Consistent observations of facets in special and discrete orientations suggest that these facets must be favored by nature and possibly associated with a local minimum of interfacial energy. Their formation may be attributed to the nucleation process in which a low-energy interface is selected.[11] Verification of this energy argument requires determination of the interfacial energy of a relaxed structure, as a function of the five variables that constrain the macroscopic geometry of W.-Z. ZHANG, Professor, and D. QIU and X.-P. YANG, Doctoral Candidates, are with the Department of Materials Science and Engineering, Tsinghua University, Beijing, 100084, P.R. China. Contact e-mail: zhangwz@ tsinghua.edu.cn F. YE, formerly Doctoral Candidate, Department of Materials Science and Engineering, Tsinghua University, is Postdoctoral Fellow with the Eco-Materials Center, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki, 305-0044, Japan. This article is based on a presentation made in the “Hume-Rothery Symposium on Structure and Diffusional Growth Mechanisms of Irrational Interphase Boundaries,” which occurred during the TMS Winter meeting, March 15–17, 2004, in Charlotte, NC, under the auspices of the TMS Alloy Phases Committee and the co-sponsorship of the TMS-ASM Phase Transformations Committee. METALLURGICAL AND MATERIALS TRANSACTIONS A
the interface. At present, a sophisticated calculation of interfacial energy variation in five dimensions (5D) for a given material system remains a challenging task. However, researchers have successfully rationalized many observations of reproducible irrational habit planes or prominent facets using geometric models. These models usually evaluate the degree of matching in an interface as an indication of energy. The fcc/bcc system is the most extensively studied system, both for its simplicity and its broad application. A pioneer investigation was made by Hall et al.,[12] who proposed a structural ledge model to account for the observed irrational habit plane
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