Invariant Deformation Element Model Interpretation to the Crystallography of Diffusional Body-Centered-Cube to Face-Cent
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INTRODUCTION
IN recent decades, many rival models were developed to account for the crystallography of the products of phase transformations. The most notable one is the phenomenological theory of martensite crystallography.[1,2] A concept of phase transformation invariant plane is the connection between martensite and austenite in a nondiffusion phase transformation. An invariant plane can be regarded as such a plane containing two invariant lines (ILs). If a habit plane (HP) of a precipitation system contains only one IL, the transformation system is a kind of diffusion phase transformation. There has been much effort devoted to finding a powerful and generalized theory for crystallography of precipitation in terms of the phenomenological crystallographic model. The earliest one is the phase transformation IL concept, which was proposed by Dahmen[3] and has been extensively applied for explanation of diffusion phase transformations.[4,5] The IL model lends a rational explanation to most crystallographic characteristics of precipitation systems including three facets, long axis (or IL), and orientation relationship (OR). However, the IL model cannot resolve the dislocation structure in a HP, multiple orientation relationship (multi-OR), or precipitation in a complicated precipitation system. Based on the O-lattice concept, which was developed from the coincident site lattice (CSL) and displacement shift complete (DSC) lattice,[6] the O-line model was implied by Zhang and Weatherly[7] and systematically used for interpretation of multi-OR and dislocation structure. Besides the preceding phenomenological HONGWEI LIU, GUANGCAI SU and JIANMIN ZENG, Professors, and WEIZHOU LI and ZHILIU HU, A/Professors, are with the School of Materials Science and Engineering, Guangxi University, Nanning 530004, P.R. China. Contact e-mail: microscopy. [email protected] JIANGWEN LIU, Professor, is with the School of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, P.R. China. Manuscript submitted May 5, 2011. Article published online June 6, 2012 3636—VOLUME 43A, OCTOBER 2012
theories, other geometric theories were also developed, such as the topological model for interface defects,[8] which discussed mainly dislocation and disconnection in the interface area, structural ledges,[9] the edge-to-edge matching model,[10–12] the planar interphase boundary migrating mechanism (Moire´ fringe mechanism),[13] and the invariant deformation element model (IDE model) developed recently by the current author.[14] All of the preceding models already realized the important role of dislocation in precipitation systems. The concept of accounting phase transformations was developed from the invariant plane (MPMC) to the IL model and then to the IDE model. Although dislocation has been widely taken into account, it is seldom realized that the direction (not the mode) of the Burgers vector in the matrix (not in precipitate) is actually invariant for diffusional phase transformations. For example, the O-line model deduce
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