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INTRODUCTION

BASED on Khachaturyan’s microelastic theory and the Landau free energy,[4] a phenomenological timedependent Ginzburg-Landau (TDGL) kinetic equation (phase-field model)[5] was widely employed to simulate microstructural evolution during phase transformations, such as solidification,[6] precipitation,[7] spinodol decomposition,[8,9] and martensitic transformation (MT) with improper[10] and proper[11] types, etc. The MT is different from the diffusional solid-state transformations described by the classic Gibbs thermodynamics, as it possesses certain unique features, such as twin structures, transformation reversibility, and shape memory effect, etc. The mechanisms of the forward and reverse MTs are both scientifically interesting and technologically important. They are responsible for such phenomena as thermoelasticity, pseudoelasticity, and the shape memory effect. The first three-dimensional computer simulation based on phase-field model was proposed by Wang and Khachaturyan for the improper cubic fi tetragonal MT.[10] This simulation generates a realistic threedimensional pattern of the martensitic structure with multidomain twinned martensitic plates. Moreover, the model predicted the major structural characteristics of the martensite during the entire transformation including nucleation, growth, and eventually the formation of internally twinned plates. The three-dimensional model [1–3]

JIAO MAN, Doctor, JIHUA ZHANG, and YONGHUA RONG, Professors, are with the School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. China. Contact e-mail: [email protected] NING ZHOU, Post Doctoral, is with the Department of Materials Science and Engineering, The Ohio State University, Columbus, OH 43210. Manuscript submitted December 23, 2009. Article published online November 17, 2010 1154—VOLUME 42A, MAY 2011

of the proper MT based on TDGL kinetic equations was first proposed by Artemev et al.[11] Computer simulation was also carried out for a dilatationless cubic-tetragonal MT with parameters corresponding to the Fe-31 pct Ni alloy.[11] Their simulation demonstrated that the presence of a nonzero volumetric component in the transformation strain significantly affected the MT. The phase-field model was employed by Zhang et al.[12] to study the heterogeneous nucleation mechanism in the face-centered cubic (fcc) to body-centered cubic MT. The simulation results indicated that when the undercooling and the defect potency reached a critical value, the embryo lost its metastability and began to grow until the transformation was completed. Xu and Morris[13] were the first to study the reverse MT by computer simulation using Khachaturyan’s microelastic theory. They revealed various factors influencing the reverse transformation and the hysteresis in MT, such as elastic strain energy. However, in their simulation, the variations of energy during microstructural evolution of MT including the martensite nucleation stage was not referred. Mn-rich Mn-Cu alloys are known to exhibit a fcc parent phas