Computer simulations of phase decomposition in real alloy systems based on the modified khachaturyan diffusion equation
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INTRODUCTION
THEORETICAL investigations on the diffusion-controlled phase transformation have been performed by many researchers. Since Cahn and Hilliard[l,2] proposed the nonlinear diffusion equation in the 1960s, many researchers have attempted the theoretical analysis of phase decomposition on the basis of the equation.t2-7] Cahn,[4] assuming the interdiffusion coefficient to be independent of composition, derived the well-known linear theory of spinodal decomposition. However, the theory is only valid for the early stage of phase decomposition of an alloy because of the neglect of the nonlinear term in the diffusion equation. Since then, the researcher's interest moved to the precise evaluation of the nonlinear term. Swanger et al.,[5] Langeret al., ~61and TsakalakostT] analyzed the phase decomposition process on the basis of such a point of view. However, various assumptions and omissions were made in their calculations, because it was extremely difficult to get the analytical solution of the nonlinear term in the differential equation. Since the recent developments of computers have made the numerical analysis of the diffusion equation possible without any omission, computer simulations have become useful in understanding the dynamics of phase transformations. Nishimori and Onuki,tsl investigating the phase decompositions in the elastically constrained materials, have studied the morphological changes of microstructure which depend on the anisotropy of the elastic constrain, the effects of external stress, and the inhomogeneity of elastic moduli. Miyazaki and co-worker, ~9-~21 accomplished the computer simulations of the phase decompositions in various alloy systems by using a polynomial free energy equation of solute composition or a free energy based on the regular solution approximation and showed many interesting simulation results, such as the competitive growth among the composition peaks,t9,1o.H] the spectrum behavior of the
TOSHIYUKI KOYAMA, Research Fellow, TORU MIYAZAKI, Professor, and ABD EL-AZEAM M. MEBED, Postgraduate Student, are with the Department of Materials Science and Engineering, Nagoya Institute of Technology, Nagoya 466, Japan. Manuscript submitted December 21, 1994. METALLURGICALAND MATERIALSTRANSACTIONSA
X-ray small angle scattering with phase decomposition,Vn and so on. These calculations are essentially based on the Cahn-Hilliard's flux equation. Recently, Khachaturyan's group rl3,1*lproposed a new calculation method for phase decomposition on the basis of the Onsager equation. This theory has many advantages over the Cahn-Hilliard's diffusion equation, such as the availability of order/disorder transformations, a shorter calculation time, precise evaluations of the excess free energy caused by the compositional variations, and so on. Khachaturyan's method is considered to be very useful for the basic understanding of the phase decomposition process. However, the composition and the temperature dependencies of the atomic interchange energy W have not been taken into account i
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