Computer simulation study of short-range order hardening
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INTRODUCTION
A M O N G various hardening mechanisms of a solid solution, the short-range order hardening (SROH) effect has not been paid much attention. This is mostly because the effect is intrinsically insignificant, and therefore, an experimental separation from major hardening effects, such as elastic contribution, due to the size difference between solute and solvent is not readily performed. In fact, a recent experiment on Cu-10 at. pct Au undertaken by Buttner and Nembach f~l concluded that the SROH is negligibly small based on the measurements of yield stress, diffuse X-ray scattering, and electric resistance. The origin of the SROH has been, since the first prediction of Fisher I21 and Flinn, t3~ ascribed to an increment of the internal energy due to the destruction of equilibrium atomic bonds caused by slip of a dislocation. Then, the essential quantities which determine the magnitude of the SROH are atomic interaction energies and atomic correlation functions. Given the geometry of slip, the estimation of the SROH is therefore reduced to a subject of statistical thermodynamics. The estimation of the atomic correlation functions is the central concern of statistical thermodynamics. Since the atomic bonds are replaced with further distant atoms after the passage of a dislocation, an explicit incorporation of wide-range atomic correlations in the free energy formula is indispensable for the study of the SROH. The cluster variation method (hereafter C V M ) , [4] which is a theoretical tool that provides improved results in various thermodynamic calculations by expanding a basic cluster, may be best suited for this purpose. Mohri et al. ISj first applied the CVM to the study of SROH for an Ising system and revealed new aspects which are hardly accessed by Bragg-Williams-type calculations, on which Fisher's and Flinn's original works are based. Furthermore, recent development of various energy expansion schemes I6'71 enables one to extract atomic interaction energies from the total energy which is obtained by an ab initio calculation. Hence, together with the CVM, recent efforts of thermodynamic calculation have been directed from prototype calculations for Ising systems toward the first-principles evaluation for realistic alloy systems. However, all of the free energy formulas developed so far are not entirely satisfactory in T. MOHRI, Associate Professor, and J. TSUTSUMI, Graduate Student, are with the Department of Metallurgical Engineering, Hokkaido University, Sapporo 060, Japan. O. SASAKI, formerly with Dai Nippon Printing Company, Tokyo 162, is Research Engineer with the Central Research Institute, Dai Nippon Printing Co., Ltd., Kashiwa 227, Japan. K. WATANABE, formerly with the Department of Metallurgical Engineering, Hokkaido University, is Professor with the Department of Industrial Engineering, Hokkaido Institute of Technology. Manuscript submitted April 25, 1989. METALLURGICALTRANSACTIONSA
taking the effect of local lattice relaxation into account. The lattice has been assumed to be either rigid
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