A Study on First Principle Calculation of Alloy Phase Diagram by Monte Carlo Simulation
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A STUDY ON FIRST PRINCIPLE CALCULATION OF ALLOY PHASE DIAGRAM BY MONTE CARLO SIMULATION Hideaki Sawada, Atsushi Nogami, Wataru Yamada and Tooru Matsumiya Advanced Materials 8 Technology Research Laboratories, Nippon Steel Corporation, 1618 Ida, Nakahara-ku, Kawasaki 211, JAPAN
ABSTRACT A method of first principle calculation of alloy phase diagram was developed by the coinbination of first principle energy band calculation, cluster expansion method (CEM) and Monte Carlo (MC) simulation, where the effective multi-body potential energy for the flip test in MC simulation was obtained by the decomposition of the total energy by GEM. This method was applied to Cu-Au binary system. The calculated phase diagram agreed with that of CVM by introducing the dependence of the lattice constant on the concentration of the whole system. Furthermore an attempt of introducing the effect of local lattice relaxation was performed by the consideration of the local concentration. The order-disorder transition temperature became closer to the experimental value by adjustment of the local lattice constant depending on the concentration in the local region consisted of up to the second nearest neighbors of the atom tested for flipping.
INTRODUCTION The first principle calculations of alloy phase diagram have been performed by the combination of band calculation, CEM[1] and CVM[2] or MC simulation [3, 4, 5]. Mohri et al. applied these methods to binary phase diagram of noble metals by the use of CVM [6]. In their calculations the order-disorder transition temperatures were overestimated when the difference of atomic radius between two atom was very large such as Cu-Au system, because no effect of the local lattice relaxation was incorporated in their model. Several researchers attempted to introduce global and local relaxation [5, 7, 9, 8]. In present study we choose the combination of CEM and MC from the viewpoints that the entropy can be evaluated more precisely in MC simulation than in CVM and that MC is suitable for introducing the effect of the local lattice relaxation. As the first step of this study, the volume optimization mechanism is incorporated in MC simulation by introducing the concentration dependence of the effective potential using the relationship between the lattice constant and the concentration of the whole system. As the second step, introduction of the effect of the local lattice relaxation is examined by the use of the local effective potentials determined by the local concentration around the atom for the flip test. This method is applied to Cu-Au binary system by the use of the same potentials as CEM-CVM calculations [10].
CALCULATION Monte Carlo Simulation The general flow of the calculation for MC simulation is shown in Fig 1. The input data are temperature, chemical potential difference between A-atom and B-atom, initial assignment of atom on each atom site and the multi-body potential. The flip test procedure is performed as follows. There are 8 tetrahedra which include an atom of flipping consideration as
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