First-principle Thoery of Phase Stability, Phase Equilibria and Phase Transition of Ordered Compounds
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0980-II02-01
First-Principle Thoery of Phase Stability, Phase Equilibria and Phase Transition of Ordered Compounds Tetsuo Mohri Division of Materials Science and Engineering, Hokkaido University, Kita-13 Nishi-8, kita-ku, Sapporo, 060-8628, Japan
ABSTRACT First-principles theory of alloys is based on electronic structure calculation at the ground state and statistical mechanics calculation at finite temperatures. The former clarifies the stability of an ordered compound against competing phases and the latter is employed mainly to derive a phase diagram. The author performed a series of first-principles investigations on binary alloy systems including noble metal alloys, semiconductor alloys and Fe-based alloy systems by combining FLAPW electronic structure total energy calculations with Cluster Variation Method. Recently, the theoretical framework is extended even to calculate microstructural evolution process. By exemplifying Fe-based alloy systems, the progress of the first-principles calculation is reviewed and future prospect is discussed. INTRODUCTION First principles calculation was initiated by electronic structure total energy calculations for ordered compounds. Then, by combining with statistical mechanics method such as Cluster Variation Method [1] and Monte Carlo simulation, phase boundaries for some systems have been derived based on atomic numbers of constituent elements. In order to assures the versatility of such calculations, one needs to expand the theoretical frameworks and develop efficient algorithms for low symmetric crystal structures and multi component systems. The extension of the first principles calculation to time dependent phenomena such as phase transformation is another challenging subject. In particular, in view of the recent progress of Phase Field Method [2], the development of a hybrid model [3-6,27,28] which incorporates electronic structure calculations and Cluster Variation Method into the Phase Filed Method is promising. In the present report, brief reviews of the first principles calculation of ground state energetics and phase equilibria for Fe-Ni and Fe-Pd systems are attempted, and recent challenge of the extension to L10-disorder phase transformation of Fe-Pd system is summarized. Finally, the remaining problem of the time scaling is discussed. GROUND STATE ANALYSIS AND PHASE STABILITY The ground state analysis was initiated way back to the beginning of 1970th. Two schemes are addressed. One is based on linear programming [7,8] and the other is called method of inequality [9]. In both the approaches, most stable ordered phases were successfully identified in the
L11 0.5 Chalcopyrite
Formation e nergy
v 2 , 2 v 2 ,1
A 3B
A 2B AB
AB 3
A
0.0
B P4 P2 P1 P3
L10
Figure 1. Ground state diagram for fcc at 50at% within the first and the second nearest neighbor pair interactions [10].
Figure 2. Schematic diagram of heats of formation of ordered phases [10].
ground state diagram under a set of given atomic interaction energies and composition. Shown in Fig. 1 [10] is
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