First-Principles Calculations of Phase Equilibria and Transformation Dynamics of Fe-Based Alloys Tetsuo Mohri, Munekazu Ohno, and Ying Chen (Submitted December 29, 2004; in revised form February 28, 2005) Theoretical procedures of first-principles calculations of phase stability and phase equilibria are summarized. The present scheme is shown to be able to reproduce the transition temperatures with surprisingly high accuracy for Fe-Pd and Fe-Pt systems. The main emphasis of the present report is placed on the extension of the first-principles calculation to transition dynamics cal- culations. This is performed by combining the cluster variation method with the phase-field method via a coarse graining operation. The time evolution process of antiphase boundaries associated with L1 0 ordering for Fe-Pd system is demonstrated. Keywords cluster expansion method, cluster variation method, coarse graining, Fe-Pd system, first-principles cal- culation, L1 0 ordered phase, ordering dynamics, phase field method 1. Introduction Recent progress in first-principles calculations of phase diagrams has been remarkable, and for certain systems, the transition temperatures are obtained with surprisingly high accuracy. [1-5] Although several approaches to first-princi- ples phase diagram calculations are available, main schemes based on a combination of electronic structure total energy calculations with statistical mechanics methods such as the cluster variation method [6] or Monte Carlo simulations are well established. Remaining problems in the future direction of the first- principles calculations of phase stability and phase equilib- ria can be summarized as (a) extension to a multicomponent systems, (b) application to a low symmetry structures, and (c) separate introduction of chemical interaction and other interactions, such as magnetic interactions. Extension to multicomponent systems is a requirement for practical pur- poses, but applying a brute force first-principles calculation to a multicomponent system is a questionable approach. In particular, in view of excellent tools of the CALPHAD-type software packages supported by powerful databases, one needs to focus on the well-tuned problems for which only first-principles calculation can provide answers. The second subject of the low-symmetry structure, in a sense, shares the common background with the first subject. Most of the first-principles calculations performed so far have centered around a high-symmetry structure, such as a cubic structure. In order for the first-principles calculation to be a versatile tool for a wide class of alloy systems, it is desirable that a calculation procedure be established at least for tetragonal and hexagonal structures. Note that symmetry does not necessarily refer to the Bravais lattice. The lowest energy state of a given alloy system is realized by local atomic displacement at each lattice point, which breaks the global symmetry of the entire lattice. Hence, even if the global lattice symmetry is characterized in terms of the Bra- vais lattice, local structure is generally topologically disor- dered and atomistic calculations need to incorporate such a low symmetry in the calculations. Recent development in the Continuous Displacement Cluster Variation Method (CDCVM) [7-12] had made it a potential theoretical tool, and further development is urged. The settlement of the third subject is a sheer necessity in connection with the current study on Fe-based alloy systems. As has been reported in the authors’ recent articles, [1-5] magnetism plays an essential role in the phase stability of Fe-Ni, Fe-Pd, and Fe-Pt alloy systems. Although spin- polarized electronic structure calculations reveal the signifi- cance of magnetism, the separation of the atomic interaction energies into chemical and magnetic energy contributions have not been attempted. It is plausible that a number of unsettled subjects in the Fe-based phase diagram calcula- tions originate from the neglect of the separate treatment of the two contributions. Among such problems is the signifi- cant deviation of the congruent composition of L1 0 ordered phase found in the Fe-Pd phase diagram. [13] Despite various attempts, the authors have not been able to reproduce the shifting of the congruent composition from 1:1 stoichiom- etry. The double-Ising type formulation is believed to be necessary for introducing interaction energies of different origins. Apart from the settlement of these subjects in the phase diagram calculations, the other direction in which the first- This paper was presented at the International Symposium on User Aspects of Phase Diagrams, Materials Solutions Conference and Ex- position, Columbus, Ohio, 18-20 October, 2004. Tetsuo Mohri, Division of Materials Science and Engineering, Gradu- ate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan; Munekazu Ohno, Division of Materials Science and Engineer- ing, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan and Technical University-Clausthal, Robert-Koch Str. 42, D-38678, Clausthal-Zellerfeld, Germany; and Ying Chen, Department of Quantum Engineering and System Science, School of Engineering, The University of Tokyo, Tokyo 113-8655, Japan. Con- tact e-mail: tmohri@eng.hokudai.ac.jp. JPEDAV (2006) 27:47-53 DOI: 10.1361/105497106X92790 1547-7037/$19.00 ©ASM International Basic and Applied Research: Section I Journal of Phase Equilibria and Diffusion Vol. 27 No. 1 2006 47