[SY-A8] Symposium A-8

[SY-A8] Phase-field model for microstructure change in L1₀ type ordering with lattice distortion

^○Ryuichiro Oguma¹, Long-Qing Chen², Syo Matsumura³ (1.Fukuoka Univ., Japan, 2.The Pennsylvania State Univ., United States of America, 3.Kyushu Univ., Japan)

Domain structures consisting of multiple off-phase variants are generally formed in ordering process in binary alloy systems. The L1₀ type order is formed in AB type alloys on the basis of an fcc lattice. The crystal structure is tetragonal. Therefore three orientational variants can be formed depending on which of <100> directions corresponds to c-axis and two translational variants are possible for each of them; six distinct crystallographic variants exist in this type of order. The present authors previously developed a phase-field formulation for ordering process of L1₀ type in binary alloys, taking into account the symmetry of the crystal structure. In the L1₀ structure the fcc lattice is divided into four simple cubic sublattices. The atomic occupation probabilities on the sublattices are represented by three independent order parameters and a composition parameter. If the state of order of atomic arrangement is represented by a point in the three dimensional Euclidean space spanned by the three order parameters, the six equivalent variants are defined by the six tips of a regular octahedron centered on the origin for the disordered state. A mean-field free energy is defined in a form of Landau type expansion with the order parameters and the composition parameter. In this presentation we further consider the effect of the lattice distortion. An elastic energy is introduced with eigen strains according to Khachatrian's method. The interface energy automatically reflects the direction of c-axis and satisfies symmetries of cubic, tetragonal and orthorhombic structures. Kinetic equations for time-evolution of the order parameters and the concentration are derived from the Ginzburg-Landau type thermodynamical potential. Formation of domain structures was simulated by treating the kinetic equations numerically in a three-dimensional cell scheme. The microstructures obtained are compared with experimental results of TEM observation.