Mesoscopic TDGL model for formation of domain structures in D0₁₉ type ordering

The present authors recently presented the time-dependent Ginzburg-Landau (TDGL) formulation for L1₂ type ordering process in binary alloys, taking into account the symmetrical relationships of these ordered phases. Extending the formulation, the authors have developed the TDGL model for microstructural evolution of D0₁₉ type ordering. The D0₁₉ structure based on hcp is divided into four equivalent sublattices. The site occupation probabilities are given as a function of three order parameters and a composition parameter. Multiple types of variants of the structures are represented by the order parameters. Mean-field free energies are defined in a form of Landau type expansion with the order parameters and the composition parameter. Interfacial energies due to local variations of degrees of order and composition are given in a gradient square approximation. Kinetic equations for time-evolution of the order parameters and the composition one are derived from the Ginzburg-Landau type potential consisting of the mean-field free energies and the interfacial energy terms. Three-dimensional numerical simulations based on the kinetic equations have been performed, and the domain structures obtained are compared with a TEM image of Cu₃Sn alloy.