Abstract
The present authors have developed a Time-dependent Ginzburg-Landau (TDGL) model for microstructural evolution of D019 type ordering, taking into account the crystal symmetry of the ordered phase. 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. We distinguish characteristic off-phase boundaries observed in Transmission Electron Microscopy (TEM) images in such as Cu3Sn and Ti3Al, and performed three-dimensional numerical simulations based on the kinetic equations.
