Application of TDGL Model to B2 Type Ordering with Two Step Phase Separation in Fe-Ni-Al Alloys

Abstract

Formation of domain structures in two-step phase separation in Fe-based Fe-Ni-Al alloys are investigated by applying a time-dependent Ginzburg-Landau (TDGL) model. The present authors recently developed a TDGL formulation for ordering processes of B2 and D0₃ in binary alloys, taking into account the symmetrical relationships between these ordered phases. In this formulation, multiple types of variants of the structures are represented by three order parameters which can be measured independently through crystal structure factors. Mean-field free energies are defined in a form of Landau type expansion with the order parameters and a 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. On the other hand, coauthors have investigated domain structures in two-step phase separation of Fe-based Fe-Ni-Al alloys. The evolution of three-dimensional domain structures and composition profiles has been analyzed by electron tomography imaging and energy-dispersive X-ray spectroscopy. In this work the authors performed three-dimensional numerical simulations assuming the thermal processing. The results of the simulations well reproduced the characteristics of the micro-structures obtained from the observations.