Application of TDGL Model to B2 Type Ordering with Two Step Phase Separation in Fe-Ni-Al Alloys
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Application of TDGL Model to B2 Type Ordering with Two Step Phase Separation in Fe-Ni-Al Alloys Ryuichiro Oguma1, Syo Matsumura2, Minoru Doi3, Satoshi Hata4, Keisuke Ogata5 1
Department of Applied Physics., Fukuoka University, Fukuoka 814-0180, Japan Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, Fukuoka 819-0395, Japan 3 Department of Mechanical Engineering, Aichi Institute of Technology, Toyota 470-0392, Japan 4 Department of Electrical and Material Science, Kyushu University, Kasuga 816-8580, Japan 5 Interdisciplinary Graduate School of Engineering Science, Kyushu University, Kasuga 816-8580, Japan 2
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. INTRODUCTION Substitutional solid solutions of Fe-Ni-Al alloy can be considered to be A3B type of pseudo binary alloy system where Fe and Ni/Al are related to major and minor atoms, respectively. The crystal structure is based on the fundamental bcc lattice. In disordered A2 state, atoms occupy the lattice sites randomly. The ordered structure of B2 type is formed by ordering reaction of A and B atoms between the first nearest neighbors. It comprises two simple-cubic type sublattices with different compositions. In the B2 phase, two types of variants exist depending on which of the two sublattices are preferably occupied by the A and B atoms. Anti-phase boundaries (APBs) with displacement a/4 are formed where the two variants come into contact. Here a is the lattice constant of a unit cell shown in Fig. 1(a). Co-authors Ogata et al. observed the two step phase separation of
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