Interplay of ordering and spinodal decomposition in the formation of ordered precipitates in binary fcc alloys: Role of second nearest-neighbor interactions

Abstract

In this paper, the possible interaction of ordering and phase separation tendencies in the formation of an ordered precipitate phase (A₃B/L1₂) within a binary supersaturated fcc solid solution is investigated using computational thermodynamics based on a generalized Bragg–Williams model incorporating first and second nearest-neighbor interactions. The formulation synthesizes and expands upon previous works and incorporates a strong pedagogical approach to elucidate the essential elements of the problem. The diffusional pathways governing microstructural development are predicted to be more complex, allowing for a multiplicity of decomposition mechanisms when second nearest-neighbor interactions are incorporated into the solution energetics, even in this mean field approximation. These higher order interactions markedly influence phase equilibria and phase stability. Ordering and clustering tendencies are not mutually exclusive but can occur synergistically, e.g. a conditional spinodal decomposition is predicted contingent on prior ordering of initially non-stoichiometric, disordered solid solutions. The role of second nearest-neighbor interactions on thermodynamic stability is discussed explicitly and compared to the classic treatments limited to first nearest-neighbor interactions only.

Keywords:

• generalized Bragg–Williams model
• congruent ordering and precipitation
• spinodal decomposition
• ordering instability

Acknowledgements

The authors dedicate this contribution to Professor Armen Khachaturyan for his intellectual leadership in the field of phase transformations and microstructural development for almost four decades. Professor Khachaturyan's classic book Theory of Structural Transformations in Solids ushered in a new era of quantitative understanding of the fundamentals governing microstructural evolution accompanying various solid state reactions and provided a foundation for the more recent successes of computational thermodynamic and kinetic approaches applied to material structure. For the senior authors (WAS and DEL), he has been a friend, teacher and colleague over the many years since coming to the United States and he has informed and inspired our research and teaching in countless ways. Finally, WAS wishes to thank the National Science Foundation (NSF/DMR) for the continued support of his research and scholarship at the University of Pittsburgh and now at the University of Virginia.