Modeling the structure and thermodynamics of high-entropy alloys
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Modeling the structure and thermodynamics of high-entropy alloys Michael Widoma) Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA (Received 19 April 2018; accepted 14 June 2018)
High-entropy and multiprincipal element alloys present exciting opportunities and challenges for computational modeling of their structure and phase stability. Recent interest has catalyzed rapid development of techniques and equally rapid growth of new results. This review surveys the essential concepts of thermodynamics and total energy calculation, and the bridge between them provided by statistical mechanics. Specifically, we review the electronic density functional theory of alloy total energy as applied to supercells and special quasirandom structures. We contrast these with the coherent potential approximation and semi-empirical approximations. Statistical mechanical approaches include cluster expansions, hybrid Monte Carlo/molecular dynamics simulations, and extraction of entropy from correlation functions. We also compare first-principles approaches with Calculation of Phase Diagrams (CALPHAD) and highlight the need to augment experimental databases with first-principles derived data. Numerous example applications are given highlighting recent progress utilizing the concepts and methods that are introduced.
I. INTRODUCTION
Modeling the structure and the thermodynamics of multicomponent materials presents a number of interesting and exciting scientific challenges. Recently developed multicomponent alloy systems stand in contrast to traditional alloys, which traditionally contain just one or two primary constituent chemical species, with other species present in small concentrations. Current research pays increasing attention to multiprincipal element alloy1,2 (MPEA) systems containing many chemical species. Special effort is given to complex concentrated alloys,3 in which several elements are present simultaneously in high concentrations. Cases where the elements substitute freely are known as concentrated solid solution alloys4 (CSSAs), while the specific case where multiple elements are present in high concentration, and they also substitute freely, are termed high-entropy alloys2 (HEAs). This review focuses on CSSAs and HEAs. Stabilization of a single phase through entropy of mixing is a foundational notion of HEAs. The ideal configurational entropy of chemical substitution, X Schem ¼ kB xa ln xa ; ð1Þ a
is maximized when all elements substitute freely, which inhibits separation into multiple phases. It is also
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2018.222 J. Mater. Res., 2018
maximized when all lat
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