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Abstract

Statistical-thermodynamic models for the description of ordering in non-stoichiometric intermetallic phases can be very helpful for the design of new functional materials for various purposes. Here, we present a review of methods for describing B2 (BCC) and L12 (FCC) – type binary alloys. The free energy of binary alloys where ordered structures are formed, is evaluated by statistical approaches employing applications of the Bragg–Williams–Gorsky mean-field approximation. In the original mean field method, the degree of order in the neighborhood of a given site in the crystal is determined by the average state of order throughout the macroscopic crystal. Actually, the force tending to produce long-range order depends on the fluctuations in the configuration, an effect which is neglected in the mean field approximation but is taken under consideration, e.g., in the Quasi-Chemical Approach (QCA) by Guggenheim and its advanced applications, in various sophisticated treatments using the Cluster Variation Method (CVM) originally developed by Kikuchi, as well as in the Defect Correlation Model (DCM). The latter model is a less sophisticated method based on the simultaneous description of short-range order and long-range order by use of properly defined non-overlapping clusters. All these methods allow the “pure” mean-field results to be substantially refined, particularly at high temperatures, and for alloys with large deviations from the stoichiometric composition. Defect concentration-alloy composition diagrams and activity-alloy composition diagrams are shown for several methods with focus on the QCA and DCM approaches. The calculated results are compared with each other and with experimental data on thermodynamic and structural properties from the literature.