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Using Re-W \sigma-phase ﬁrst-principles results in the Bragg-Williams approximation to calculate ﬁnite-temperature thermodynamic properties
First-principles (FP) calculations of total energies for 32 different configurations of Re-W σ phase were used to fit a compound energy formalism (CEF) Hamiltonian that was used in phenomenological Calphad method calculations to model finite-temperatures thermodynamic properties. A comparison with Connolly-Williams method–cluster variation method (CWM-CVM) calculations indicates that the first-principles CEF (FP-CEF) describes temperature-dependent site occupancies as well as the CWM-CVM approximation within the temperature range of interest for applications. This result seems to indicate that the Bragg-Williams approximation (BWA) is sufficient to describe the Re-W σ phase. A complete Re-W phase diagram is calculated using the FP-CEF Hamiltonian for the σ phase. Differences between the phase diagrams, and single phase properties calculated both with, and without, the first-principles results are striking. It is expected that using the FP-CEF σ-phase description that takes into account the first-principles energetics will yield more reliable extrapolations into higher-order system.