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First-principles-based phase diagrams and thermodynamic properties of TCP phases in Re-X systems (X = Ta, V, W)
The structural stability of topologically close-packed phases in binary transition metal alloys is investigated with a combination of first-principles calculations based on density-functional theory and the Bragg–Williams–Gorsky approximation for the description of the configurational entropy. For a variety of different (i) exchange–correlation functionals, (ii) pseudopotentials, and (iii) relaxation schemes, for the relevant phases in Re–X (X = Ta, V, W) binary systems, we compare the energy of formation at T = 0 K, as well as the phase diagrams and site occupancies at finite temperatures. We confirm previous findings that the configurational entropy plays a stabilising role for complex phases in these systems at elevated temperatures. Small differences in the calculated energy of formation for different exchange–correlation functionals, pseudopotentials and relaxation schemes are expected, but give rise to qualitatively different phase diagrams. We employ these differences in order to estimate the order of magnitude of the standard deviation necessary in the qualitatively-reliable calculation of phase diagrams and site occupancies. In an attempt to determine the accuracy that is required to assure a qualitatively correct prediction of phase diagrams, we modify our first-principles results numerically by random variations with the determined standard deviation as maximum amplitude. Taking the order of site occupancies and the set of stable phases as simple criteria for a qualitatively correct prediction, we find that the accuracy required for the energy of formation of the individual configurations in these systems is approximately 5 meV/atom (≈0.5 kJ/mol at).