Integrated modeling of molar volume of the sigma phase aided by first-principles calculations

Abstract

The volume modeling of the sigma phase is an indispensable complement to the integrated computational material design of technologically important materials, such as high-alloy steels and Ni-based superalloys. The molar volume of the sigma phase is influenced by both the atomic mixing (the volume variation affected by this factor is caused by composition alteration rather than site occupation change) and atomic order (i.e. atomic constituent distribution or site occupancy preference on inequivalent sites of a crystal). In the present work, we developed a new integrated thermodynamic and molar volume model to consider physically both mixing and order factors. The integrated model was built within the compound energy formalism (CEF), enabling the thermodynamic calculations to determine equilibrium site occupancies for the subsequent volume calculations. The model parameters of the CEF were assigned by using the first-principles calculated energies and molar volumes of the complete sets of ordered configurations of the sigma phase, as well as the extrapolated molar volumes of the pure elements in the hypothetic sigma phase structure. Such extrapolation for pure elements is based on the experimental data from the literature and the first-principles calculations. We applied the integrated model to study the binary compounds, e.g. Cr-Co, Cr-Fe, Cr-Mn, Mo-Fe, Mo-Mn, Mo-Re, Re-Cr, Re-Fe, Re-Mn, Nb-Al, Ta-Al, V-Fe, V-Ni, and ternary compounds Cr-Fe-X (X = Co and Ni). The integrated thermodynamic and molar volume databases can predict successfully the molar volume of the binary and ternary sigma compounds. As most experimental volume data were measured at room temperature and atmospheric pressure, and the first-principles calculations were performed at 0 K, the present model parameters are valid at about room temperature and atmospheric pressure.