Comparison of the Site Occupancies Determined by Combined Rietveld Refinement and Density Functional Theory Calculations: Example of the Ternary Mo–Ni–Re σ Phase

Abstract

The site occupancies of the Mo–Ni–Re σ phase have been studied as a function of the composition in the ternary homogeneity domain by both experimental measurements and calculations. Because of the possible simultaneous occupancy of three elements on the five sites of the crystal structure, the experimental determination of the site occupancies was achieved by using combined Rietveld refinement of X-ray and neutron diffraction data, whereas calculation of the site occupancies was carried out by using the density functional theory results of every ordered (i.e., 3⁵ = 243) configuration appearing in the ternary system. A comparison of the experimental and calculation results showed good agreement, which suggests that the topologically close-packed phases, such as the σ phase, could be described by the Bragg–Williams approximation (i.e., ignoring the short-range-order contributions). On the other hand, the atomic distribution on different crystallographic sites of the Mo–Ni–Re σ phase was found to be governed by the atomic sizes. Ni, having the smallest atomic size, showed a preference for low-coordination-number (CN) sites, whereas Mo, being the largest in atomic size, preferred occupying high-CN sites. However, the preference of Re, having intermediate atomic size, varied depending on the composition, and a clear reversal in the preference of Re as a function of the composition was evidenced in both the calculated and experimental site-occupancy results