Influencing factors of atomic order in the binary sigma phase

Abstract

The sigma phase can serve as a prototype of intermetallic phases when investigating the atomic order (i.e. atomic constituent distribution or site occupancy preference on inequivalent sites of a crystal structure), as the sigma phase bears a broad homogeneity range and there are numerous experimental site occupancy data available for the sigma phase. The present work brings new insights into the influencing factors of atomic order in the binary sigma phase. We calculated the atomic volumes and atomic charges of the constituent elements of 32 stoichiometric end-member compounds (i.e. the complete set of ordered configurations) of the binary sigma phase by using first-principles calculations. The calculation results show that besides the size factor and the number of valence electrons, the total number of electron shells is found as the third factor that affects the atomic order of the sigma phase. Moreover, the calculation results indicate that between the two constituent elements, the one with larger atomic size, smaller number of valence electrons or smaller total number of electron shells prefers occupying large coordination number (CN) sites (i.e. 4f, 8i1 and 8j) and the other prefers occupying small CN sites (i.e. 2a and 8i2). Furthermore, we dissociated the effects of individual influencing factors on atomic order of the sigma phase combining with the measured site occupancies from the literature.