Atomic interactions in C15 Laves phases

The C15 phase (Fd3¯m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Fd\bar{3}m$$\end{document}) has been extensively studied by several methodologies to evaluate its atomic interactions. Ideally ordered at the AB2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$AB_2$$\end{document} composition, this Laves phase is known to present a non-stoichiometry domain accommodated by substitutional atomic disorder at high temperature. With the Cu–Mg system as an example, a cluster expansion method study revealed that first neighbors pair interaction is positive yielding a favorable mixing of Cu and Mg atoms in 16d site and a homogeneity extended in the Mg-richer side. To guide the thermodynamic modeling of the C15 phase, special quasi-random structure cells have been generated at several compositions to simulate atom mixing with and without the merging of 8a and 16d sites. Combined with electronic density functional theory, calculation on several systems (Ta–V, Cr–Nb, Mo–Zr and Cr–Ti) was done to estimate the mixing energies on the two different sublattices. The results are compared to published assessments and open a discussion on the acceptability of the traditional thermodynamic model.