Explaining the entropy forming ability for carbides with the effective atomic size mismatch.

To quickly screen for single-phased multi-principal-element materials, a so-called entropy forming ability (EFA) parameter is sometimes used as a descriptor. The larger the EFA, the larger is the propensity to form a single-phase structure. We have investigated this EFA descriptor with atomic relaxations in special-quasi-random structures and discovered that the EFA correlates inversely with the lattice distortion. Large effective atomic size differences lead to multi-phase compounds, and little size differences to single-phase compounds. Instead of configurational entropy, we therefore demonstrate the applicability of the Hume-Rothery rules to phase stability of solid solutions even in compositionally complex ceramics.