Can Hume-Rothery rules predict single-phase high-entropy rocksalt oxide phases?

In the quest for understanding and tailoring the formation and properties of entropically stabilised ceramics, rocksalt-structured (MgNiCoCuZn)O occupies a central place. To date, most of the reported high-entropy rocksalt oxides (HERSOs) are derivatives of the original (MgNiCoCuZn)O, and only a couple of other novel HERSOs have been synthesised. To pave the way for the discovery of new HERSOs, we seek rapid and effective methodologies for screening large compositional spaces such as those associate with high entropy oxides. In this letter, we analyse modifications of the Hume-Rothery (HR) rules that govern the formation of solid-solution metallic alloys. We propose that HERSOs can form based on maintaining an oxidation state of +2 for all cations and a low value for the coefficient of variation associated with the lattice constants of the unmixed constituent oxides in a (hypothetical or actual) rocksalt phase. As a result of applying Hume-Rothery-inspired rules, we provide an heuristic explanation for the synthesizability of three experimentally realised HERSOs, and list a significant number of other HERSO compositions that can potentially be realised via similar methodologies. The rules devised in this work for HERSOs should provide guidance for future synthesis efforts, and we expect that community use could lead to further refinements as well as to modifications for application-specific screening.