Maximizing Misfit Cation Solubility in Rock-Salt High-Entropy Oxides

To explore and quantitatively map the cation-size mismatch solubility limits in high-entropy oxides (HEOs), we report on Ca²⁺ substitution in prototypical MgCoNiCuZnO, because while isovalent, Ca²⁺ is 38% larger than its partners’ average ionic radii. Using the thermodynamics-grounded bond-length distribution descriptor, we identify Ca²⁺–Cu²⁺ interactions as the primary prospective lattice destabilizer. Bulk synthesis powder diffraction confirms at most 4% Ca²⁺ solubility with Cu at 950°C, modestly rising to at most 5% after Cu removal at 1150°C. We then employ far-from-equilibrium pulsed-laser deposition to investigate metastable solubility; epitaxial films incorporate 10% Ca²⁺ with Cu and a full 20% Ca²⁺ without, doubling and quadrupling the respective bulk limits. Ca²⁺ incorporation enables deterministic control of the lattice parameter through composition, producing a 4.2% out-of-plane lattice expansion over a 10% Ca²⁺ window in MgCoNiCuZnO and a 2.6% expansion over a 20% Ca²⁺ window in the Cu²⁺-free system. Overall, our results demonstrate both the extended solubility that is possible in HEO systems, particularly when accessing metastable states through quenching from high-energy plasma, and that the specific constellation of solid solvent cations can be rationally engineered to leverage or minimize bond-length distributions when largely misfit cations are added, thus expanding the accessible compositional space.