Thermodynamic origin of medium-entropy stabilization in multicomponent rock-salt oxides

Abstract: High entropy oxides are commonly associated with high configurational entropy ($ΔS_{conf}\geq$ 1.61R) corresponding to five equimolar cations occupying a crystallographic sublattice. However, recent experimental observations indicate that medium-entropy compositions may also exhibit entropy-stabilized rock-salt phases, raising an important question regarding the minimum entropy required for phase stabilization. In this work, we employ a first-principles thermodynamic framework to investigate the stability of rock-salt oxides containing two to five principal cations components analogous to (Ni$<em>{0.8}$Cu$</em>{0.2}$)O, (Ni$<em>{0.6}$Cu$</em>{0.2}$Zn$<em>{0.2}$)O, (Ni$</em>{0.4}$Cu$<em>{0.2}$Zn$</em>{0.2}$Co$<em>{0.2}$)O, (Ni$</em>{0.2}$Cu$<em>{0.2}$Zn$</em>{0.2}$Co$<em>{0.2}$Mg$</em>{0.2}$)O. Density functional theory, MCSQS-based structural modeling, and finite-temperature Gibbs free-energy analysis are combined to quantify the roles of enthalpy mixing ($ΔH_{mix}$), configurational ($ΔS_{conf}$), vibrational ($ΔS_{vib}$), and electronic contributions towards ($ΔS_{elec}$) entropy change in governing phase stability. The results show that $ΔS_{conf}$ alone is not a universal descriptor of phase stability. While the two-cation system is enthalpy-stabilized but three-, four- and five-cation systems become thermodynamically stable at high-temperature due to entropy-driven reduction of the Gibbs free energy. These findings demonstrate that single-phase rock-salt oxides are not restricted to the conventional high-entropy limit and that medium-entropy compositions can also be stabilized under suitable thermodynamic conditions.