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

High entropy oxides are commonly associated with high configurational entropy ($\Delta S_{conf}\geq$ 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$_{0.8}$Cu$_{0.2}$)O, (Ni$_{0.6}$Cu$_{0.2}$Zn$_{0.2}$)O, (Ni$_{0.4}$Cu$_{0.2}$Zn$_{0.2}$Co$_{0.2}$)O, (Ni$_{0.2}$Cu$_{0.2}$Zn$_{0.2}$Co$_{0.2}$Mg$_{0.2}$)O. Density functional theory, MCSQS-based structural modeling, and finite-temperature Gibbs free-energy analysis are combined to quantify the roles of enthalpy mixing ($\Delta H_{mix}$), configurational ($\Delta S_{conf}$), vibrational ($\Delta S_{vib}$), and electronic contributions towards ($\Delta S_{elec}$) entropy change in governing phase stability. The results show that $\Delta S_{conf}$ 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.