For the first time, an approach coupling the variable charge model based on a tight-binding approach within the second moment approximation (SMTB-QB) and the Effective Site Energy (ESE) is used to obtain the phase diagram of a mixed oxide. SMTB-QB allows one to calculate the site energies of all atoms in random solid solution for the ${\mathrm{SnTiO}}_2$ mixed oxide. These energies are analyzed within the ESE model as a function both of the local environment (number of Sn nearest neighbors) and of the nominal concentration. The almost symmetrical miscibility gap is well reproduced by Monte Carlo simulations. The ESE model shows that the apparent symmetry of the phase diagram actually comes from two highly asymmetrical thermodynamic forces. The local effect that induces a homoatomic short range order (SRO) dominates when Sn is the minority element, while the nonlocal effect that does not induce SRO dominates when Sn is the majority element. This result demonstrates that the ESE model's ability to analyze the driving forces that govern phase diagrams, which has been widely demonstrated for bimetallic alloys, also extends to mixed oxides.

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• Phase transitions
• Thermodynamics
• 3-dimensional systems
• Oxides
• Mean-field & cluster methods
• Monte Carlo methods