Thermodynamics of Oxides with Substitutional Disorder: A Microscopic Model and Evaluation of Important Energy Contributions

The first‐principles calculation of finite‐temperature phase stability and thermodynamic properties of multicomponent oxides presents a significant challenge. The time scale on which substitutional disorder occurs prevents the use of standard simulation methods, and a correct description of entropic effects requires that excitation energies can be calculated accurately on the scale of k B T . A model is presented in which substitutional disorder is parameterized with a cluster expansion. The thermodynamics of this model can be easily obtained with lattice model statistical mechanics. The only input required to the procedure is a description of bonding in the system, which is used to calculate the energy of ordered ionic configurations. This method is applied to the CaO‐MgO, Gd 2 O 3 ‐ZrO 2 , CaO‐ZrO 2 systems, and to Li x CoO 2 ( x between 0 and 1) electrodes for rechargeable lithium batteries. In almost all cases, a correct description of the charge state of the ions is essential to obtain the proper mixing behavior. Only for a highly ionic material such as CaO‐MgO does the charge state of the ions remain unvaried upon mixing. We find that approximate energy models that employ fixed charges will tend to overestimate the energy required for mixing, hence the order‐disorder transition temperature.