Solid solutions are ubiquitous in materials chemistry and are a staple of different applications such as white LED phosphors , superconductors and catalysis . Their widespread application has warranted many studies into the formation of these solid solutions with many physical, 10-12 electronic and magnetic properties also investigated. The rise of computational research methods has allowed for rapid evaluation of different solid solutions. However, predicting the ability of two end members to form a solid solution is a non-trivial task with various methods proposed. The cluster-expansion methodology is a popular approach for this purpose as it can fit density functional theory (DFT) data to a model Hamiltonian and was used by Li and coworkers to explore the (Ga 1-x Zn x )(N 1-x O x ) solid solution. However this work builds on assumptions from experimental data which may not always be readily available for new systems.