Finding stable multi-component materials by combining cluster expansion and crystal structure predictions

A desired prerequisite when performing a quantum mechanical calculation is to have an initial idea of the atomic positions within an approximate crystal structure. The atomic positions combined should result in a system located in, or close to, an energy minimum. However, designing low-energy structures may be a challenging task when prior knowledge is scarce, specifically for large multi-component systems where the degrees of freedom are close to infinite. In this paper, we propose a method for identification of low-energy crystal structures within multi-component systems by combining cluster expansion and crystal structure predictions with density-functional theory calculations. Crystal structure prediction searches are applied to the Mo 2 AlB 2 and Sc 2 AlB 2 ternary systems to identify candidate structures, which are subsequently used to explore the quaternary (pseudo-binary) (Mo x Sc 1– x ) 2 AlB 2 system through the cluster expansion formalism utilizing the ground-state search approach. Furthermore, we show that utilizing low-energy structures found within the cluster expansion ground-state search as seed structures within crystal structure predictions of (Mo x Sc 1– x ) 2 AlB 2 can significantly reduce the computational demands. With this combined approach, we not only correctly identified the recently discovered Mo 4/3 Sc 2/3 AlB 2 i -MAB phase, comprised of in-plane chemical ordering of Mo and Sc and with Al in a Kagomé lattice, but also predict additional low-energy structures at various concentrations. This result demonstrates that combining crystal structure prediction with cluster expansion provides a path for identifying low-energy crystal structures in multi-component systems by employing the strengths from both frameworks.