First-principles study of mixing in the system of layered dichalcogenides MoS2-WS2

The thermodynamic stability and mixing behavior of the MoS₂-WS₂ system were investigated using a cluster expansion model constructed from density functional theory (DFT) calculations. The alloy cluster expansion approach enabled the efficient sampling of atomic configurations, overcoming the computational limitations of direct DFT calculations. The accuracy of the cluster expansion model was validated against additional DFT calculations, achieving a root-mean-squared error close to 1.0 × 10⁻⁴ eV/atom and R2 = 0.74. The mixing energy landscape was analyzed to determine the existence of ordered ground-state structures and assess the stability of solid solutions. The results indicate that MoS₂-WS₂ forms a stable solid solution across the full compositional range, with specific ordering tendencies at a broad range of intermediate atomic concentrations of tungsten, from XW = 0.33 to 0.66. The constructed convex hull suggests a multitude of ground states in this range with ordering patterns of a single solute atom residing in a hexagon of solvent atoms within a single layer. Generally small mixing energy values imply a dominant role of entropy at synthesis temperatures. The findings provide insight into the thermodynamic factors governing mixing in transition metal dichalcogenide MoS₂-WS₂ solid solutions, contributing to the rational design of materials based on them.