### Description

## Equilibrium Phase Diagrams of Two-dimensional Alloys from First Principles

John Cavin and Rohan Mishra

Alloying is a successful strategy for tuning the phases and properties of two-dimensional (2D) transition metal dichalcogenides (TMDCs). To accelerate the synthesis of TMDC alloys, we present a method for generating temperature-composition equilibrium phase diagrams by combining first-principles total-energy calculations with thermodynamic solution models. This method is applied to three representative 2D TMDC alloys: an isostructural alloy, MoS_{2(1-x)}Te_{2x}, and two heterostructural alloys, Mo_{1-x}W_{x}Te_{2} and WS_{2(1-x)}Te_{2x}. Using density-functional theory and special quasi-random structures, we show that the mixing enthalpy of these binary alloys can be reliably represented using a sub-regular solution model fitted to the total energies of relatively few compositions. The cubic sub-regular solution model captures 3-body effects that are important in TMDC alloys. By comparing phase diagrams generated with this method to those calculated with previous methods, we demonstrate that this method can be used to rapidly design phase diagrams of TMDC alloys and related 2D materials.