While 2D materials attract considerable interests for their exotic electronic and mechanical properties, their phase behaviour is still largely not understood. This work focuses on (Mo:Ti) S2 binary alloys which have captured the interest of the tribology community for their good performance in solid lubrication applications and whose chemistry and crystallography is still debated. Using electronic structures calculations and statistical mechanics we predict a phase-separating behaviour for the system and trace its origin to the energetics of the d-band manifold due to crystal field splitting. Our predicted solubility limits as a function of temperature are in accordance with experimental data and demonstrate the utility of this protocol in understanding and designing TMD alloys.

Funding Information: This project has received funding from the European Union Horizon2020 research and innovation programme under grant agreement No. 721642: SOLUTION. The authors acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work. The authors are grateful to the UK Materials and Molecular Modelling Hub for computational resources, which is partially funded by EPSRC (EP/P020194/1). TP acknowledges the support from the project OPVVV Novel nanostructures for engineering applications No. CZ.02.1.01/0.0/0.0/16_026/0008396 supported by EU/MSMT.
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