Order-disorder phase transitions in the two-dimensional semiconducting transition metal dichalcogenide alloys Mo(1−x)W(x)X(2) (X = S, Se, and Te)

A combination of density functional theory, an empirical model, and Monte Carlo simulations is used to shed light on the evolution of the atomic distribution in the two-dimensional semiconducting transition metal dichalcogenide alloys Mo(1−x)W(x)X(2) (X = S, Se, and Te) as a function of the W concentration and temperature. Both random and ordered phases are discovered and the origin of the phase transitions is clarified. While the empirical model predicts at x = 1/3 and 2/3 ordered alloys, Monte Carlo simulations suggest that they only exist at low temperature due to a small energetic preference of Mo-X-W over Mo-X-Mo and W-X-W interactions, explaining the experimental observation of random alloy Mo(1−x)W(x)S(2). Negative formation energies point to a high miscibility. Tunability of the band edges and band gaps by alteration of the W concentration gives rise to a broad range of applications.