LAUSR

In this work, we report an ab initio study of the structural and thermodynamic properties of two-dimensional transition-metal dichalcogenides (2D-TMDC) alloys, Mo(1–x)W x (S, Se, Te)2, using the cluster expansion framework to compute the Helmholtz free energy of alloys as a function of alloy composition and temperature, in the framework of the generalized quasi-chemical approximation. We consider alloying only on the metal sublayer. Our results indicate a weak dependence of the structural properties (lattice constants, nearest-neighbor bond lengths, and layer width) on the alloy composition (i.e. concentrations of W and Mo atoms), in line with the very similar values of the atomic radii of Mo and W atoms. A stronger dependence on the chalcogen is obtained, a trend that reflects the larger variations in atomic radii among the three chalcogen species. As a function of composition, the structural parameters we examined show similar trends, with negligible bowing (i.e. deviations from a Vegard’s law interpolation between end compounds), for the three alloys. Moreover, already at 300 K the behavior of these structural features as a function of composition is very similar to that of the standard-regular-solution (SRS) high-temperature limit. In contrast, the electronic band gaps of the the three alloys as a function of composition show small but significant bowing, as high as −1% to −2% near the x = 0.5 alloy composition. Similarly to the structural features, the band gaps attain the high-temperature SRS limit already at 300 K. Regarding thermodynamic properties, we obtain negative values of the internal energy of mixing for the three alloys over the full range of compositions. Therefore, the theoretical alloying phase diagram for the three alloys is featureless, with stability of a fully-mixed alloy at all temperatures and compositions, with no miscibility gap (hence no bimodal nor spinodal decomposition lines). The thermodynamic potentials (mixing internal energy, mixing entropy, and mixing free energy) reach the high-temperature limit at ∼1000 K, the temperature range of synthesis of 2D-TMDC alloys. These trends of structural and electronic properties of the 2D-TMDC alloys are due to the very similar atomic radii and the nearly identical coordination chemistry of Mo and W. Our results are in agreement with experimental work on the alloying of Mo and W atoms, for samples of Mo(1–x)W x S2 monolayer alloys, that found that the random mixed alloy is the thermodynamically stable state for this alloy, with no segregation or phase separation.