  First principles phase diagram calculations, that included van der Waals
interactions, were performed for the bulk transition metal dichalcogenide
system $(1-X) \cdot WS_{2} - (X) \cdot WTe_{2}$. To obtain a converged phase
diagram, a series of cluster expansion calculations were performed with
increasing numbers of structure-energies, ($N_{Str}$) up to $N_{Str}=435$, used
to fit the cluster expansion Hamiltonian. All calculated formation energies are
positive and all ground-state analyses predict that formation energies for
supercells with 16 or fewer anion sites are positive; but when $\approx 150
N_{Str} \leq 376$, false ordered ground-states are predicted. With $N_{Str}
\geq 399$, only a miscibility gap is predicted, but one with dramatic asymmetry
opposite to what one expects from size-effect considerations; i.e. the
calculations predict more solubility on the small-ion S-rich side of the
diagram and less on the large-ion Te-rich side. This occurs because S-rich
low-energy metastable ordered configurations have lower energies than their
Te-rich counterparts.
