A first principles phase diagram calculation, that included van der Waals interactions, was performed for the 3D bulk system (1 - X) · MoS2 - (X) · MoTe2. Surprisingly, the predicted phase diagram has at least two ordered phases, at X ≈ 0:46, even though all calculated formation energies are positive; in a ground-state analysis that examined all configurations with 16 or fewer anion sites. The lower-temperature I-phase is predicted to transform to a higher-temperature I'-phase at T ≈ 500 K, and I' disorders at T ≈ 730 K. Both these transitions are predicted to be first-order, and there are broad two-phase fields on both sides of the ordered regions. Both the I- and I'-phases are predicted to be incommensurate, i.e., aperiodic: I-phase in three dimensions; and I'-phase in two dimensions.
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