  Common substitutional isovalent semiconductor alloys usually form disordered
metastable phases with positive excess formation enthalpies ({\Delta}H). In
contrast, monolayer alloys of transition metal dichalcogenides (TMDs) MX2 (M =
Mo, W; X = S, Se) always have negative {\Delta}H, suggesting atomic ordering,
which is, however, not yet experimentally observed. Using first-principles
calculations, we find that the negative {\Delta}H of cation-mixed TMD alloys
results from the charge transfer from weak Mo-X to nearest strong W-X bonds and
the negative {\Delta}H of anion-mixed TMD alloys comes from the larger energy
gain due to the charge transfer from Se to nearest S atoms than the energy cost
due to the lattice mismatch. Consequently, cation-mixed and anion-mixed alloys
should energetically prefer to have Mo-X-W and S-M-Se ordering, respectively.
The atomic ordering, however, is only locally ordered but disordered in the
long range due to the symmetry of TMD monolayers, as demonstrated by many
energetically degenerate structures for given alloy compositions. Besides, the
local ordering and disordering effects on the macroscopic properties such as
bandgaps and optical absorptions are negligible, making the experimental
observation of locally ordered TMD alloys challenging. We propose to take the
advantage of microscopic properties such as defects which strongly depend on
local atomic configurations for experiments to identify the disordering and
local ordering in TMD alloys. Finally, quaternary TMD alloys by mixing both
cations and anions are studied to have a wide range of bandgaps for
optoelectronic applications. Our work is expected to help the formation and
utilization of TMD alloys.
