α-MoC1–x
has
recently
attracted extensive attention in heterogeneous catalysis for its unique
catalytic properties. As a nonstoichiometric material, the performance
of α-MoC1–x
is closely related
to its intrinsic carbon vacancy, but the knowledge regarding the structural
nature associated with the vacancy is still lacking. In this work,
we perform a cluster expansion (CE) study to reveal the vacancy distribution
on α-MoC1–x
(001) and (111)
surface. Considering that a large number of symmetrically distinct
clusters are needed to build accurate CE models for multicomponent
surface systems, we adopt the strategy of utilizing the machine-learning
force field to efficiently generate thousands of training data. With
the effective cluster interactions on the α-MoC1–x
(001) and (111) surfaces, Monte Carlo simulations
are conducted to model the surface vacancy distribution behaviors.
The surface-bulk difference as well as the surface effects on configurational
properties are revealed. It is found that the carbon atom tends to
segregate to the topmost layer of the α-MoC1–x
(001) surface and the vacancy tends to segregate
to the topmost layer of the α-MoC1–x
(111) surface. We also predict the structures of the topmost
layer of (001) and (111) surface under the simulated reaction condition,
which can provide important insights into catalyst modeling and design
for α-MoC1–x
-related catalytic
systems. The scheme to build surface CE models developed in this work
can be generally used in theoretical modeling of heterogeneous catalytic
surfaces with configurational disorder.