Devices based on
two-dimensional (2D) materials such as graphene
and molybdenum disulfide have shown extraordinary potential in physics,
nanotechnology, and electronics. The performances of these applications
are heavily affected by defects in utilized materials. Although great
efforts have been spent in studying the formation and property of
various defects in 2D materials, the long-term evolution of vacancies
is still unclear. Here, using a designed program based on the kinetic
Monte Carlo method, we systematically investigate the vacancy evolution
in monolayer graphene on a long-time and large spatial scale, focusing
on the variation of the distribution of different vacancy types. In
most cases, the vacancy distribution remains nearly unchanged during
the whole evolution, and most of the evolution events are vacancy
migrations with a few being coalescences, while it is extremely difficult
for multiple vacancies to dissolve. The probabilities of different
categories of vacancy evolutions are determined by their reaction
rates, which, in turn, depend on corresponding energy barriers. We
further study the influences of different factors such as the energy
barrier for vacancy migration, coalescence, and dissociation on the
evolution, and the coalescence energy barrier is found to be dominant.
These findings indicate that vacancies (also subnanopores) in graphene
are thermodynamically stable for a long period of time, conducive
to subsequent characterizations or applications. Besides, this work
provides hints to tune the ultimate vacancy distribution by changing
related factors and suggests ways to study the evolution of other
defects in various 2D materials.