  Graphene is a two-dimensional carbon material which exhibits exceptional
properties, making it highly suitable for a wide range of applications.
Practical graphene fabrication often yields a polycrystalline structure with
many inherent defects, which significantly influence its performance. In this
study, we utilize a Monte Carlo approach based on the optimized Wooten, Winer
and Weaire (WWW) algorithm to simulate the crystalline domain coarsening
process of polycrystalline graphene. Our sample configurations show excellent
agreement with experimental data. We conduct statistical analyses of the bond
and angle distribution, temporal evolution of the defect distribution, and
spatial correlation of the lattice orientation that follows a stretched
exponential distribution. Furthermore, we thoroughly investigate the diffusion
behavior of defects and find that the changes in domain size follow a power-law
distribution. We briefly discuss the possible connections of these results to
(and differences from) domain growth processes in other statistical models,
such as the Ising dynamics. We also examine the impact of buckling of
polycrystalline graphene on the crystallization rate under substrate effects.
Our findings may offer valuable guidance and insights for both theoretical
investigations and experimental advancements.
