Phase-field crystal model for heterostructures

Atomically thin two-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possibility of choosing many constituent components and their proportions allows optimization of these materials to specific requirements. The wide adaptability comes with a cost of large parameter space making it hard to experimentally test all the possibilities. Instead, efficient computational modeling is needed. However, large range of relevant time and length scales related to physics of polycrystalline materials poses a challenge for computational studies. To this end, we present an efficient and flexible phase-field crystal model to describe the atomic configurations of multiple atomic species and phases coexisting in the same physical domain. We extensively benchmark the model for two-dimensional binary systems in terms of their elastic properties and phase boundary configurations and their energetics. As a concrete example, we demonstrate modeling lateral heterostructures of graphene and hexagonal boron nitride. We consider both idealized bicrystals and large-scale systems with random phase distributions. We find consistent relative elastic moduli and lattice constants, as well as realistic continuous interfaces and faceted crystal shapes. Zigzag-oriented interfaces are observed to display the lowest formation energy.