  Today the study of two-dimensional (2D) materials has become one of the key
objectives of materials science. Unlike their three-dimensional counterparts,
2D materials can simultaneously demonstrate unique transport and mechanical
properties due to their dimensionality and quantum size effect. In their
fabrication and application, 2D materials are usually located on top of the
substrate or combined into heterostructures, which makes their structures and
properties strongly depend on the nature and quality of the environment. Here,
we present a novel method for studying the atomic structures of two-dimensional
materials and epitaxial thin films on arbitrary substrates. The method can
predict successful stages of epitaxial growth and the regions of stability of
each atomic configuration with experimental parameters of interest. We
demonstrate the performance of our methodology in the prediction of the atomic
structure of MoS2 on Al2O3 (0001) substrate. The method is also applied to
study the CVD growth of graphene and hexagonal boron nitride on Cu (111)
substrates. In both cases, stable monolayer and multilayer structures were
found. The stability of all the structures in terms of partial pressures of
precursors and temperature of growth is predicted within the ab initio
thermodynamics approach.
