RESUMO
We extend the three-point XPFC model of Seymour & Provatas (Seymour & Provatas 2016 Phys. Rev. B93, 035447 (doi:10.1103/PhysRevB.93.035447)) to two components to capture chemical vapour deposition-grown graphene, and adapt a previous two-point XPFC model of Greenwood et al. (Greenwood et al. 2011 Phys. Rev. B84, 064104 (doi:10.1103/PhysRevB.84.064104)) into a simple model of two-component graphene. The equilibrium properties of these models are examined and the two models are compared and contrasted. The first model is used to study the possible roles of hydrogen in graphene grain boundaries. The second model is used to study the role of hydrogen in the dendritic growth morphologies of graphene. The latter results are compared with new experiments.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.
RESUMO
A comprehensive study is presented for the influence of misfit strain, adhesion strength, and lattice symmetry on the complex Moiré patterns that form in ultrathin films of honeycomb symmetry adsorbed on compact triangular or honeycomb substrates. The method used is based on a complex Ginzburg-Landau model of the film that incorporates elastic strain energy and dislocations. The results indicate that different symmetries of the heteroepitaxial systems lead to distinct types of domain wall networks and phase transitions among various surface Moiré patterns and superstructures. More specifically, the results show a dramatic difference between the phase diagrams that emerge when a honeycomb film is adsorbed on substrates of honeycomb versus triangular symmetry. It is also shown that in the small deformation limit, the complex Ginzburg-Landau model reduces to a two-dimensional sine-Gordon free energy form. This free energy can be solved exactly for one dimensional patterns and reveals the role of domains walls and their crossings in determining the nature of the phase diagrams.
