Commensurate-incommensurate solid transition in the 4He monolayer on γ-graphyne

Path-integral Monte Carlo calculations have been performed to study the He-4 adsorption on gamma-graphyne, a planar network of benzene rings connected by acetylene bonds. Assuming the He-4-substrate interaction described by a pairwise sum of empirical He-4-carbon interatomic potentials, we find that unlike alpha-graphyne, a single sheet of gamma-graphyne is not permeable to He-4 atoms in spite of its large surface area. One-dimensional density distributions computed as a function of the distance from the graphyne surface reveal a layer-by-layer growth of He-4 atoms. A partially-filled He-4 monolayer is found to exhibit different commensurate solid structures depending on the helium coverage; it shows a C-2/3 commensurate structure at an areal density of 0.0491 angstrom(-2), a C-3/3 structure at 0.0736 angstrom(-2), and a C-4/3 structure at 0.0982 angstrom(-2). While the promotion to the second layer starts beyond the C-4/3 helium coverage, the first He-4 layer is found to form an incommensurate triangular solid when compressed with the development of the second layer.