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

Path-integral Monte Carlo calculations have been performed to study the He4 adsorption on γ-graphyne, a planar network of benzene rings connected by acetylene bonds. Assuming the 4He-substrate interaction described by a pairwise sum of empirical 4He-carbon interatomic potentials, we find that unlike α-graphyne, a single sheet of γ-graphyne is not permeable to 4He 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 4He atoms. A partially-filled 4He monolayer is found to exhibit different commensurate solid structures depending on the helium coverage; it shows a C2/3 commensurate structure at an areal density of 0.0491 Å-2, a C3/3 structure at 0.0736 Å-2, and a C4/3 structure at 0.0982 Å-2. While the promotion to the second layer starts beyond the C4/3 helium coverage, the first 4He layer is found to form an incommensurate triangular solid when compressed with the development of the second layer.