Interlayer interaction and mechanical properties in multi-layer graphene, Boron-Nitride, Aluminum-Nitride and Gallium-Nitride graphene-like structure: A quantum-mechanical DFT study

In present study, we investigated mechanical, electronic and interlayer properties of mono, bi and 3layer of Boron-Nitride (B-N), Aluminum-Nitride (Al-N) and Gallium-Nitride (Ga-N) graphene sheets and compared these results with results obtained from carbonic graphenes (C-graphenes). For reaching this purpose, first we optimized the geometrical parameters of these graphenes by using density functional theory (DFT) method. Then we calculated Young's modulus of graphene sheet by compressing and then elongating these sheets in small increment. Our results indicates that Young's modulus of graphenes didn't changed obviously by increasing the number of layer sheet. We also found that carbonic graphene has greatest Young's modulus among another mentioned sheets because of smallest equilibrium distance between its elements. Next we modeled the van der Waals interfacial interaction exist between two sheets with classical spring model by using general form of Lennard-Jones (L-J) potential for all of mentioned graphenes. For calculating L-J parameters (ε and σ), the potential energy between layers of mentioned graphene as a function of the separation distance was plotted. Moreover, the density of states (DOS) are calculated to understand the electronic properties of these systems better.