Directional anisotropy, finite size effect and elastic properties of hexagonal boron nitride

Classical molecular dynamics simulations have been performed to analyze the elastic and mechanical properties of two-dimensional (2D) hexagonal boron nitride (h-BN) using a Tersoff-type interatomic empirical potential. We present a systematic study of h-BN for various system sizes. Young's modulus and Poisson's ratio are found to be anisotropic for finite sheets whereas they are isotropic for the infinite sheet. Both of them increase with system size in accordance with a power law. It is concluded from the computed values of elastic constants that h-BN sheets, finite or infinite, satisfy Born's criterion for mechanical stability. Due to the the strong in-plane sp(2) bonds and the small mass of boron and nitrogen atoms, h-BN possesses high longitudinal and shear velocities. The variation of bending rigidity with system size is calculated using the Foppl-von Karman approach by coupling the in-plane bending and out-of-plane stretching modes of the 2D h-BN.