Analytical optimization of the lattice parameter using the binding energy calculated in the quasi-classical approximation

Abstract

The dependence of the static binding energy of a crystal on the crystal structure as calculated in the initial quasi-classical approximation is shown to allow the equilibrium lattice parameter to be found analytically. The application of this method to boron nitride modifications leads to lattice parameters that coincide with experimental values to within several percent. This method gives lattice parameters of 2.66, 3.49, and 2.44 A for the BN hexagonal layer and the cubic c-BN and “ideal” wurtzite-like w-BN crystals, respectively. The corresponding binding energies are estimated to be 23.2, 14.1, and 13.6 eV/mol, respectively.