Ab initiocalculations of third-order elastic constants and related properties for selected semiconductors

Abstract

We present theoretical studies for the third-order elastic constants ${C}_{ijk}$ in zinc-blende nitrides AlN, GaN, and InN. Our predictions for these compounds are based on detailed ab initio calculations of strain-energy and strain-stress relations in the framework of the density functional theory. To judge the computational accuracy, we compare the ab initio calculated results for ${C}_{ijk}$ with experimental data available for Si and GaAs. We also underline the relation of the third-order elastic constants to other quantities characterizing anharmonic behavior of materials, such as pressure derivatives of the second-order elastic constants ${c}_{ij}^{\ensuremath{'}}$ and the mode Gr\"uneisen constants for long-wavelength acoustic modes $\ensuremath{\gamma}(\mathbf{q},\mathbf{j})$.