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

We present theoretical studies for the third-order elastic constants Cᵢⱼₖ 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 Cᵢⱼₖ 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 cᵢⱼ^' and the mode Gr\"uneisen constants for long-wavelength acoustic modes γ(q,j).