Correlations for single-crystal elastic constants of compound semiconductors and their representation in isomechanical groups

A correlation is presented for the single-crystal elastic constants (C-ij) of elemental (and IV-IV), III-V, and II-VI semiconductors with the diamond cubic, sphalerite, and wurtzite crystal structures. Both experimental data and theoretical calculations based on density functional theory follow the correlation. The elastic constants can be represented by an empirical linear relation that is a simple function of melting temperature T-M and mean atomic volume Omega with C-ij=A(ij)+B-ij(k(B)T(M)/Omega), where k(B) is Boltzmann's constant. The empirical constants A(ij) and B-ij are different for each of the groupings of semiconductors considered, which are identified as isomechanical groups. This correlation is similar in form to other correlations in the literature for diffusion data of materials that indicate the significance of the melting temperature as a scaling for lattice dynamic properties of materials.