Elastic constants of random solid solutions by SQS and CPA approaches: the case of fcc Ti-Al

Special quasi-random structure (SQS) and coherent potential approximation (CPA) are techniques widely employed in the first-principles calculations of random alloys. Here we scrutinize these approaches by focusing on the local lattice distortion (LLD) and the crystal symmetry effects. We compare the elastic parameters obtained from SQS and CPA calculations, taking the random face-centered cubic (fcc) Ti1-xAlx (0 <= x <= 1) alloy as an example of systems with components showing different electronic structures and bonding characteristics. For the CPA and SQS calculations, we employ the Exact Muffin-Tin Orbitals (EMTO) method and the pseudopotential method as implemented in the Vienna Ab initio Simulation Package (VASP), respectively. We show that the predicted trends of the VASP-SQS and EMTO-CPA parameters against composition are in good agreement with each other. The energy associated with the LLD increases with x up to x = 0.625 similar to 0.750 and drops drastically thereafter. The influence of the LLD on the lattice constants and C12 elastic constant is negligible. C-11 and C-44 decrease after atomic relaxation for alloys with large LLD, however, the trends of C-11 and C-44 are not significantly affected. In general, the uncertainties in the elastic parameters associated with the symmetry lowering turn out to be superior to the differences between the two techniques including the effect of LLD.