Quasi-harmonic temperature dependent elastic constants from first principles

We present our implementation of the temperature dependent elastic constants (EC) in the thermo_pw software, a driver of the Quantum ESPRESSO routines for the calculation of material properties. The calculation can be done within either the quasi-static or the quasi-harmonic approximations (QHA) and can provide both the isothermal and isoentropic EC. Within the QHA, isothermal EC are computed from second derivatives with respect to strain of the Helmholtz free energy, derived from the phonon frequencies computed via Density Functional Perturbation theory for several strained configurations.
The calculation is parallelized on images and can evaluate simultaneously the dynamical matrices at different geometries, q-points, and irreducible representations. We expect that the method can take advantage from the next generation of parallel machines with thousands of CPUs for any size of the unit cell of the solid.
We apply our method to several metals (Al, Ag, Au, Cu, Pd, and Pt) and semiconductors (Si and BAs). The results are compared with the available experimental data. Moreover the effect of finite temperature electronic excitation as well as of the exchange and correlation functional are discussed.