Calculating elasticity of aluminum at high temperature and pressure including anharmonicity

Accurately calculating the elastic constants in crystals at high temperature and pressure from first-principles requires the inclusion of anharmonic effects, but current calculations in the literature rarely include anharmonicity due to computational cost. Here we calculate the elastic constants of aluminum using density functional theory where anharmonic effects are explicitly included by employing the quasiharmonic approximation with free energy perturbation theory. The computational cost is minimized by using the irreducible derivative method for computing phonons and phonon interactions. We calculate the thermal expansion, second order elastic constants, and third order elastic constants up to high temperatures and pressures in aluminum and compare to experimental measurements where available.