First-principles prediction of crystal structures at high temperatures using the quasiharmonic approximation

We show here how first-principles quasiharmonic approximation (QHA) calculations in its simplest statically constrained form can be used to predict crystal structures at high temperatures. This approximation has been extensively used to investigate thermodynamic properties of Earth forming minerals and has offered excellent results for the major mantle phases at relevant conditions. We carefully compare QHA predictions of crystal structures using the local density approximation with crystallographic data in $\mathrm{Mg}\mathrm{Si}{\mathrm{O}}_3$ perovskite at high pressures and temperatures. Small but systematic deviations in the lattice parameters (at most 0.3%) appear at high temperatures $(T>2000\mathrm{K})$ and are associated with the development of deviatoric thermal stresses. An iterative scheme is proposed to eliminate these spurious thermal stresses and further improve the quality of the predictions of this popular and successful thermodynamics method.