Role of dynamical instability in the ab initio phase diagram of calcium

In the 32-119 GPa pressure range and at room temperature, a simple cubic phase was reported for calcium in many different experiments. Standard linear response theory, both within density functional perturbation theory and frozen phonon calculations, presents dynamical instabilities for the simple cubic structure in the whole pressure range. Many other possible candidate phases, as well as several possible stabilization mechanisms for the simple cubic phase, have been proposed as the result of ab initio predictions but the role of temperature on the relative stability of the different phases has not been systematically investigated. We revisit the stability of the three most important candidate phases of calcium for the intermediate pressure range and for various temperatures, taking explicitly into account thermal corrections relative to electronic as well as phononic entropy and anharmonic contributions. This corrects the discrepancies among previous theoretical results and experiments and presents a different picture of the temperature driven phase transition, which results from dynamical anharmonic stabilization of simple cubic and destabilization of the tetragonal phase.