High-pressure phases of calcium: Prediction of phase VI and upper-pressure phases from first principles

Abstract

Comparing enthalpies among the crystal structures which have recently been determined by experiments or been predicted by first-principles calculations, we have reconstructed the phase diagram of calcium and found further high-pressure phases. Our phase diagram predicts that the phase V of an orthorhombic $Cmca$ structure exists only in a small pressure range narrower than 10 GPa and it transforms to another phase, phase VI of an orthorhombic $Pnma$ structure. In addition, we found that the phase VI prevails about 20 GPa range and transforms to still another phase, phase VII of a tetragonal $I4/mcm(00\ensuremath{\gamma})$ structure at 135 GPa and finally takes the hexagonal-close-packed structure above 495 GPa. Calculated results of the superconducting transition temperature ${T}_{c}$ on the basis of our phase diagram suggest that ${T}_{c}$ of 25 K, which is the experimentally reported highest value in calcium, should have been observed in the phase VI or phase VII, rather than in phase V.