# Phases of Ca from first principles

## Abstract

Structures and properties of many of the phases of Ca under pressure are calculated from first principles by a systematic procedure that minimizes total energy E with respect to structure under the constraint of constant volume V. The minima of E are followed on successive sweeps of lattice parameters for 11 of 14 Bravais symmetries for one-atom-per-cell structures. The structures include the four orthorhombic phases. Also included are the hexagonal close-packed and cubic diamond phases with two atoms per primitive cell. No uniquely orthorhombic phases are found; all one-atom orthorhombic phases over a mega-bar pressure range are identical to higher-symmetry phases. The simple cubic phase is shown to be stable where it is the ground state. The number of distinct one-atom phases reduces to five plus the two two-atom phases. For each of these phases the Gibbs free energy at pressure p, G(p), is calculated for a non-vibrating lattice; the functions G(p) give the ground state at each p, the relative stabilities of all phases and the thermodynamic phase transition pressures for all phase transitions over a several-megabar range. © 2009 IOP Publishing Ltd.