Equilibrium lines and crystal phases under pressure

A crystal phase in equilibrium under changing pressure traces out a line in structure space where each point corresponds to a structure. Along that equilibrium line the structure and all static properties describe the static behavior of the phase, including two sets of elastic constants and the bulk modulus. We discuss and illustrate the calculation of the equilibrium line and the properties from both the Gibbs free energy and the internal energy. We show that the bulk modulus, which gives a stress to strain ratio along the equilibrium line, has a universal relation independent of pressure to that set of elastic constants which control the stability, but not to the set of elastic constants appearing in the stress-strain relations at constant pressure. © 2009 IOP Publishing Ltd.