Electronic Theory of Phase Transitions in Ca, Sr, and Ba under Pressure

The transitions induced by temperature and pressure between the face-centered cubic (fcc) and the body-centered cubic (bcc) phases in the alkaline earth metals---Ca, Sr, and Ba---are analyzed by computing the differences in Gibbs free energy between the two phases in the framework of the nearly-free-electron and harmonic approximations. At the absolute zero of temperature and pressure, the observed fcc in Sr and bcc in Ba were found to have the lower internal energy; in Ca, however, identical analysis led to lower energy in bcc rather than the observed fcc. An fcc-bcc transition characterized by a change in the sign of the difference in free energies in Sr at 0^∘{}K was found at a critical pressure Pc~10 kbar; at zero pressure, it was found at a critical temperature, Tc~150^∘K. Both these results agree only qualitatively with the observed Pc~36 kbar and Tc~830^∘K. Ca and Ba, already bcc at absolute zero, showed no phase transition.