Hybridization and the fcc-bcc Phase Transitions in Calcium and Strontium

Abstract

The effect of $s-d$ hybridization on the phase stabilities of calcium and strontium is studied as a function of temperature and pressure within the context of the generalized pseudopotential theory. The inclusion of hybridization is found to favor the fcc structure at all pressures and, in particular, is necessary to explain the observed fcc structure in these metals at zero temperature and pressure. Phase boundaries are calculated by equating the free energy of the fcc structure to that of the bcc structure. Temperature-induced phase transitions are predicted to occur at 555 °K in calcium and 625 °K in strontium, as compared with the experimentally observed values of 721 and 830 °K, respectively. The transition temperature $T_c$ is found to increase with pressure $P$ for both metals. The predicted $\frac{d{T}_c}{dP}$ is qualitatively correct but quantitatively too large for calcium, while of the wrong sign for strontium. However, in the simple-metal limit of no hybridization, $\frac{d{T}_c}{\mathrm{dP}}$ is calculated to be negative in both cases. This suggests that the experimental behavior at nonzero pressures can be explained by an appropriate balance of pseudopotential and hybridization contributions to the free energy.