Contribution of electronic excitations to the entropy of crystals: The relative stabilities of the hcp, fcc, and bcc structures among the transition metals

The entropy contributions to the relative stability of one crystal structure versus another due to electronic excitations are calculated in lowest order. While the electronic contribution is but a small part of the total entropy of a crystal, the change in these terms with change in structure is as large as the entropy changes inferred from experiment. One will not have a complete accounting of such entropy effects until there are detailed estimates of the phonon contributions. However, the present results offer the possibility of dividing the experimental values into electronic and phonon terms and attributing to each the temperature dependence of their leading terms when doing thermodynamic calculations.