Correlation Effects on the Electronic Specific Heat of Sodium

Abstract

The effect of the martensitic transformation in sodium on measured values of its specific heat is analyzed. It is shown that the only important effect at low temperatures is to produce a mixture of the two phases. The measured specific heat is very closely given by the sum of the specific heats of each phase measured separately. An analysis of the various experimental measurements gives the result that the effective mass of conduction electrons in the bcc high-temperature phase is greater than 1.5 times the free electron mass while in the hcp low-temperature phase the corresponding value is less than 1.21. Using further experimental data it is estimated that the effective masses in the bcc high-temperature phase and the hcp low-temperature phase are 1.7 and 1.1 times the free electron value, respectively. These effective mass values imply that there is substantial contact of the Fermi surface in the hcp structure with the "$A$" faces of the Brillouin zone. The large effective mass in the bcc phase indicates a large enhancement of the specific heat of the conduction electrons in sodium by correlation and electron-phonon interaction effects. The correlation effects alone appear to increase the specific heat of a free electron gas at a density corresponding to $r_s=3.96\mathrm{}$ (in units of the Bohr radius) by about 40%.