Phonon spectrum and thermal energy of sodium by Toya’s method with a modified interference factor

Abstract

Toya has recently used the Hartree-Fock method to study the interaction of lattice vibrations with the electrons in a metal. This has been used to calculate the phonon spectrum and C v of sodium. Since Toya’s original expressions give a slightly exaggerated contribution for the Umklapp processes they have been modified by multiplying the argument of Bardeen’s interference factor ( g function) by a constant which is taken to be 1·04. Some evidence for the correctness of this modification has been presented. The calculated dispersion relations for the waves propagated in the three principal symmetry directions as well as the C v are found to be in very good agreement with the experimental results above 40 °K. There is some degree of disagreement below this temperature which may possibly be due to the existence of two phases.