Participation of the electron gas in lattice vibrations

Abstract

The vibration spectrum and the specific heats of gold have been studied by two models in order to test whether the electrons participate in the complete vibration spectrum of a crystal. The two models represent the extreme cases given by de Launay, one of which ignores the effect of electrons on the lattice vibration while the other assumes its full participation for all the frequencies. Frequencies have been calculated for the 1000 points of the Brillouin zone and the specific heats have been evaluated by the sampling technique. The choice of this metal for calculation was dictated by the fact that, on account of the large discrepancy in the Cauchy relation, the difference between the lattice frequencies of the two models is expected to be very high. It is found that the central force model does not predict the value of the Cv of the metal at all correctly, while de Launay's model is in qualitative agreement with experiment above 15°K. De Launay's idea that electrons participate only in the non-dispersive region of the spectrum thus appears to be wrong.