The ordinary transport properties of the noble metals

The Fermi Surfaces in Cu, Ag and Au are now known to be greatly distorted, with thick ‘necks’ passing through the zone boundaries. In this paper we enquire whether such an electronic structure is quantitatively consistent with the observed transport coefficients. The mathematical model is quite simple; the shape of the Fermi surface is made to depend on a single parameter which can be interpreted as the pseudo-potential of the {111} atomic planes acting on an orthogonalized plane wave, giving rise to an energy gap of 5–10 ev at the zone boundaries. Various integrals over the Fermi surface can then be evaluated by elementary methods, and compared with the corresponding experimental quantities. The electronic specific heat and optical mass in the pure metals are consistent with the model. The galvanomagnetic effects are shown to depend a great deal on the anisotropy of the electron relaxation time, whose variation with energy is also probably the electron relaxation time, whose variation with energy is also probably the main determinant of the sign of the thermoelectric power. A better theory of electron-phonon interaction is needed before this, and the electrical and thermal conductivities, can be calculated accurately. Generally speaking there is no evidence which directly contradicts the rigid band model, except perhaps the effect of alloying on the optical absorption edges and on the electronic specific heat, but there are still many experimental and theoretical gaps in our knowledge.