Conductivity of Monovalent Metals

Abstract

The conductivity of monovalent metals is computed from the Bloch theory under the assumption that the wave functions of the electrons are nearly the same as those of free electrons throughout the major part of the volume. The perturbation potential resulting from the Debye elastic waves, which produce transitions between the electronic states, is the sum of two terms: (1) the change in the total potential of the ions, which are assumed to move rigidly with the elastic waves, and (2) the change in the potential of the self-consistent field of the valence electrons. The second part tends to compensate the first. Scattering of electrons through angles greater than 2 ${\sin }^{-1\mathrm{}}$ $2^{-\frac{2}{3}}$ (∼79°) results from the "Umklappprozesse" of Peierls. It is shown that the probability of these transitions joins smoothly with the probability of transitions of the ordinary type, so that the probability is a continuous function of the angle of deflection, and transitions through all angles are possible. Comparison with experiment is made through Bethe's interaction constant $C$, which is a measure of the average scattering power of the elastic waves. Table I gives the theoretical and experimental values of $\frac{C}{\zeta }$, where $\zeta$ is the Fermi energy. Reasonable agreement is obtained for Na and K, but the theoretical values of $C$ for the remaining monovalent metals are somewhat too small.