Resistance of Monovalent Metals

Abstract

With the detailed knowledge available at present of the nature of the metallic state, an attempt has been made to estimate quantitatively the resistivity of the monovalent metals. It is shown that the older conception of a "deformable" potential gives for Na a resistivity about 9 times too high. In our new formulation the resistivity is simply due to the fact that in a distorted crystal the proper solutions are not of the type of progressive waves, but linear combinations of these. The transition probabilities can be worked out under the assumptions that the charge distribution of the conduction electrons almost compensates the electrostatic potential due to the shift of the ions from their equilibrium positions and that in the undistorted crystal the periodic factor $u_k$ in the wave functions $u_k\exp \left(2\mathrm{}\pi i\mathbf{k}·\mathbf{R}\right)$ does not depend sensibly on the wave number k. In this case only the average electronic density and not the exact form of the wave functions and potentials is found to be relevant. The result can be expressed by an interaction constant $C$, which measures the average scattering effectiveness of the elastic waves. The computation gives $\frac{C}{E_0}=0.84\mathrm{}$, where $E_0$ is the Fermi energy. The empirical values are for Na 0.77, K 0.81, Cu 1.12, Ag 1.21, Au 1.19.