A Theory of Electrical Conduction in Metals

Abstract

The electrons are assumed to have kinetic energy corresponding to the thermionic work function $W$ and to move on orbits which form a space lattice with a constant $\ensuremath{\delta}$ of the same order as that of the positive ions ${\ensuremath{\delta}}_{1}$. At each critical point of an orbit, each of the six directions are taken as equally probable. Treating the problem as a kind of Brownian motion and applying the virial theorem, the specific conductivity $\ensuremath{\sigma}$ is found approximately equal to $0.6\ifmmode\times\else\texttimes\fi{}\frac{N{e}^{2}(\frac{{\ensuremath{\delta}}^{2}}{h})eW}{\overline{E}}$, when $\overline{E}$ is the mean heat content of one degree of freedom of the metal. The observed and calculated values of $\ensuremath{\sigma}$ (taking $\ensuremath{\delta}={\ensuremath{\delta}}_{1}$) are in fair agreement for Ag, Au and Cu. For Na, $\ensuremath{\sigma}(\mathrm{obs}.)$ is twice $\ensuremath{\sigma}(\mathrm{calc}.)$. Better agreement would be obtained if $\ensuremath{\delta}$ were taken as $1.5{\ensuremath{\delta}}_{1}$, but uncertainty as to the values of $W$ and as to the error introduced by applying the virial theorem to discontinuous processes makes this of little significance.