Changes in the Electrical, Thermal, and Thermoelectrical Properties of Monovalent Metals by Lattice Distortions

In this paper we study theoretically the effect of static lattice distortions on the electrical resistivity, electronic thermal conductivity, and absolute thermoelectric power of monovalent metals. We base our work on a transport equation which follows from straightforward quantum-statistical arguments. Employing an iteration method, we reduce this equation to a set of integral equations in one independent variable, and solve this set explicitly for $T\gg \Theta$. We are thus able to study the three effects of interest for a distorted metallic lattice at high temperatures, and to obtain information concerning the anisotropy of a metal, containing certain types of imperfections, in a much wider temperature range. We prove the striking result that our transport equation yields the same results as the simplified one employed by Mackenzie and Sondheimer, provided that $T\gg \Theta$ and that the effect of the lattice distortions on the three properties mentioned above is small. To illustrate our general formulas, we treat in detail the case of an array of parallel edge dislocations. We express our results in terms of a quantity $Q$, which is proportional to the ratio of the changes in absolute thermoelectric power and electrical resistivity. For plastically deformed noble metals, the observed values of $Q$ are appreciably larger than the corresponding theoretical values for dislocation arrays of the type mentioned above.