Thermoelectric Phenomena in Crystals and General Electrical Concepts

Abstract

It is shown that when an electric current passes across an interface where the crystal orientation changes there is a Peltier heat, but no corresponding jump of potential. This demands that we analyze the action of an impressed e.m.f. into two aspects. The following definitions are suggested: (1) energy per unit time delivered by the source when current $i\mathrm{flows}=i\times \mathrm{working}\text{'}\text{'}$ e.m.f.; (2) $i=\frac{(\mathrm{driving}\text{'}\text{'}\mathrm{e}.\mathrm{m}.\mathrm{f}.\mathrm{}-\Delta \mathrm{V})}{\Delta R}$. In ordinary isotropic materials this analysis is not necessary, but it is necessary in unequally heated materials in which thermal currents are flowing. In an unequally heated metal the "driving" e.m.f. between two points at a temperature difference $d\tau$ is $-\frac{d\tau \int 0^{\tau }\sigma d\tau }{\tau }$, and the "working" e.m.f. between the same two points is $\sigma d\tau$. It is shown that these expressions demand that the current convect with it the energy $\frac{\tau \int 0^{\tau }\sigma d\tau }{\tau }$, which must be described as thermal energy. We are able in these terms to give a thermodynamically consistent account of the energy transformations in all parts of a thermo-electric circuit. The theoretical significance of a thermal energy which depends on the direction of current flow is emphasized. The argument may be extended from crystals to ordinary isotropic substances. A number of questions peculiar to crystals are discussed. The existence of an internal Peltier heat when the direction of current flow changes is proved, and the importance of this effect for all theories of conduction is emphasized. Some fine structure seems demanded in a metal which is not ordinarily taken into account. Equipartition cannot hold, but the thermal energy of the electrons is of the same order of magnitude as that given by equipartition. Formulas are derived for the internal Peltier heat as a function of the direction of current flow, for the surface heats and for the two latent heats of evaporation of electrons. The possible existence of a Volta difference of potential between different faces of the same crystal is recognized. An argument is drawn from the connection with the photo-electric effect suggesting that this Volta difference may possibly vanish.