Interpretation of Transport Measurements in Electronically Conducting Liquids

Abstract

Measurements of the electrical conductivity $\sigma$, the thermoelectric power $\alpha$, and the Hall coefficient $R$ are tabulated and examined. The properties are found to evolve smoothly as a function of the magnitude of $\sigma$, which ranges from ${10}^5$ to ${10}^{-12\mathrm{}}$ ${\mathrm{\Omega }}^{-1\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$. For $\sigma >5000\mathrm{}$, conventional metallic properties are found. For $\sigma <100\mathrm{}$, the conductivity is due to the hopping of localized electrons. Attention is focused on the intermediate range of $\sigma$ values, within which $\sigma$ and $\alpha$ exhibit the characteristics of a $p$-type semiconductor, with $\frac{\mathrm{dp}}{\mathrm{dT}}>0\mathrm{}$, while the behavior of $R$ is $n$ type and metallic. A number of problems associated with the semiconductor interpretation are discussed, and it is suggested that the Hall coefficient measurements are more significant than has generally been believed. The traditional procedures by which information about electronic properties have been deduced from transport measurements are carefully reexamined. It is demonstrated that $\sigma$ and $\alpha$ on one hand, and $R$ on the other, measure different and essentially independent aspects of electronic behavior. The apparently contradictory nature of the data in the intermediate $\sigma$ range is shown to result from the use of restrictive assumptions and specialized language of the crystalline solid state. A generalized language is developed which can more adequately describe electronic properties in noncrystalline material. Four, rather than two, basic categories of $n$- and $p$-type behavior are defined. A simple model is presented which can describe the transport characteristics which predominate in the different ranges of conductivity.