Lorenz Number of Chromium

Abstract

The thermal and electrical conductivities $\ensuremath{\kappa}$ and $\ensuremath{\sigma}$, respectively, have been measured for chromium between approximately 1.5 and 330\ifmmode^\circ\else\textdegree\fi{}K in order to determine the Lorenz number $L=\frac{\ensuremath{\kappa}}{\ensuremath{\sigma}T}$. Since at 330\ifmmode^\circ\else\textdegree\fi{}K these data agree with the higher-temperature measurements by Powell and Tye, an analysis has been developed to encompass both sets of data. Although $L$ shows the usual metallic behavior at low temperatures, at all temperature above 90\ifmmode^\circ\else\textdegree\fi{}K it is greater than the expected Sommerfeld value (${L}_{0}=2.445\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ ${\mathrm{V}}^{2}$/${\mathrm{deg}}^{2}$). It is not possible to account for this anomaly by the usual assumption of a lattice component of thermal conductivity without allowing the component itself to become anomalous. Klemens has pointed out that anomalous values of $L$ are expected in transition metals at high temperatures because the Fermi skin begins to encompass their complicated band structure. Analysis of $L(\mathrm{Cr})$ in these terms shows that the transport coefficients can be separated into two factors: one which has the temperature dependence of single definite scattering processes above and below the N\'eel temperature, and another which is the integral of a quantity that has the characterisitics of the known band structure. Since this integral is temperature-dependent, it is possible to state that certain anomalies in the transport properties of chromium are due to its band structure. It appears that above the Ne\'el temperature Cr may be approaching nondegeneracy.