Lorenz Number of Chromium

The thermal and electrical conductivities $\kappa$ and $\sigma$, respectively, have been measured for chromium between approximately 1.5 and 330°K in order to determine the Lorenz number $L=\frac{\kappa }{\sigma T}$. Since at 330°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°K it is greater than the expected Sommerfeld value ($L_0=2.445\mathrm{}\times {10}^{-8\mathrm{}}$ ${\mathrm{V}}^2$/${\mathrm{deg}}^2$). 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 $L\left(\mathrm{Cr}\right)$ 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 Néel 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 Neél temperature Cr may be approaching nondegeneracy.