Thermal Resistivity of Potassium between 1.5 and 15 K

Abstract

The thermal resistivity of single-crystal and polycrystalline potassium specimens having residual-resistance ratios between 195 and 6500 has been measured between 1.5 and 15 K. It is found that theoretical calculations based on semiclassical ideas are in reasonably good agreement with the experimental data, particularly for the more impure specimens at low temperatures. The role of umklapp scattering is clearly evident. Although the umklapp processes can contribute as much as 50% to the total thermal resistivity, the simple expression $W=\frac{A}{T}+B{T}^{2}$, obtained by only considering normal scattering, describes the results remarkably well up to about 10 K. Depending upon the purity, the values of $B$ ranged from 2.38 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$ cm/W to 1.53 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$ cm/W, indicating a deviation from Matthiessen's rule of about 50%. The magnitude of the calculated thermal resistivity is very near the experimental result for impure specimens but the calculated values are too high for the purer specimens. It is shown that when impurity scattering is dominant, a variational calculation of the electron-phonon thermal resistance should be quite accurate. In pure specimens the calculations are not expected to be nearly as good; reasons for this are discussed. At high temperatures, above 6 to 8 K, the theoretical temperature dependence is in considerable disagreement with the experimental results. Deviations from Matthiessen's rule, as well as other possible reasons for this discrepancy, are discussed. Our data are in qualitative agreement with that of Mac-Donald, White, and Woods; however, contrary to the observations of Stauder and Mielczarek, we observe no anomalous behavior in the thermal conductivity of potassium. Reasons for the differences between our results and those of Stauder and Mielczarek are presented and discussed. We conclude that the thermal resistance of potassium can be understood very well within the framework of existing theoretical work. In specimens of low and intermediate purity the contribution of lattice thermal conduction can be appreciable and should be taken into account when making comparisons with theory.