Lattice Thermal Conductivity, Nernst-Ettinghausen Effect, and Specific Heat in Antimony at Low Temperature

Abstract

The lattice thermal conductivity, the high-field Nernst-Ettinghausen thermoelectric coefficient, and the specific heat of antimony have been determined in the temperature range 0.4-2.4°K. Thermal-conductivity results confirm the predominance of phonon-electron normal scattering in the lowest range of temperatures with the expected $T^2$ law. The dramatic increase in the lattice thermal conductivity above 1.5°K is thought to be due to the inability of the electrons to scatter phonons with wave numbers $q>\mathrm{}2\mathrm{}{k}_F$, where $2k_F$ is the diameter of a charge carrier's Fermi pocket. An effective scattering Debye temperature of ${\Theta }^{*}=\left(\frac{2k_F}{q_D}\right)\Theta \approx 25°$K is in good agreement with experimental results. Nernst-Ettinghausen results give the total electronic density of states $Z=(1.10\mathrm{}\pm 0.07)\times {10}^{33}$ ${\mathrm{erg}}^{-1\mathrm{}}$ ${\mathrm{cm}}^{-3\mathrm{}}$; the presence of a phonon-drag contribution is confirmed and discussed. The specific-heat results, $C=(116.5\mathrm{}\pm 6.4)T+(211.0\pm 5.3)T^3+1.97\mathrm{}\pm 0.23)T^{-2\mathrm{}}$ in μJ ${\left(\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{°}\mathrm{K}\right)}^{-1\mathrm{}}$, are compared with the results of transport measurements and with recent specific-heat determinations.