Lattice Conductivity, Lorenz Numbers, and Nernst-Ettingshausen Effect in Tungsten at Liquid-Helium Temperatures

A further analysis of previously published measurements of the dc electrical and thermal transport coefficients of a tungsten crystal is presented. The coefficients were measured as functions of a strong magnetic field at several temperatures in the range of liquid ${\mathrm{He}}^4$. Problems in separating the lattice thermal conductivity from the electronic thermal conductivity by a simultaneous study of the magnetoresistivities are discussed. The limiting conductivity obtained from such a study of the tungsten data is found to be in reasonable agreement with calculations based on the assumption of strongly coupled phonons scattered by nearly free electrons. From the same data, the Lorenz number is deduced as a function of temperature and found to be in excellent agreement with an electron-electron scattering formula given by Ziman. The transverse (Hall and Righi-Leduc) conductivities are used to deduce a transverse Lorenz number which displays an unexpected temperature dependence that is not explained. An apparent phonon drag effect, very similar to that found by Long et al. in the transverse (Nernst-Ettingshausen) thermoelectric coefficient of antimony, is found in the tungsten data for the same coefficient, and is quantitatively explained by a simple model. An electronic specific-heat coefficient is also deduced from the Nernst-Ettingshausen data, and is found to have a value intermediate to the results of augmented-plane-wave (APW) and relativistic augmented-plane-wave (RAPW) Fermi surface calculations.