Seebeck Effect in Sodium Tungsten Bronze

The Seebeck coefficients of metallic NaₓWO₃ were measured as functions of the sodium concentration x from $x=0.9$ to $x=0.4$, and as functions of the temperature from 4.2 to 300^∘{}K. The diffusion contribution did not confirm the x^-2/3 dependence predicted by free-electron theory and suggested by earlier data. The lattice contribution at low temperatures contained a term due to normal electron-phonon processes and a term due to umklapp electron-phonon processes. The umklapp phonon drag increased with increasing sodium concentration, a result that would be expected if the Fermi surface increases with increasing sodium concentration. The Seebeck coefficient of tetragonal crystals was anisotropic with S_⊥SII=1.3 at 300^∘{}K.