Seebeck Effect in Sodium Tungsten Bronze

Abstract

The Seebeck coefficients of metallic ${\mathrm{Na}}_x\mathrm{W}{\mathrm{O}}_3$ were measured as functions of the sodium concentration $x$ from $x=0.9\mathrm{}$ to $x=0.4\mathrm{}$, and as functions of the temperature from 4.2 to 300°K. The diffusion contribution did not confirm the $x^{-\frac{2}{3}}$ 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 $\frac{S_{\perp }}{S_{\mathrm{II}}}=1.3\mathrm{}$ at 300°K.