Phonon-Drag Thermopower in Cu-Al and Cu-Si Alloys

Abstract

The thermoelectric power of Cu-Al and Cu-Si alloys has been determined from 4.2 to 320\ifmmode^\circ\else\textdegree\fi{}K. Assuming that the thermopower is separable into diffusion and phonon-drag components, the change in phonon-drag thermopower $\ensuremath{\Delta}{S}_{g}$ is determined for Cu+0.77 at.% Al and Cu+1.12 at.% Si. The change in phonon-drag thermopower is analyzed using the method developed by Huebener for lattice vacancies in gold. Scattering of phonons by impurities is assumed to follow a Rayleigh scattering law with relaxation time ${\ensuremath{\tau}}_{i}={(a{\ensuremath{\omega}}^{4})}^{\ensuremath{-}1}$. From the change in phonon-drag thermopower it is found, for 0.77 at.% Al in Cu, that $a=(0.9\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}43}$ ${\mathrm{sec}}^{3}$, while for 1.12 at.% Si in Cu, $a=(6.5\ifmmode\pm\else\textpm\fi{}2.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}43}$ ${\mathrm{sec}}^{3}$. These results are compared with the scattering parameter computed from the mass-difference term in Klemen's theory for scattering of low-frequency lattice waves by point imperfections. For Cu-Al, the results indicate that phonon scattering can be accounted for by the mass-difference term. The results for Cu-Si indicate that the mass-difference contribution to phonon scattering is of the same magnitude as the contribution from the combined effects of the elastic strain field and changes in the elastic constants of interatomic linkages.