Size Effect on Phonon Drag in Platinum

Abstract

Thermoelectric measurements with thermocouples consisting of thin platinum foils and 0.254-mm-diam platinum wire have been carried out between 4.2 and 310°K. The thickness of the foils was 1.6×${10}^{-3\mathrm{}}$ to 8×${10}^{-3\mathrm{}}$ mm. The difference $\Delta S$ between the thermoelectric power of the foils and the wire was separated into the electronic component $\Delta S^e$, caused by the electron scattering at the crystal surface, and the phonondrag component $\Delta S^g$, resulting from the phonon scattering at the crystal surface. From the phonon-drag component $\Delta S^g$ the phonon mean free path ${\lambda }_0$ in the bulk material was determined as a function of the temperature. Above 60°K (approximately the temperature of the phonon-drag peak) the relation ${\lambda }_0=(1.1\mathrm{}\times {10}^{-5\mathrm{}})e^{64°\mathrm{K}/T}$ mm was found, in agreement with the expectation that in this temperature range ${\lambda }_0$ is mainly limited by phonon-phonon umklapp processes. The pre-exponential factor in ${\lambda }_0$ is within a factor of two in agreement with the value calculated from Klemens's theory. From the electronic component $\Delta S^e$, the derivative of the electron mean free path $l$ with respect to the electron energy $E$ was found to be ${\left\{\frac{\partial \ln l}{\partial E}\right\}}_{E_F}=3.4\mathrm{}\pm 0.8$ ${\mathrm{}\left(\mathrm{eV}\right)\mathrm{}}^{-1\mathrm{}}$. Measurements of the electrical-resistivity difference between the foils and the wire yielded for the electron mean free path in platinum the value $l=(6.4\mathrm{}\pm 1.0)\times {10}^{-7\mathrm{}}$ cm at 296°K.