Size Effect on Phonon Drag in Platinum

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 to 8×{}10^-3 mm. The difference ΔS between the thermoelectric power of the foils and the wire was separated into the electronic component ΔSᵉ, caused by the electron scattering at the crystal surface, and the phonondrag component ΔSᵍ, resulting from the phonon scattering at the crystal surface. From the phonon-drag component ΔSᵍ the phonon mean free path λ₀ 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 λ₀=(1.1×10^-5)e^64^∘K/T mm was found, in agreement with the expectation that in this temperature range λ₀ is mainly limited by phonon-phonon umklapp processes. The pre-exponential factor in λ₀ is within a factor of two in agreement with the value calculated from Klemens's theory. From the electronic component ΔSᵉ, the derivative of the electron mean free path l with respect to the electron energy E was found to be ∂lnl∂E_EF=3.4±0.8 (eV)^-1. 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±1.0)×10^-7 cm at 296^∘{}K.