A plot of against temperature for a high-purity bar of a metal shows three readings:…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Electronic transport in solids · Electronic transport in solids

Solid State Physics, Ch Two currents, two forces: Wiedemann-Franz and thermoelectricity

Problem

A plot of κ/σT\kappa/\sigma T against temperature for a high-purity bar of a metal XX shows three readings: 2.44×10−8 W Ω K−22.44\times10^{-8}\,\mathrm{W\,\Omega\,K^{-2}} for all T<5 KT<5\,\mathrm{K}; a minimum of 1.55×10−8 W Ω K−21.55\times10^{-8}\,\mathrm{W\,\Omega\,K^{-2}} at T≈25 KT\approx25\,\mathrm{K}; and 2.20×10−8 W Ω K−22.20\times10^{-8}\,\mathrm{W\,\Omega\,K^{-2}} at T=300 KT=300\,\mathrm{K}. ((a)) Express each of the three readings as a multiple of the Lorenz number L0=2.44×10−8 W Ω K−2L_0=2.44\times10^{-8}\,\mathrm{W\,\Omega\,K^{-2}}. ((b)) Each point on this curve is built from two separate measurements on the same bar. State the boundary condition (in terms of the electrical current) under which each of σ\sigma and κ\kappa is measured. ((c)) Explain, in terms of the angle and the energy change of a scattering event, why the ratio dips below L0L_0 at 25 K25\,\mathrm{K} and why it recovers only partially by 300 K300\,\mathrm{K}.

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