Tungsten's Hall coefficient is measured to be

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

Tungsten's Hall coefficient is measured to be RH=−1.18×10−11 m3 C−1R_H=-1.18\times10^{-11}\,\mathrm{m^3\,C^{-1}}, negative as for electron-like carriers. A bar of tungsten is connected to a voltmeter with lead (Pb) leads across a temperature difference ΔT=30 K\Delta T=30\,\mathrm{K}; the reading is ΔV=−90 μV\Delta V=-90\,\mu\mathrm{V} (hot end relative to cold, cold end as reference, S=−ΔV/ΔTS=-\Delta V/\Delta T). Lead's own absolute Seebeck coefficient near 300 K300\,\mathrm{K} is SPb=+1.0 μV K−1S_{\rm Pb}=+1.0\,\mu\mathrm{V\,K^{-1}}. Someone argues: "the reading gives tungsten's Seebeck coefficient directly as SW=−ΔV/ΔT=+3.0 μV K−1S_{\rm W}=-\Delta V/\Delta T=+3.0\,\mu\mathrm{V\,K^{-1}}, positive; since the Hall coefficient is negative (electron-like), a positive Seebeck coefficient contradicts it, so tungsten must be an unusually dirty sample." ((a)) Identify the two errors in this argument. ((b)) Compute tungsten's correct absolute Seebeck coefficient from the data given.

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