A metal X has a measured Hall coefficient

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 metal X has a measured Hall coefficient RH=+0.30×10−10 m3 C−1R_H=+0.30\times10^{-10}\,\mathrm{m^3\,C^{-1}}, positive as for hole-like carriers. A researcher clamps a bar of metal X between two blocks held at a temperature difference ΔT=25 K\Delta T=25\,\mathrm{K}, connects a copper voltmeter across the ends, and reads ΔV=+175 μV\Delta V=+175\,\mu\mathrm{V} (hot end relative to cold, measured with the cold end as reference, S=−ΔV/ΔTS=-\Delta V/\Delta T). Copper's own absolute Seebeck coefficient at 300 K300\,\mathrm{K} is SCu=+1.8 μV K−1S_{\rm Cu}=+1.8\,\mu\mathrm{V\,K^{-1}}. The researcher argues: "the reading gives the metal's Seebeck coefficient directly as SZn=−ΔV/ΔT=−7.0 μV K−1S_{\rm Zn}=-\Delta V/\Delta T=-7.0\,\mu\mathrm{V\,K^{-1}}, which is negative (electron-like); since the Hall coefficient said holes, one of the two measurements must be faulty." ((a)) Identify the two errors in this argument. ((b)) Compute metal X's correct absolute Seebeck coefficient from the data given.

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