A metal has a face-centred cubic structure with

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Free electrons, energy bands and electronic structure

Condensed Matter Physics, Ch Tight binding, band filling and the three kinds of solid

Problem

A metal has a face-centred cubic structure with a=4.10 A˚a = 4.10\ \mathrm{\mathring{A}}. Its first band is completely full, its second band holds exactly one electron per atom, half its capacity, and no other band holds any electrons. ((a)) Using Chapter 8's free-electron formula, RH=−1/neR_H = -1/ne, with nn taken as this band's electron density (one electron per atom), predict the Hall coefficient. ((b)) Explain why Chapter 8's simple formula should get the sign and rough size right here but gave the wrong sign entirely for aluminium.

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