A transition metal has a d band wide holding the usual states per atom (both spins…

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

Solid State Physics, Ch Tight binding and the band structures of real materials

Problem

A transition metal has a d band 3.0 eV3.0\,\mathrm{eV} wide holding the usual 1010 states per atom (both spins counted). Assuming the Fermi level sits near the middle of this band, where the density of states can be taken as roughly uniform, estimate ((a)) the density of states at the Fermi level, D(EF)D(E_F), in states per eV per atom; ((b)) the electronic heat-capacity coefficient γ\gamma, in mJ mol−1K−2\mathrm{mJ\,mol^{-1}K^{-2}}, using γ=π23kB2D(EF)\gamma=\frac{\pi^2}{3}k_B^2D(E_F) per mole of atoms.

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