A hypothetical crystal has three atoms in its primitive cell

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

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

Problem

A hypothetical crystal has three atoms in its primitive cell, contributing

2

3

and

3

valence electrons respectively. ((a)) How many valence electrons sit in the primitive cell, and how many bands would this fill exactly if nothing more happens in three dimensions? ((b)) The crystal's measured resistivity at room temperature is

1.5\times10^{-6}\ \mathrm{\Omega\,m}

, about

88

times copper's. Explain, using an idea from this chapter, how this is possible even though your count in (a) predicts a full set of bands with a gap above them. ((c)) What does the resistivity suggest about this crystal's band overlap compared with calcium's?

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