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
Grey tin has the diamond structure, with four valence electrons on every atom. A student argues: 'The conventional cubic cell holds 8 atoms, so it holds 32 valence electrons; since one band holds 2 electrons per primitive cell, this fills 32/2=16 bands.'
((a)) What is wrong with this reasoning?
((b)) Redo the count correctly, and say how many bands are exactly filled.