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For the case of metals, we observed that metals often have nearest-neighbours in excess of the maximum valency (for example, 8 for Li, which has only one valence electron) and that metals display great conductivity. On this basis, it was suggested that electrons are delocalised over the solid, and we used LCAO (linear combination of AO) over all the valence orbitals to form a band - the 2s band in this case.

The above is from section two in MIT's solid state lecture notes here. They talk about the above two points suggesting an atom in a metal lattice can interact with a large number of others. This then leads to thinking in terms of the orbitals of the "system" or the entire "macromolecule"

However, for non-metallic solids, like diamond for example, bonds are viewed as sp3 localised bonds and the number of nearest neighbours equals how many covalent bonds it can form, and it has poor conductivity as well. The poor conductivity is often explained by saying the band gap($E_g$) to the conduction band is large. But I don't understand the meaning of forming a band in this context, when the assumption we used of delocalised electrons over the entire solid doesn't hold.

Also, the description for the formation of the valence and conduction band for diamond is given in terms of sp3 orbitals combining to the form the bands. Why is hybdridisation (from VBT/VSEPR) being brought in to the picture here?

xasthor
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1 Answers1

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Existence of band structure is the result of Bloch theorem, which predicts that electron spectrum in a periodic potential consists of continuous patches, states being label by a continuous number/vector $\mathbf{k}$ and a discrete band index $n$. Thus, the existence of bans is the consequence of crystal structure.

Excess of valency comes into play when distinguishing metals and semiconductors - in metals it results in the last band typically not completely filled, which means that there are mobile electrons present. On the other hand, in diamond structure, characteristic of Carbon, Silicon, and Germanium, all the bonds are saturated and we can distinguish last fully filled band (valence band) and the first empty band (conduction band). Similar situation takes place for close elements, as in GaAs or AlGaAs - which are combinations of elements of valencies three and five.

Roger V.
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