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Lets say I have a monatomic chain of atoms in which the electrons are nearly free. I know how to solve this, we end with energy gaps at the Brillouin zone boundaries.

Now lets say every other atom is slightly different (or the length of alternating bonds is slightly different). How does this affect the situations?

I think the following will happen - we double the lattice vector and hence half the size of the Brillouin zone. -we will double the number of electrons (each Brillouin zone will still have the same amount of available states though).

I would also think that the size of the energy band gap alternates.

Is there anything else that would happen?

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