Posted by Steve Simon on May 31, 2013, 7:11 am, in reply to "Fermi energy of nearly free electron model"
Yes, i think the word "nearly" here is perhaps a bit confusing. I believe you are meant to approximate gold as a free electron gas in both of the latter two parts of the question. At any rate, it is perfectly consistent to assume gold is a free electron gas (stating this as an assumption!). It certainly fits the observed property that gold is a metal.
You might wonder if gaps might open up in the dispersion due to the periodic potential (i.e., this could be the "nearly free" part). However, this should not change the answer very much. Since gold has a half-filled BZ (it has an odd number of electrons), most of the fermi surface is not near to the BZ boundary, so the periodic potential does not change the shape of the fermi surface (or fermi energy) too much. In truth actually the fermi surface of gold *does* touch the fermi surface and forms a small tube between BZs, so the periodic potential must lower the fermi energy a little bit.
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