Effect of Compression on Fermi Energy.

[Cheetox]

I know that when a metal is compressed its fermi energy is increased. I would attempt to explain this by saying, "as the volume has been decreased, so has the allowed number of particle in a 3D box states, thus as we have the same number of electrons and fewer allowed states, and the pauli exclusion principle does not allow electrons to occupy the same states, electrons will be pushed into higher n values of the particle in a box states as the ones below are already occupied and thus the highest energy states occupied at 0K will increase and thus the fermi energy will increase."

Is this the correct way to think about the effect of compression on a metal? Is there a more elegant way of stating the above?

cheers

 

[rmanoj]

Thinking in terms of the particle-in-a-box model, as the box becomes smaller, the eigenenergies themselves shift upwards. So if the number of electrons is conserved, then the max-energy state that is occupied will also shift upwards and that is, by definition, a state corresponding to the Fermi energy. Generalize this intuitive model to an infinite crystal with periodic boundary conditions.

 

[charng]

Yes, this is a correct way to think about the effect of compression on a metal. Another way to explain it is that as the volume decreases, the distance between atoms decreases, leading to a higher electron density. This higher electron density then leads to a higher Fermi energy, as more electrons are packed into the available energy states. Additionally, the compression may also cause a change in the band structure of the metal, which can also affect the Fermi energy. Overall, the increased electron density due to compression leads to a higher Fermi energy in a metal.