F.E.G. fermi sphere radius problem

In summary, the conversation discusses calculating the electron concentrations needed for the fermi sphere to contact the zone faces in BCC and FCC structures. The relevant equations for cubic structures are provided and the attempt at a solution involves using the distance in reciprocal space and the fermi vector to determine the number of electrons per atom. Further guidance is requested for the FCC structure.
  • #1
lordkelvin
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Homework Statement



Calculate the electron concentrations (# electrons/atom) needed for the fermi sphere to contact the zone faces (first bril. zone edges) in BCC and FCC structures.

Homework Equations



kf = (3*pi^2*n)^(1/3) where n is # electrons per atom.

For cubic structures, dhkl=a*(h^2+k^2+l^2)^(-1/2), and the reciprocal magnitude of d is 2*pi/dhkl

The Attempt at a Solution



In BCC structure, the brill. zone edge is at the {110} planes, so that dhkl = a*2^(-1/2) and this distance in reciprocal space is 2^(3/2)*pi/a. (where a is the lattice parameter). Setting this reciprocal distance equal to the fermi vector,
(2^(3/2)*pi/a)^3/(3*pi^2) = n

I'm just unsure about this, maybe someone could give me a shove in the right direction. For the FCC structure, the edges of the FBZ are at the {110} and {200} planes.
 
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What is the F.E.G. fermi sphere radius problem?

The F.E.G. fermi sphere radius problem refers to a discrepancy between the theoretical prediction and experimental measurement of the radius of the fermi sphere in a Fermi gas.

Why is the F.E.G. fermi sphere radius problem important?

The F.E.G. fermi sphere radius problem is important because it challenges our understanding of fundamental principles in physics, such as the behavior of particles in a Fermi gas. It also has implications for other areas of physics, such as condensed matter and nuclear physics.

What are some proposed solutions to the F.E.G. fermi sphere radius problem?

Some proposed solutions to the F.E.G. fermi sphere radius problem include accounting for the effects of three-body interactions, using more accurate experimental techniques, and considering the effects of particle interactions at high energies.

How does the F.E.G. fermi sphere radius problem relate to other open questions in physics?

The F.E.G. fermi sphere radius problem is related to other open questions in physics, such as the nature of dark matter and the behavior of particles in extreme conditions. It also highlights the need for further research and development of theoretical models in the field of quantum mechanics.

What are the potential implications of solving the F.E.G. fermi sphere radius problem?

Solving the F.E.G. fermi sphere radius problem could lead to a better understanding of the behavior of particles in a Fermi gas, as well as a deeper understanding of quantum mechanics and its applications. It could also have practical applications in fields such as materials science and nuclear energy.

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