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Homework Help: F.E.G. fermi sphere radius problem

  1. Nov 13, 2011 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant 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

    3. 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.
  2. jcsd
  3. Mar 12, 2016 #2
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