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Homework Help: Brillouin Zone of BCC lattice?

  1. Mar 2, 2009 #1
    I'm answering a question where it becomes necessary to know the closest face of the BZ in a bcc structure. The answer is given as +/- (2*pi) / (sqrt(2)*a) where a is the cubic lattice parameter.

    I would have thought the Answer would have been sqrt(3)*a / 4. Where does the pi come from?

    Cheers in advance.
     
  2. jcsd
  3. Mar 2, 2009 #2

    lanedance

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    Homework Helper

    are you working the reciprocal lattice? i think the pi comes about in the transformation to reciprocal lattice
     
  4. Mar 2, 2009 #3
    The reciprocal lattice of BCC is FCC. The 2pi comes from teh definition of the reciprocal lattice:
    b1=2pi/Volume (b2xb3) etc.

    The reciprocal FCC has a side of 4Pi/a. In FCC the nearest neighbors of a corner are the centers of adjacent faces, at distance sqrt(2)/2 * (size of cube).
    The Brillouin zone is at half this distance so it will be
    1/2*(sqrt(2)/2)*(4pi/a) = pi*sqrt(2)/a = 2pi/(a*sqrt(2))
     
  5. Mar 3, 2009 #4
    cheers!
     
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