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Bcc lattice

  1. Feb 14, 2013 #1
    Hi, i have problems understanding the Brilluoin zone to the bcc lattice

    First, i wonder what the distances are, from the origo to the brillouin zone plane borders.
    I firts thought it would be half the distance of the basis vectors (mine are 2pi/a, where a is my lattice constant, BUT its only true for 2-D calculations for square lattices.

    I know that the distances in 3D should be |G-vector|/2, and i take the smallest possible G.

    But i still dont know

    ANyone who knows how to find the distances from origo to the first BZ zone boundaries, knowig that the basis vector in the reciprocal space is 2pi/2?are they all the same??
  2. jcsd
  3. Feb 15, 2013 #2
    I think if the direct lattice constant is a, then the reciprocal lattice constant would be[itex]2\pi/a[/itex] hence your favorite distance is [itex](\pi/\sqrt2)a[/itex].
  4. Feb 15, 2013 #3
    Thanks a lot. and this goes eveforryone of the 12 directions in the BZ?
  5. Feb 15, 2013 #4
    No, it was for the four direction located in the middle of the figure 4.16 Ashcroft & Mermin. you can easily calculate it for remained 8 directions (see the figure).
  6. Feb 15, 2013 #5
    ok thanks. im jut interested in the 110-direvtion, from origo to N,in the Ʃ-direction
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