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Aug6-07, 09:12 AM
P: 5
Help, first Brillouin zone and K points

Quote Quote by meopemuk View Post
The shape of the 1st BZ is determined by the lattice periodicity. Positions of k points in the Brillouin zone are determined by the size and shape of the crystal. Usually, periodic boundary conditions are applied on the crystal boundary, so the crystal as a whole is assumed to form a periodic unit cell. The size of this unit cell is huge, so the distance between k-points is very small. For all practical purposes one can assume that the crystal is infinite, and that actual positions of the k-points have no physical significance, and summations over k-points can be replaced by integrations in the k-space.

I am now constructing a crystal of theoretically finite size. Can I understand as that, for a triangular lattice, the positions of k points exactly form a "triangular lattice" too in the 1st BZ? Thanks a lot!