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First Brillouin Zone





Before explaining what a Brillouin zone is, let’s make some definitions







Now we finally can define a First Brillouin zone





First Brillouin zone calculation method for Reciprocal lattice point P-


  1. Calculate Reciprocal lattice primitive vectors.
  2. Find the mid point, M, between P and all other lattice points.
  3. Calculate a plane which is located at M and perpendicular to P-M.
  4. First Brillouin zone is all points in space which could be reached by not crossing any plane calculated in 3.

My program generates first Brillouin zones, using steps 2-4 of this algorithm.

Link to program explanations can be found here.

This program also calculates Fermi surfaces.

Explanations on Fermi surfaces can be found here.

Other programs and explanations, prepared in the Physics Department of the Technion can be found here