Brillouin Zones

Support for finding First Brillouin Zones and Irreducible BZs (following the method of Jorgensen et al.) was introduced in c2x 2.41.

The result can be output as a bare list of vertices, in either absolute (--verts) or fractional (--verts_frac), or it can be output in a form for easy visualisation in Jmol or visualisation in VMD. K-points can be reduced to the first or irreducible Brillouin zone with the -r option.

fcc Brillouin zones

The FCC reciprocal space cell (white), first Brillouin zone (red), irreducible Brillouin zone (green) and reduced even k-point mesh (cyan).


The volume of the Brillouin Zone is the volume of the reciprocal space unit cell is the reciprocal of the volume of the real space unit cell. The volume of the IBZ is the volume of the BZ divided by the number of symmetry operations in k-space. That is the theory, and c2x should warn if its output disagrees.

The code is full of horrid floating-point comparisons. One may get different (better) results by adjusting the tolerance with which these are made, e.g. -e=1e-8. I'd be interested if this is ever necessary.

The Brillouin functionality of c2x is in part a solution looking for a problem. If you have suggestions on how it could be made more useful, then feel free to contact mjr19. The domain is