Is the First Brillouin Zone Unique Despite Non-Unique Primitive Vectors?

[Niles]

Hi

We know that there is no unique primitive cell, meaning there is no unique choice of primitive vectors. Now, when we find our reciprocal primitive vectors, then we can construct the first Brillouin zone (FBZ) by using the Wigner-Seitz method.

But we know that primitive vectors are not unique, so if we construct the FBZ by using these vectors (via the Wigner-Seitz method), then how do we know that we have found the unique FBZ?


Niles.

 

[caffenta]

Primitive cells not being unique simply means that you can choose different cells to represent a particular lattice. It does not mean that a specific cell is necessarily not unique. There is only one first Brillouin zone, but it is not the only choice of unit cell for the reciprocal lattice.

EDIT: It's the Wigner-Seitz method that makes the Brioullin zones (1st, 2nd, ...) unique.