# High symmetry points

1. Sep 14, 2008

### saray1360

hi,

I have found a website in which it has described how to find high symmetry points for wurtzite structure. Here is its address:
http://cmt.dur.ac.uk/sjc/thesis_mcg/node53.html

But, as I know these points are being used for standard numbers of atoms for example in a wurtzite system we should have 4 atoms in the unit cell and if we change the number of atoms these points change!

Please let me know how I can calculate the high symmetry points for a unit cell with 12 atoms in a hexagonal lattice such as wurtzite structure of ZnO nanowires?

Thanks,
Sara

2. Sep 14, 2008

### JustinLevy

The brillouin zone is determined by the lattice symmetry, not the placement (or number) of atoms in the unit cell.

What they are describing there (which "paths in k-space" along which to calculate the bandstructure), there have appeared some standards for each lattice symmetry, but ultimately it is a just a convention: We'd like to have and represent the bandstructure in the entire brillouin zone, but it is far easier to represent slices of this. Which slices are important to you, or is enough to feel like you "covered enough" is up to you or just a convention.

A similar problem you probably have seen is how one represents the electron orbitals for materials. It is just difficult to represent higher dimensional data. Usually we cut a plane (or line) through and show the densities on this surface, or show a 3-D model with the surface of a constant chosen density for the orbital.

3. Sep 16, 2008

### saray1360

Dear all,

It is trivial, but please let me know how I can clculate high symmetry points for hexagonal lattice. I know the points are gamma, A, H , L, M and K but I do not know how to calculate them. For example I have a k-point grid in reciprocal lattice as follows:

7.0 0.0 0.0
0.0 7.0 0.0
0.0 0.0 5.0

Please do help me, it is really urgent for me.

Regards,
sara

4. Nov 12, 2010