Good afternoon all,
The plan for at least in the 2D system a and b is the following:
- Get reciprocal lattice vectors a and b from you lattice vectors.
- Draw vectors a, b, -a, -b, a+b, and -a-b in paper.
- Bisect them. (It should be the equation of a straight line passing mid-distance from the vector, and forming a 90 degree angle with the vector, which is what a bisector is.)
- Determine the points where two consecutive bisectors join, by writing down the equations of their straight lines and making them equal.
- The points where bisectors cross are your high symmetry points. And this process, repeated for all pairs of vectors in point 2, give you the first Brillouin zone.
I got the following:
When i started calculating the bisector equations it got really messy and I hope to get someone to help continue the work or find a suitable reference to know how we got the BZ.