The Brillouin zones of a lattice are an important concept in solid state physics. This tool lets you see the 3D Brillouin zones of an arbitrary bravais lattice.
https://tobycrisford.github.io/bravais-lattice-fermi-surfaces/
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Thanks for sharing this tool.
I remember I’ve seen some images for electron clouds (atomic orbitals (?)), which are round. So, I was surprise that the Brillouin zones are so sharp-edged. At least zone 1 cases look like the cells of a 3D Voronoi diagram.
Is it true that zone 1 are always convex polyhedrons?
For zone 2 and 3 I see they are not convex any more.
Sometimes calculations take quite a long time, and this makes the user wonder whether the browser has crashed. My suggestion is to move the calculations in a web worker, so that the main JS thread is not blocked. You may also show some progress bar, if it is possible to estimate it.
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Thanks for the feedback! The higher brillouin zones can be slow, and your suggestions sound good. I’ve spent a lot of time in the last week or so getting it to this point, so it might take me a while to get round to those changes, but they’re going on my list!
I had to google Voronoi diagrams, but I think you’re exactly right. The first Brillouin zone consists of the region of space which is closest to the central point of the lattice (technically the reciprocal lattice), which if I understand right is what a Voronoi diagram is? And yes, that’s why the first Brillouin zone will always be convex.
I believe the second Brillouin zone is then the region of space which has that central point of the lattice as its second closest lattice point, and so on. Those shapes don’t have to be convex.
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