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jocke_x1

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_{h}?) and see if it remains the same or at a point in the reciprocal lattice. My problem is that i dont know how to do it explicitly. How do I find the matrix representations of the operations?

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- Thread starter jocke_x1
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jocke_x1

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M Quack

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Doing this by matrix multiplication is tedious. It is much easier to do graphically.

You know the operations are

* 4-fold (90 deg) rotations about the face normals of the cube

* 3-fold (120 deg) rotations about the body diagonals of the cube

* 2-fold (180 deg) rotations about the face diagonal (translated so it goes through the center of the cube).

* Inversion symmetry k--> -k.

* all of the above followed by inversion symmetry.

Find the symmetry elements that leave k in place. These form the little co-group.

Once you have found all of them, you can check that they form a group (sub-group of Oh).

Be careful with vectors on the border of the Brillouin zone boundary. They may change place to a new positions that is related to the old one by a reciprocal space vector. Such positions are equivalent and the symmetry element belongs to the little co-group.

Whatever is left throws k elsewhere. All the positions you get in this way form the star of k.

You can check your results on the Bilbao crystallography server

http://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-kv-list

(you will understand the output once you understand how to do this by hand :-) )

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