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November 4th, 2011, 02:45 AM   #1
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calulating the verticies of a unit cell

Hi, this is my first post. i hope its in the best place - if not then maybe someone can point me to the right place.

So im really stuck on one particular issue regarding unit cells. Basically, i know how each of the atoms in a cell can be generated using symmetry operators but i need to know how i generate the vertices for the unit cell itself.

For example in the simple case where a = b = c = 5 and alpha = beta = gamma = 90 the Cartesian coordinates for the vertices (where the origin is one of the vertices) would be:

(0,0,0) origin, (5,0,0), (5,5,0), (0,5,0), (0,0,5), (5,0,5), (0,5,5), (5,5,5)

Ok but what are the Cartesian positions of the vertices given alpha = beta = gamma = 80 (for example)? I have a commercial piece of software which gives the values as:

(0,0,0) origin, (4.870,0.729,0.86, (4.870,5.653,1.736), (0,4.924,0.86, (0,0,5), (4.870,0.729,5.83, (0,4.924,5.86, (4.870,5.653,6.736)

but i really need to know how you do this calculation!! I have tried using cords and trigonometry and i can get this to work for 2 dimensions, but if there are 3 dimensions (i.e. the 3rd angle is not 90) then the values are not correct i guess because of the non-90 3rd angle.

Many thanks in advance for any help someone can give!

matt
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