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I have the following problem :

I generate GaAs (zinc blende structure) supercells, and then I want to replace some As atoms by N atoms. Let's say I have fcc conventional cell repeated twice in the x, y and z direction so that I have a total of 64 atoms, 32 of Ga and 32 of As. 8 atoms per conventional cell times 2x2x2 = 64. Then I replace 2 of the As atoms by N atoms so that there are

[tex]

\frac{64!}{2! 62!} = \frac{64 \times 63}{2} = 2016

[/tex]

possibilities. Of course since the supercell is repeated to infinity there will be a lot of equivalent configurations.

My question is: Is there any way using group theory to determine which of the 2016 possible configurations are equivalent?

If no one knows the answer can anyone suggest a good book about group theory applied to crystal structures?

Thanks!

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# Group theory and crystal structure

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