The application of the partial Patterson method and the thirteenfold hexagonal superstructure of Cu7As6Se13

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Abstract
Derivative structures based upon sphalerite or galena often exhibit hexagonal superstructures characteristic of a peculiar thirteenfold multiplicity. A synthetic semiconductor, Cu7As6Se13, is one of the examples. Crystals of Cu7As6Se13 are rhombohedral with a = 8.71 Å, α = 105°41′. The space group is R3. The unit cell referred to hexagonal axes has dimensions a = 14.025 Å, c = 9.61 Å, and there are three formula units per cell. As an example of the application of the partial Patterson method, the superstructure was solved based upon a three-dimensional Patterson function synthesized with superstructure reflections alone.The structure is a distortion structure based upon sphalerite. The maximum distortion from sphalerite is around 0.2 Å. In terms of the theory of derivative crystal structures, it has been shown that the thirteenfold superstructures are smallest probable ones for rhombohedral distortion structures based upon sphalerite or galena.

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