A symmetry-adapted-function analysis of plastic crystals. Application to 1-cyanoadamantane at room temperature

X-ray diffraction of plastic crystals is investigated by using the decomposition of the orientational average density of the atoms on symmetry-adapted functions. For a cubic lattice, the molecular librational amplitude is related to the order of the cubic harmonics to be used. For a rigid molecule with 3m symmetry in a cubic lattice, the symmetry-adapted functions and the rotator functions are given up to order 12. The plastic phase structure of 1-cyanoadamantane, C₁₁H₁₅N, which is f.c.c., Z = 4 and a = 9.813 (3) Å, has been studied in the Fm3m space group. The orientational average density of the cyano group has a very sharp maximum in the [001] directions not completely describable (R_w = 15.4%) with cubic harmonics of order only up to 12. All the results obtained with this method agree very well with the corresponding ones from the Frenkel model structure of this compound.