The structure factor of orientationally disordered crystals: the case of arbitrary space, site and molecular point group

Abstract

The rotational form factor will be derived for the most general case of crystal, site and molecular symmetry (including non-crystallographic molecular point groups). Linear combinations of spherical harmonics adapted to the proper symmetry are used throughout. Their number as well as the number of free parameters of the orientational probability function is computed. Rules are given about how many parameters can be determined independently. Their number depends on the geometry of the molecule. The paper also includes the case of several symmetrically equivalent orientationally disordered molecules per unit cell.

Comparison between structural analyses of plastic and brittle crystals

“…In adamantane there exist a priori three 'independent' shells (12~ # 12~) (Prandl, 1981) corresponding to the secondary (Cs) and tertiary (Ct) C atoms and to the secondary H atoms. However, in X-ray diffraction, only the C atoms are important and will be considered in the following.…”

Atomic Dispacement Parameter Nomenclature. Report of a Subcommittee on Atomic Displacement Parameter Nomenclature

“…(u) or T(h) have been used for special problems (e.g. curvilinear motion, molecular disorder); see Johnson & Levy (1974), Press & Hiiller (1973) and Prandl (1981). Again, these expansions do not seem yet to have entered routine crystallographic work.…”

Numerical structure factor calculation of orientationally disordered molecules

“…The small amount of information inevitably increases the number of free parameters. The way back from the scattering density distribution to the orientational distribution function is in general not unique (Prandl, 1981) and it is also difficult to constrain the parameters in such a way that the two distribution functions are everywhere positive or zero (H/iller & Press, 1979). Therefore, a good refinement can lead to an unphysical result.…”