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Modern X-ray and neutron diffraction techniques can give precise parameters that describe dynamic or static displacements of atoms in crystals. However, confusing and inconsistent terms and symbols for these quantities occur in the crystallographic literature. This report discusses various forms of these quantities, derived from probability density functions and based on Bragg diffraction data, both when the Gaussian approximation is appropriate and when it is not. The focus is especially on individual atomic anisotropic displacement parameters (ADPs), which may represent atomic motion and possible static displacive disorder. The first of the four sections gives background information, including definitions. The second concerns the kinds of parameter describing atomic displacements that have most often been used in crystal structure analysis and hence are most commonly found in the literature on the subject. It includes a discussion of graphical representations of the Gaussian mean-square displacement matrix. The third section considers the expressions used when the GaussJan approximation is not adequate. The final section gives recommendations for symbols and nomenclature.

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Single-crystal X-ray diffraction data for anthracene, flail10, have been measured at six temperatures from 94 to 295 K. Positional and displacement parameters for C and H atoms were refined at each temperature by conventional least-squares techniques. The derived anisotropic displacement parameters for the C atoms at each of the six temperatures were corrected for the contributions of the internal modes and were then analyzed to determine translational (T) and librational (L) tensors describing the rigid-body molecular motion. Although the resulting T and L tensors agree well with those measured and calculated previously at room temperature, the shrinkage of the L tensor with crystal cooling appears somewhat anomalous. The unexpected behavior is concentrated in the component of L associated with the long molecular axis, a component that is, as a consequence of the molecular geometry, relatively poorly determined. Therefore, while the possibility of some subtle, temperature-dependent structural change, such as a molecular reorientation, cannot be ruled out, neither can it be endorsed. This study underlines how the geometry of the molecule being studied can limit the quality of the rigid-body thermal-motion description determined by diffraction methods.

An extensive analysis of polymorphic crystalline systems of organic compounds in which at least one member has a high number of molecules in the asymmetric unit (Z′ > 2) has been carried out. Crystal structures are compared by traditional methods based on crystallographic cell reductions and powder patterns, as well as from stability considerations by comparing the distribution of molecule-molecule energies in the packing coordination sphere. The combination of these methods allows a safer detection of genuine polymorphism, since real space and reciprocal space information are seen to be complementary. In many cases, a clear-cut difference between polymorphic structures appears. However, there are also cases where X-ray structure determinations of "new" polymorphs can be better interpreted merely as low-quality redeterminations of previously found phases. The present study provides improved crystal structure recognition methods and clarifies some details of the molecular organization in crystal structures with high Z′. We discuss problems of how polymorphs are to be defined and make some suggestions about the conditions under which one polymorph or the other may be formed.

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