Generalized atomic displacements in crystallographic structure analysis

An attempt is made to summarize both theoretical and experimental aspects of generalized atomic displacement parameters (ADP's) in crystalline matter. Generalized displacement parameters are used to describe the weakening of Bragg intensities via the anharmonic (static or thermal) Debye-Waller factor (DWF) and its real-space counterpart, the generalized atomic probability density function (p.d.f.). The lattice dynamical base of the harmonic and anharmonic thermal DWF is discussed. It is pointed out that the static DWF frequently contains higher-order terms. The mathematical base for an experimental determination of generalized ADP's is given. The most popular current formulations (one-particle potential and statistical approaches) are reviewed and their individual limitations are discussed. Likewise the demands put on the quality and extent of experimental data are assessed. Some aids to the interpretation of generalized ADP's established by crystallographic least-squares procedures are given and a Monte-Carlo method for the calculation of errors in p.d.f. maps is presented. Finally, some prospects for future work are outlined and a more frequent comparison of theoretical calculations and experimental determinations of generalized ADP's is advocated.