Motion in crystals: the molecular mean field model

Abstract

The problem of describing collective atomic motion in molecular crystals is reviewed from the point of view of normal coordinate analysis in its mean square amplitude form. There are two related problems with this approach: (1) The apparent lack of information on correlation between atomic motion inherent in atomic displacement parameters as determined from elastic diffraction experiments. (2) The need to identify molecular deformation coordinates associated with low frequencies and therefore with large amplitudes. Within the limits of the harmonic approximation the first problem can be solved by considering mean square amplitudes obtained at different temperatures. The second problem can be approached by analyzing and visualizing the deviations of atomic displacement parameters from rigid body behavior or, alternatively, by looking for static deformations of molecular fragments closely related in structure to the molecule whose atomic displacement parameters are to be analyzed. Some of the above points are illustrated with the help of the atomic displacement parameters of H 8 Si 8 O 12 , determined at 100 and 10K.