LATTICE-DYNAMICAL CALCULATION OF ATOMIC DISPLACEMENT PARAMETERS (ADPs). Carlo M. Gramaccioli and Francesco Demartin, Università degli Studi, Via Botticelli 23, I-20133, Milano, Italy, Tullio Pilati, CNR-CSRSRC, Via Golgi 19, I-20133 Milano, Italy

ADPs comparable with the corresponding values obtained from crystal structure refinement can be derived from Born-von Karman lattice dynamics. A rigid ion model has been assumed, where atomic charges and VFF parameters have been deduced from best fit to the vibrational frequencies of a series of similar compounds, either molecular crystals or even ionic, non-molecular inorganic compounds, such as most minerals.

Besides confirming the physical meaning of ADPs, a detailed interpretation of atomic motion is allowed, also in terms of internal degrees of freedom of atomic groups and their correlated motion. The possibility of correcting bond lengths for thermal motion in the most general case is also provided, since the correlation tensors between the displacement of different atoms can be obtained as by-products; particularly interesting is the link to spectroscopic and thermodynamic properties, and the possibility of checking if empirical potentials are transferable.

In comparison with the parallel interpretation of motion which can be obtained by fitting the individual ADPs, a way which is presently preferred by most crystallographers, the main difficulties of our theoretical calculations are the need of adequate knowledge of empirical potentials, which still have to be developed for many groups of substances, and the harmonic approximation, since no satisfactory model of this kind has yet been developed for anharmonic motion.

However, at least in some problematic instances (pyrope, almandine), where anharmonic behaviour has long been claimed, joint examination of crystallographic and thermodynamic properties compared with the theoretical model has provided a consistent explanation based on harmonic motion and order-disorder transformations.