A geometric centroid principle and its application.
A new concept of approximation for rigid point sets is suggested. As a necessary condition of optimality, the principle of the conjoint centroid is proved: to achieve a best approximation, certain co-sets must conjoin their centroids. The practical use of the centroid principle, and how it opens up a non-classical method of modelling various aspects of orientational disorder in crystals, is demonstrated. The principle is applied to the interpretation of density data, to the prediction of high-pressure conformations through qualitative simulations, and to the prediction and computation of disordered sets of possible reorientation pathways which explain the shape of the electron-density distribution reconstructed from diffraction experiments. It is also demonstrated how an inversion of the centroid principle can be used to model forces between the parts of the disordered structures.
Mädler
F
F
Hahn-Meitner-Institute Berlin, D-14109 Berlin, Germany. maedler@hmi.de
Behrends
E
E
Knorr
K
K