Crystal structure prediction by ionic network analysis: the example of (p-T-X)-structure relationships in olivines

The method of Ionic Network Analysis (INA) is defined by reference to the known crystal structures of olivine minerals. It is based on a reversible transformation between two alternative representations of ionic crystal structures: (a) the crystallographic and (b) the interactional. Whereas the former encompasses unit-cell parameters and atomic coordinates, the latter consists of selected interaction vectors between ions. Since the lengths and orientations of these vary only slightly between crystal structures obtained under systematically varying (p, T, X) conditions, they may be used to predict the crystal structures at intermediate (p, T, X) values by interpolation. Two interactional networks are constructed, one for the anions and the other for cations. As both networks lead to independent calculated values of the unit-cell parameters, it is possible to exploit the known, continuous (p, T, X) variations of cell parameters as normative constraints for the prediction of atomic coordinates within a predictive structural refinement procedure. Continuously varying structurally based parameters such as the volumes of cation coordination polyhedra may likewise be used. The choice of olivines for developing the method has been guided by the availability of pressure, temperature and compositional structural data for them. However, the ideas are expounded sufficiently generally for the method to be applied to other minerals.