A note on the distortion theorem.

The distortion theorem is a conditional statement that establishes the certain relations between the variation of the mean bond length and the variation of the valence of a central ion of a coordination polyhedron. It was found that in some principal cases the conditional part of the distortion theorem is not necessary. A combinatorial evaluation of the distortion theorem and a theoretical analysis of the bond length-bond valence correlation were performed. An extension of the distortion theorem is proposed.

Predicting the lattice constants of the ternary pyrochlores A2B2O6O'.

The pyrochlores A2B2O6O' attract much attention because of their physical properties. Several models which relate chemical compositions of ternary pyrochlores with lattice constants have been proposed. Analysis of these models shows that some of them are statistically inadequate and cannot be used. Statistical models to predict lattice constants of ternary pyrochlores A2B2O6O' have been derived using multiple linear regression analysis.

Ab initio determination of heavy oxide perovskite related structures from precession electron diffraction data.

Two complex perovskite-related structures were solved by ab initio from precession electron diffraction intensities. Structure models were firstly derived from HREM images and than have been confirmed independently using two and three-dimensional sets of precession intensities. Patterson techniques prove to be effective for ab initio structure resolution, specially in case of projections with no overlapping atoms. Quality of precession intensity data may be suitable enough to resolve unknown heavy oxide structures.