The co-ordination number rule and the rule of hardness, powerful tools to rationalize inorganic structures

Abstract

The co-ordination number rule and the rule of hardness are developed in detail to rationalize inorganic co-ordination structures. We demonstrate how even very complex structures can be understood and sometimes predicted starting from primary co-ordination numbers of cations only. We remind the reader of relations between cation and anion co-ordination numbers and their use for the derivation of connectivity formulas of a Niggli type. We show how the hardness of the ions is responsible for their particular position within a structure. Furthermore, we derive a measure of segregation of the different ions within the structures and also of their electrostatic imbalance in relation to Pauling's rule of charge sums, and we interpret such structural details in the context of simple numeric relations of co-ordination numbers together with specific "chemical" effects.

A DFT study on the correlation between topology and Bader charges: Part III, the development of charge, “size” and coordination in alkali and alkaline earth titanates(IV)

“…And going along with the reduction of coordination numbers this changes the catenation of coordination polyhedra and the topology of the structures. (We have described the development from local organization in coordination polyhedra to the long range topology in an earlier paper [13]. )…”

“…We have shown [13] how segregation may be classified and even quantified by combining stoichiometric coefficients and coordination numbers in a simple calculus, and we have demonstrated that not only chemically very different elements segregate in a structure but that there is also a sort of "numeric" separation due to high coordination numbers for the A type cations alone with the strong catenation of A polyhedra resulting from it. It would be worthwhile to examine the development of charges in combination with such segregation parameters in more detail.…”

A study on AB2O6compounds, Part V: a DFT study on charge balance as driving force for structural organisation

“…In earlier papers [2,16] we have described how the local situation of co-ordination forcibly defines principles of organisation for the whole structural ensemble. To know how all steps of this puzzle are realised in detail would allow us to predict structures beforehand.…”

“…In earlier papers we have described how the local situation of coordination determines the overall structure. We cannot go into detail here and rather refer to our papers [2,3,16] where we have described the interdependencies of stoichiometric coefficients a, b and c and co-ordination numbers p, q and r in A a p B b q C c r compounds. From these numbers we can derive a minimum number of non-equivalent anions in the structure.…”

Twinning in chalcostibite revisited

“…CHARDI2015: Nespolo and Guillot, 2016). The structure of minerals is commonly described as based on cation-centred polyhedra, but the importance of the alternative interpretation as anioncentred polyhedra has been repeatedly emphasized (see, e.g., Krivovichev et al, 2013;Beck, 2014;Eon and Nespolo, 2015). As it was already pointed out by Hofmann (1933), both types of metal atoms are very close to the (104) plane (Fig.…”