Charge distribution as a tool to investigate structural details: meaning and application to pyroxenes

The charge distribution (CD) method, previously introduced as a development of the bond-valence (BV) approach, is applied for the first time to mineral structures, and specifically to pyroxenes. CD essentially involves the distribution of the Effective Coordination Number (ECoN) of a cation among all the neighboring anions. This distribution is then interpreted in terms of distribution of 'charges', where 'charge' represents the formal oxidation state. Differently from BV, the CD description depends upon the geometry of each coordination polyhedron, which is characterized through ECoN (a non-integer number). The contribution of each cation-oxygen bond to ECoN, labelled 'bond weight', corresponds to the bond strength in the BV method, but it is defined in terms of bond-length ratio in each polyhedron and not as a function of the cation-oxygen pair. The ratio q/Q of the formal oxidation number to the computed charge can be interpreted as a measure of the correctness of the structure (cation ratio) and of the degree of over- or under-bonding (anion ratio). A similar interpretation is not possible for the analogous quantities obtained through the BV approach. The analysis in terms of CD of the pyroxene chains (from 101 structures) shows different trends as a function of composition, temperature and pressure; in particular it shows a different behaviour of the two crystallographically independent chains of orthopyroxenes and of P2(1)/c clinopyroxenes.