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

Abstract

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 P21/c clinopyroxenes.

Crystal structures and polymorphism of Sr₄[Al₆O₁₂]SO₄

“…The positional deviations of all atoms in the unit cell were necessarily less than 0.004 nm, which is within the resolution limit of the three-dimensional EDDs. We have also confirmed the validity of the structural model by the charge distribution method, 24), 25) in which the ratio of the formal oxidation number (q) to the computed charge (Q) of cation [= (q/Q) cation ] indicates the correctness of the structure determination. Actually, the (q/Q) Sr -, (q/Q) Al -, and (q/Q) S -values are all close to unity (Table S2).…”

Reinvestigation of the LuFeO3(ZnO)m Homologous Series: Insights from Charge Distribution Analysis on the Effect of the Coordination Polyhedra Shape on the Cation Distribution

“…It is thus more related to the geometry of each coordination polyhedron, rather than to the true crystal chemistry, as instead is the BV. Since the Q computed according to CD is the result of the distribution of q, it is suitable to investigate isomorphic substitutions of cations with di!erent q: a distribution giving QOq indicates the possible presence of a mistake in the assigned site occupancy (6).…”

Does mathematical crystallography still have a role in the XXI century?

“…The concept of coordination number itself has been the object of critical considerations (Hoppe, 1970) and generalizations (Hoppe, 1979;O'Keeffe, 1979). To judge up to what distance an atom still coordinates with its neighbours, or the closely related question of accounting for the bond-length distribution in irregular coordination polyhedra, different methods have been proposed, such as bond valence (see a review in Urusov, 1995), resonance bond number (Boisen et al, 1988;Rutherford, 1991Rutherford, , 1998a and charge distribution (Hoppe et al, 1989;Nespolo et al, 1999Nespolo et al, , 2001.…”