ЩОДО ВИЗНАЧЕННЯ КООРДИНАЦІЙНОГО ЧИСЛА В МОДЕЛІ ЗВ’ЯЗКОВОЇ ВАЛЕНТНОСТІ

Анотація

The bond valence model (BVM) in its modern form is widely used in mineralogy and structural inorganic chemistry as a powerful yet convenient tool for validating crystal structures and for predicting interatomic distances in the crystal structures of known chemical composition and presupposed bond network. Bond valence (BV) s_AX is defined as the part of the classical atomic valence shared with each A–X cation-anion bond in a given [AX_n] coordination sphere. The valence of a bond (measured in valence units, v.u.) is considered to be a unique function of the bond length; and the most commonly adopted empirical expression for the relationship between the bond valences s_AX and the bond lengths r_AX is the equation s_AX = exp[(r₀ – r_AX)/b], where r₀ and b are the empirically determined constants (BV parameters) for a given A/X ion (atom) pair.

The BV parameters r₀ and b are typically derived by fitting the above s_AX = f(r_AX) equation to a representative set of well determined coordination spheres under the constraint that the sums of the s_AX values calculated for the central atoms of the considered coordination shells are equal or as close as possible to the oxidation state (atomic valence) expected for these atoms. The BV parameters determined in this way can readily be used for validating newly determined crystal structures via bond valence summation and for predicting bond lengths. Unfortunately, the physical limit of the coordination sphere has presently no the universally adopted definition; so, in calculating the BV parameters, researchers set the limit(s) from their personal opinions and preferences. As a result of the absence of the adopted definition for the limit of the coordination sphere, the BV parameters (r₀; b) determined for the same ion pair in different works could be incompatible with each other.

The main goal of this work is to present the rigorous and structure-oriented definition for the limit of the coordination sphere, successfully used by the author over the last decade: the shortest distance from the central cation to another cation in a given crystal structure is taken as the physical limit of the coordination sphere under consideration.