Bond softness sensitive bond-valence parameters for crystal structure plausibility tests

Based on a description of bond valence as a function of valence electron density, a systematic bond softness sensitive approach to determine bond-valence parameters and related quantities such as coordination numbers is elaborated and applied to determine bond-valence parameters for 706 cation–anion pairs. While the approach is closely related to the earliersoftBVparameter set, the newsoftNC1parameters proposed in this work may be simpler to apply in plausibility checks of crystal structures, as they follow the first coordination shell convention. The performance of thissoftNC1bond-valence parameter set is compared with that of the previously derivedsoftBVparameter set that also factors in contributions from higher coordination shells, and with a benchmarking parameter set that has been optimized following the conventional choice of a universal value of the bond-valence parameterb. The results show that a systematic adaptation of the bond-valence parameters to the bond softness leads to a significant improvement in the bond-valence parameters, particularly for bonds involving soft anions, and is safer than individual free refinements of bothR0andbfrom a limited number of reference cation environments.

Structural Formability of ABO3-Type Perovskite Compounds: Bond Valence Analysis

On the basis of a total of 382 ABO3-type compounds, the structural formability of ABO3-type perovskite compounds is investigated by using the bond valence model method. A new two-dimensional structural map approach for predicting the formability of ABO3-type perovskite compounds that relies on the ideal bond distances with the combination of bond valence parameter, coordination number and oxidation state is proposed. The sample points representing compounds of forming perovskite and non-perovskite are distributed in distinctively different regions. Some misclassified compounds are analyzed and some new compounds are tested within the new structure map. The developed approach can be used to search for new perovskite and perovskite-related compounds by screening all possible elemental combinations.

New lanthanide–nitrogen bond-valence parameters

The bond-valence parameters (R ij ), which connect bond valences and bond lengths, have been computed for lanthanide–nitrogen bonds. It has been found that values of bond-valence parameters decrease with increasing lanthanide atomic number in coordination compounds, and that they are smaller than the R ij parameters of inorganic compounds. As expected, the lanthanide–nitrogen bond-valence parameters are larger than lanthanide–oxygen bond-valence parameters. There are no obvious dependencies between the number of N atoms in the coordination sphere and the bond-valence parameter value.

The correlation between metal oxidation state and bond valence parameters for M—O bonds (M = V, Fe and Cu). A simple method to search for the metal oxidation-state independent parameter pairs

Based on the latest available crystal data and the reported bond valence parameters, the linear correlation between the bond valence parameter

Influence of pressure on the lengths of chemical bonds

An expression to describe the force that a chemical bond exerts on its terminal atoms is proposed, and is used to derive expressions for the bond force constant and bond compressibility. The unknown parameter in this model, the effective charge on the atoms that form the bond, is determined by comparing the derived force constants with those obtained spectroscopically. The resultant bond compressibilities are shown to generally agree well with those determined from high-pressure structure determinations and from the bulk moduli of high-symmetry structures. Bond valences can be corrected for pressure by recognizing that the bond-valence parameter, R 0, changes with pressure according to the equation{\rm d}R_0/{\rm d}P = 10^{-4} R_0^4/(1/B-2/R_0)\; \rm{\AA\,\,GPa}^{-1}

Relationship between bond valence and bond softness of alkali halides and chalcogenides

Established bond-valence parameter tables rely on the assumption that the bond-valence sum of a central atom is fully determined by interactions to atoms in its first coordination shell. In this work the influence of higher coordination shells is tested in detail for bonds between lithium and oxygen. It is demonstrated that the sum of the weak interactions with atoms of the second coordination shells significantly contributes to the valence sum and should therefore not be neglected. Since the independent refinement of the two parameters R 0 and b is hardly possible from the limited range of bond lengths occurring in the first coordination shell, the restriction of bond-valence sums to contributions from nearest neighbours implicated another far-reaching simplification: the postulation of a universally fixed value of the bond-valence parameter b which characterizes the shape of the bond-valence pseudopotential for the respective atom pair. However, recent more sophisticated applications of the bond-valence concept, e.g. to model ion-transport pathways in solid electrolytes, demand sensible estimates of the bond-valence sums for mobile ions not only at their equilibrium sites but also at interstitial sites and bottle-necks of transport pathways. Calculations of bond valences at these non-equilibrium sites require the knowledge of the actual shape of the bond-valence pseudopotential. A systematic route to a more realistic estimate of b for alkali halides and chalcogenides is developed in this work from an empirical correlation between b and the absolute softnesses of the interacting particles.

Studies on bond and atomic valences. I. correlation between bond valence and bond angles in SbIII chalcogen compounds: the influence of lone-electron pairs

In the present bond-valence concept the bond-valence parameter ro is treated as constant for a given pair of atoms, and it is assumed that the bond valence sij is a function of the corresponding bond length Dij , and that the atomic valence is an integer equal to the formal oxidation number for Vi derived from stoichiometry. However, from a statistical analysis of 76 [SbIIIS n ] and 14 [SbIIISe n ] polyhedra in experimentally determined structures, it is shown that for SbIII—X bonds (X = S, Se), ro is correlated with {\bar \alpha} i , the average of the X—Sb—X angles between the three shortest Sb—X bonds. This is interpreted as a consequence of a progressive retraction of the 5s lone-electron pair from the SbIII nucleus, which can be considered as continuous change of the actual atomic valence act Vi of Sb from +3 towards +5. A procedure is derived to calculate an effective atomic valence eff Vi of SbIII from the geometry, {\bar \alpha} i and Dij , of the [SbIII Xn ] polyhedra, which approximates act Vi and is a better description of the actual valence state of SbIII than the formal valence for Vi . Calculated eff V SbIII are found to vary between +2.88 and +3.80 v.u. for [SbIIIS n ] and between +2.98 and +3.88 v.u. for [SbIIISe n ] polyhedra. It is suggested that a corresponding modification of the present bond-valence concept is also required for other cations with lone-electron pairs.