Abstract
Published two-body bond-valence parameters for cation-oxygen bonds have been evaluated via the root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180,194 filtered bond lengths from 31,489 coordination polyhedra. Values of the RMSD range from 0.033-2.451 v.u. (1.1-40.9% per unit of charge) with a weighted mean of 0.174 v.u. (7.34% per unit of charge). The set of best published parameters has been determined for 128 ions and used as a benchmark for the determination of new bond-valence parameters in this paper. Two common methods for the derivation of bond-valence parameters have been evaluated: (1) fixing B and solving for R(o); (2) the graphical method. On a subset of 90 ions observed in more than one coordination, fixing B at 0.37 Å leads to a mean weighted-RMSD of 0.139 v.u. (6.7% per unit of charge), while graphical derivation gives 0.161 v.u. (8.0% per unit of charge). The advantages and disadvantages of these (and other) methods of derivation have been considered, leading to the conclusion that current methods of derivation of bond-valence parameters are not satisfactory. A new method of derivation is introduced, the GRG (generalized reduced gradient) method, which leads to a mean weighted-RMSD of 0.128 v.u. (6.1% per unit of charge) over the same sample of 90 multiple-coordination ions. The evaluation of 19 two-parameter equations and 7 three-parameter equations to model the bond-valence-bond-length relation indicates that: (1) many equations can adequately describe the relation; (2) a plateau has been reached in the fit for two-parameter equations; (3) the equation of Brown & Altermatt (1985) is sufficiently good that use of any of the other equations tested is not warranted. Improved bond-valence parameters have been derived for 135 ions for the equation of Brown & Altermatt (1985) in terms of both the cation and anion bond-valence sums using the GRG method and our complete data set.
Highlights
Many people have investigated correlations between deviations from Pauling’s second rule (Pauling, 1929) and bondlength variations in crystals (e.g. Baur, 1970, 1974; Donnay & Allmann, 1970; Pyatenko, 1972; Brown & Shannon, 1973; Ferguson, 1974), generally developing quantitative relations between bond length and the strength of a bond
As part of other work examining the dispersion of bond lengths in inorganic crystals, we have used the Inorganic Crystal Structure Database (ICSD) to extract bond lengths for all atoms of the periodic table of elements bonded to oxygen, as a function of oxidation state and coordination number
We have an effective method for the derivation of bond-valence parameters, and have determined that (1) the minimization should be done on the cation bond-valence sums, while the anion bond-valence sums are verified a posteriori, and (2) the most useful level of universality remains on the basis of ion pairs
Summary
Many people have investigated correlations between deviations from Pauling’s second rule (Pauling, 1929) and bondlength variations in crystals (e.g. Baur, 1970, 1974; Donnay & Allmann, 1970; Pyatenko, 1972; Brown & Shannon, 1973; Ferguson, 1974), generally developing quantitative relations between bond length and the strength of a bond. Brown’s latest list of published bond-valence parameters (Brown, 2013) contains 1749 sets of bond-valence parameters for the equation of Brown & Altermatt (1985), for 1350 unique ion pairs, and counts 340 sets of bond-valence parameters for 194 cations bonded to oxygen. We (1) evaluate published bond-valence parameters for 128 cations bonded to oxygen, using a very large set of bond lengths that have undergone rigorous filtering; (2) investigate many alternative algebraic forms of the bondvalence—bond-length relation; (3) evaluate different fitting methods used in the derivation of bond-valence parameters; (4) determine new bond-valence parameters for 135 cations bonded to oxygen
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