Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen.
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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.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 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.
Affiliation: Geological Sciences, University of Manitoba, 125 Dysart Road, Winnipeg, Manitoba R3T 2N2, Canada.
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. No MeSH data available. |
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Mentions: While the GRG optimization has proved to be much more effective than an iterative search method, the use of a search algorithm generally raises concern as to whether the minimization obtained is a local minimum as opposed to the global minimum. Mills & Christy (2013 ▸) show that contour plots of RMSD as a function of Ro and B for Te4+ and Te6+ are smooth and concave in shape, but the plots only cover a narrow range of values around the extracted parameters. In Fig. 1 ▸ we show (for Fe3+) that the shape remains concave over a much larger range of values, and no maxima, saddle points or other minima are observed. As a result, convergence can only lead to the global minimum. Note that both Fig. 1 ▸ and the plot of Mills & Christy (2013 ▸) show that the contour lines can have a pronounced oval shape; thus different combinations of values for Ro and B can lead to the same level of fit over a non-negligible range of values for the cations (although different parameters from one contour line may give different anion BVS), which may be deceptive in an iterative search for the global minimum. |
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Affiliation: Geological Sciences, University of Manitoba, 125 Dysart Road, Winnipeg, Manitoba R3T 2N2, Canada.
No MeSH data available.