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Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen.

Gagné OC, Hawthorne FC - Acta Crystallogr B Struct Sci Cryst Eng Mater (2015)

Bottom Line: 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 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.

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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.


Bond-valence parameter Ro as a function of mean bond length for the 90 multiple-coordination-number ions
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fig3: Bond-valence parameter Ro as a function of mean bond length for the 90 multiple-coordination-number ions

Mentions: Here we will examine trends in the bond-valence parameters derived with the GRG method for the 90 ions with two or more coordination numbers. We begin with the relation between the bond-valence parameter Ro and the mean bond length of a pair of ions. Fig. 3 ▸ shows our new values for Ro as a function of mean bond length. The correlation is not strong (R2 = 0.457), although it changes slightly by removing the two lower outliers (H+, Li+; R2 = 0.516). Certain groups of ions of similar crystal-chemical behavior also show significant correlation (e.g. alkali metals, R2 = 0.937; alkaline-earth metals, R2 = 0.962). Attempts to relate the individual parameters Ro and B directly to other physical properties of the ions were not successful.


Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen.

Gagné OC, Hawthorne FC - Acta Crystallogr B Struct Sci Cryst Eng Mater (2015)

Bond-valence parameter Ro as a function of mean bond length for the 90 multiple-coordination-number ions
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4591556&req=5

fig3: Bond-valence parameter Ro as a function of mean bond length for the 90 multiple-coordination-number ions
Mentions: Here we will examine trends in the bond-valence parameters derived with the GRG method for the 90 ions with two or more coordination numbers. We begin with the relation between the bond-valence parameter Ro and the mean bond length of a pair of ions. Fig. 3 ▸ shows our new values for Ro as a function of mean bond length. The correlation is not strong (R2 = 0.457), although it changes slightly by removing the two lower outliers (H+, Li+; R2 = 0.516). Certain groups of ions of similar crystal-chemical behavior also show significant correlation (e.g. alkali metals, R2 = 0.937; alkaline-earth metals, R2 = 0.962). Attempts to relate the individual parameters Ro and B directly to other physical properties of the ions were not successful.

Bottom Line: 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 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.

View Article: PubMed Central - HTML - PubMed

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.