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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.


Determination of the curvature of the bond-valence relation by a match of the a priori bond valences to their observed bond lengths.
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fig2: Determination of the curvature of the bond-valence relation by a match of the a priori bond valences to their observed bond lengths.

Mentions: The network equations were derived for each of the 51 crystal structures to determine their a priori bond valences using the method of Rutherford (1990 ▸). The a priori bond valences were then compared with their respective experimental bond lengths, for a total of 481 pairs. The resulting plot is shown in Fig. 2 ▸. A series of simple equations were then fitted to the data points by least-squares minimization. These equations are considered next.


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

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

Determination of the curvature of the bond-valence relation by a match of the a priori bond valences to their observed bond lengths.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig2: Determination of the curvature of the bond-valence relation by a match of the a priori bond valences to their observed bond lengths.
Mentions: The network equations were derived for each of the 51 crystal structures to determine their a priori bond valences using the method of Rutherford (1990 ▸). The a priori bond valences were then compared with their respective experimental bond lengths, for a total of 481 pairs. The resulting plot is shown in Fig. 2 ▸. A series of simple equations were then fitted to the data points by least-squares minimization. These equations are considered next.

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.