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. 2009 Dec;109(12):6858-919.
doi: 10.1021/cr900053k.

Recent developments in the methods and applications of the bond valence model

Ian David Brown  1
Affiliations
Free PMC article

Recent developments in the methods and applications of the bond valence model

Ian David Brown. Chem Rev. 2009 Dec.
Free PMC article
No abstract available

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Figures

Figure 1
Figure 1
Bond fluxes in the (110) plane of rutile, TiO2. Copyright 1999 International Union of Crystallography. Reproduced with permission from ref (9).
Figure 2
Figure 2
Portion of the bond network of an NaCl crystal. Black ions are Na+, light ions are Cl−.
Figure 3
Figure 3
Finite bond graphs for (a) NaCl (c.f. Figure 2) and (b) perovskite (c.f. Figure 21).
Figure 4
Figure 4
Finite bond graph for perovskite as a capacitive electric circuit based on Figure 3b. According to the principle of maximum symmetry, the capacitors are all identical.
Figure 5
Figure 5
Bond-valence−bond-length correlation for Ca−O bonds. The circles represent the bond fluxes calculated for a number of observed bonds. The line is calculated using eq 26 with R0 = 1.967 Å and b = 0.37 Å. Reproduced from Figure 3.1 (p. 27) from “The Chemical Bond in Inorganic Chemistry: the Bond Valence Model” by Brown, David (2002) by permission of Oxford University Press.
Figure 6
Figure 6
Consequences of different choices for the cutoff radius, Rcutoff, on the values of the bond valence parameters, R0 and b, for Li−O bonds. (a) Refined value of R0, (b) refined value of b, (c) average difference between the atomic valence and the bond valence sum calculated with the bond valence parameters refined at this cutoff, (d) bond valence at the cutoff calculated with the corresponding bond valence parameters. Copyright 2001 International Union of Crystallography. Reproduced with permission from ref (79).
Figure 7
Figure 7
Refined value of b as a function of the difference in softness between the anion and the cation calculated using eq 32. Squares are alkali halides, triangles are alkali chalcogenides, dots represent values taken from the literature. The line is a fit to the dots. All distances out to at least 6 Å were used. Copyright 2001 International Union of Crystallography. Reproduced with permission from ref.(79)
Figure 8
Figure 8
Bond-valence−bond-length curve illustrating the distortion theorem by showing how the average bond length increases from 2.56 to 2.62 Å as the valences of two hypothetical bonds change from 0.2 vu to 0.1 and 0.3 vu, that is, at constant bond valence sum.
Figure 9
Figure 9
Electronic distortion shown by lone electron pairs (dashed spheres). (a) Lone pair is nonstereoactive and (b) lone pair is stereoactive.
Figure 10
Figure 10
Schematic representation of a three-ligand seven-coordinated complex and its reduction to a simple planar pseudotrigonal description using the valence vector model. Copyright 2006 International Union of Crystallography. Reproduced with permission from ref (129).
Figure 11
Figure 11
The Ag+ conduction paths in the unit cell of α-AgI with ΔV = 0.05 vu. Reproduced with permission from ref (135), copyright 2000 by American Physical Society.
Figure 12
Figure 12
Average observed coordination number (⟨NB⟩ = Nb) of anions plotted against the residual valence (CDA = Cb) for (a) borates, (b) uranyl minerals, and (c) sulfates. Copyright 2008 Oldenbourg Wissenschaft Verlag GmbH. Reproduced with permission from ref (149).
Figure 13
Figure 13
(a) Lewis acid strength of Fe2+ plotted against the number of transformer water molecules; (b) same as (a) but with the range of basicities of the structural unit superimposed. Copyright 2008 Oldenbourg Wissenschaft Verlag GmbH. Reproduced with permission from ref (149).
Figure 14
Figure 14
Cation radii in borates in Å plotted against the cation Lewis acid strength. The lines show the different trends for (a) infinitely polymerized borates, (b) finitely polymerized borates and (c) unpolymerized borates. Adapted from ref (146). Copyright 2001 Oldenbourg Wissenschaft Verlag GmbH. Adapted with permission from ref (151).
Figure 15
Figure 15
Ag+ conduction paths in α-AgI modeled at 525 K using the reverse Monte Carlo method. In contrast to Figure 11 which shows the conduction paths in the time and space averaged structure that conforms to the space group symmetry, this figure shows the localized paths at a specific hypothetical point and at a particular time with the atoms displaced from their average positions by thermal motion. Reproduced with permission from ref (135). Copyright 2000 by the American Physical Society.
Figure 16
Figure 16
Variation in the bond valence sums (AV) as a function of the O2− parameter, u, of each of the ions in the spinels MgCr2O4 (top) and NiAl2O4 (bottom). The predicted value of u is the one which gives the bond valence sums for each ion that correspond to their atomic valence. With kind permission of Springer Science + Business Media from Phys. Chem. Miner. “Cation ordering in NiAl2O4 spinel by a 111 systematic row CBED technique” 27 (1999) 112, Tabira and Withers, Figure 4.
Figure 17
Figure 17
Modulation of the bond valence sums in GaS1.82 around Ga (top, contour interval 0.1 vu) and S (bottom, contour interval 0.05 vu) as a function of the two additional dimensions. Solid lines are positive contours, broken lines are negative. Over the whole crystal the environments around Ga and S will sample all of the regions shown in this diagram. Copyright 2003 International Union of Crystallography, Reproduced with permission from ref (192).
Figure 18
Figure 18
Structure of the B4O72− ion. Open circles represent O2−, filled circles represent B3+. The central O2− is proposed to be the labile anion.
Figure 19
Figure 19
Bond-valence−bond-length plot for O−H bonds. The points plot the valence against the observed bond lengths for a number of accurately determined hydrogen bonds. The thick line is a fit to these points, the thin line is an interpolation of the correlation that would be expected if the repulsion strain between the terminal O2− ions were absent. Reproduced from Figure 7.1 (p.77) from “The Chemical Bond in Inorganic Chemistry. The Bond Valence Model” by Brown, David (2002). By permission of the Oxford University Press.
Figure 20
Figure 20
Example of a Steiner plot. See text for details. Copyright 2003 American Chemical Society. Reproduced with permission from Picazo, O.; Alkorta, I.; Elguero, J. J. Org, Chem.2003, 68, 7485.
Figure 21
Figure 21
Group of eight unit cells of the cubic perovskite structure ABX3. The B cations (black) are octahedrally coordinated by X anions (white). The octahedra are linked through shared corners to form a cubic network. The A cations (gray) occupy the centers of the cubes formed by the linked octahedra.
Figure 22
Figure 22
Global instability index, G, plotted against the tolerance factor, t, for all known ABO3 compounds assuming that each adopts the cubic perovskite structure. The 3:3 compounds lie on the solid line, the 2:4 compounds lie on the dash line and the 1:5 compounds lie on the dotted line. The horizontal line at G = 0.2 vu represents the upper stability limit of the cubic strncture. Adapted from ref (221). Copyright 2007 International Union of Crystallography. Reproduced with permission.
Figure 23
Figure 23
A 2 Å thick slice through a silver iodide molybdate glass showing the Ag+ conduction pathways. Light parts correspond mainly to I−−, the dark parts to O2−-coordinated, Ag+. Reproduced with permission from ref (135), copyright 2000 by American Physical Society.
Figure 24
Figure 24
(a) Outer sphere complexes hydrogen bonded to the surface and the equivalent diffuse double layer capacitor. (b) Inner sphere complexes directly bonded to the surface and the equivalent diffuse triple layer capacitor.
Figure 25
Figure 25
Acetyl phosphate group in E2P showing the bonding of the Mg2+ ion. The numbers above the bonds are the lengths in Å, the numbers below are the bond valences. Copyright 2004 American Society for Biochemistry and Molecular Biology. Reproduced with permission from ref (289).
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References

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    1. Pauling L. J. Am. Chem. Soc. 1929, 51, 1010.
    1. Bragg W. L. Z. Kristallogr. 1930, 74, 237.
    1. Baur W. H. In Structure and Bonding in Crystals, Vol. II; O’Keeffe M., Navrotsky A., Eds.; Academic Press: London, 1981; Chapter 31.