Bond Valence Sum Calculations

The most commonly adopted empirical expression for the variation of bond length with bond valence is  

If the BVS rule is not satisfied (i.e. when the BVS are not very near to the formal charges for the ions) this may indicate metastability. In LaNiOa.s, for example, BVS calculations give a lanthanum valence of -1-2.63 and valences of -1-2.20 and -1-2.13 for the octahedral and square planar nickel cations, respectively. Although the Ni cation prefers square planar coordination, this oxide readily takes up oxygen upon heating in undergoing a stmctural transition to the perovskite LaNiOs, where the BVS are -1-3.05 and -1-3.01 for lanthanum and nickel, respectively (Alonso et al., 1997). The following worked example illustrates how to use Eqs. 3.20 and 3.21 with Table 3.7. 

TABLE 3.7. Bond-Valence Parameters for Some Halides, Nitrides, Oxides, Phosphides, and Sulfides 

Two sets of crystallographic data are given below for the bond lengths between Ti + and 0 in an oxide where the formal charge on titanium is +4. Each titanium ion is octahedrally coordinated by oxygen and the bond lengths given are those for the two axial, T-0(2), and four equatorial, Ti-0(1), distances. Use BVS calculations to predict which data are the most plausible. 

From Table 3.7, the bond valence parameter, / ,y, for the Ti -O bond is 1.815. Substituting the values for the various parameters in Eqs. 3.20 and 3.21 yields 

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Fig. 12.8. The bond valence sums calculated around Eu (Eu2) on the surface of the EuS layer and Eu + (Eul) inside the layer as a function of the position along the incommensurate wave (phase t). Reproduced with permission from Cario et al. (1999).

We would like to thank D. P. Norton and J. T. Luck for the preparation of the samples used for this work, J. Halbritter and Z. G. Ivanov for valuable comments and J. Buban for performing the bond-valence sum calculations. This research was sponsored by NSF under grant No. DMR-9503877 and by... 

The crystals of [V 0S04(H20)4]-S04-[H2N(C2H4)2NH2] contain two types of piperazines (one disordered with two essentially equal components and one situated about the crystallographic center of symmetry). The crystallographic data, the results of the bond valence sum calculations and manganometric titrations of the reduced vanadium(IV) sites, and charge balance consideration indicate that all piperazines are doubly protonated. 

I was characterized by powder X-ray diffraction (PXRD), energy dispersive analysis of X-rays (EDAX), chemical analysis, thermogravimetric analysis (TGA) and IR spectroscopy. EDAX analysis indicated the ratio of Mn S to be 3 2. The presence of fluorine was confirmed by analysis and the percentage of fluorine estimated by EDAX in a field emission scanning electron microscope was also satisfactory. Thermogravimetric analysis also confirms the stoichiometry of the compound. Bond valence sum calculations and the absence of electron density near fluorine in the difference Fourier map also provide evidence for the presence of fluorine. The sulfate content was found to be 30.8% compared to the expected 32% on the basis of the formula. 

I Mo(IV) complexes Mo(V) complexes I Mo(VI) complexes Figure 2.12 A graphical display of the results of Bond Valence Sum calculations. 

Random structure methods have proved useful in solving structures from X-ray powder diffraction patterns. The unit cell can usually be found from these patterns, but the normal single-crystal techniques for solving the structure cannot be used. A variation on this technique, the reverse Monte Carlo method, includes in the cost function the difference between the observed powder diffraction pattern and the powder pattern calculated from the model (McGreevy 1997). It is, however, always necessary to include some chemical information if the correct structure is to be found. Various constraints can be added to the cost function, such as target coordination numbers or the deviation between the bond valence sum and atomic valence (Adams and Swenson 2000b Swenson and Adams 2001). 

The EXAFS spectrum of a metal atom in a protein gives the lengths of the bonds between the metal and its ligand atoms with sufficient accuracy to calculate their bond valences. In principle it can also determine the number of each type of bond that the metal forms, but the results are much less reliable. However, calculation of the bond valences sum for the possible environments allows one to determine not only the coordination number but also the oxidation state of the metal atom (Thorp 1992 Hati and Datta 1995 Scarrow et al. 1996 Bell et al. 1997 Clark-Baldwin et al. 1998 Dooley et al. 1998). 

Palenik, G. J. (1997ft). Bond valence sums in coordination chemistry using oxidation state independent i o values. A simple calculation of the oxidation states of titanium in compounds containing Ti-N, Ti-O, and Ti-Cl bonds. Inorg. Chem. 36, 3394-7. 

Bond valence sum (BVS) analysis, developed by Brown (43) to calculate metal oxidation states in materials such as high-temperature superconductors and zeolites, has recently been shown by Thorp (44) to be predictive for metalloenzymes and model compounds. On the basis of crystallographic data, the empirical parameters r0 and B are determined. These values can then be used to calculate oxidation states from known coordination environments or coordination numbers from known oxidation states and bond lengths. The requisite equations are... 

Taking into account the structural diversity of the (n)-PB and (n)-HB structures as well as the existence of their intergrowths, the number of phases that can be obtained in the U-Mo-W-0 system can be extremely high. Kovba [19] pointed out that one of the reasons for such rich diversity is the variable valences of U, Mo and W. Indeed, even in the simplest (2)-PB phase (3-UOM02O7 [22-24], the formal valence of U is questionable. Assuming the hexavalent oxidation state for Mo, the formal valence of U should be A+. However, Bums et al. [26] calculated bond-valence sum incident upon the U site as 5.17 vu. Special spectroscopic investigations would be desirable in order to clarify the situation. 

Bond valence sum is calculated using interatomic distances and empirical bond valence parameters tabulated for each type of the bond. The analysis was conducted using VaList software [A.S. Wills and I.D. Brown, VaList, CEA, France (1999)], available from ftp //ftp.ill.fr/pub/dif/valist/. 

For application to YBCO, it has been pointed out that bond-valence calculations are empirical and cannot be used to determine the valences of the elements involved to better than around 10% [11.43]. However, in the case of the boundary structures observed here, the atomic positions can only be determined with an accuracy of 0.1 A, making any errors induced by the bond-valence sum analysis second order. As such, the bond-valence sums can be used to indicate positions where the valence of the elements involved changes considerably, although relating the magnitude of the change to properties must be approached with care. 

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