Determining valence

Typically lattice-induced strain results in the bonds around one cation being stretched and the bonds around another cation being compressed as found in BaRuOs (10253) by Santoro et al. (1999, 2000). When this happens, the valence sum rule will be violated around the cations in question but the valence still distributes itself as uniformly as possible among the bonds, so that the experimental bond valences determined from the bond lengths remain as close as possible to the theoretical bond valences. For this reason the BSI is typically smaller than the GII for lattice-induced strains, though the opposite is true for compounds with electronically induced strain where the valence sum rule remains well obeyed. 

Bargar, J. R., Brown, G. E. Jr, and Parks, G. A. (1997a). Surface complexation of Pb(II) at oxide water interfaces I. XAFS and bond valence determination of mononuclear and polynuclear Pb(II) sorption products on aluminum oxides. Geochim. Cosmochim. Acta 61, 2617-37. 

The fact that the co-ordination number for so many elements is six, and is generally independent of the nature of the co-ordinated groups, has made A. Werner suggest that the number is decided by available space rather than affinity, and that six is usually the maximum number which can be fitted about the central atom to form a stable system. Consequently, the co-ordination number represents a property of the atom which enables the constitution of molecular compounds to be referred back to actual linkings between definite atoms. A molecular compound is primarily formed through the agency of secondary valencies and, just as primary valencies determine the number of univalent atoms or their equivalent which can be linked to a central atom, so secondary valencies determine the number of mols. which can be attached to the central atom. The secondary valency is often active only towards definite mol. complexes, and hence the formation of additive compounds with other mol. complexes does not occur. Accordingly, the number of secondary valencies which are active towards different molecules is not always the same. 

Wachter ( ) have presented a very clear example of this behaviour in their studies of the moment formation in TmSe Te under pressure where both mixed valency, or intermediate valence (IV), and semiconductor to metal transition are found. The particular interest of this case is not only that these materials have been extensively characterized, but also because they show, from comparison of valences determined by two different experimental methods, that a unique picture which considers only one type of... 

Bargar, J.R. et al., XAFS and bond-valence determination of the structures and compositions of surface functional groups and Pb(ll) and Co(ll) sorption products on single-crystal a AI2O3, J. Colloid Inter/. Sci., 185, 473, 1997. 

One should strictly make a distinction between ideal bond valence defined theoretically from the bond graph in Section 10.3.2 and experimental bond valence determined from the observed bond lengths using Equations 10.1 or 10.2. Except in the situations described in Section 10.6, tbe two differ only by the experimental uncertainty... 

Tafto J, Krivanek OL (1982) Site-specific valence determination by electron energy-loss spectroscopy. Phys Rev Lett 48 560-563... 

Cosandey F., Su D., Sina M., Pereira N., Amatucci G. G. Fe valence determination and Li elemental distribution in lithiated FeOojFi.s/C nanocomposite battery materials by electron energy loss spectroscopy (EELS), Micron 2012, 43, 22-29. 

Then one may introduce orthogonal atomic orbitals oj and b , which are excited atomic orbitals of A and B orthogonalized to a and b, and one will generate single and double excitations towards these virtual MOs from either neutral (0i, 2) or ionic (< 3, valence determinants. 

I aS - bd / 2 combination will always correspond to the lowest (b) exact state, which dissociates into ground-state atoms. The ground state has very large components in the model space, on neutral determinants only for large interatomic distances, and on neutral and ionic valence determinants at short interatomic distances. The two lowest eigenstates of H2 should definitely belong to the target space. 

The transferability of a valence effective Hamiltonian defined on H2 to H clusters therefore faces a series of basic difficulties, which leaves little hope of success. The situation would be even worse of course if one dealt with boron or carbon atoms since for C2 already one should introduce strongly hybridized (for instance C(p ) + C(p )) or m tiply ionic (for instance C -I- C (s p )) states which are unbound. The choice of the target space is already impossible on the diatom, and the definition of an exact (Bloch, des Cloizeaux,...) effective Hamiltonian from knowledge of the spectrum of the diatom is either impossible or perfectly arbitrary. Even if it were possible, the treatment of B4 or C4 would introduce some multiply ionic valence determinants for which the assessment of an effective energy would be impossible. 

In concluding this brief history, it is worth noting that the atomic double-well model has ramifications in the discussion of orbital localization in solids, and is therefore germane to the problems associated with valence determinations in solids and compounds containing rare earths. 

In what follows, two separate problems that should be clearly distinguished are discussed. The first is to find a method of determining the individual bond valences appearing in Eq. (2) - a partial solution to the problem which is of practical utility in many instances is presented. The second problem is the determination of bond valences from experimental data (bond lengths). As bond lengths are affected by factors other than bond valence, bond valences determined in this way are referred to as apparent bond valences and symbolized v. The sum of apparent bond valences for all the bonds to a given atom are called the apparent valence, V,. ... 

Doublet ground state for mixed valence Determine the magnitude of / in terms of t for which the model system defined in Fig. 6.4 has a doublet ground state. 

The application of Mjy y absorption to valence measurements is still at its infancy at this time, although first studies were started already in 1973 by Ottewell et al. (1973) and recently continued by Kaindl et al. (1983b, 1984) and by van der Laan et al. (1986). Analytic procedures for the extraction of the 4f occupation numbers from two complicat l and superimposed Mjy y final-state multiplets require the existence of reliable theoretical calculations of their intensities and positions in each valence state, which are available only recently (Thole et al. 1985). In addition the special experimental problems of Mjy y absorption, e.g., saturation effects and surface shifts diminish drastically the potential of Mjy y absorption as a tool for high-precision valence determinations. 

Various analytical procedures are applied to extract valence numbers from Lm spectra. They are based on a deconvolution of two superimposed and shifted single-peaked sub-spectra taken either from experimental or from numerical reference spectra. Within Av = +0.1 the different techniques yield the same results on identical spectra. An estimate of the absolute and relative uncertainties may be obtained from table 3. It lists the valence numbers from most of the Lnui spectra published from 1975 until 1986. These numbers have been worked out by more than ten different laboratories. Obviously the numbers extracted from identical systems agree fairly well in spite of the fact that they have been obtained with the use of quite different deconvolution techniques. Large systematic deviations (>0.1) from the average numbers (where available) should be attributed to different experimental results rather than to the specific valence determination procedure. 

Valenee numbers of Tm,Se extracted from My absorption data (Kalkowski et al. 1985a, Kaindl et al. 1985) are found to coincide with p, according to eq. (8). The origin of the discrepancy between the valence determination from Lm absorption, magnetic susceptibility and XPS on one hand and My absorption on the other hand, is not clear at this time. Probably it is due to the special experimental problems of M absorption (d. sections 4.3.1 and 5). 

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