Chemical or Isomer Shift

FIGURE 4.57 Effect of the coulombic interaction in the energy levels of 57Fe. 

The Physical Chemistry of Materials Energy and Environmental Applications 

FIGURE 4.58 57Fe Mossbauer absorption spectrum resulting from isomer shift. 

The isomer shift is caused because the emitter and the absorber 57Fe nuclei in the Mossbauer experiment have different electronic charge densities at the position of the nucleus [137-140], Consequently, we get a small shift in the difference of the energy levels given by [137-140] 

The isomer shift gives information about electron density at the nucleus, the valence of the tested atom, and the structure of the environment of the surroundings of the tested atom. 

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The chemical or isomer shift (8) is a linear function of electron density (due to electrons occupying s orbitals) at the nucleus. This, in turn, is influenced by many factors (oxidation state, spin state, -character i n the c bonds, dn back-bonding, ionicity), and correlations are not simple. For low-spin complexes 8 is rather independent of oxidation state from —2 to +2. Even Fe(CN) and Fe(CN) have almost identical 8 values. For high-spin compounds, however, 8 varies markedly with formal oxidation state and indeed provides an excellent means of establishing it. A few examples of how Mossbauer spectra can be employed in studying the chemistry of iron will now be given others will be mentioned as appropriate below. 

This internal pressure effect may actually be quite general in Mbssbauer effect studies of small particles, as discussed by Schroeer et al. for the recoil-free fraction (156) and the isomer shift (157). In addition, Schroeer (152) has summarized a number of origins for Mossbauer parameters being particle size dependent. Thus, from the above discussion, it seems apparent that a priori particle size determination using the recoil-free fraction, quadrupole splitting, or isomer shift is not possible for an arbitrary catalytic system. However, the "experimental calibration of these parameters, which not only facilitates particle size measurement, may also provide valuable information about the chemical state (e.g., electronic, defect, stress) of the small particles. This point will be illustrated later. 

The electron density i/ (0)p at the nucleus primarily originates from the ability of s-electrons to penetrate the nucleus. The core-shell Is and 2s electrons make by far the major contributions. Valence orbitals of p-, d-, or/-character, in contrast, have nodes at r = 0 and cannot contribute to iA(0)p except for minor relativistic contributions of p-electrons. Nevertheless, the isomer shift is found to depend on various chemical parameters, of which the oxidation state as given by the number of valence electrons in p-, or d-, or /-orbitals of the Mossbauer atom is most important. In general, the effect is explained by the contraction of inner 5-orbitals due to shielding of the nuclear potential by the electron charge in the valence shell. In addition to this indirect effect, a direct contribution to the isomer shift arises from valence 5-orbitals due to their participation in the formation of molecular orbitals (MOs). It will be shown in Chap. 5 that the latter issue plays a decisive role. In the following section, an overview of experimental observations will be presented. 

Apart from the determination of nuclear parameters, the Mossbauer transition in Os, especially the 36.2 and 69.6 keV transitions, are suited for chemical applications. As shown below, the 36.2 keV level, in spite of its large half-width, can be well used for the measurement of isomer shifts, whereas the 69.2 keV state is favorable for the characterization of electric quadrupole or magnetic dipole interactions. Both Mossbauer levels are populated equally well by the parent isotope lr, and simultaneous measurement is possible by appropriate geometrical arrangement. 

We have learned from the preceding chapters that the chemical and physical state of a Mossbauer atom in any kind of solid material can be characterized by way of the hyperfine interactions which manifest themselves in the Mossbauer spectrum by the isomer shift and, where relevant, electric quadrupole and/or magnetic dipole splitting of the resonance lines. On the basis of all the parameters obtainable from a Mossbauer spectrum, it is, in most cases, possible to identify unambiguously one or more chemical species of a given Mossbauer atom occurring in the same material. This - usually called phase analysis by Mossbauer spectroscopy - is nondestructive and widely used in various kinds of physicochemical smdies, for example, the studies of... 

Apart from the determination of the structures of stannylenes by diffraction methods (X-ray or electron diffraction) many other physico-chemical techniques can be exployed to characterize these compounds more completely. Besides the classical methods such as IR-, Raman-, PE-, UV- and NMR-spectroscopy, MoBbauer-119 m-tin spectroscopy is widely used for the determination of the oxidation states of tin atoms and of their coordination 1n8-12°-123>. jt is not in the scope of this report to study the dependence of MoBbauer constants such as isomer shift and quadrupole splitting on structural parameters. Instead, we want to concentrate on one question Which information can we deduce from the structure of stannylenes to evaluate their reactivity ... 

Equation (10) shows that the isomer shift IS is a direct measure of the total electronic density at the probe nucleus. This density derives almost exclusively from 5-type orbitals, which have non-zero electron densities at the nucleus. Band electrons, which have non-zero occurrence probabilities at the nucleus and 5-type conduction electrons in metals may also contribute, but to a lesser extent. Figure 3 shows the linear correlation that is observed between the experimental values of Sb Mossbauer isomer shift and the calculated values of the valence electron density at the nucleus p (0). The total electron density at the nucleus p C ) (Eq. 10) is the sum of the valence electron density p (0) and the core electron density p (0), which is assumed to be constant. This density is not only determined by the 5-electrons themselves but also by the screening by other outer electrons p-, d-, or /-electrons) and consequently by the ionicity or covalency and length of the chemical bonds. IS is thus a probe of the formal oxidation state of the isotope under investigation and of the crystal field around it (high- and low-spin Fe may be differentiated). The variation of IS with temperature can be used to determine the Debye temperature of a compound (see Eq. (13)). 

The potential of the SW approach to systematize inneratomic properties and processes can be easily illustrated by reconsidering chemically induced nuclear lifetime variations which, among others, are of relevance to the calibration problem of Moessbauer isomer shifts. Highly excited atom states carrying single or multiple vacancies in inner shells form another promising subject of SW simulations. In the latter case the results of a DV-Xa study of the K-shell x-ray satellite intensities of metal fluorides can be used for a comparative assessment of both methods. 

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