Nuclear transition

Up to the present time, the Mossbauer effect has been observed with nearly 100 nuclear transitions in about 80 nuclides distributed over 43 elements (cf. Fig. 1.1). Of course, as with many other spectroscopic methods, not all of these transitions are suitable for actual studies, for reasons which we shall discuss later. Nearly 20 elements have proved to be suitable for practical applications. It is the purpose of the present book to deal only with Mossbauer active transition elements (Fe, Ni, Zn, Tc, Ru, Hf, Ta, W, (Re), Os, Ir, Pt, Au, Hg). A great deal of space will be devoted to the spectroscopy of Fe, which is by far the most extensively used Mossbauer nuclide of all. We will not discuss the many thousands of reports on Fe... 

Not all nuclear transitions of this kind produce a detectable y-ray for a certain portion, the energy is dissipated by internal conversion to an electron of the K-shell which is ejected as a so-called conversion electron. For some Mossbauer isotopes, the total internal conversion coefficient ax is rather high, as for the 14.4 keV transition of Fe (ax = 8.17). ax is defined as the ratio of the number of conversion electrons to the number of y-photons. 

However, in contrast, the resonance effect increased by cooling both the source and the absorber. Mdssbauer not only observed this striking experimental effect that was not consistent with the prediction, but also presented an explanation that is based on zero-phonon processes associated with emission and absorption of y-rays in solids. Such events occur with a certain probability/, the recoil-free fraction of the nuclear transition (Sect. 2.4). Thus, the factor/is a measure of the recoilless nuclear absorption of y-radiation - the Mdssbauer effect. 

The entity ot is the so-called isomer shift calibration constant, c is the speed of light, Co is the electric constant, and Eq is the nuclear transition energy. (The Coulomb constant k = l/(47rco), which was dropped in (4.1), is re-inserted here.) A comprehensive derivation of this expression is found in [8, 9]. 

In those cases where we are dealing with nuclear transitions which are a mixture of multipolarity Ml and E2 with a mixing parameter 5 defined by = ((/i E2 h))l ((/i I M111/2)) (positive or negative), one obtains the extended relation... 

In anisotropic crystals, the amplitudes of the atomic vibrations are essentially a function of the vibrational direction. As has been shown theoretically by Karyagin [72] and proved experimentally by Goldanskii et al. [48], this is accompanied by an anisotropic Lamb-Mossbauer factor/which in turn causes an asymmetry in quadra-pole split Mossbauer spectra, for example, in the case of 4 = 3/2, f = 1/2 nuclear transitions in polycrystalline absorbers. A detailed description of this phenomenon, called the Goldanskii-Karyagin effect, is given in [73]. The Lamb-Mossbauer factor is given by... 

Fig. 7.53 Transmission Mossbauer spectra of the 137, 155, and 187 keV nuclear transitions of 186,188,190qj taken with sources emitting an unsplit line and (a) Os02-absorber (rj 0), (b) OSP2-absorber (rj 0.74). The curves are the results of least-squares fits. The vertical bars indicate the positions and relative intensities of the individual hyperfine components (from [254])...

There are two iridium isotopes, ir and Ir, suitable for Mossbauer spectroscopy. Each of them possesses two nuclear transitions with which nuclear resonance absorption has been observed. Figure 7.58 (from [266]) shows the (simplified) nuclear decay schemes for both iridium Mossbauer isotopes the Mossbauer transitions are marked therein with bold arrows. The relevant nuclear data known to date for the four Mossbauer transitions are collected in Table 7.1 at the end of the book. 

It is a matter of historical interest that Mossbauer spectroscopy has its deepest root in the 129.4 keV transition line of lr, for which R.L. Mossbauer established recoilless nuclear resonance absorption for the first time while he was working on his thesis under Prof. Maier-Leibnitz at Heidelberg [267]. But this nuclear transition is, by far, not the easiest one among the four iridium Mossbauer transitions to use for solid-state applications the 129 keV excited state is rather short-lived (fi/2 = 90 ps) and consequently the line width is very broad. The 73 keV transition line of lr with the lowest transition energy and the narrowest natural line width (0.60 mm s ) fulfills best the practical requirements and therefore is, of all four iridium transitions, most often (in about 90% of all reports published on Ir Mossbauer spectroscopy) used in studying electronic stractures, bond properties, and magnetism. 

Nuclear absorption of incident X-rays (from the synchrotron beam) occurs elastically, provided their energy, y, coincides precisely with the energy of the nuclear transition, Eq, of the Mossbauer isotope (elastic or zero-phonon peak at = E m Fig. 9.34). Nuclear absorption may also proceed inelasticaUy, by creation or annihilation of a phonon. This process causes inelastic sidebands in the energy spectrum around the central elastic peak (Fig. 9.34) and is termed nuclear inelastic scattering (NIS). 

Here, A is the nearly isotropic nuclear coupling constant, I is the nuclear spin (Iun = I), and m is the particular nuclear spin state. It may be observed that the zero field splitting term D has a second-order effect which must be considered at magnetic fields near 3,000 G (X-band). In addition to this complication nuclear transitions for which Am = 1 and 2 must also be considered. The analysis by Barry and Lay (171) of the Mn2+ spectrum in a CsX zeolite is shown in Fig. 35. From such spectra these authors have proposed that manganese is found in five different sites, depending upon the type of zeolite, the primary cation, and the extent of dehydration. 

X-rays, often used in radiation chemistry, differ from y-rays only operationally namely, X-rays are produced in machines, whereas y-rays originate in nuclear transitions. In their interaction with matter, they behave similarly—that is, as a photon of appropriate energy. Other radiations used in radiation-chemical studies include protons, deuterons, various accelerated stripped nuclei, fission fragments, and radioactive radiations (a, /, or y). 

The nuclear transitions are very sensitive to the local environment of the atom, and Mossbauer spectroscopy is a sensitive probe of the different environments an atom occupies in a solid material. By analyzing the chemical shifts and quadrupole splitting in Mossbauer spectra of samples containing Mossbauer-ac-tive nuclei, information on the state of oxidation and the local structure can be obtained. Only a few nuclei can be used for this purpose, so this method has limited but powerful applications. 

Figure 5.1 Resonant absorption of y-radiation by a nucleus can only take place in the solid state because of recoil effects. The excited nucleus of a free atom emits a y-photon with an energy EirER, whereas the nucleus in the ground slate of a free atom can only absorb a photon if it has an energy equal to Eo+ER. As the linewidth of nuclear transitions is extremely narrow, the emission spectrum does not overlap with the absorption spectrum. In a solid, a considerable fraction of events occurs recoil free (ER=0), and here the emission spectrum overlaps completely with the absorption spectrum (provided source and absorber have the same chemical environment).

Figure 5.5 The four most common types of Mossbauer spectra observed in iron-containing catalysts along with the corresponding nuclear transitions. Also indicated is how the Mossbauer parameters are derived from the spectra.

Theoretical considerations leading to a density functional theory (DFT) formulation of the reaction field (RF) approach to solvent effects are discussed. The first model is based upon isolelectronic processes that take place at the nucleus of the host system. The energy variations are derived from the nuclear transition state (ZTS) model. The solvation energy is expressed in terms of the electrostatic potential at the nucleus of a pseudo atom having a fractional nuclear charge. This procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy, since all integrations involved are performed over [O.ooJ The quality of the approximations made are discussed within the frame of the Kohn-Sham formulation of density functional theory. 

Formulation of the insertion energy within the Nuclear Transition State (ZTS) Model. 

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