A Mossbauer spectrum

This is the basic form of a Mossbauer spectrum a plot of transmission versus a series of Doppler velocities between source and absorber (i.e. versus the eflfective y-ray energy), the absorption line being Lorentzian in shape with a width at half-height corresponding to IF. The various factors influencing the transmission spectrum are illustrated schematically in Fig. 1.7, which is self-explanatory. 

It should not be forgotten that the excited absorber nuclei re-emit the y-ray within 10 s. However, if the internal conversion coefficient is high, correspondingly fewer y-rays will be emitted. More important, however, the re-emission is not directional but takes place over the full 4.-r solid angle. Consequently the number of secondary events recorded at the detector in a collimated transmission experiment are few and are usually neglected. 

We shall return to the theoretical discussion again in Chapter 3 to see how the spectrum can be influenced in detail by various properties of the resonant nucleus and by the extra-nuclear electrons. Before then, however, it will be convenient to outline the experimental techniques of Mossbauer spectroscopy and this forms the subject of the next chapter. 

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The Debye temperature is usually high for metallic systems and low for metal-organic complexes. For metals with simple cubic lattices, for which the model was developed, is found in the range from 300 K to well above 10 K. The other extreme may be found for iron in proteins, which may yield d as low as 100-200 K. Figure 2.5a demonstrates how sharply/(T) drops with temperature for such systems. Since the intensity of a Mossbauer spectrum is proportional to the... 

The recoil-free fraction / is an important factor for determining the intensity of a Mossbauer spectrum. In summary, we notice from inspecting (2.14)-(2.17) and Fig. 2.5a that... 

Fig. 3.12 Contributions to a Mossbauer spectrum given in counts per channel. A b is the nonreso-nant background from scattered y-radiation and X-ray fluorescence in source and absorber...

Although the EFG of a given system can be easily determined from a Mossbauer spectrum, it may be rather difficult to relate it to the electronic structure of the Mossbauer atom. In order to visualize a few typical cases, the computation of the EFG is described in the following for some selected charge distributions. A comprehensive quantum chemical interpretation of the quadrupole sphtting will be given in Chap. 5. 

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... 

The intensity of a Mossbauer spectrum depends not only on the recoil-free fractions of the source and the absorber and on the number of absorbing nuclei, but also on the linewidth of the absorption lines and on whether or not saturation effects occur. The following approximate expression is valid for relatively thin absorbers [17] ... 

Expression (5-6) indicates that the intensity of a Mossbauer spectrum is only proportional to the concentration of Mossbauer atoms if the term (1 -trnJAl l) 1. 

Another parameter that one can extract from a Mossbauer spectrum is the quadrupole splitting. The 3/2 state in either iron or tin is degenerate with respect to an asymmetric electrostatic field, and in such a field these levels will be split into dz 3/2 and 1/2 levels. One can observe transitions either to or from these two levels to the ground state, and this is the quadrupole splitting. It is actually e qQ, where eq is the electrostatic field gradient—i,e., the second derivative of the potential with respect to the coordinate—and eQ is the nuclear quadrupole moment. The typical quadrupole split spectrum for iron is shown in Figure 6, in which the cubic (octahedral) symmetry around the iron atom is de-... 

The spin states of the iron(II) atoms have been verified with Mossbauer spectroscopy. A Mossbauer spectrum recorded at room temperature, shows two doublets... 

Figure 2-3 A Mossbauer spectrum for an orthopyroxene sample with ferrosilite mole fraction of 1.1% equilibrated at 900°C. The solid curve is the fit to the spectrum, and the dashed curves are individual fit lines. The residual is also shown (shifted upward by 0.989 units so that it can be shown clearly). The area ratio of two Ml peaks to two M2 peaks is 0.2367 0.0055. Fe " is negligible. The cation distribution (or formula) of this orthopyroxene (4 cation and 6 oxygen basis) is as follows tetrahedral site, Alo.oi8Si1.982 Ml Fe0.0041Mg0.9776Ti0.0007Al0.0176 M2, Cao.ooi6Feo.oi72Mgo.9803-There is also minor amount of Na (0.0004) and Mn (0.0005) in M2 site. From Wang et al. (2005).

A Mossbauer spectrum that has helped to corroborate the structure of cyclooctatetraene iron tricarbonyl is shown in Figure 27-12. The separation of the two absorption peaks in Figure 27-12 corresponds to a sample Doppler velocity of 1.23 mm sec-1. This Doppler effect means that there is the very small energy difference of 1.4 X 10 6 kcal mole 1 in the two transitions shown. 

Doppler velocity may provide a Mossbauer spectrum with a large increase in the signal to noise ratio compared to that obtained in the transmission mode. The type of radiation used to generate the scattered Mossbauer spectrum depends on the internal conversion coefficient a a large value of a, which favors the emission of X rays by the Mdssbauer isotope, makes X-ray detection appropriate, while a small value of a favors y-ray detection. 

It is through the changes in the electronic structure of the chemisorbed species or the surface that MGssbauer spectroscopy can be used in the study of surface interactions between gases and surface sites. Because a Mossbauer spectrum represents a sum of the contributions from the various interactions present, in contrast to an average value, information may also be deduced about the nonuniformity of the surface for the studied chemisorption or catalytic process. In such studies, the Mossbauer isotope may be part of the catalytic surface and/or present in the chemisorbed species, as illustrated in the following examples. 

The most comprehensive information obtained from a Mossbauer spectrum is contained in Bint that depends on the magnetic hyperfine tensor A and, through (S), on the ZFS, the electronic g tensor (and exchange couplings when we consider polynuclear systems). For samples containing randomly oriented molecules, such as poly crystalline powders or molecules in frozen solution, the Mossbauer spectrum depends on the orientation of the molecule relative to the direction of the applied field,4 6 which is fixed in the laboratory and is generally either parallel or perpendicular to the direction of Mossbauer radiation. As a consequence, the spectrum is a powder average from which we have to extract the various tensor quantities of... 

In Mossbauer spectroscopy, we encounter two types of expectation values for the electronic spin4 6 that we illustrate briefly for an iron site with S = 1/2 and g 2, taking the applied field along z. If the spin relaxation rate (spin flips between the Ms= + 1/2 and Ms= —1/2 sublevels) is slow compared to the nuclear precession frequency (which is typically 10—30 MHz Larmor precession around Bint or quadrupole precession), the nucleus senses the Fe atom in either the Ms= + 1/2 or Ms =1/2 state during the absorption process. In this case, we have (Sz) = + 1/2 for spin up and (Sz) = —1/2 for spin down. Each electronic level produces a Mossbauer spectrum, and these two spectra are weighted by the probability (given by the... 

Figure 5.4 provides a schematic diagram of a Mossbauer experiment in transmission mode with a moving single-line source and the absorbing sample in fixed position. A Mossbauer spectrum is a plot of the y-ray intensity transmitted by the sample, against the velocity v of the source. The latter is related to the... 

Equation (5-6) indicates that the intensity of a Mossbauer spectrum is only proportional to the concentration of Mossbauer atoms if the term (1 — trnat/4ra) x 1. This is so when absorbers are thin, and when the lines are broader than the natural linewidth. For heavier samples, saturation effects come into play. In case of a sextet, the factor fo in Eq. (5-7) forms the reason that the outer peaks are more affected than the inner peaks, with the result that the line intensity ratios become lower than the expected value of 3 1. 

Figure 4.55 shows a Mossbauer spectrum obtained with a spectrometer similar to that shown in Figure 4.54, that is, in transmission geometry. 

A Mossbauer spectrum contains different absorption peaks. The relative intensity, position, and shape of the absorption peaks composing the spectrum are related to the hyperfine interactions affecting the sample nuclei. The 57Co nuclei contained in the source are included in a solid matrix, such as a face-centered cubic (FCC) rhodium, which only affects the position of the emission line but does not split it [140],... 

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