Factors determining the Mossbauer spectrum

A Mossbauer spectrum is characterised by the number, shape, position and relative intensity of the various absorption lines. These features result from the nature of the various hyperfine interactions and their time dependence, as well as on any motion of the Mossbauer nuclei. 

The total absorption intensity of the spectrum is a function of the concentration ofMossbauernuclei in the absorber and the cross-sections of the nuclear processes involved. This absorption intensity, together with the signal-to-noise ratio of the detection system and the total number of counts, determine the quality of the Mossbauer spectrum and the accuracy with which information can be obtained from it. It should be noted that Mossbauer spectroscopy is not generally an appropriate technique for measuring the total concentration of a certain nuclide within a system because it is usually relatively insensitive to small concentrations and because the absorption intensity depends on a number of other factors which may be difficult to quantify. However, relative concentrations of different chemical forms of the Mossbauer nuclide can frequently be obtained, such as the relative concentration of the element in different oxidation states. 

The following sections will consider the various hyperfine interactions and other effects which determine the nature of the Mossbauer spectrum, and will also consider briefly how these factors relate to the types of information that can be obtained by Mossbauer spectroscopy. 

The isomer shift of the absorption lines in the Mossbauer spectrum, also sometimes known as the chemical shift, the chemical isomer shift or the centre shift, is a result of the electric monopole (Coulomb) interaction between the nuclear charge distribution over the finite nuclear volume and the electronic charge density over this volume. This shift arises because of the difference in the nuclear volume of the ground and excited states, and the difference between the electron densities at the Mossbauer nuclei in different materials. In a system where this electric monopole interaction is the only hyperfine interaction affecting the nuclear energy levels, the nuclear ground and excited states are unsplit, but their separation is different in the source and absorber by an amount given by the isomer shift 5. 

The eflecis on (he nuclear energy levels of Fe of (n) the isomer shift and (b) the quadrupole splitting. The Mossbauer absorption transitions and the resulting spectra, which give the isomer shift S and the quadrupole splitting A, are also shown. 

---

For example, the Mossbauer spectrum of a BaFcsAlgOig catalyst for combustion of methane is given in Fig. 4 ((S). This spectrum has been fitted with four sextets that correspond to the four octahedral crystallographic sites of the structure that may be occupied by the ferric ions, thus leading to a different atomic environment for each of them. From the relative intensities of the four sextets used for the fit and considering equal / factors for the corresponding species, it is possible to determine the respective occupation of these sites by iron. Alternatively, only a complete Rietveld analysis of the powder X-ray diffraction pattern of the catalyst would have enabled such a determination. 

Since the Mossbauer effect is intimately related to any motion of the emitting or absorbing nucleus on either a microscopic or macroscopic scale, Mossbauer spectroscopy provides a potential means by which information on nuclear dynamics, and hence on the dynamics of a system in which the Mossbauer nucleus acts as a probe, can be obtained. Any motion of the Mossbauer nucleus can influence the Mossbauer spectrum in two ways. Firstly, because this motion may be related to the vibrational properties of the system it can influence the recoil-free fraction and hence the absorption intensity of the spectrum itself. Since the absolute absorption intensity is dependent on a large number of other factors, which may be diflicult to determine accurately, any change in recoil-free fraction is most usefully followed as a function of temperature in order to obtain information on the vibrational properties of the system. The second way in which the effects of any motion of the Mossbauer nucleus in the source or absorber are manifested is in the Mossbauer spectroscopic linewidths, as this motion can be thought of as an additional Doppler motion which may partially smear out the resonant absorption. Since the linewidths are also... 

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... 

This relation is only valid for a crystal with isotropic /-factor. The effect of crystal anisotropy will be treated in Sect. 4.6.2. The function h(6) describes the probability of finding an angle 6 between the direction of the z-axis and the y-ray propagation. In a powder sample, there is a random distribution of the principal axes system of the EFG, and with h 6) = 1, we expect the intensity ratio to be I2J li = I, that is, an asymmetric Mossbauer spectrum. In this case, it is not possible to determine the sign of the quadmpole coupling constant eQV. For a single crystal, where h ) = — 6o) 5 delta-function), the intensity ratio takes the form... 

Here, L(v) is a lineshape function that integrates to unity, v is the frequency,/ is the Lamb-Mossbauer factor, and the desired side bands have an area fraction / that is proportional to which hence determines the relative peak heights in a NIS spectrum. More details are provided in Appendix 2 (Part III, 3 of CD-ROM). An equivalent and often more suggestive display of the NIS spectrum is the PVDOS approach, which describes the NIS signal in terms of the partial vibrational density of states ... 

The evaluation of a Mossbauer spectrum implies the determination of the physical parameters, the isomer shift, Debye-Waller factor, and electric and magnetic hyperfine fields. When flue-... 

The fundamentals of SSS are based on the theory of impurity centers in a crystal. The optical spectrum of an organic molecule embedded in a matrix is defined by electron-vibrational interaction with intramolecular vibrations (vibronic coupling) and interaction with vibrations of the solvent (electron-phonon coupling). Each vibronic band consists of a narrow zero-phonon line (ZPL) and a relatively broad phonon wing (PW). ZPL corresponds to a molecular transition with no change in the number of phonons in the matrix (an optical analogy of the resonance -line in the Mossbauer effect). PW is determined by a transition which is accompanied by creation or annihilation of matrix phonons. The relative distribution of the integrated intensity of a band between ZPL and PW is characterized by the Debye-Waller factor ... 

---