Mossbauer spectroscopy electric quadrupole interaction

Equation (4.15) would be extremely onerous to evaluate by explicit treatment of the nucleons as a many-particle system. However, in Mossbauer spectroscopy, we are dealing with eigenstates of the nucleus that are characterized by the total angular momentum with quantum number 7. Fortunately, the electric quadrupole interaction can be readily expressed in terms of this momentum 7, which is called the nuclear spin other properties of the nucleus need not to be considered. This is possible because the transformational properties of the quadrupole moment, which is an irreducible 2nd rank tensor, make it possible to use Clebsch-Gordon coefficients and the Wigner-Eckart theorem to replace the awkward operators 3x,xy—(5,yr (in spatial coordinates) by angular momentum operators of the total... 

Mossbauer spectroscopy senses the hyperfine interactions, which are present at the nucleus of the Mossbauer isotope. The electrical monopole interaction causes the isomer shift and the electric quadrupole interaction leads to the quadrupole splitting, which in the case of Fe causes a two-line Mossbauer pattern. The magnetic dipole interaction leads to a magnetically split six-line pattern (Figure 4). In the following text, these interactions and their deduction from Mossbauer spectra will be discussed. 

The recently synthesized Au(V) complex fluorides of the form A AuFjwith A = Xe2F, XeRJ, and Cs have been studied by Mossbauer spectroscopy with the 77.3 keV gamma resonance of Au. The values obtained for isomer shift and electric quadrupole interaction are in harmony with the assigned oxidation state Au(V), as well as with the octahedral shape of the AuFj anion. 

The existence of an electric quadrupole interaction is one of the most useful features of Mossbauer spectroscopy. The theory is closely related to that used in nuclear quadrupole resonance spectroscopy [14, 15). Any nucleus with a spin quantum number of greater than / = 4 has a non-spherical charge distribution, which if expanded as a series of multipoles contains a quadrupole term. The magnitude of the charge deformation is described as the nuclear quadrupole moment Q, given by... 

The existence of an electric quadrupole interaction is one of the most useful features of Mossbauer spectroscopy. The energy levels in the presence of an electric field gradient (e.f.g.), q, are ... 

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... 

Spieting H. (1984) The Electric Field Gradient and the Quadrupole Interaction, In Long GJ (ed), Mossbauer spectroscopy applied to inorganic chemistry, Vol. 1. Plenum Press, New York, p 77. 

Orbital degrees of freedom are one of the important parameters to discuss the ordered ground states in materials. Orbital occupancy reflects electric field gradient (EFG) at nuclei. Then, Mossbauer spectroscopy can detect orbital occupancy of electrons, especially d or f electron cases. Electronic orbits in f electrons are usually called electronic quadrupole moments. Electronic quadrupole moments directly interact with nuclear quadrupole moments, which are observed as nuclear quadrupole interactions. Since the nuclear quadrupole moment in the Mossbauer transition is relatively large, 3.1 barn, the nuclear quadrupole interaction is relatively easy to detect as asymmetry of spectra even when hyperfine fields are observed. 

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