Quadrupole splitting asymmetry

Isomer shift versus a-iron at RT Quadrupole splitting Asymmetry parameter... 

Figure 4.54 The effect of an electric field gradient (EFG) creating asymmetry in the electron distribution round a gold nucleus, leading to a quadrupole splitting in the Mossbauer spectrum. (Reproduced with permission from Gold Bull., 1982,15, 53, published by World Gold Council.)...

Most valuable chemical information can be extracted from Mbssbauer parameters such as the isomer shift (5), the quadrupole splitting (AEq), the magnetic splitting (AEm), and the asymmetry parameter (n). 

Since the EFG component E and the asymmetry parameter rj = (Fee Vyy)/V,. in the PAS are invariants of the EFG, the two similar arrangements of the charge q shown in Fig. 4.7a, b must produce the same quadrupole splitting (because energies do not depend on the choice of the coordinate system). 

With h 6) - 1/sin 0)5(0 — Oq), one obtains the same result as given by (4.58), which implies that the anisotropy of the/factor cannot be derived from the intensity ratio of the two hyperfine components in the case of a single crystal. It can, however, be evaluated from the absolute/value of each hyperfine component. However, for a poly-crystalline absorber (0(0) = 1), (4.66) leads to an asymmetry in the quadrupole split Mossbauer spectrum. The ratio of l-Jh, as a function of the difference of the mean square amplitudes of the atomic vibration parallel and perpendicular to the y-ray propagation, is given in Fig. 4.19. 

Both Fe(ll)(TPP) and Fe(II)(OEP) have positive electric quadrupole splitting without significant temperature dependence which, however, cannot be satisfactorily explained within the crystal field model [117]. Spin-restricted and spin-unrestricted Xoi multiple scattering calculations revealed large asymmetry in the population of the valence orbitals and appreciable 4p contributions to the EFG [153] which then was further specified by ab initio and DFT calculations [154,155]. 

To calculate the nuclear quadrupole moment from the measured quadrupole splitting, it is necessary to know the electric field gradient, q, at the Te nucleus as well as the asymmetry parameter, rj. These can be calculated in the Townes and Dailey approximation (4) by knowing the chemical bonding in Te. 

Dr. Clifford Yes, the quadrupole splitting for iron in rare earth oxides was perhaps 1% times the value reported in any of the iron oxides themselves. This is probably caused by the fact that in the iron oxides the asymmetry in the crystal is in the second coordination sphere. In other words, it is caused by the presence or absence of the nearest iron atoms in the lattice, whereas in the rare earth oxides, it s an oxygen deficiency in the first coordination sphere of the iron, assuming that the iron took a normal lattice position in the rare earth oxide. 

Due to the electric quadrupole interaction, the Mi = 1/2 and Mi = 3/2 components of the 7 = 3/2 state of 57Fe split up, giving rise to the quadrupole splitting. Derived from the interaction of the nuclear quadrupole moment with the electric field gradient at the iron nuclei, AEq provides information about the asymmetry of the electron density around the iron nucleus. The electric field gradient at the iron nucleus can be calculated to obtain AEq (97). Since both 6 and AEq are related to the electron density at the nucleus, basis sets with an enlarged flexibility at the core region... 

Fig. 28. Asymmetry of quadrupole split peaks due to the Gol danskii-Karyagin effect. 7t = +j - transition a — i - i transition c = (27t/7)2( - <.x2 . z and x are parallel and perpendicular, respectively to the surface normal. Figure according to Suzdalev and Makarov (208).

Two parameters describe the quadrupole interaction there are the quadrupole splitting and the asymmetry parameter, rj, which is defined as,... 

Mossbauer spectroscopy also provides structural information.97-100 In particular it is possible to deduce from peak asymmetry the separate appearance of surface atoms as size is decreased they cause an increase in intensity of quadrupole splitting, and two quadropole components indicate two kinds of surface atoms.97 Au1 and Au111 species are also sometimes recognised,99 and sometimes not.98... 

Mossbauer spectroscopy has proved to be a very valuable tool in tin chemistry. The isomer shift (IS) is a measure of the 5s electron density at the tin nucleus while the quadrupole splitting (QS) is a measure of the electric field gradient (due to the asymmetry of the electron cloud) at the tin nucleus. On going from the plus two to the plus four oxidation state tin loses 5s electron density. Since the tin nucleus expands on absorption of the 23.9 keV photon during the Mossbauer experiment, the greater the s electron density at the nucleus the more positive the isomer shift will be (56, 57). Therefore, tin(II) compounds have higher isomer shift values than do tin(IV) compounds. The isomer shift of /3 tin (2.56 mm/sec relative to BaSnOa) is commonly used as the dividing point between divalent and tetravalent tin (58-60). 

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