Quadrupole splitting , Mossbauer

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. 

Table 3. Experimental ratios of quadrupole split Mossbauer lines of deoxy mb single crystals under various orientations...

As the interest in doped cobaltate perovskites boosted around the turn of the millennium due to the discovery of the CMR effect, the need for Mossbauer studies of these oxides became evident. The repeated measurements [36] showed that the Co emission Mossbauer spectra of the Lao.8Sro.2Co03 3 (Figs. 19.16 and 19.17) resemble those published by Bhide et al. [35] that is, between 78 and 191 K, they consist of a paramagnetic doublet and a magnetic s tet with broad lines, while above 218 K only an unresolved quadrupole-split Mossbauer spectrum Is observed. The temperature at which... 

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.)...

The various, solid-state stereochemistries just described may often be distinguished fairly readily by " Sn Mossbauer spectroscopy 5-9, 452), particularly from the value of the quadrupole splitting parameter, AEq (see Table II). 

Sn Mossbauer Quadrupole Splittings for Organotin Compounds OF Known Stereochemistry... 

For example, octahedral quadrupole splitting observed for the cis-octahedral analogs 7,8). More recently, temperature-dependent Mossbauer measurements have been used in conjunction with Raman spectroscopy to determine molecular weights 453) and lattice rigidity 460) of various organotin compounds. 

Table 1. The 72-atom model examined by different theoretical methods. The energy differences (AE in kcal/mol) are calculated with respect to the lowest SCF energy. q(Fe) stands for Mulliken population charges on the Fe atoms q(S) and SS(b.i.) are the Mulliken population charges and the bond index for the bridging S atoms, respectively AEq is the calculated Mossbauer quadrupole splitting constant [mm/sec]. The PUHF spin states are those projected from the UHF wavefunction with 5 = 5,. 

PUHF, yield the lowest energies as well as reasonable Mossbauer quadrupole splitting constants, A Jq. 

Figure 2A. Schematic diagram of Mossbauer parameters isomer shift (6), quadrupole splitting (AEq) and magnetic dipole splitting of the nuclear energy states of 57pe leading to various hyperfine splitting in Mossbauer spectra.

The results of the XRD measurement showed that the Fe jAl, jPO catalyst was almost in amorphous state. Only a very broad peak at 29 of ca. 23 degree was observed. The Mossbauer spectroscopic study on this catalyst showed one doublet of iron with the isomeric shift of 0.31 mm s (a-Fe was used as the reference) and the quadrupole splitting of 0.62 mm s. These parameters are very close to those observed for FePO [13, 14], suggesting that the iron cation in the catalyst is tetrahedrally coordinated with oxygen and isolated by four PO tetrahedral units. Such coordination circumstance was suggested to be a key factor for the iron site effective for the oxidation of CH to CHjOH by H -Oj gas mixture [15]. 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

Principally, stmctural information can be obtained from the quadrupol splitting in the Mossbauer spectra of tin (IV)-compounds by the calculation of expectation regions... 

The spin state of the compounds XFe(R2dtc)2 is 3/2 (64). Mossbauer spectra of ClFe(Et2 tc)2 in solution are almost identical with the spectrum of the six-coordinated Fe(Et2magnetic susceptibility and in the isomer shift and quadrupole splitting parameters suggests a geometrical correspondency in solution, which can be attained by the binding of a solvent molecule to the sixth coordination site of the ClFe(Et2[Pg.98]

Fig. 4.6 Quadrupole splitting of the excited state of Fe with I = 3/2 and the resulting Mossbauer spectrum. Quadrupole interaction splits the spin quartet into two degenerate sublevels 7, OT/) with energy separation A q = 2 q. The ground state with I = 1/2 remains unsplit. The nuclear states are additionally shifted by electric monopole interaction giving rise to the isomer shift 8...

In a conventional Fe Mossbauer experiment with a powder sample, one would observe a so-called quadrupole doublet with two resonance lines of equal intensities. The separation of the lines, as given by (4.36), represents the quadrupole splitting The parameter Afg is of immense importance for chemical applications of the Mossbauer effect. It provides information about bond properties and local symmetry of the iron site. Since the quadrupole interaction does not alter the mean energy of the nuclear ground and excited states, the isomer shift S can also be derived from the spectrum it is given by the shift of the center of the quadrupole spectrum from zero velocity. 

The experimentally observed quadrupole splitting AEq for Fe in inorganic compounds, metals, and solids reaches from 0 to more than 6 mm s [30, 32]. The range of AEq for other Mossbauer isotopes may be completely different because of the different nuclear quadrupole moment Q of the respective Mossbauer nucleus, and also because the EFG values may be intrinsically different due to markedly different radial distributions of the atomic orbitals (vide infra). As Q is constant for a given isotope, variations in the quadrupole coupling constants eQV can only arise from... 

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