Mossbauer 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... 

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...

Pure nuclear magnetic hyperfine interaction without electric quadrupole interaction is rarely encountered in chemical applications of the Mossbauer effect. Metallic iron is an exception. Quite frequently, a nuclear state is perturbed simultaneously by... 

Fig. 4.13 Combined magnetic hyperfine interaction for Fe with strong electric quadrupole interaction. Top left, electric quadrupole splitting of the ground (g) and excited state (e). Top right first-order perturbation by magnetic dipole interaction arising from a weak field along the main component > 0 of the EFG fq = 0). Bottom the resultant Mossbauer spectrum is shown for a single-crystal type measurement with B fixed perpendicular to the y-rays and B oriented along...

The low-temperature Mossbauer spectra of the spinel type oxides, NiCr204 [14,18] (Fig. 7.6b) and NiFe204 [3, 18], have been found to exhibit combined magnetic dipole and electric quadrupole interaction (Fig. 7.7). For the evaluation of these spectra, the authors have assumed a small quadrupolar perturbation and a large magnetic interaction, as depicted in Fig. 7.3 and represented by the Hamiltonian [3]... 

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. 

Figure 1. Hyperfine interactions for Fe nuclei, showing the nuclear energy level diagram for (a) an unperturbed nucleus (b) electric monopole interaction (isomer shift) (c) electric quadrupole interaction (quadrupole splitting) and (d) magnetic dipole interaction (hyperfine magnetic splitting). Each interaction is shown individually, accompanied by the resulting Mossbauer spectrum.

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 ... 

The determination of peak intensities becomes a more complicated issue in the case of combined hyperfine magnetic dipole and electric quadrupole interactions (for the case of Fe see, e.g., Kundig (1967) and Housley et al. (1969)), or when the Mossbauer transition has a mixed (most often Ml + E2) multipole character (for the case of Ru see, e.g., Foyt et al. (1975)). Further factors influencing the relative peak intensities will be discussed in O Sect. 25.2.7.5. 

Fig. 4.5. Quadrupole Splitting in with I = 3/2 in the excited state and / = 1/2 in the ground state. The I = 3/2 level is split into two sub-levels by electric quadrupole interaction while the ground state with 7=1/2 does not split because there is no spectroscopic quadrupole moment in a nucleus with I = 1/2. The levels of 7 = 3/2 and 7 = 1/2 are shifted by electric monopole interaction (giving rise to isomer shift). Inset shows the schematic of resultant Mossbauer spectrum...

As an example, the effect of the electric quadrupole interaction in a Mossbauer nucleus with 7=3/2 in the excited state and I = 1/2 in the ground state, as is the case in Fe and Sn. is given in Figure 10. The quadrupole interaction gives rise to a doublet with the splitting... 

Fig. 4.4. Mossbauer spectra of RbFeF4 taken over a range of temperature up to 135 K. The changes in the spectra in the region between 120 and 135 K occur as a result of the changing ratio of the strengths of the electric quadrupole interaction, which is essentially temperature independent, and the magnetic hyperfine field, which decreases quickly as the temperature approaches the Neel temperature of 133 1 K. The broadened lines observed in spectra taken just below the Neel temperature are due to changes in hyperfine field within the range of temperature stability of the apparatus. (Rush, Simopoulos, Thomas Wanklyn, 1976.)...

Fig. 4.5. Mossbauer spectra of a single crystal of RbFeCI, taken with the gamma-ray beam directed perpendicular to the principal axis of the electric field gradient. The spectrum at 4.2 K shows no magnetic interaction. The spectrum at 1.3 K is produced by the situation illustrated in Figure 4.3(d) where a strong electric quadrupole interaction is combined with a weaker magnetic interaction whose effective magnetic field is perpendicular to the principal axis of the electric field gradient. (Baines et al 1983.)...

Fig. 4.25. Schematic Mossbauer spectra to demonstrate how asymmetric line-widths can arise in a magnetic sextet spectrum. The independent effects of the electric quadrupole interaction and the magnetic dipolar contribution to the hyperfine field are shown separately in (u) and (h) respectively and these effects are summed in (c). An equally probable site has a combined electric quadrupole interaction and magnetic dipolar contribution to the hyperfine field of opposite sign and this spectrum is shown in (d). Sites with both signs of interaction are present in the material and therefore (c) and (d) are added to give the spectrum shown in (e). Finally the distribution in magnitude as well as sign of the interactions is included in the spectrum shown in (/) which models the actual conditions in a real solid. It is seen that the resulting spectrum has linewidths Fj where F, >F4, r2

In the case of an additional electric quadrupole interaction (when > 0), as is shown in (d), the substates of the excited state with m/ = 3/2 and 1/2 shown in (c) are pairwise shifted up and downwards in energy in opposite directions by the so-called first-order quadrupole shift This leads to an asymmetry of the resulting splitting pattern in the Mossbauer spectrum, as shown in the lower part of (d). 

Electric quadrupole interaction between the nuclear quadrupole moment and an inhomogeneous electric field at the nucleus. The observable Mossbauer parameter is the quadrupole splitting AEq . The information derived from the quadrupole splitting refers to oxidation state, spin state and site symmetry. 

Figure 4 (A) The splitting of the excited level of a Fe nucleus due to the electric quadrupole interaction A. (B) The corresponding Mossbauer spectrum.

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