Quadrupole hyperfine spectrum

Fig. 11. Quadrupole hyperfine spectrum of Np in Np metal. The bar diagram shows the decomposition into two quadrupole patterns meaning that Np occupies two lattice sites with different local symmetries. In both cases the electric field gradient is not rotationally symmetric (rj 0). The fit (solid line) includes the Goldanskii-Karyagin effect (see text). The dashed line shows the spectrum expected in case of full isotropy. [Taken from Dunlap et al. (1970).]...

Figure 8.34. Nuclear quadrupole hyperfine structure of the J = 1 level of 7Li79Br (v = 0) in zero field. The largest splitting is due to the quadrupole interaction involving the 79 Br nucleus, and the smaller splitting arises from the sLi nucleus. The transitions indicated are resonsible for the resonances shown in the experimental spectrum presented in figure 8.35.

Other physical properties also show that the iron cores of native ferritins and bacterioferritins are different. Mossbauer spectra of ferritins measured as a function of temperature (Fig. 1) show quadrupole split doublets, with an isomer shift typical of Fe +, gradually being replaced as the temperature is lowered (between about 50 and 15 K) by a magnetic hyperfine spectrum (30, 31). The transition temperature, Tb, is lower than the ordering temperature, Tord (240 K) observed for bulk ferrihydrite (32), because of fluctuations in the direction of mag-... 

The 14N quadrupole hyperfine structure was analyzed from the MW spectrum and the nitrogen nuclear quadrupole coupling constants (NQCC) for aniline-Hy are determined as follows xaa = 2.34, Xbb = 1-86 and Xcc = —4.20 MHz38. 

The collapse of a six-line hyperfine spectrum with decreasing relaxation time is illustrated by the calculated spectra in Fig. 3.8 [44] for a " Fe nucleus in a fluctuating magnetic field and a fixed electric field gradient for different values of the electronic relaxation time. If the fluctuation rate is very slow compared to the precession frequency of the nucleus in the field H, the full six-line hyperfine pattern is observed. If the fluctuation rate is extremely rapid the nucleus will see only the time-averaged field which is zero and a symmetric quadrupolar pattern will be seen. At intermediate frequencies the spectra reflect the fact that the 2> -> transitions which make up the low-velocity component of the quadrupole doublet relax at higher frequencies than do the I I i> and -]-> -> transitions which... 

Only brief details are available for anhydrous iron(III) sulphate it gives a paramagnetic spectrum at room temperature [111] with a chemical isomer shift of 0-39 mm s and a quadrupole splitting of 0-60 mm s" [9]. A sharp magnetic hyperfine spectrum is seen at 1-8 K with a field of 550 kG [98]. 

The first reported Mossbauer spectrum of a-Fe203 was by Kistner and Sunyar [1], who thereby recorded the first chemical isomer shift and electric quadrupole hyperfine interactions to be observed by this technique. With a single-line source the room-temperature spectrum comprises six lines from a hyperfine field of 515 kG the chemical isomer shift (Table 10.1) is... 

The oxide CeFeOa has been prepared and shown to be analogous to the other rare-earth orthoferrites [124]. The Curie temperature is 719 K, and the quadrupole perturbation on the hyperfine spectrum (e) changes sign at 230 K as the result of electronic spin reorientation with respect to the crystal axes and hence the electric field gradient tensor. The spins are perpendicular to the c axis above 230 K, but parallel to it below that temperature. 

The temperature dependence of the magnetic field and quadrupole interaction in erbium metal have been followed between 4-2 and 40 K and analysed [142]. An estimate of —1-9(4) bam was suggested for the excited-state quadra-pole moment. In a more detailed study, the line intensities of the hyperfine spectrum in a single crystal of Er metal have been correlated with the magnetic structure previously determined by neutron diffraction methods [143]. 

In paramagnetic substances, it is necessary to compare tr with tl If tr < < tl so that the orientation of the electronic spins fluctuates very rapidly, the internal magnetic field seen by the nucleus will average to zero and there will be no magnetic interactions. This appears to be the case with the ferrous hemoglobins and one observes unbroadened, nearly symmetric, quadrupole doublets. If on the other hand tr > > TL, magnetic hyperfine interactions can occur and one may expect line broadening and perhaps even a fully resolved hyperfine spectrum. 

When both magnetic and quadrupole hyperfine interactions are present simultaneously the general interpretation of the spectrum can be quite complex. Since both interactions are direction-dependent it is necessary to know the angle between the principal axis of the e.f.g. tensor and the magnetic axis. Solutions are not too complicated if one interaction is weak and can be considered to be only a perturbation on the principal interaction. In many cases it is not possible to use such a simplified treatment and a complete analysis is required. 

The principal isotope of copper is Cu which has a nuclear spin / of 3/2 both chlorine and bromine have naturally occurring isotopes ( C1, Cl, Br, Br) with spins of 3/2, so that extensive quadrupole hyperfine splitting is to be expected. The spectrum ofCuCl shown in figure 10.37 arises from the J = 1 0 rotational transition the J = 0 level does not have a quadrupole splitting but if the Cl and Cu nuclear... 

In practical applications it may happen that the magnetic and quadrupole hyperfine interactions occur simultaneously and the spectra are superimposed on one another. Such a case for iron is presented in Fig. 11 where the effect of first-order quadrupole perturbation on a magnetic hyperfine spectrum is shown. It is evident that the detailed interpretation of this Mossbauer spectrum is quite complex. 

The two absorption peaks, appearing in the measured Mossbauer spectrum as a consequence of electric quadrupole hyperfine interaction, are called a doublet. 

The fine structure of atomic line spectra and the hyperfine splittings of electronic Zeeman spectra are non-symmetric for those atomic nuclei whose spin equals or exceeds unity, / > 1. The terms of the spin Hamiltonian so far mentioned, that is, the nuclear Zeeman, contact interaction, and the electron-nuclear dipolar interaction, each symmetrically displace the energy, and the observed deviation from symmetry therefore suggests that another form of interaction between the atomic nucleus and electrons is extant. Like the electronic orbitals, nuclei assume states that are defined by the total angular momentum of the nucleons, and the nuclear orbitals may deviate from spherical symmetry. Such non-symmetric nuclei possess a quadrupole moment that is influenced by the motion of the surrounding electronic charge distribution and is manifest in the hyperfine spectrum (Kopfer-mann, 1958). 

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...

Let us now consider a pure quadrupole spectrum which leads to the hyperfine splitting as shown schematically in Fig. 4.18. For the intensity ratio /2//1, we obtain... 

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. 

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