Quadrupole perturbation

The perturbation of the four substates of the excited 7 = 3/2 manifold by induces a typical asymmetry of the resulting magnetically split Mossbauer spectrum as pictured at the bottom of Fig. 4.10 for positive the inner four lines, 2-5, are shifted to lower velocities, whereas the outer two lines, 1 and 6, are shifted to higher velocities by equal amounts. In first order, the line intensities are not affected. For negative the line asymmetry is just inverted, as the quadmpole shift of the nuclear 1/2 and 3/2 states is opposite. Thus, the sign and the size of the EFG component along the field can be easily derived from a magnetic Mossbauer spectrum with first-order quadrupole perturbation. 

Ru has a nuclear ground state with spin /g = 5/2 and a first excited state with 4 = 3/2" ". Electric quadrupole perturbation of Ru was first reported by Kistner [110] for Ru02 and ruthenocene this author has also evaluated the ratio of the nuclear quadrupole moments to be QJQ > 3. The sign and magnitude of the individual quadrupole moments are given in Table 7.1 (end of the book). 

Fig. 4 Relaxation pathways between quadrupole-perturbed Zeeman levels of / = 3/2 nuclear spin. Reprinted from [50]...

For a nonzero electric field gradient tensor V at the Ti sites, we expect for each Ti isotope 27 resolved quadrupole perturbed NMR fines. The frequency... 

Fig. 2 Ti quadrupole perturbed NMR spectrum of BaTiOs in the cubic PE phase. The sharp 1/2 -1/2 central lines are sitting on a broad satellite backgroimd...

The quadrupole perturbed NMR spectriun of Rb (I = 312) consists of the central hne and two satelUte Unes. In D-RADP-x the nuclear quadrupole couphng constant decreases linearly with x from 9.6 MHz (x = 0) to 6.6 MHz (x = 0.95) [10], whereas the Larmor frequency amounts to 98.163 MHz in a Bo field of 7 T. Due to the substitutional disorder, and the corresponding loss of the translational invariance, the satelHte transitions are inhomogeneously broadened that much, that only the central transition can be directly observed. The position of the corresponding resonance line can be calculated using standard NMR-NQR theory [16], where the second order shift is given by ... 

The last two terms are small second-order dipole-dipole and dipole-quadrupole perturbation corrections. The numerical values of all these terms for the example of the lslOfc state are as listed in Table 5. 

Key Words Dipolar glasses, Ferroelectric relaxors, Conducting polymers, NMR line shape, Disorder, Local polarization related to the line shape, Symmetric/asymmetric quadrupole-perturbed NMR, H-bonded systems, Spin-lattice relaxation, Edwards-Anderson order parameter, Dimensionality of conduction, Proton, Deuteron tunnelling. 

NMR is a powerful technique for providing information about the distribution and dynamics of local RFs, characteristic of such systems. While the quadrupole-perturbed NMR line shape analysis gives details about the distribution of local RFs, spin-lattice relaxation (SLR) studies can give information on the dynamics in the frustrated state of these systems. From the literature, it can be seen that most of the NMR experiments have been carried out in RADP mixed systems and its deuterated analogues. ETFI group published a number of results21-23 on various mixed crystals. 

Blinc et al.4 in a classic paper on the NMR line shapes in PGs have presented the relation between the RF distribution and the quadrupole-perturbed NMR line shape for both first-order and second-order quadrupole effects. Static as well as time fluctuating RFs have been considered. By evaluating the local RF distribution, Blinc et al.4 have evaluated the Edwards-Anderson (qEA) order parameter. 

SLR time results provide novel information on the temperature dependence and distribution of local RFs and their dynamics. A direct evidence for incoherent phonon-assisted deuteron tunnelling in H-bonded systems has been observed from NMR experiments. The use of quadrupole-perturbed ID 2H NMR spectroscopy and in particular 2D 2H NMR exchange spectroscopy has found to be very promising as regards elucidating the details of the hydrogen dynamics. 

J. P. Adloff, Application to Chemistry of Electric Quadrupole Perturbation of y-y Angular Correlations, Radiochim. Acta 25, 57 (1978)... 

Figure 2.8. Energy level diagram of a spin- /2 system showing the Zeeman interaction and the first- and second-order quadrupole perturbation of the energy levels.

Figure 2.9. The quadrupole perturbed powder patterns for an I = nucleus. A. The outer satellite transitions to first-order. B. The second-order quadrupolar broadening of the central transition with...

Figure 2.14. The MAS centreband of a second-order quadrupole perturbed powder pattern as a function of the asymmetry parameter t for an I = >2 nucleus with Xq = 3.2 MHz at t o = 95 MHz.

Blinc et a/.177,178 performed 47Ti(/— 5/2) and 49Ti(/= 7/2) quadrupole-perturbed NMR experiments with very high-quality single crystal of BaTiCV The authors observed that in the paraelectric cubic phase T> Tc, the narrow central 1/2) transition lines are surrounded by a broad... 

Fig. 3.5 The effect of a first-order quadrupole perturbation on a magnetic hyper-fine spectrum for a f transition. Lines 1,2 and 5,6 have equal separations only when there is no quadrupole effect acting, or when cos 0 =- 1 / 3.

Fig. 10.1 Spectra of a-Fc203 at 162 0 K (below Morin temperature) and at 371-3 K (above Morin temperature). Note the reversal in sign of the quadrupole perturbation as shown by the spacings of the outer lines. [Ref. 3, Fig. 1]...

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. 

Another use for a saturating comb is to initialize the populations of quadrupole perturbed Zeeman levels, when only one pair of levels can be irradiated. As already discussed in III.C.3., Avogadro and Rigamonti used a very long ( 1800 pulses ) saturating comb on the central transition of... 

Fig. 11.8. Neutron scattering spectra (a) quasi-elastic and (b) elastic scattering on CSHSO4 samples recorded with IN6 time of flight and IN 10 Doppler-back scattering spectrometers, respectively, at the Institut Laue-Langevin . (c) The intensity of the elastic component (I ) for a fixed window is compared with the conductivity plot as a function of temperature (with permission), (d) Temperature dependence of the deuteron quadrupole perturbed NMR spectra of CSDSO4 at a general orientation near the O - III transition (with permission).

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. 

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