Quadrupole shift

The value of is given by the component of the EFG tensor along the main quantization axis. Therefore, in this example where the EFG is axial (77 = 0) with the main component the quadrupole shift is eQVzJ - This is just half the quadrupole splitting that would be observed in an unperturbed quadrupole spectrum without a magnetic field at the nucleus. 

Quadrupole Shifts in High-Field Magnetic Spectra... 

Fig. 4.11 Angular dependence (Scos d - 1 + 77sin 0cos2(/)) of the first-order quadrupole shift, Eq in high-field Mossbauer spectra. Left side > 0 and r/ = 0. Right side r] = 1 viewed in...

Fig. 4.12 Surface plots of the EFG tensor as determined from the angular dependence of the first-order quadrupole shift, Eq of high-field magnetic Mossbauer spectra. The plots visualize the value of the function (3cos 0 - 1 + rysin d cos20) for > 0 and ry = 0 (a), r] = 0.3 (b), and 77 = 1 (c)...

Distinct quadrupole shifts do occur as well in magnetically split spectra of single-crystals, poly crystalline powder or frozen solution samples. In all three cases, the line shifts obey the simple first-order expression at high-field condition. 

In contrast, soft magnetic solids and paramagnetic systems with weak anisotropy may be completely polarized by an applied field, that is, the effective field at the Mossbauer nucleus is along the direction of the applied field, whereas the EFG is powder-distributed as in the case of crystallites or molecules. In this case, first-order quadrupole shifts cannot be observed in the magnetic Mossbauer spectra because they are symmetrically smeared out around the unperturbed positions of hyperfine fines, as given by the powder average of EQ mj, d, in (4.51). The result is a symmetric broadening of all hyperfine fines (however, distinct asymmetries arise if the first-order condition is violated). 

The value is derived from a zero-field spectrum recorded at 150 K. A q could not be determined at 4.2 K because the compound is in the limit of slow paramagnetic relaxation and the strong unquenched orbital moment forces the internal field into the direction of an easy axis of magnetization. As a consequence, the quadrupole shift observed in the magnetically split spectra results only from the component of the EFG along the internal field and the orientation of the EFG is not readily known dbabh is a bulky N-coordinating amide... 

In the case of quadrupole nuclei with spin Z> 1/2, the frequency at the center of gravity, v g, of the CT is shifted by the second-order quadrupole shift ... 

If the nucleus feels both a magnetic field and an electric field gradient, and the electric quadrupole interaction is small, then the excited levels shift as indicated in Fig. 10.20e. The result is that only the inner four lines of the sextet are equidistant. This type of spectrum is measured from bulk Fe2C>3, with a magnetic hyperfine field of 51.5 T and a small quadrupole shift on the absorption peaks of 0.10 mm/s. 

In the presence of a small simultaneous electric quadrupolar interaction, the split levels are shifted by an amount s, which is called the quadrupole shift parameter and is given by the following ... 

Simulation of the complete DOR spectrum (centreband plus the spinning sidebands) will yield the NMR interaction parameters (Sun et al. 1992, Cochon and Amoureux 1993, Amoureux and Cochon 1993). However, it is most usual to perform the experiment to give improved resolution and simply quote the measured peak position which appears at the sum of the isotropic chemical and second-order quadrupole shifts. DOR experiments at more than one applied magnetic field will allow these different contributions to be separated and hence provide an estimate of the quadrupole interaction via the combined quadrupole effect parameter Pq... 

Table Bl.12.3 Spin-dependent factory(7) for the isotropic second-order quadrupole shift.

In high magnetic fields, M, Wq and the quadrupole shift can be calculated using perturbation theory. Taking = 0 for simplicity, the first-order shift is... 

In the supercages of HY zeolite, the difference in chemical shift (8cs( Xe) - 8cs( Xe)) of the two NMR-observable isotopes Xe, which is sensitive to the electric-field gradient (EFG), and Xe, which is not sensitive to EFG, is -5 ppm at room temperature. The latter value is due to the second-order quadrupole shift of Xe and provides us with the EFG generated by the framework of this microporous material 16.3xl0 V.m . ... 

It follows from the quadrupole splitting, which increases when the temperature is raised, that the quadrupole shift should also increase with rising temperature T. The weak... 

The quadrupole shift is eliminated by averaging the frequency measurements on three orthogonal orientations, resulting in a fractional uncertainty of 0.5 x 10 I Estimation of all of the systematic effects (electric fields, gravity, second-Doppler effect, etc.) have yielded a correction of 1.727 Hz, with a total fractional uncertainty of 7.2 X 10" . The absolute frequency of the transition was measured with a frequency comb vs cesium to be 1064,721,609,899,144.94 Hz, with a statistically limited total fractional uncertainty of 9.1 x 10 , which is the most accurate absolute measurement of an optical frequency to date. 

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