First-order quadrupole splittings

Zeeman and first order quadrupole splitting for the nucleus (nuclear spin I = /2). A = Cq(3cos — 1)/8/ /(27 — 1).[ 1 The angle 0 defines the orientation of the principle axis of the (crystalline) sample with respect to the field direction. 

Fig. 7.4. Cl NMR spectrum (derivative of absorption signal) of poly-y-benzyl-L-glutamate solutions of CH2CI2 at 25°C showing a first-order quadrupole splitting. The peptide mole fraction was 0.140. (From Ref. [125])...

First-order static quadrupole effects give for the chlorine and bromine nuclei rise to spectra analogous to that shown in Fig. 7.4. First-order quadrupole splittings have been determined for Cl in the hexagonal mesophase of the dodecyltrimethylammonium chloride-water system [1Z6 405] and for Br in the hexagonal mesophase of the hexadecyltrimethyl-ammonium bromide-water system [Z21], (The hexagonal mesophase is built... 

The Pr resonance in PrV04 at 4.2 K, e.g., shows a nice five-line pattern due to first-order quadrupole splitting by the 7=5/2 Pr nucleus, if the magnetic field is applied parallel to the [110] plane of the crystal. ... 

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. 

At the present time it is unclear whether the spin echo decay spectroscopy approach successfully demonstrated for Na is generally transferable to other alkali ion nuclei such as Li and Cs. The latter two isotopes have moderately small electric quadrupole moments causing first order quadrupolar splittings that are comparable to the radio frequency excitation window. As a result, the 7i-pulse length is ill-defined in many situations and the contribution of dipolar coupling of the observed spins to nuclei in the outer Zeeman levels is difficult to quantify. Nevertheless, some promising initial results on cesium borate... 

The Splitting Av again reflects first-order quadrupole interaction, but also the degree of order in the mesophase, quantified by the ordering factor S . The two quantities are connected by Equation (3.7). 

Fig. 7.2. Powder patterns for I = 3/2 showing (a) NMR spectrum in the presence of first-order quadrupole effects and (b) the effect on the central component in the spectrum of second-order effects. The spectra are shown relative to the central point, with Ap and denoting first- and second-order quadrupole splittings,...

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). 

A first-order quadrupole interaction pattern is observed in the partly ordered liquid crystal systems [NbCp(CO)4]/nematic phase 4 (nine-line pattern). Polycrystalline [NbCp(CO)4] exhibits a comparable spectrum at 1.53 T but a second-order pattern (split central component) arises at 0.27 T. ... 

Fig. 4.10. The left side of the scheme represents the starting situation of pure Zeeman splitting, as described by (4.48) and shown before in Fig. 4.9. In this example, the field B = (0,0,B), which defines the quantization axis, is chosen as the z-direction. The additional quadrupole interaction, as shown on the right side of Fig. 4.10, leads to a pair-wise shift of the Zeeman states with mj = 3/2 and mi = 1/2 up- and down-wards in opposite sense. In first order, all lines are shifted by the same energy as expected from the m/-dependence of the electric...

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. 

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...

Figure 5.1 The effect of quadrupole interactions on an / = 3/2 nucleus in a magnetic field. The Zeeman interaction splits the levels by an equal amount, cot, (the Larmor frequency in frequency units). The central +1 /2 to -1 /2 transition is unaffected by first order coupling co j however, second order coupling, co , affects all transitions.

Equation (16) is very important because it imcovers two central ideas. First, the second-order frequency splitting depends inversely on the Larmor frequency, thus the importance of this term diminishes with increasing external magnetic field strength. Second, the k=0 term has no orientation dependence (Do 0 = 1) or, in other words, it is an isotropic term. This means that the isotropic shift observed in the NMR spectriun of a quadrupolar nucleus has, in addition to the usual isotropic chemical shift, a contribution from the quadrupole cou-phng, which is given by... 

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