Quadrupole spectra

Allen reviews the experimental techniques and the information which can be obtained from pure quadrupole spectra of solids (28). The quadrupole coupling constant is determined by the curvature of the potential field near the nucleus (i.e., the second derivative of V with respect to distance). Therefore it is influenced by changes of the electron distribution near the nucleus. The method is, of course, restricted to compounds containing at least one nucleus with a nonzero quadrupole moment, and reveals only the electron distribution near that nucleus. Thus it is not applicable to the nuclei H , G , or O, but it does apply to D, N , CP, and 

Allen lists quadrupole coupling constants for a number of chlorine substituted acetic acids and acetamides (29, 28), and he discusses results for solid HCl. Although it is clear that he expects an effect of H bonding and anticipates the direction, Allen s data do not suffice to establish it. 

More recendy, O Konski and Flautt have made quadrupole resonance studies of solid ammonia (1543). They observe a 12.6 percent decrease of the coupling constant upon condensation of NHj gas, and attribute the change to an increase of ionic character upon formation of H bonds. The even larger shift for ND (21 percent) is hence interpreted as evidence that deuterium bonds are stronger than the hydrogen bonds. 

Sidgwick and Callow were among the first to list criteria of formation of m/ramolecular H bonds (1875a). Their conclusion that ring formation is present in the ortho compounds is based upon the absence of the effects of the intermolecular H bonding shown by meta and para compounds. This chapter will provide many examples of the resulting nearly normal character of chelated compounds. 

Some of the important substances in which H bonds are formed are proteins, polypeptides, sugars, lignins, gelatin, starch, and other substances from living tissues. This area shares with polymer formation a prominent position among the most intriguing chemical problems. The 

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Fig. 4.14 Magnetically perturbed quadrupole spectra simulated for powder distributions of the EFG (Vzz > 0) with an applied field B = 4T which is fixed in the laboratory system perpendicular to the y-beam/ The value of the quadrupole splitting is kept constant at AEq = +4 mm s For negative quadrupole splitting (V z < 0), the spectra would be inverted on the velocity scale. Note the difference in relative intensities for the spectrum for ry = 0 and the single-crystal type spectrum given in Fig. 4.13. Similar patterns are obtained for B y...

Livingston, R. Pure Quadrupole Spectra the Substituted Methanes. J. chem. Physics 19, 1434 (1951). 

Figure 15.17. Deuterium quadrupole spectra static (top) and magic angle spinning at 1 kHz (bottom).

The quadrupole spectra will have several degenerate transitions, and the appropriate summations are listed in Table 3.2 and Appendix 2. A dipole f f transition shows 1 1 intensity for a polycrystalline sample, and 5 3 and 1 3 intensity ratios for a single crystal with the y-ray axis perpendicular to and parallel to the principal axis of a symmetric electric field gradient tensor. 

Fig. 3.6 The effect of orientation upon the intensities of magnetic and quadrupole spectra for a f -> i transition.

Anisotropy effects have also been calculated to be detectable as an alteration of the intensity ratios in magnetic hyperfine spectra [61]. For quadrupole spectra with higher spin states it is sometimes possible to observe intensity discrepancies between the m = 0, m = 1, and the 1 -> ibi groups of transitions, each of which has different angular properties. Examples are to be found in I2 [62] and IBr, ICl [63] where vibrational anisotropy is assumed. 

The substituted perovskite phases Sr(TaFe) 03, Pb(NbFe)i03 and SrTi03 lT5Sr(TaFe)j03 give quadrupole spectra which can be simulated theoretically by assuming a random distribution of cations on the iron site and an electric field gradient which arises solely from the cation randomisation [117]. 

Livington, R., and Zeldes, H. 1955, "Tables of Eigenvalues for Pure Quadrupole Spectra, Spin 5/2 and 7/2," Oak Ridge National Laboratory Report ORNL-1913. 

Ion traps are also simple in design, modest in cost, and capable of rapid scanning for GC-MS apphcations. The spectra generated often differ from classical quadrupole spectra, and some ions may undergo dissociation or ion/molecule collisions inside the ion trap. 

The conventional, and very convenient, index to describe the random motion associated with thermal processes is the correlation time, r. This index measures the time scale over which noticeable motion occurs. In the limit of fast motion, i.e., short correlation times, such as occur in normal motionally averaged liquids, the well known theory of Bloembergen, Purcell and Pound (BPP) allows calculation of the correlation time when a minimum is observed in a plot of relaxation time (inverse) temperature. However, the motions relevant to the region of a glass-to-rubber transition are definitely not of the fast or motionally averaged variety, so that BPP-type theories are not applicable. Recently, Lee and Tang developed an analytical theory for the slow orientational dynamic behavior of anisotropic ESR hyperfine and fine-structure centers. The theory holds for slow correlation times and is therefore applicable to the onset of polymer chain motions. Lee s theory was generalized to enable calculation of slow motion orientational correlation times from resolved NMR quadrupole spectra, as reported by Lee and Shet and it has now been expressed in terms of resolved NMR chemical shift anisotropy. It is this latter formulation of Lee s theory that shall be used to analyze our experimental results in what follows. The results of the theory are summarized below for the case of axially symmetric chemical shift anisotropy. 

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