Axial symmetry powder pattern

Powder patterns of crystals with axial symmetry yield the value of qQ but do not, of course, give the direction of the axis of symmetry. Line shapes to be expected for the magnetic resonance in this situation have been calculated (95) and for / = %, the shape is illustrated in Fig. 11 for polycrystalline corundum (a-AbOs). 

This shape of the powder pattern is that predicted (5) for an 7 = nucleus in axial symmetry. This situation occurs for the Al nuclei in a-AljOs which is a hexagonal close-packed array of oxygen atoms with the aluminum atoms ordered in of the holes octahedrally coordinated with oxygen atoms. 

Magic angle spinning averages all tensors to axial, with their symmetry axes all coincident with the rotor s axis. Then the anisotropic parts of all tensors will scale to zero when the rotor is tilted to the magic angle cos-1 Vj = 54.74° = 54°44 and the spectral powder patterns are narrowed to sharp liquidlike lines. 

FIGURE 7.8 Schematic representation of a powder pattern for anisotropic chemical shielding, (a) Typical pattern for axial symmetry where [Pg.195]

This expression shows that the chemical shielding anisotropy (CSA) leads to a variation of the resonance frequency with orientation according to the familiar (3 cos2 0—1) dependence and thus produces typical powder patterns, as illustrated in Fig. 7.8 for axial and nonaxial symmetries. 

As mentioned earlier, the symmetry at Si is slightly distorted octahedral, the site being surrounded by 6 oxide ions. Therefore, Nff at Si and CuH (also in a similar environment are expected to have similar e.s.r. spectra. The spectrum of CuH ion would be the more complex, however, because of hyperfine interaction with the magnetic nuclei Cu and Cu s. In contrast, all but 1-2 % (Ni i) of the Ni nuclei are non-magnetic. The e.s.r. spectrum of a sodium-reduced Ni (5 %)Y sample in which most of the Ni ions are believed to be at Si is shown in fig. 8. This powder-pattern spectrum is characteristic of a system with an axially symmetric -tensor ... 

As shown in Fig. 1, a typical 15N powder pattern of a peptide reveals axial symmetry because the electronic structure around the nitrogens of the peptide bonds is nearly symmetrical around the axes of the N-H bonds. In such cases, the orientation of the principal axis is difficult to determine even from a singlecrystal study. The directions of the two principal values, crn and dipolar interactions between the nitrogen and the adjacent... 

Figure 7.8. Simulated fijll- and half-field powder pattern ESR spectra of triplet states for different values of E/D (see text) [59] (a) = 0 the triplet wavefunction is axially symmetric. The pattern contains singularities at // (hv D/2 - /8hv)/gli and steps at D)/gP. (b) 0 E <. D/i the axial symmetry of the wavefunction is broken. The singularities occur at...

Chemical-shift anisotropy is very sensitive to molecular structure and dynamics. Each nucleus can be pictured as being surrounded by an ellipsoidal chemical-shift field, A, arising from the influences of neighboring spins, as described by Eq. (4). If the molecules in the sample have no preferred orientational order, these tensors will be randomly distributed, and the line-shape is predictable. If the shielding is equivalent in all directions = (5yy = zi, A is spherical), a symmetric peak, like shown that in Fig. 29a, will be observed at qjso, which is defined in Eq. (5). Axial symmetry = Gyy A is, more or less, football-shaped) results in a powder pattern like that shown in Fig. 29b. In this case, the tensor elements may be labeled CTy ) and (g x and Gj ). If there is no symmetry in the chemical-shift field (gxx is a flattened football), then the... 

Figure 29 Powder patterns for shielding tensor A with (a) spherical symmetry (b) axial symmetry (c) no symmetry. 

Figure 2.8 Typical powder-pattern spectra observed in polycrystalline solids Chemical Shift under (a) cubic, (b) axial, and (c) non-axial symmetries (d) Dipolar interaction between two spins 1/2 (I and S) Quadrupolar interaction for spins e) 1 and f) 3/2, considering an EFG with axial symmetry. The zero of the frequency scale in each case corresponds to the frequency associated with isotropic average (as occurring in liquids). The parameter A depends on the anisotropy of the tensors describing each of the interactions.

Figure 2 (A,B) The span (fi) describes the breadth of powder patterns according to the difference between the and S33 components of the CS tensor. (C)-(F) The skew (k) describes the shape of powder patterns according to symmetry of the CS tenson (C) axial, (D) nonaxial, (E) nonaxial, and (F) axial symmetry. Skew values are provided...

Fig. 10.20. Theoretical spectral patterns for NMR of solid powders. The top trace shows the example of high symmetry, or cubic site symmetry. In this case, all three chemical shift tensor components are equal in value, a, and the tensor is best represented by a sphere. This gives rise to a single, narrow peak. In the middle trace, two of the three components are equal, so the tensor is said to have axial site symmetry. This tensor is best represented by an ellipsoid and gives rise to the assymetric lineshape shown. If all three chemical shift components are of different values, then the tensor is said to have low-site symmetry. This gives rise to the broad pattern shown in the bottom trace.

For powder photographs, the use of the charts described on p. 143 and in Appendix 3 will show whether the substance is cubic, tetragonal, or hexagonal if it is not, the numerical methods of indexing the patterns of crystals of low symmetry may be tried or, if it is. possible to pick out single crystals, or if the specimen can be recrystallized to give suitable crystals, the unit cell dimensions may be determined by the methods described earlier. A search may then be made in the tables of Donnay and Nowacki (1954), in which, for each crystal system, the species are arranged in order of the axial ratios. 

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