Chemical shift tensor powder pattern

It is apparent from Eq. (20.17) that in a rigid, solid sample the chemical shift will depend on its orientation with respect to the applied field. A sample having all like carbon nuclei with the same orientations—as in a single crystal—will exhibit chemical shifts that vary as the crystal is rotated in the applied magnetic field. In a powdered sample, all possible crystalline orientations are present, so the NMR spectrum will COTisist of the chemical shift tensor powder pattern. 

Two theoretical [6] chemical shift tensor powder patterns are illustrated in Figure 5.4(a),(b). Principal values 022 and <733 are indicated, and their isotropic averages, o-j, are given as dotted lines. In the axially symmetric case (b), (7 and are the resonant frequencies observed when the principal-axis system is aligned and J. to the applied field. Molecular motion will narrow... 

Figure 5.4 Schematic chemical shift tensor powder pattern for an axially asymmetric (a) and axially symmetric (b) tensor. The isotropic chemical shift values

Although potentially capable of providing motional and orientational information, the chemical shift tensor powder pattern contributes significantly to the broadening of solid state NMR spectra (see Figure 5.1(b)) and often... 

Fig. 3. Example spectra from the one-dimensional dipolar-shift experiment taken from reference 7. (a) (Top) Experimental l3C chemical shift anisotropy powder pattern for Ru(C5H5)2 and (below) for comparison, the dipolar shift l3C spectrum for the same compound, (b) Calculated dipolar-shift lineshapes for different angles (indicated) between the lH-13C dipolar and chemical shift anisotropy tensor principal z-axes.

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.

Here cto is the isotropic shift (1/3 [cti, 0-21 -1- ct3,]) and tree is the projection of the chemical shift tensor along the spinning axis and defined analogously to Eq. (3). In general this latter term produces a powder pattern when summed over nuclei at all orientations. However, when cos 0 = l/J3, the powder pattern collapses and only the isotropic value remains, i.e., CTjj/ = 0-5,. If this magic angle is misset by e radians, then (9)... 

Efforts to understand the state of hydrogen in metals and metal hydrides have involved the use of NMR for many years. This study combines the conventional solid state NMR techniques with more recently developed high-resolution, solid state NMR techniques (5,6). Conventional NMR techniques furnish information on dipolar interactions and thus can furnish static geometrical information on hydrogen positions and information on proton motion within such solids. The newer multiple pulse techniques suppress proton-proton dipolar interaction and allow information on other, smaller interactions to be obtained. This chapter reports what the authors believe is the first observation of the powder pattern of the chemical shift tensor of a proton that is directly bonded to a heavy metal. 

The isotropic chemical shift is the average value of the diagonal elements of the chemical shift tensor. Advances in solid state NMR spectroscopy allow one to determine the orientation dependence, or anisotropy, of the chemical shift interaction. It is now possible to determine the principal elements of a chemical shift powder pattern conveniently, and the orientation of the principal axes with more effort. Hence, instead of settling for just the average value of the chemical shift powder pattern, one can now aim for values of the three principal elements and the corresponding orientations in a molecular axis system. 

The resulting principal values of the 13C chemical shift tensors of the C60 carbons are 8n = 228 ppm, 822 = 178 ppm, and 833 = -3 ppm. Tycko et al reportet the experimental values 8n = 213 ppm, S22 = 182 ppm, and 833 = 33 ppm obtained from low temperature measurements of a powder pattern spectrum (18). However, the spectra have a low signal to noise ratio and a wide slope so that a larger error for the experimental value can be assumed. The chemical shift anisotropy of 217 ppm corresponds quite well with the spectral range of about 200 ppm reported by Kerkoud et al for low temperature single crystal measurements (19). 

Chemical shift spectra of PTFE obtained at 259° are shown in Figure 1. These lineshapes, for three different samples of varying crystallinity, may be seen to be a linear combination of two lineshapes one is characteristic of an axially symmetric powder pattern and the other of an isotropic chemical shift tensor. At this temperature these two lineshapes differ greatly and may be numerically decomposed. 

For polycrystalline samples, the angular dependence of the chemical shift in Equation 1 results in a broad powder pattern , which can be calculated by assuming a random distribution of 0k (e.g., a constant increment of 0k with intensities proportional to sin(0k)). The powder pattern provides information on the size and symmetry of the chemical shift tensor from which useful structural and dynamical information can be obtained. However, it is usually very difficult to resolve separate powder patterns for phases that contain more than one type of crystallographic site, because the frill width of the powder pattern (811 - 833) typically exceeds the range in 8i. 

Figure 1 Solid-state NMR powder patterns, dominated by chemical shift anisotropy effects (a) spherically symmetric chemical shift tensor, (b) axially symmetric chemical shift tensor, (c) asymmetric chemical shift tensor. Top traces theoretical powder patterns bottom traces powder patterns broadened by other anisotropic interactions or chemical shift distribution effects.

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