Powder patterns resolving

MAS Si speetnim of a sample of sodium disilieate (Na Si O,) erystallized from a glass is shown as an example. Whilst the statie speetnim elearly indieates an axial ehemieal shift powder pattern, it gives no evidenee of more than one silieon site. The MAS speetnim elearly shows four resolved lines from the different polymorphs present in die material whose widths are 100 times less than the ehemieal shift anisotropy. 

This compound has two crystallographically distinct vanadium sites. While the static spectrum is a superposition of two powder patterns of the kind shown in Figure 3, MAS leads to well-resolved sharp resonances. Weak peaks denoted by asterisks are spinning sidebands due to the quadrupolar interaction. 

Figure 2 shows 29Si solid state NMR data of high-silica ZSM-5 with 24 crystallographic Si positions, 15 of which are well enough resolved in the MAS NMR spectrum to be assigned to crystallographic positions. The CSA parameters are determined by simulation of the lineshapes of the powder pattern as obtained from the 2D experiment. 

In a high symmetry crystal system, very few peaks occur in the powder pattern, and they are often well resolved and well separated. It is then possible to measure their position and intensity with accuracy, and by the methods we described earlier, index... 

The other general way of resolving powder patterns from different chemical sites is to generate multidimensional NMR spectra in which the desired powder patterns (or magic-angle spinning sideband patterns) are resolved in one dimension, separated according to (for instance) isotropic chemical shift in another dimension. These techniques are discussed below in the relevant section for each type of nuclear spin interaction. 

Because of the general similarities in the diffraction patterns, and the lack of clearly resolvable distinguishing peaks, they employed the Rietveld method (Young 1993). In the Rietveld method, the entire experimental diffraction pattern for each solid phase is used as a basis for comparison. For structure determination using powder diffraction, this comparison is made with a structural model used to generate a calculated pattern. In quantitative analysis of polymorphic phases, the known crystal stmctures are used to generate the standard diffraction patterns and these are then refined against the experimental powder pattern of the mixture to obtain the relative amounts of the polymorphs. 

Preliminary results for on a Cu/Zn/Al methanol synthesis catalyst show a fairly narrow (a few tens of ppm) resonance at 350 ppm (Fig. 34) (95). It has been ascribed to Knight-shifted CO on copper, but its relative sharpness might indicate that it is actually the low-field divergence of a chemical-shift powder pattern (the corresponding high-field discontinuity being overlapped by the rest of the spectrum). In principle, a study of the spin lattice relaxation time could resolve the issue. 

One way to obtain highly resolved, selective, solid state information plus uniquely defined information on the orientation-dependencies of spin interactions is to perform NMR experiments on oriented single crystals. However, for various reasons, such single crystal NMR experiments appear impractical in standard applications to organometallic chemistry. The vast majority of solid state NMR experiments on organometallic compounds are— and probably will be— performed on polycrystalline powder samples. In principle, also for polycrystalline powders, all relevant information on spin interactions is contained in the shape of the powder patterns obtained imder static conditions. The problem then is the extraction of well-defined single parameters from such lineshapes resulting from either a multitude of resonances and/or the simultaneous presence of multiple spin interactions. In practice, it turns out that only very rarely is this possible. 

The following numbers of monosaccharide residues per molecule were reported by Ott a-diainylose, 22 a-tetraamylose, 12 a-octaamylose, 63 /3-triamylose or /3-hexaamylose, 6 cellulose, 3 licheiiin, 7 starch, 2 and inulin, 6. The x-ray powder patterns published by Ott appear weak and poorly resolved, lending an additional item of doubt to an already tenuous argument. Herzog examined several known substances by Ott s method out of seven cases, only one was reasonably close to the correct value while the others were off by 40 to 500 %. 

More recently, the static NMR spectra of 16 potassium compounds have been obtained by Bastow (1991) using a solid pulse echo sequence. Most of these compounds have relatively small dipolar coupling, resulting in sharp powder pattern features of the observed central transition. Accurate simulations allowed the values of xq and T to be determined and also indicated very small CSA contributions. Most of these model compounds contain only 1 potassium site, but even those compounds with 2 inequivalent K sites could be sufficiently resolved to allow accurate and unambiguous simulation (Bastow 1991). The NMR interaction parameters for potassium compounds are collected in Table 8.8. 

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. 

It is well known that resolved enantiomers and the racemic mixtures of dissymmetric substances ordinarily crystallize in different space groups,37 so it is natural to use quantitative XRPD as a means to determine the enantiomeric composition. This approach was demonstrated in the case of ibuprofen, taking advantage of the differing powder patterns of the resolved enantiomers and the racemate.38 The detection limits for either form (in the presence of the other form) were very similar, being approximately 3.3% w/w. 

Whereas within the family of the cubic Prussian blue analogs a large number of lattice constants have been determined, little attention has been devoted so far to polymeric cyanides not belonging to the cubic system. It must be emphasized, however, that polynuclear cyanides having unit cell symmetries other than cubic are by no means rare exceptions. Hexacyanometalates(III) of Zn2+ and Cd2+ are obtained not only in a cubic modification but also as samples with complicated and not yet resolved X-ray patterns of definitely lower symmetry than cubic (55). The exact conditions for obtaining either modification are not yet known in detail. The hexacyanoferrates(II), -ruthenates(II), and -osmates(II) of Mn2+ and several modifications of the corresponding Co 2+ salts show very complicated X-ray powder patterns which cannot be indexed in the cubic system (55). Preliminary spectroscopic studies show the presence of nearly octahedral M C6-units in these compounds, too. 

MAT) to resolve powder lineshapes arising from chemical shift anisotropy.5 The MAT experiment was developed by Gan6 and is a two-dimensional experiment, which resolves chemical shift anisotropy powder patterns in f2 according to their isotropic chemical shifts in /j. The whole experiment is conducted under very slow MAS. Under very slow MAS, the spectrum approximates to that of a static (non-spinning) experiment, and it is this feature that produces static-like powder patterns in the f2 dimension of the MAT experiment. 

Fig. 2. The MAT experiment applied to poly(2-hydroxypropyl ether of bisphenol A)5 (top) to examine the 180° ring flips affecting 13C 4 and 5. (a) The complete two-dimensional MAT spectrum.5 The projection in f2 is effectively the lineshape that would be recorded for a powder sample. As this spectrum clearly shows, the chemical shift anisotropy powder patterns from the nine 13C sites in this polymer are extensively overlapped and would not be resolved without the aid of this MAT experiment, (b) The powder lineshapes for each 13C site taken from the two-dimensional spectrum in (a).5 Those for carbons 4 and 5 show distortions of the lineshape shoulders typical of motional averaging, in this case from 180° phenyl ring flips.

For some systems, the presence of two or more interactions, and two or more chemically distinct sites induce so strong overlaps between the different contributions that the analysis of the NMR powder spectra is too intricate to be possible. Even when the powder pattern singularities are well resolved, it is not unusual that the eigenvalues of the interaction tensor do not show any obvious anomaly at a phase transition. In that case, only a complete determination of the interaction tensor (including the direction of the principal axes) may lead sufficient information to characterize the different phases. 

In the NMR spectrum, the dipolar interaction represents itself as a line splitting. For isolated pairs of unlike spins, the i and j spin resonances are each split into a doublet with a splitting of 2d , for like spins a doublet with a splitting of 3d is found. For powder samples a so called Pake powder pattern is found instead of the doublet. Resolved splittings are only observable for fairly well isolated spin systems consisting of two or a very few spins (e.g., the proton pair of the crystal water in gypsum [9]). For extended spin systems, a broad and rather featureless resonance line is observed. 

---