Powdered crystals, lineshape

Bisquaric acid was also studied by 13C CPMAS NMR between 123 and 523 K, with powdered crystals.173 This material has also potential for nonlinear optical and dielectric applications. The low-temperature spectra resolve three peaks instead of four in SQA. This compound has no dipole moment, and no phase transition was detected in the studied temperature range, although the lineshape suggests the occurrence of a phase transition below 373 K. An explanation proposed by the authors is the lack of resolution due to the accidental overlapping of the two resonances of the C OH and C — O carbons participating to the HBs, an interpretation also supported by GIAO ab initio chemical shift calculations. 

Peak widths. The lineshapes and linewidths of peaks in a powder XRD pattern depend on the crystallinity of the sample, as well as features of the instrumentation and the data collection procedure. In particular, peaks in the powder XRD pattern may be broadened as a consequence of small crystallite size. If the powder XRD patterns of two samples with the same crystal structure have significantly different linewidths, the visual appearance may differ substantially, especially in regions of significant peak overlap. 

In organic radicals in solution, the y-factor anisotropy cannot be detected one needs oriented samples. In crystals of free radicals, this anisotropy is easily measured—for example, in crystals of sodium formate (Na+ HCOO-) the principal-axis components are gxx = 2.0032, gyy = 1.9975, and gzz = 2.0014. If there is some spin-orbit interaction in an organic molecule (e.g., if a compound contains S or Cl), then y-values as high as 2.0080 are encountered. In disordered powders with narrow EPR lineshapes, the y-factor anisotropy can produce considerable distortion in the overall signal, due to averaging of the y-tensor. 

If the single crystal is now pulverized so that all C—D bond orientations are equally probable, the powder will display the well-known Pake doublet lineshape (Fig. 2, bottom), which is the sum of all the individual doublet spectra. The separation of the two sharp peaks, for which 0 = 90°, characterizes the width of the spectrum Av = y4 e qQlh). This quantity is known as the quadrupolar splitting. The functional form of the Pake doublet arises from a combination of two factors. First, the relative number of C—bonds oriented at a given angle with respect to the magnetic field varies as sin 6. Second, the transformation from angular to frequency terms of the function 3(cos 0 - l)/2 yields /i(v) = - 2v)- for < v < v J2 and /jfv) (v, -i- 2v)- /2... 

Figure 1.11 (a) Single crystal type (selected orientations of 0 = 0°, 55° and 90°) and (b) first derivative powder type EPR lineshapes for a randomly oriented S = 1 /2, / = 1/2 spin system with uniaxial symmetry. The angular dependence curve (0 vs field) for m, = 1/2 is shown in (c). 

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 NMR internal interaction symmetric second-rank tensors are characterized by three eigenvalues, and three angles are required to orient the corresponding PAS with respect to crystal axes. Only the eigenvalues of the interaction tensors can be extracted from a powder spectra by least-squares fitting of the lineshape. Although absolute orientations cannot be obtained,... 

The peculiar temperature and composition dependence of the valence of chemically collapsed phases of SmS was first observed in the system Sm1 xGdxS (55). Recently a phase diagram in the (x, T)-plane has been proposed for this system (41) as well as for CeTh alloys (44). When cooled below about 200 K the chemically collapsed phases of SmS show a dramatic lattice expansion, in some cases with explosive character (55) and disintegration of the crystal into a black powder. An example of this transition towards a more divalent state of Sm on cooling in SmAs 18 S 82 and Sm 81 Y19S is shown in Fig. 22 and 23, where we show the data of Poliak et al (63). The temperature dependent configurational mixing of Sm ions which is directly visualized in the XPS data is the source of the anomalous temperature dependence of the lattice constant. No detailed analysis of the dependence of the Sm 4/lineshape on temperature... 

In this formula, I is the nuclear quantum number, r(Bj) the first derivative lineshape function, B the resonance position and P the transition probability. 0 and i are the Euler angles expressing the orientation of the magnetic field vector B with respect to the principal axes of the tensors. Integration is needed since in powder samples, the crystallites take all possible orientations with respect to the magnetic field. Since the principal tensor axes and the crystal axes are assumed to be coincident, integration can be restricted to one octant of the unit sphere. 

Figure 7.7 shows an example of the energy of the spin sublevels of the triplet state as a function of H for // [a-, H y, and // z [61]. The behaviour of the spin energy levels is orientation-dependent [61], and the fields-for-resonance for the allowed Am = 1 transitions vaiY with the orientation of H relative to the triplet axes. Most ESR and ODMR studies of triplets states in biological molecules [58] and triplet excitons in crystalline semiconductors [55] have consequently been performed on single crystals. All of the samples described in this chapter, however, were polycrystalline or amorphous, and the triplet resonance lineshape is therefore the powder pattern obtained by averaging the spectra over all orientations [62]. Simulated powder pattern spectra for different values of E/D are shown in Figure 7.8 ... 

H O CP experiments are not routine. One problematic issue is the orientation dependency of the quadrupolar interaction. As a result, only a fraction of the nuclear spins in a powder satisfies the Hartmann—Hahn matching condition, leading to distorted lineshapes. Ando and co-workers [14,16,17] recorded a series of H—CP static spectra of polypeptides. The resultant spectra exhibit clear lineshape distortions, as a result of the combination of the CP experiment and low magnetic field detections. Witterbort and co-workers [28,52,97] successfully apphed a modified H—CP sequence in single-crystal experiments of bio- and organic molecules to regain sensitivity. 

There have been several studies of shift anisotropy in paramagnetic solids, obtained from the orientation analysis of powder lineshapes. Bloembergen [76], Rundle [77], and Poulis and Hardeman [78] analyzed the orientation dependent shifts in single crystals of hydrated Cu salts at low temperatures. McGarvey and Nagy [79, 80] have investigated the temperature dependence of static powder spectra of uranocene U(CgHg)2, a system where all the protons are chemically equivalent. 

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