Single crystal, lineshape

The O KVV lineshape is severely altered by impurities in the sintered HTSC s, and no single crystal lineshape data have been reported. The O KW Uneshapes for CuO and CuiO have been reported (16), and they have the primary dp or p features, respectively, around 19 eV. A very small satelUte appears around 7 eV in CuaO which we attribute to the pp state. A much larger and broader satelUte around 7 to 14 eV in CuO appears, which we attribute to the d p state around 14 eV as weU as a smaUer amount... 

Fig. 2 Schematic representation of the 13C NMR signal of a single crystal containing the functional group AB, oriented (A) perpendicular to the applied field, and (B) parallel to the applied field. The lineshape in (C) represents the NMR signal of a polycrystalline sample with a random distribution of orientations yielding the chemical shift anisotropy pattern displayed. (From Ref. 15.)...

An example of the application of this lineshape is shown in Fig. 2a for the free induction decay of 19F in a single crystal of CaF2 for B0 along the [1,0,0]... 

Fig. 2. (a) The free induction decay, G(t) for 19F in a single crystal of CaFi for B0 along [1,0,0]. The experimental points are given by circles and crosses from the CW and pulse measurements, respectively, and the theoretical curve is that of Eq. (14), corresponding to an exponential decay multiplied by a sine function. Note that F(t) is equivalent to G(t) in the present notation. Reproduced with permission from A. Abragam, The Principles of Nuclear Magnetism, p. 121, Oxford University Press, London, 1961. (b) The lineshape in the frequency domain corresponding to the Fourier transform of the theoretical curve. 

Structural studies of systems that cannot be obtained as pure single crystals are beset with serious difficulties. This problem can be solved with the use of ESR techniques if the lineshape or spin-relaxation parameters of the ESR signals from a paramagnetic center respond suitably to the approach of another paramagnetic center. Two types of spin-spin interactions can be distinguished (1) dipole-dipole interaction arises because... 

When the H- H dipole-dipole interaction can be measured for a specific pair of H nuclei, studies of the temperature dependence of both the H NMR line-shape and the H NMR relaxation provide a powerful way of probing the molecular dynamics, even in very low temperature regimes at which the dynamics often exhibit quantum tunnelling behaviour. In such cases, H NMR can be superior to quasielastic neutron scattering experiments in terms of both practicality and resolution. The experimental analysis can be made even more informative by carrying out H NMR measurements on single crystal samples. In principle, studies of both the H NMR lineshape and relaxation properties can be used to derive correlation times (rc) for the motion in practice, however, spin-lattice relaxation time (T measurements are more often used to measure rc as they are sensitive to the effects of motion over considerably wider temperature ranges. 

For the partially deuterated benzoic acid (C6D5COOH), the solid state H NMR spectrum is dominated by the intra-dimer H- H dipole-dipole interaction. In a single crystal, both tautomers A and B are characterised by a well-defined interproton vector with respect to the direction of the magnetic field (Fig. 1). Proton motion modulates the H- H dipole-dipole interactions, which in turn affects the H NMR lineshape and the spin-lattice relaxation time. It has been shown that spin-lattice relaxation times are sensitive to the proton dynamics over the temperature range from 10 K to 300 K, and at low temperatures incoherent quantum tunnelling characterises the proton dynamics. A dipolar splitting of about 16 kHz is observed at 20 K. From the orientation dependence of the dipolar splitting, the... 

Figure 1 Experimental and simulated EPR spectra of oxidized CooA at pH 7.4. Experimental conditions temperature, 2 K microwave frequency, 35.106GHz microwave power, 20p,W 100 kHz field modulation amplitude, 0.4 mT time constant, 128 ms scan time, 4 min. Lower traces, in absorption line-shape (due to rapid-passage conditions), are the experimental spectrum (blue) and a digital integration of the simulated spectrum (red). Upper traces in first-derivative lineshape are a digital derivative of the experimental spectrum (blue) and the simulated spectrum (red). Simulation parameters component (a) g = [2.60, 2.268, 1.85], (b) g = [2.47, 2.268, 1.90] Gaussian single-crystal linewidths (half-width at half-maximum) W = [500, 200, 400] MHz. Simulated spectra for (a) and (b) are added in the ratio 2 1 to give the summed spectrum shown...

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 Mg MAS spectrum of Mg(OH)2 (brucite) is broad (Figure 8.10B), but shows a quadrupolar lineshape from which 8iso and Xq values of 14.1 ppm and 3.15 MHz were determined (MacKenzie and Meinhold 1993). These values are in reasonable agreement with a single crystal study of Mg(OH)2 in which the linewidth was found to... 

Ge NMR is subject to great difficulty, and is seldom studied. Recently reported spectra from single crystal germanium with differing isotope contents show quadrupo-lar lineshapes arising from local lattice distortion related to isotopic disorder (Verkhovskii et al. 2000). 

Fig. 17. Schematic of the nonadecane/urea-inclusion compound. From left to right single-crystal experiment by rotation around the channel axis. Critical inhomogeneous linebroadening on approaching the transition temperature from above, with a lineshape invariant by rotation around c hole burning in the last spectrum proves the inhomogeneous nature of the broadening. Schematic of rotation patterns that gives the chain orientation in the low-temperature phase.

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