Lineshapes powder

Further evidence for the unique nature of the shock-formed point defects is the dispersion in ESR lineshape characteristic of conductivity at temperatures above 30 K. In shock-modified powder the conductivity is constant down to 2 K, indicating that the electrons responsible for the conductivity are not trapped. These observations indicate that shock-modified rutile is in a physical defect state that has not been obtained in more conventional vacuum-reduction defect studies. 

The stochastic theory of lineshape has been developed by Anderson and Weiss [157], by Kubo [158], and by Kubo and Tomita [159] in order to treat the narrowing of spectral lines by exchange or motion, a generalized formulation having been subsequently presented by Blume [31]. We consider below an application of the theory of Blume to the specific problem of relaxation between LS and HS states in Mossbauer spectra of powder materials which is based on the formulation by Blume and Tjon [32, 33], Accordingly, the probability of emission of a photon of wave vector Ik and frequency m is given as [160] ... 

Fig. 2 Mechanically oriented bilayer samples as a membrane model for ssNMR. (a) Illustration of the hydrated lipid bilayers with MAPs embedded, the glass supports, and the insulating wrapping, (b) A real sample consists of 15 stacked glass slides, (c) Schematic solid-state 19F-NMR lineshapes from an oriented CF3-labelled peptide (red), and the corresponding powder lineshape from a non-oriented sample (grey), (d) Illustration of typical orientational defects in real samples - the sources of powder contribution in the spectra...

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. 

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.

As a consequence of the small quadrupole moment of Li, the quadrupolar interaction in solid state NMR spectra is much smaller for Li than for Li. This has been used to advantage for the determination of the Li chemical shift anisotropy from the Li static solid state powder spectrum of 2,4,6-tris(isopropyl)phenyllithium (see below) . Applying MAS up to 10 kHz, the CSA contributions to the lineshape can be completely ehminated in most Li spectra of organolithium compounds. If the measurement of the quadrupolar... 

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. 

Figure 1 Typical lineshape for a powdered solid (After ref. 1, page 169)...

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. 

In Figure 2, these lineshapes are decomposed into the isotropic lineshape and the axially symmetric powder pattern lineshape. This same procedure was used for eight samples. 

Obtaining information from powder pattern lineshapes (or sideband patterns) always involves matching the experimental lineshapes to those obtained from simulation, and the simulations necessarily involve some model for the molecular motion. This model dependency is an inevitable limitation on this general method for studying molecular motion. The vast majority of studies assume some kind of Markov model for the motion,4 that is, it is assumed that the nucleus/molecule jumps between A discrete sites and that the time taken to... 

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