Line broadening in solids

The single-mode laser naturally gives less output power than a multimode laser with the same active volume since its induced emission is concentrated into a smaller frequency range. This loss in intensity, however, is much less than one would expect from the ratio of linewidths or from the reduction in oscillating mode number 3i. 32,41) jbis is due to the fact, that not only atoms with the exact transition frequency can contribute to the induced emission, but also those inside the homogeneous linewidth which is determined by collision processes in the case of gas lasers or by crystal line broadening in solid lasers... 

Group 18. - A 3He NMR study has been made of line-broadening in solid 3He-4He mixtures below 50 mK.571 2H NMR spectroscopy was used to study impurity-helium solids prepared by injecting deuterium atoms and mole-cules into superfluid He. Pulsed He NMR data were reported for solid He in a silver sinter down to temperatures of 400 pK.573 He NMR was used to characterise 3He nanoclusters embedded in h.c.p. 4He.574 Ferromagnetism of two-dimensional solid 3He has been investigated by SQUID NMR.575... 

Line broadening in solid-state NMR arises from spin interactions which can be described in first order by coupling tensors of rank two (cf. Section 3.1) [Hael, Mehl, Schl], The spin interactions are either linear or bilinear in the spin operator. Linear interactions are the Zeeman interaction, the chemical shielding, and the interaction with the rf field. Bilinear interactions are the J coupling, the dipole-dipole coupling, and the quadrupolar interaction. In isotropic materials like powders, glasses, and undrawn polymers, wide lines are observed as a result of an isotropic orientational distribution of coupling tensors. 

In the preceding section, we discussed methods of suppressing dipolar interactions as a means of eliminating spin diffusion in relaxation measurements, but dipolar interactions are also the principal source of line-broadening in solid-state spectra, and therefore suppression of dipolar interactions also offers the possibility of obtaining high resolution spectra of solids in which chemical shift information is discernible. It is this, rather than the suppression of spin diffusion that has been the motivation in the development of these techniques, particularly the multiple pulse sequences. 

The issue of what causes line broadening in solid-state NMR was thoroughly investigated by Su et al To understand the linewidth contributions to membrane protein NMR spectra, T2 relaxation times of uniformly labeled residues which show that the homogeneous line widths are determined by conformation-independent factors, including residual dipolar coupling, J-coupling, and intrinsic T2 relaxation. Examples of this were shown by TAT and other peptides. 

Anisotropic line broadening in solids often leads to a situation in which only one dominant hyperfine interaction is resolved, the one for the atom at which the spin is localized. In fluid media, however, anisotropic contributions average, lines are narrower, and a multitude of hyperfine interactions may be resolved. This situation is frequently observed for proton couplings in n radicals, where the electron spin is distributed throughout a network of conjugated bonds. Examples can be found in Ref. 23. 

We have referred to the various interactions which can cause line broadening in the solid state. One of these, which is normally not a problem in liquid state NMR, is due to the fact that the chemical shift itself is a tensor, i.e. in a coordinate system with orthogonal axes x, y and z its values along these axes can be very different. This anisotropy of the chemical shift is proportional to the magnetic field of the spectrometer (one reason why ultra-high field spectrometers are not so useful), and can lead in solid state spectra to the presence of a series of spinning sidebands, as shown in the spectra of solid polycrystalline powdered triphenylphosphine which follows (Fig. 49). In the absence of spinning, the linewidth of this sample would be around 75 ppm ... 

The anisotropies that lead to line broadening in isotropic ESR spectra influence solid-state spectra more directly. Accordingly a more complex spin Hamiltonian is required to interpret such spectra ... 

The nucleus is quadrupolar (spin 7/2, natural abundance 99.76%), and thus, the spectra can be affected by both the first- and second-order quadru-pole interaction, though the second-order broadening is generally not the largest source of line broadening in these materials. In general, three major anisotropic interactions influence the line shapes seen in the NMR spectra of solid samples (i) the qua-... 

A. Meissner, P. Bloch, E. Humpfer, M. Spraul and O. W. Sorensen, Reduction of inhomogeneous line broadening in two-dimensional high-resolution MAS NMR spectra of molecules attached to swelled resins in solid-phase synthesis, J. Am. Chem. Soc., 1997, 119, 1787-1788. 

The S groups stabilized at the solid surface can differ in their chemical nature. In the disordered (amorphous) solids, to which silica refers and which are of most practical and theoretical interest, the variations in the spatial structure are inevitable. These variations cause variations in the properties of even those S groups having chemically identical composition of their coordination spheres and give rise to the inhomogeneous line broadening in the spectra of these groups and to their kinetic inequivalence. In this work, special emphasis is placed on the questions associated with these problems. 

Before going into some detail on the applied techniques, we shall first summarise the causes of line broadening in the spectra of solids. Line broadening in 13C NMR spectra of solids will be discussed below. 

A discussion on line broadening in the spectra of large molecules may be best introduced by describing the spectral results obtained for naphthalene when present as a low-concentration substitutional solid solution with durene at very low temperatures 1 2>. 

The surface effect discussed above is an aspect of inter-molecular relaxation in molecular solids is that associated with the depth of the molecule from the sample surface. This effect manifests itself as an apparent line-broadening in UPS spectra, other contributions to line-broadening also exist. These, as well as some specific mechanisms that lead to the observed intermolecular polarization effect will be discussed below. 

Figure 3. Solid State CP/MAS NMR Spectra of Unreacted IHSS Elliot Silt Loam Soil and IHSS Pahokee Peat. LB=line broadening in Hz.

The second factor that contributes to line broadening for solids is chemical shielding anisotropy (the term chemical shift anisotropy should be avoided in this context, since, strictly speaking, chemical shift is a scalar quantity and cannot be anisotropic). In solution, the observed chemical shift is the average of the shielding of a nucleus over all orientations in space, as the result of molecular tumbling. In a solid, shielding of a specific nucleus in a... 

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