Line-broadening, sources

As discussed in Section 13.1, line broadening sources are manifold. In the previous subsections two of the most common ones were considered size (Section 13.2.1) and strain (Section 13.2.2) broadening. It is therefore legitimate to wonder to what extent different line broadening sources can be distinguished from the effects observed in a PD pattern. To discuss this point, two types of lattice defects that affect the line profile are considered. 

Unfortunately, few cases can be properly described under the assumptions of Equations (14) or (15) (or by other possible combinations " ) real life cases usually do not match perfectly any simple combination of Lorentzian or Gaussian profiles. Generally speaking the additivity rule for different IB components is not known a priori, so using Equations (14), (15) or other combinations of terms is somewhat arbitrary, unless specific assumptions are made on the line broadening sources." ... 

One can think of several other possible line broadening sources. Expressions for the FT may be analytical but also numerical in some cases, as for the grain... 

Natural line broadening is usually very small compared with other causes of broadening. However, not only is it of considerable theoretical importance but also, in the ingenious technique of Lamb dip spectroscopy (see Section 2.3.5.2), observations may be made of spectra in which all other sources of broadening are removed. 

Besides the instrumental effects (mainly experimental resolution) the main sources of line broadening are ... 

It is quite common to observe that the lines in a nitroxide spectrum show variations in width. One feature which contributes to this is the anisotropy of the nitroxide grouping, as a consequence of which the high field component of the nitrogen triplet may be perceptibly broadened. This effect is particularly noticeable when free tumbling of the nitroxide molecule is restricted either by the viscosity of the solvent or when the radical is incorporated into a very large (e.g. polymer) molecule. This selective line broadening is, of course, one of the principal sources of information in spin-labelling experiments (Berliner, 1976). 

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-... 

Line broadening due to inhomogeneity in the static magnetic field. Ho, as well as in the rf pulse Hj, can contribute to the observed resonance. However, studies of standard sairples, of known natural linewidths, enable the contributions from this source to be determined. In the present case these causes contribute only a few percent, i.e., a few Hz, to the total linewidth and are thus inconsequential to the present problem. Before discussing the different motional contributions to the linewidth. 

For non-viscous liquids, where the cibove condition will be expected to be fulfilled, narrow resonances are observed, when only this source of line broadening is involved. 

The Time Dependent Processes Section uses time-dependent perturbation theory, combined with the classical electric and magnetic fields that arise due to the interaction of photons with the nuclei and electrons of a molecule, to derive expressions for the rates of transitions among atomic or molecular electronic, vibrational, and rotational states induced by photon absorption or emission. Sources of line broadening and time correlation function treatments of absorption lineshapes are briefly introduced. Finally, transitions induced by collisions rather than by electromagnetic fields are briefly treated to provide an introduction to the subject of theoretical chemical dynamics. 

In experimental measurements, such sharp 8-function peaks are, of course, not observed. Even when very narrow band width laser light sources are used (i.e., for which g(co) is an extremely narrowly peaked function), spectral lines are found to possess finite widths. Let us now discuss several sources of line broadening, some of which will relate to deviations from the "unhindered" rotational motion model introduced above. 

Following Eq. 4 there are three different sources of line broadening adding to the natural line width AB, which reflects the lifetime of the final state (Heisenberg uncertainty principle) and in some cases an unresolved spin orbit splitting. In first approximation, 7)... 

The line-shape of a true (undistorted) EPR spectrum should be independent of the acquisition parameters, and therefore to assess spectral distortion one can compare spectra acquired with different parameters. Figure 15.6 illustrates the effect of modulation amplitude on EPR line-shape. The central line-width (peak-to-peak width AHpp = 1.6 G) remains unchanged when the modulation amplitude is increased from 0.5 to 1 G while at a modulation amplitude of 10 G, distortion and line-broadening (AHpp = 6.4 G) can be clearly observed. The main sources of spectral distortions are modulation amplitude, microwave power, and scanning rate (speed). These are discussed in the following sections. 

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