Other Sources of Line Broadening

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. 

Anti-phase domain boundaries, are three-dimensional mistakes typical of several intermetallic systems undergoing disorder/order transformations. APBs also act on the apparent domain size, but selection rules are totally different 

To conclude this overview on the most common sources of line broadening it is worth considering the instrumental profile. As discussed in Chapters 5 and 6, wavelength dispersion, sample absorption and instrument optics generally produce a finite width IP that is regarded as an extrinsic profile, even if absorption is actually a sample related property. The IP is always present in a PD pattern, combined with the intrinsic profile produced by microstructural features and lattice defects present in the studied sample. 

The traditional approach to treat the IP is based on deconvolution techniques. In fact, it can be shown that the PD profile is a convolution ((8 ) of profile components produced by different sources [IP, size (S), strain (D), faulting (F), etc.]  

In principle this is a robust method, but it has several practical drawbacks. Eliminating background and overlap with other peak profiles can be difficult, if not impossible in many cases of practical interest the broader the profiles i.e. the more suitable to a LPA) the more peak overlapping is inevitably present in the PD pattern. In addition, the Stokes method involves a numerical procedure for the Fourier analysis, so it is exposed to all the downsides related to signal sampling and truncation. 

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Since its first description in 1971 [35], gel-phase NMR was applied to peptide chemistry by Manatt and coworkers [36, 37], These authors used 13C NMR to determine the extent of chloromethylation of crosslinked polymers and 19F NMR to monitor protection-deprotection reactions. These two nuclei are the most commonly used in these types of studies, mainly because of their significant chemical shift dispersion, which can alleviate in part the resolution loss due to the non ideal linewidth obtained in the gel state. Apart from restricted molecular motion, that shortens T2 because of an efficient transverse relaxation, other sources of line-broadening derive from magnetic susceptibility variations within the sample (due to the physical heterogeneity of the system) and residual dipolar couplings. 

No systematic study seems to have been reported concerning other sources of line broadening yet crystalline strains or impurities may explain the breadth or even the failure to observe some lines. 

This is a remarkable result because it implies that the linecenter cross section for an absorption transition from the electronic ground state to several of the lowest lying electronically excited states, including forbidden transitions, will be approximately equal to the square of the wavelength. However, in order for this to be true, other sources of line broadening, such as collision broadening... 

Equation (58) reveals that the amplitudes of the lines and peaks decrease, while their widths increase, in proportion to grad. This broadening becomes significant when it approaches or exceeds the value of AB j, which includes all other sources of line broadening. 

In Chap.10 several techniques have been presented which allow the Doppler width to be overcome. Provided that all other sources of line broadening could be eliminated, the spectral resolution of these techniques can reach at least in principle the limit imposed by the natural linewidth at... 

While MAS and CP-MAS are often sufficient to resolve chemical sites for nuclei like C, P and Si, this is not the case for other nuclei such as ZAl, and B. The reason is that the first group of nuclei have spin while the second have higher spin. Nuclei with spin greater than are subject to electric quadrupole effects, in addition to chemical shift, and these effects present a significant additional source of line-broadening. Because the quadrupole anisotropy in the presence of a strong magnetic field does not transform simply like a 2nd rank tensor, it cannot be... 

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. 

As the refractive index difference diminishes, calculated and experimental values of the peak width differ significantly, and sources of peak broadening other than attenuation must be considered. These include both Brownian movement and lattice distortions or microcrystallinity due to the presence in the lattice of smaller or larger particles. Line broadening as a result of such defects would be most apparent in highly transparent suspensions, where more planes contribute to the diffraction. 

It would appear that measurement of the integrated absorption coefficient should furnish an ideal method of quantitative analysis. In practice, however, the absolute measurement of the absorption coefficients of atomic spectral lines is extremely difficult. The natural line width of an atomic spectral line is about 10 5 nm, but owing to the influence of Doppler and pressure effects, the line is broadened to about 0.002 nm at flame temperatures of2000-3000 K. To measure the absorption coefficient of a line thus broadened would require a spectrometer with a resolving power of 500000. This difficulty was overcome by Walsh,41 who used a source of sharp emission lines with a much smaller half width than the absorption line, and the radiation frequency of which is centred on the absorption frequency. In this way, the absorption coefficient at the centre of the line, Kmax, may be measured. If the profile of the absorption line is assumed to be due only to Doppler broadening, then there is a relationship between Kmax and N0. Thus the only requirement of the spectrometer is that it shall be capable of isolating the required resonance line from all other lines emitted by the source. 

Nuclear spins can be considered as dipoles that interact with each other via dipolar couplings. While this interaction leads to strongly broadened lines in soUd-state NMR spectroscopy, it is averaged out in isotropic solution due to the fast tumbUng of the solute molecules. In Uquid-state NMR spectroscopy, the dipolar interaction can only be observed indirectly by relaxation processes, where they represent the main source of longitudinal and transverse relaxation. 

This very simple case is rare because of the small wavelength shifts involved but has been observed for mercury-202 [235]. A cooled low-pressure mercury-202 microwave source and a low-pressure mercury vapour atom cell were used, to ensure minimal line broadening (0.0002 nm at the 253.7 nm line). Only mercury-202 and mercury-200 could be determined in this way, as the other isotopic lines showed overlap, and even this was only possible as, for mercury, low-temperature, low-pressure atom cells can be used. 

A controversial problem is the cause of the pronounced asymmetry of some ESR spectra, while others are symmetric or only slightly asymmetric.At least four reasons have been suggested to explain this asymmetry. First, highly pure phenothiazine can be prepared only by using special techniques when the radical is prepared, by chemical methods in particular, small amounts of other radicals (e.g., 3-hydroxy-S ) may be present with the predominant species in the system. Superposition of the signals from the impurities upon the main spectrum may lead to asymmetry. Another source of asymmetry may be the so-called asymmetrical broadening, due to the dependence of the line width on the value of (the projection of the nuclear spin on the direction of the magnetic field).If this... 

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." ... 

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