Side-bands

At this point it is worth comparing the different techniques of contrast enliancements discussed so far. They represent spatial filtering teclmiques which mostly affect the zeroth order dark field microscopy, which eliminates the zeroth order, the Schlieren method (not discussed here), which suppresses the zerotii order and one side band and, finally, phase contrast microscopy, where the phase of the zeroth order is shifted by nil and its intensity is attenuated. 

Unlike broadband data, narrowband data provide the ability to directly monitor, trend, and alarm specific machine-train components automatically by the use of a microprocessor for a window of frequencies unique to specific machine components. For example, a narrowband window can be established to directly monitor the energy of a gear set that consists of the primary gear mesh frequency and corresponding side bands. 

At low rotation rates, less than the chemical shifts anisotropy, however, the powder spectra contained disturbing side bands dispersed among the isotropic chemical shifts. In order to discriminate between sidebands and isotropic resonances two spectra obtained at different spinning speeds were multiplied together or the differentiation was made by visual inspection. 

Fig. 19.5 C-CP/MAS NMR spectra for sample 5 (a) and 11 (b). The asterisks indicate rotational side bands.

The peaks at 20 and 220 ppm are rotational side bands, their position depends on the rotation speed. In principle, the presence of carbon could also lead to the formation of TiC. However, the precursor contains no Ti-C bonds and thus TiC formation is not very likely. The peak maximum for the static line of... 

Here, L(v) is a lineshape function that integrates to unity, v is the frequency,/ is the Lamb-Mossbauer factor, and the desired side bands have an area fraction / that is proportional to which hence determines the relative peak heights in a NIS spectrum. More details are provided in Appendix 2 (Part III, 3 of CD-ROM). An equivalent and often more suggestive display of the NIS spectrum is the PVDOS approach, which describes the NIS signal in terms of the partial vibrational density of states ... 

Dipolar coupling and 3C shielding anisotropy cause unequal intensity of spinning side bands. The scalar coupling enabled magic angle rotation to distinguish two sets of sub-spectra.58... 

With most spectrometers, you have a choice of either 100 kHz or a lower frequency of field modulation. The higher frequency generally gives better S/N, but if the lines are unusually sharp (<0.08 Gauss), 100 kHz modulation leads to side bands , lumps in the line shape that confuse the interpretation of the spectrum. This effect is illustrated in Figure 1.12. Under such circumstances, use the lower frequency for which the sidebands are closer together and thus less likely to be a problem. 

Fig. 3.18. Synthetic spectrum of a red giant, Tes = 4500 K, log g = 2.25 in the region of the strong Mg i b lines (see Fig. 3.9). The upper spectrum is the same with atomic lines switched off and shows molecular bands of MgH. The horizontal lines show the central and side bands of the Lick Mg2 index. Adapted from Mould (1978).

Fig. 11.5 Differential phase contrast detection of patterned protein in a 10 mm by 30 mm region, (a) Protein height signal showing ridges of protein in a checker board pattern, (b) Side band demodulated signal image in which the carrier frequency of the ridges is removed to show only the protein envelope. Reprinted from Ref. 21. with permission. 2008 Optical Society of America...

Here a third selection rule applies for linear molecules, transitions corresponding to vibrations along the main axis are allowed if Aj = 1. The A/=0 transition is only allowed for vibrations perpendicular to the main axis. Note that because of this selection rule the purely vibrational transition (called Q branch) appears in the gas phase spectrum of C(X but is absent in that of CO. In both cases, two branches of rotational side bands appear (called P and R branch) (see Fig. 8.3 for gas phase CO). 

It leads to unsymmetrical excitation bands in respect to the sideband number n. However, the scaling factor remains unchanged if both the side band number n and the phase increment A ip change sign... 

If the time-dependent Hamiltonian does not commute with itself at all times, then one does not necessarily observe a sharp side-band spectrum under MAS. Only for spinning... 

Hartmann-Hahn cross polarization between two low-y nuclei has been successfully used to record chemical-shift correlation spectra between 13C and 15 N nuclei. Cross polarization between two low-y nuclei suffers from a high sensitivity to the exact matching condition at one of the side bands of the Hartmann-Hahn condition [101]. Adiabatic methods (APHH-CP) can eliminate most of this sensitivity and lead to high transfer efficiencies [34, 62, 90]. 

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