Two-Sided Bands

The so-called coordinate, or international, notation refers to the mutual orientation of the coordinate axes and symmetry elements [11], The notation always starts with the letterp, referring to the translation group. Axis a is directed along the band, axis b lies in the plane of the drawing, and axis c is perpendicular to this plane. The first, second, and third positions of the symbol after the letter p indicate the mutual orientation of the symmetry elements with respect to the coordinate axes. If no rotation axis or normal of a symmetry plane coincides with a coordinate axis, the number 1 is placed in the corresponding position in the symbol. The coincidence of a rotation axis, 

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Similarly, a pendulum with a soft, flexible shaft has one natural frequency of oscillation, and several definite multiples of it, if the shaft is bending. However, as shown in Fig. 13.1, if two pendula are loosely coupled by a soft spring (or two guitar strings by a piece of rubber), there will still be a most-likely natural frequency, but two "side-band frequencies" will appear. 

In the ENDOR/TRIPLE technique (also called Special TRIPLE) both transitions are induced simultaneously [14,15] by modulating a carrier of frequency with a frequency, v iple, resulting in two side bands... 

When the output of such a tuneable monochromatic laser is sent through an electrooptic modulator, the phase and thus the frequency of the transmitted laser wave is modulated and the frequency spectrum consists of the carrier and two side-band frequencies, where the side-bands have opposite phases (Figure 1). At a modulation frequency of Q=l GHz, the separation of the sidebands from the carrier is about equal to the Doppler width of the absorption lines. If this modulated laser beam is detected after transmission through the absorption cell, the... 

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. 

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... 

In addition to anthropogenic pollution, some serpentine soils derived from Fe and Mg-rich ultramafic rocks are enriched in Ni, Cr and Co. In North America, ultramafic rocks form two discontinuous bands along the east and west side of the continent. The largest area of ultramafic terrain is in the Klamath Mountains province of northern California and southern Oregon (Lee et al., 2001). Serpentinite is a metamorphic rock formed from low... 

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). 

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]. 

Figure 5.9 Two examples of dynamic induced band-shape effects, (a) Weak coupling an absorption single line of the Yb + ion in LiNbOs (denoted by an arrow) is accompanied by the appearance of phonon side bands (reproduced with permission from Montoya et al., 2001) (b) Strong coupling the broadband luminescence of the Cr + ion in LiNbOs (reproduced with permission from Camarillo et al., 1992).

Piezoelectric microbalance The piezoelectric microbalance is a resonant frequency device. The piezoelectric effect is the development of a charge on some crystals such as quartz when a stress is applied the stress may be mechanical (e.g., added weight) or electrical. Such crystals may be used as part of a resonance circuit to provide very stable, narrow-band frequencies the quartz crystal is plated on two sides with a thin conducting layer and leads are connected to the resonance circuit so the crystal replaces an LC network. The obtained frequency of vibration (pu) depends on a number of parameters of the crystal but is usually 5-10 MHz. However, if a mass (Am) becomes attached to one side of the crystal, it changes the resonant frequency by an amount At , such that... 

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