Parallel dispersion mode

In addition, Echelle spectrometers are often used [50], By combination of an order-sorter and an Echelle grating either in parallel or in crossed-dispersion mode, high practical resolution (up to 300 000) can be realized with an instrument of fairly low focal length (down to 0.5 m) (Fig. 94). Therefore, the stability as well as the luminosity are high. By using an exit slit mask with a high number of preadjusted slits, highly flexible and rapid multielement determinations are possible. 

Equations (3.2) and (3.3) are approximate formulae for spectrometers of modem design without lenses. The actual value for the VG prism spectrometer used in our HB-501 STEM is about 1.8 pmeV. In parallel detection mode, the dispersion achieved is usually further magnified by quadmpole lenses. A single quadmpole produces a line focus. Two such lenses in series can act as a... 

Apart from gratings used at low orders, so-called echelle gratings can be used. Their groove density is low (a up to 1/100 mm) but therefore order numbers of up to 70 can be used [50]. Here, the orders overlap and must be separated by using a second dispersive element (e.g. a prism) either with its axis parallel to that of the echelle grating or in so-called crossed-dispersion mode. In the latter case, the spectrum occurs as a number of dots with a height equalling that of the entrance slit. 

The dispersive (+ n, - m ) mode has already been seen clearly with the duMond diagrams, Figure 2.10. Here, the curves are no longer identical and the crystals must be displaced from the parallel position in order to get simultaneous diffraction. As the crystals are displaced, so the band of intersection moves up and down the curve. When the curves become very different, the K 1 and K 2 intensities are traced out separately. Then the peaks are resolved in the rocking curve, and if no better beam conditioner is available it is important in such cases to remove the K 2 component with a slit placed after the beam conditioner. A slit placed in front of the detector, with the detector driven at twice the angular speed of the specimen, also works very well. This is in effect a low resolution triple-axis measurement. 

When k E O and x E = 0, there is a purely longitudinal S wave without a magnetic field. Thus x E = 0 and x C = 0 due to Eq. (48). The dispersion relation and the phase and group velocities are the same as (51) for the EM wave. The field vectors E and C are parallel with the wave normal. Possibly this mode may form a basis for telecommunication without induced magnetic fields. 

One can show, that in this case Ic is parallel to P, P, and also to w, i.e. this solution is the dispersion relation of the LO mode. It is remarkable that wL, which now turns out to be the frequency of the LO mode, does not depend on k. cjl has no dispersion in the center of BZ 1 and is always greater than oiT because e0 > e . Eq. (11.20) is called the Lyddane-Sachs-Teller relation. 

Foam films and a foam from the aqueous and organic phases of an extraction system containing a 30% solution of tri-buthyl phosphate (TBP) in kerosene and nitric acid (1 mol dm 3) have been studied in a parallel mode [137]. The reasons for foaming and the effect of emulsion formation on foam stability were elucidated. Thus, a foam with a measurable lifetime was obtained when TBP was in concentration of 0.8 mol dm 3 which corresponded to the concentration of black spot formation. When the volume ratio of the organic to the aqueous phase was 1 5, the foam formed in the system was stabilised additionally by a highly disperse O/W emulsion. This was due to the reduced rate of drainage. These results are confirmed by the experimental data acquired with a specially constructed centrifugal extractor [136]. It makes it possible to perform an extraction process under conditions close to those in industry. 

The best way to proceed is to choose a molecule reacting along two parallel paths and measure the selectivity defined as the ratio of rate of the two parallel reactions. If the two products come from different adsorbed states requiring different surface structures, a change of selectivity with dispersion or mode of preparation of the metal may be found. The most unequivocal case is when the specific activity for one of the parallel reactions changes from one catalyst to the next, while the specific activity for the other remains unchanged. 

Figure 9-19 Phonon dispersion relation (angular frequency vs. relative wave vector) for the three-stripe phase of CH4 on the external surface of a bundle. LI, L2, and L3 are longitudinal branches, i.e., molecular motion parallel to the groove. The dotted curve is the result for a ID adsorbate at the same density. The remaining curves correspond to the dispersion relation of transverse modes. (Adapted from Ref. [89].)...

Thus the cavity polariton dispersion has a simple interpretation. Let us calculate the electric fields from eqn (10.7) for the modes (10.16). Neglecting small terms of the order of q2 /n2, the fields Ei and Et are related in these modes by Ei = —Et cot (p. Then the y-component of the fields Eu,l is equal to zero. In other words, with accuracy up to small terms (of the order of q2 /k2) the total in-plane electric field in the polaritonic modes is parallel to the dipole moment Pi for any direction of the wavevector q, and the value of the Rabi splitting energy thus does not depend on the wavevector direction. 

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