Scattering peaks

The classical counterpart of resonances is periodic orbits [91, 95, 96, 97 and 98]. For example, a purely classical study of the H+H2 collinear potential surface reveals that near the transition state for the H+H2 H2+H reaction there are several trajectories (in R and r) that are periodic. These trajectories are not stable but they nevertheless affect strongly tire quantum dynamics. A study of tlie resonances in H+H2 scattering as well as many other triatomic systems (see, e.g., [99]) reveals that the scattering peaks are closely related to tlie frequencies of the periodic orbits and the resonance wavefiinctions are large in the regions of space where the periodic orbits reside. 

M. Teubner, R. Strey. Origin of the scattering peak in microemulsion. J Chem Phys 57 3195-3200, 1987. 

N2 adsorption-desorption isotherms revealed that MCs had hi surface area (>1200 m /g) and large pore volume (>1.0 cm /g). From SAXS patterns of the prepared materials, it was confirmed that pores of SBA-15 and CMK-3 retained highly ordered 2-dimensional hexagonal type arrangement [5], while MCM-48 had 3-dimensional cubic type pore structure. It should be noted that a new scattering peak of (110) appeared in the CMK-1 after the removal of MCM-48 template. Furthermore, the pore size of CMK-1 and the wall thickness of MCM-48 were found to be 2.4 nm and 1.3 nm, respectively. This result demonstrates that a systematic transformation of pore structure occurred during the replication process from MCM-48 to CMK-1 [6]. 

To quantify this result, the structure factor S(q, t) at time t and the initial structure factor S(qy 0) were computed. As seen in experiments, a scattering peak at qmax was observed. In these simulations, qmdLX was found to corres-... 

The Landau-Ginzburg model of a ternary mixture of oil, water, and surfactant studied here was proposed by Teubner and Strey [115] on the basis of the scattering peak in the microemulsion phase. Later it was refined by Gompper and Schick [116]. Its application to various bulk and surface phenomena is described in detail in Ref. 117. 

It is usually convenient to identify the angles of the 10 most intense scattering peaks in a powder pattern, and to then list the accepted tolerance ranges of these based on the diffractometer used for the determinations. Such a representation has been developed for data obtained for racemic mandelic acid, and for its separated (S)-enantiomer, using a diffractometer system whose precision was known to be +0.15 degrees 26 [30]. The criteria are shown in Table 7.9, the form of which enables the ready identification of a mandelic acid sample as being either racemic or enantiomerically pure. It should be noted that the powder pattern of the separated (i )-enantiomer would necessarily have to be identical to that of the separated (S)-enantiomer. 

Lower limit of acceptability for scattering peak (degrees 20) Accepted angle for scattering peak (degrees 20) Upper limit of acceptability for scattering peak (degrees 20)... 

XRPD can be similarly used to differentiate between the members of a solvatomorphic system. For instance, Fig. 7.12 shows the powder patterns obtained for the anhydrate and monohydrate phases of lactose. The existence of structural similarities in the two forms are suggested in that the main scattering peaks of each form are clustered near 20 degrees 26, but the two solvatomorphs are easily differentiated from an inspection of the patterns. The differentiation could also be rendered more quantitative through the development of a table similar to that developed for the mandelic acid system. 

TXRF was used to characterize high-viscosity polymer dispersions [83], with special attention being paid to the different drying techniques and their effect on the uniformity of the deposited films. TXRF was also used as a means to classify different polymers on the basis of their incoherently scattered peaks [84], Dispersive XRF has been used to assess the level of aluminum in antacid tablets [85]. 

Thus, the application of the Bragg s equation to the scattering peak at20 = 18 and applying a correction of 20% yields an interchain distance ca 6A. As a function of the degree of sulpho-nation and relative humidity, this distance appears to be constant. 

Table 12.1—Position of the Raman scattering peak, calculated for four commonly used solvents and five excitation wavelengths from a mercury lamp.

Fig. 30. Quasielastic broadening of the neutron scattering peak observed in the paraelectric phase for the copolymer 60/40. The points represented the experimental results with their statistical error bar. The solid line is the Lorentzian function obtained after the deconvolution process described in the text...

Since protein emission spectra are generally rather broad, larger emission bandwidths can usually be tolerated. Only where it is important to resolve tyrosine fluorescence from tryptophan fluorescence and the Rayleigh scattering peak is it necessary to minimize the bandwidth. In cases where only low concentrations of material are available, it is necessary to strike a balance between resolution and light intensity in order to obtain the best possible signal-to-noise ratio. Settings of 2.5 to 10 nm are normal. 

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