Relative intensities 586 INDEX

In Raman spectroscopy the intensity of scattered radiation depends not only on the polarizability and concentration of the analyte molecules, but also on the optical properties of the sample and the adjustment of the instrument. Absolute Raman intensities are not, therefore, inherently a very accurate measure of concentration. These intensities are, of course, useful for quantification under well-defined experimental conditions and for well characterized samples otherwise relative intensities should be used instead. Raman bands of the major component, the solvent, or another component of known concentration can be used as internal standards. For isotropic phases, intensity ratios of Raman bands of the analyte and the reference compound depend linearly on the concentration ratio over a wide concentration range and are, therefore, very well-suited for quantification. Changes of temperature and the refractive index of the sample can, however, influence Raman intensities, and the band positions can be shifted by different solvation at higher concentrations or... 

Recent developments and prospects of these methods have been discussed in a chapter by Schneider et al. (2001). It was underlined that these methods are widely applied for the characterization of crystalline materials (phase identification, quantitative analysis, determination of structure imperfections, crystal structure determination and analysis of 3D microstructural properties). Phase identification was traditionally based on a comparison of observed data with interplanar spacings and relative intensities (d and T) listed for crystalline materials. More recent search-match procedures, based on digitized patterns, and Powder Diffraction File (International Centre for Diffraction Data, USA.) containing powder data for hundreds of thousands substances may result in a fast efficient qualitative analysis. The determination of the amounts of different phases present in a multi-component sample (quantitative analysis) is based on the so-called Rietveld method. Procedures for pattern indexing, structure solution and refinement of structure model are based on the same method. 

So far, we have seen that if we measure the Bragg angle of the reflections and successfully index them, then we get information on the size of the unit cell and, if it possesses any translational symmetry elements, also on the symmetry. In addition, we have seen that the intensity of each reflection is different and this too can be measured. In early photographic work, the relative intensities of the spots on the film were assessed by eye with reference to a standard, and later a scanning microdensitometer was used. In modern diffractometers, the beam is intercepted by a detector, either a charge coupled device (CCD) plate or a scintillation counter, and the intensity of each reflection is recorded electronically. 

The Collection is a source of reference patterns for pure crystalline phases. The data may be helpful in identifying known zeolitic materials and indexing their diffraction patterns. Because so many factors related to both the zeolite crystal and the diffraction instrument affect powder diffraction data, phase identification is not always straightforward and frequently requires additional data. Considerable care should be exercised in comparing calculated diffraction patterns to experimental patterns. For example, the use of fixed versus variable incident slits on a powder diffractometer can drastically change the relative intensities of a diffraction pattern, and it should be emphasized that calculated patterns are only as accurate as the structure refinements on which they are based. 

Consider first a series of eight views of the same data matrix for the intensity coefficient ii for a relative refractive index m of 1.200. Figures 1 through 8 represent different perspective viewpoints of the same three-dimensional matrix viewed from the front, right-hand side, back, etc., so as to reveal details of the simple behavior of complicated mathematical functions. 

The powder pattern of etodolac is shown in Figure 3, and a summary of the observed scattering angles, d-spacings, and relative intensities is shown in Table 1. Since the unit cell parameters of etodolac are known [9], it was possible to index the observed lines to the PbCa and these assignments are also found in Table 1. 

Examination of Eq. (6.21) shows that y(a>) is comprised of two terms that are proportional to c, 2 and that are associated with the traditional contribution to the susceptibility from state 11 ) and E2) independently, plus two field-dependent terms, proportional to a -j = c cje co /eia), which results front the coherent excitation of both II ) and E2) to the same total energy E = Ex + to) = E2+ to2. As a consequence, changing au alters the interference between excitation routes and allows for coherent control over the susceptibility. As in all bichromatic control scenarios, this control is achieved by altering the parameters in the state preparation in order to affect c1,c2 and/or by varying the relative intensities of the two laser fields. Note that control over y(ciy) is expected to be substantial if e(a>j)/e(cOj) is large. However, under these circumstances control over yfro,) is minimal since the corresponding interference term is proportional to e(a>t)/e(cQj). Hence, effective control over the refractive index is possible only at one of co( or >2. 

This is now the relative intensity of any reflected x-ray beam (A, k and l being the beam indices). Recalling that cos (rnr) may be either 1 or — 1, depending upon whether n is even or odd, it may be proved (Exercise 8) that only those reflections will show for which A, k, and l are all odd or all even. The value of /Cu diminishes as the beam indices increase thus, aside from the systematic absences mentioned, the beams of high index tend to be fainter than the beams of low index. 

Single Surfactant Systems. Relative intensity results for an equilibrium film of the block copolymer B1 in n-decane sandwiched between two water droplets at 25°C, are shown in Table II. The intensity was independent of the bulk polymer concentration within the accuracy of measurement. Assuming a constant film refractive index this implies that the film thickness is independent of surfactant concentration, and an average value of J was used for the calculation of film thickness. Coalescence occurs below a concentration of 0.1 g dm, presumably because there is insufficient... 

This procedure has been used to determine droplet size in sprays. Oseillations in the curve relating x and D can be smoothed out by the use of an incident laser beam having a broad speetral bandwidth [83]. An accumulation of independent scattering intensities from multiple scatterers ean be used to measure the mean droplet size of a group [84]. This procedure has been applied to water sprays and the experimental data confirmed by phase Doppler anemometry [85]. The applicability of the polarization ratio technique is strongly influenced by the complex refractive index of the dispersed media and is limited to media having a relative refractive index below about 1.44 [86]. 

After several tests, it is possible to estimate approximately the optimal relative intensities needed to obtain large photoinduced nonlinearities within relatively short preparation periods. The dependence of the generated SH signal is a function of the phase difference AO between the writing beams at CD and 2co frequencies. The relative phase difference AO can be varied by tilting a BK7 plate of known thickness and refractive index dispersion. ... 

Fig. 1. Powder x-ray profiles of solid Ceo at atmospheric pressure (top) and 1.2-GPa hydrostatic pressure (bottom). Dots are experimental points (approximately 70 per point), and the solid curves are least-squares fits to an fee structurewith adjustable lattice constant a. The fitted relative intensities have no physical significance in this simple model. The scattered wave vector Q = 4TTsin6/X, where 0 is the Bragg angle for these profiles wavelength = 0.71 A. Indexing of the strongest peaks is indicated. The high-Q shoulder on the (311) is the weak (222) reflection the low-Q shoulder on the (111), observed to some extent in all our nominally pure Cfio samples, is presently unidentified. The variable intensity of this shoulder has litde eflfect on the lattice constant of a particular sample, so we can safely conclude that it has no effect on the compressibility derived from the present data.

To save paper, we are here compressing notation to the vector forms for position x = x, y, z and indexes h = h,k t, and using Euler s form of the complex numbers. We will expand them back to their full forms later. Again, it is unnecessary to actually multiply by NP, which we do not even know, since it is a constant and doesn t change the relative intensities or phases of the structure factors. 

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