Scattering angle 470 INDEX

It should be noted that low-loss spectra are basically connected to optical properties of materials. This is because for small scattering angles the energy-differential cross-section dfj/dF, in other words the intensity of the EEL spectrum measured, is directly proportional to Im -l/ (E,q) [2.171]. Here e = ei + iez is the complex dielectric function, E the energy loss, and q the momentum vector. Owing to the comparison to optics (jqj = 0) the above quoted proportionality is fulfilled if the spectrum has been recorded with a reasonably small collection aperture. When Im -l/ is gathered its real part can be determined, by the Kramers-Kronig transformation, and subsequently such optical quantities as refraction index, absorption coefficient, and reflectivity. 

A relative crystallinity or "crystallinity index" has been used as an approximate method [55,56]. The simplest procedure involves determination of the intensity at a single scattering angle (26), in reference to the value for the amorphous halo at the same angular reflection. This method, for example, was useful to follow the variation of crystallinity of an iPP during isothermal melting [57]. 

Fig. 6. Lower part angular dependence of the non-normalized static scattering intensity I(q) observerd with latex particles (R=265 nm). Upper part dependence of r/q =D on the scattering angle in dynamic LS. The sharp downturn at large scattering angles results from a weak back reflection of light on the boundary of the aqueous solution to the index matching bath, that consisted of toluene. This reflection results from the difference in the refractive indices of water (n = 1.333) and toluene (n =1.51). Reprinted with permission from [182]. Copyright [1982] American Society...

Here is the in vacuo laser wavelength, n the refractive index in the scattering medium and 0 the scattering angle measured within The brackets indicate the average over all r in the... 

Figure 10.18 Dynamic light scattering (DLS) of vesicle mixtures, (a) P-index phase diagram and (b) size distributions (from DLS) for DDAB-oleate mixtures, total concentration 1 mM in 0.2 M borate buffer at pH 8.5, 25.0 °C, scattering angle 90°. (From Thomas and Luisi, 2004.)...

The independent variable s = sind 6, where X is the electron wavelength and 20 the scattering angle. The summation indices i and j refer to each of the M atoms in the molecule. The index pair k and 1 refers to a representative atom pair of the molecule studied, chosen to obtain a convenient form for I(s) and its Fourier transformed partner. fj(s) is the complex scattering amplitude of the i-th atom in the molecule and rji(s) is the argument of fj(s), /. e. 

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. 

Figure 5. Scattering intensity per unit mass of particles as a function of particle diameter for a system in which the wavelength of the incident light is 632.8 nm, the scattering angle is 90°, the particle refractive index is 1.59, and the medium refractive index is 1.33 (for example polystyrene spheres in water).

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