Intensity of scattering

Consider a three-dimensional crystal. For the scattering amplitude of a discrete system of j atoms in an elementary cell we can write a formula simUar to (5.15)  

The differential intensity calculated in that way is related to a point in the diffraction pattern corresponding to wavevector q. Usually, all multipliers are excluded, although they can be taken into account when necessary (for example cos 2 9), and the scattering intensity 7(q) is expressed in relative, electron units  

The intensity can be found from the X-ray diffraction experiment and the result compared with calculated diffraction pattern that is angular spectrum of the scattered X-ray intensity. To this effect, we should make a Fourier transform F(q) of the density function p(r) i.e. find the scattering amplitude and then take square of it, 7(q) = IF (q)l. This works well for solid crystals, but is not always convenient for liquids, liquid crystals and other soft matter materials in which the thermal fluctuations play a very substantial role. In such cases, the so-called density autocorrelation function appears to be more convenient. However, before to proceed along that way, we should separate two sources of scattering. 

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It is well known that the intensity of scattered light varies as the fourth power of the frequency, and based on this alone one would predict the Stokes lines to be less intense than the anti-Stokes by a factor of... 

A method in which the intensity of scattered radiation is measured at an angle of 90° to the source. 

Determining Concentration by Nephelometry In nephelometry, the relationship between the intensity of scattered radiation, hy and the concentration (% w/v) of scattering particles is given as... 

Spectroscopic measurements may also involve the scattering of light by a particulate form of the analyte, fn turbidimetry, the decrease in the radiation s transmittance through the sample is measured and related to the analyte s concentration through Beer s law. fn nephelometry we measure the intensity of scattered radiation, which varies linearly with the analyte s concentration. 

Figure 4.7c illustrates how x-ray diffraction techniques can be applied to the problem of evaluating 6. If the intensity of scattered x-rays is monitored as a function of the angle of diffraction, a result like that shown in Fig. 4.7c is obtained. The sharp peak is associated with the crystalline diffraction, and the broad peak, with the amorphous contribution. If the area A under each of the peaks is measured, then... 

Zimmt has reported the intensity of scattered light at various angles of observation for polystyrene in toluene at a concentration of 2 X 10" ... 

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... 

Fig. 3-8. Relationship between intensity of scattered x-rays and thickness of an aluminum-foil support. The x-ray tube was operated at 50 kv and 50 ma. A lithium fluoride analyzing crystal was used at 20 — 25°. (Authors unpublished results.)...

Beams of electromagnetic radiation of appropriate wavelength ate scattered when they interact with the gradients inherent in stractuied materials. By measuring the ways in which the intensity of scattered radiation varies as a function of the angle at which the radiation initially strikes the sample, the wavelength of the radiation, and the time, many aspects of the stmcture of materials can be inferred. 

To calculate the intensity of scattered radiation along the direction P when the incident wave is unpolarized, let the incident wave of intensity lo be resolved into two components of equal intensity... 

The last factor is equal to 1+cos 0. The combined intensity of scattered light at a distance r and in a direction specified by 6 (Fig. 43) due to all particles in unit volume (N/V) of the very dilute solution becomes... 

The correlator (6) is of the utmost importance because its generating function enters into an expression which describes the angular dependence of intensity of scattering of light or neutrons [3]. It is natural to extend expression (6) for the two-point chemical correlation function by introducing the w-point correlator ya1... (kl...,kn l) which equals the joint probability of finding in a macromolecule n monomeric units Maj.Ma> divided by (n-1) arbitrary sequences... 

Ts = intensity of scattered light transmitted by the sample Tj = intensity of incident light... 

The intensity of scattering of light by a swollen network is related to two factors. One of these is the mean square fluctuation in refractive index which is proportional to the mean squared fluctuation in Mc, with a proportionality constant determined by the difference in refractive index between the rubber and the diluent. The second is the... 

For a vibration having a frequency v, the Stokes and anti-Stokes spectra correspond to bands at v0 — v and v0 + v. The spectra are usually presented as the intensity of scattered light vs. the shift, v0 — v, in cm 1. 

When the electric field strength of the incident light is ED, the induced dipole will be m, = aE0 where a is the optical polarisability. The electric field strength of radiation scattered by the induced dipole Es, depends on second derivative of m1 with respect to time. The useful experimental quantities are intensities of scattered light (Is) and incident important light (is). These are respectively proportional to Es2 and E02, averaged over a vibrational period, i.e., from time t = 0 to 10/C, where 1 is wavelength of... 

Photon correlation spectroscopy (PCS) has been used extensively for the sizing of submicrometer particles and is now the accepted technique in most sizing determinations. PCS is based on the Brownian motion that colloidal particles undergo, where they are in constant, random motion due to the bombardment of solvent (or gas) molecules surrounding them. The time dependence of the fluctuations in intensity of scattered light from particles undergoing Brownian motion is a function of the size of the particles. Smaller particles move more rapidly than larger ones and the amount of movement is defined by the diffusion coefficient or translational diffusion coefficient, which can be related to size by the Stokes-Einstein equation, as described by... 

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