Scatter radiation

The correlation fiinction G(/) quantifies the density fluctuations in a fluid. Characteristically, density fluctuations scatter light (or any radiation, like neutrons, with which they can couple). Then, if a radiation of wavelength X is incident on the fluid, the intensity of radiation scattered through an angle 0 is proportional to the structure factor... 

It was predicted in 1923 by Smekal and shown experimentally in 1928 by Raman and Krishnan that a small amount of radiation scattered by a gas, liquid or solid is of increased or decreased wavelength (or wavenumber). This is called the Raman effect and the scattered radiation with decreased or increased wavenumber is referred to as Stokes or anti-Stokes Raman scattering, respectively. 

The reason why the spacings are equal, and not the 1-0, 2-1, 3-2,... anharmonic intervals, is explained in Figure 9.21. The laser radiation of wavenumber Vg takes benzene molecules into the virtual state Fj from which they may drop down to the v = level. The resulting Stokes scattering is, as mentioned above, extremely intense in the forward direction with about 50 per cent of the incident radiation scattered at a wavenumber of Vg — Vj. This radiation is sufficiently intense to take other molecules into the virtual state V2, resulting in intense scattering at Vg — 2vj, and so on. 

The existence of the amorphous phase of the fiber is confirmed in x-ray examination by the occurrence of a distinct intensity maximum of the radiation scattered diffusively at 2Q = 21.6 . The fraction of the amorphous phase in the fiber depends on manufacturing conditions and a possible further refining treatment. It is estimated to vary from 0.25 to 0.60. With an increase of the draw ratio and following the thermal treatment of the fiber, the proportion of the amorphous phase only reaches the lower values of this interval,... 

The Maxwell theory of X-ray scattering by stable systems, both solids and liquids, is described in many textbooks. A simple and compact presentation is given in Chapter 15 of Electrodynamics of Continuous Media [20]. The incident electric and magnetic X-ray helds are plane waves Ex(r, f) = Exo exp[i(q r — fixO] H(r, t) = H o exp[/(q r — fixO] with a spatially and temporally constant amplitude. The electric field Ex(r, t) induces a forced oscillation of the electrons in the body. They then act as elementary antennas emitting the scattered X-ray radiation. For many purposes, the electrons may be considered to be free. One then finds that the intensity /x(q) of the X-ray radiation scattered along the wavevector q is... 

This interaction leads to at least four (4) components, namely R- the radiation reflected, A- the radiation absoit>ed, T- the radiation transmitted, and S - the radiation scattered. A depiction of these interactions is given in the following diagram ... 

The turbidity may be obtained by integrating the total intensity of radiation scattered in all directions by the N/V particles per unit volume, i.e. 

Before scattering intensity measurements can be converted to molecular weights, the two corrections previously discussed—the dissymmetry correction for intraparticle interference and the extrapolation to zero concentration—must be introduced, or established to be negligible. The relationships given in the preceding sections unfortunately account rigorously for either only in the absence of the other. The theory of the concentration dependence of the scattered intensity applies to the turbidity corrected for dissymmetry, and the treatment of dissymmetry is strictly valid only at zero concentration (where interference of radiation scattered by different polymer molecules vanishes). 

Dave. J. W., "Subroutines for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere", IBM Report No. 320-3237, IBM Scientific Center, Palo Alto, California, 1968. 

RAT grinding operations. This surface layer was removed except for a remnant in a second grind. Spectra - both 14.4 keV and 6.4 keV - were obtained on the undisturbed surface, on the bmshed surface and after grinding. The sequence of spectra shows that nanophase Oxide (npOx) is eiu-iched in the surface layer, while olivine is depleted. This is also apparent from a comparison of 14.4 keV spectra and 6.4 keV spectra [332, 346, 347]. The thickness of this surface layer was determined by Monte-Carlo (MC)-Simulation to about 10 pm. Our Monte Carlo simulation program [346, 347] takes into account all kinds of absorption processes in the sample as well as secondary effects of radiation scattering. For the MC-simulation, a simple model of the mineralogical sample composition was used, based on normative calculations by McSween [355]. 

Equation (9.1) documents that quadmpole splittings A q exhibit quantum-beat spectra with period H/IuAEq superimposed over the time dependence of the nuclear decay exp(—f/t) with mean decay time t = 141 ns for Fe. In Fig. 9.2, quadmpole splittings A q = 0 and 2 mm s in the energy domain (conventional MS) are compared with those in the time domain (MS using synchrotron radiation) [7]. The QBs in the time domain spectmm for A q = 2 mm s are the result of the interference between the radiation scattered by different nuclear resonances. Consequently, their frequencies correspond to the energetic differences between these resonances. 

Radiation, Scattered—Radiation which during its passage through a substance, has been deviated in direction. It may also have been modified by a decrease in energy. 

The architecture of macromolecules is another important synthetic variable. New materials with controlled branching sequences or stereoregularity provide tremendous opportunity for development. New polymerization catalysts and initiators for controlled free-radical polymerization are driving many new materials design, synthesis, and production capabilities. Combined with state-of-the-art characterization by probe microscopy, radiation scattering, and spectroscopy, the field of polymer science is poised for explosive development of novel and important materials. New classes of nonlinear structured polymeric materials have been invented, such as dendrimers. These structures have regularly spaced branch points beginning from a central point—like branches from a tree trunk. New struc-... 

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... 

For an assembly of several free point electrons, interference occurs between radiation scattered by different centers. If the incident and diffracted beams are defined by two unit vectors, s0 and s, respectively (Fig. 1.1), the phase difference of the radiation scattered by two points, separated by the vector r, equals 27tS-r, where S is the scattering vector, equal to (s — s0)/A. Vector S bisects s and s0, and has the length 2 sin 0/X. In the physics literature, an alternative notion is commonly used. The incident and diffracted beams are defined by the vectors k... 

As emphasized earlier, the weakness of the difference intensity is a specific difficulty with this sort of experiment. The ratio between the difference and the full scattering intensity is on the order of 10 -10 This is particularly problematic in solution work, where the radiation scattered by the solute is buried in that from the solvent. A further complication arises from the interference between X-ray and optical manipulations. In fact, the intensity of... 

One can thus estimate the total light intensity incident on a given volume of air in the troposphere due to direct solar radiation, scattering, and reflection. The light absorbed in that volume can then be calculated... 

These sources are direction radiation from the sun, radiation scattered by gases and particles, and radiation reflected from the earth s surface. 

In this section, we present a few examples of instruments available for visual observation and imaging of colloids and surfaces, for measurement of sizes and for surface force measurements. Such a presentation can hardly be comprehensive in fact, that is not our purpose here. Throughout the book, we discuss numerous other techniques such as osmotic pressure measurements, light and other radiation scattering techniques, surface tension measurements,... 

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