Coherent scatter

Let us take two polymers (one deuterated and one hydrogenated) and dissolve them in a solvent (or another polymer) having a scattering length b. The coherent scattered intensity can be derived from (B 1.9.117), which gives... 

X-ray diffraction consists of the measurement of the coherent scattering of x-rays (phenomenon 4 above). X-ray diffraction is used to determine the identity of crystalline phases in a multiphase powder sample and the atomic and molecular stmctures of single crystals. It can also be used to determine stmctural details of polymers, fibers, thin films, and amorphous soflds and to study stress, texture, and particle size. 

Interference of Waves. The coherent scattering property of x-rays is used in x-ray diffraction appHcations. Two waves traveling in the same direction with identical wavelengths, X, and equal ampHtudes (the intensity of a wave is equal to the square of its ampHtude) can interfere with each other so that the resultant wave can have anywhere from zero ampHtude to two times the ampHtude of one of the initial waves. This principle is illustrated in Figure 1. The resultant ampHtude is a function of the phase difference between the two initial waves. 

THE USE OF INTENSITY OF COHERENT AND NON-COHERENT SCATTERED RADIATION OF THE X-RAY TUBE FOR THE COMPENSATION OF MATRIX EFFECTS AT THE ANALYSIS OF SOLUTIONS BY X-RAY FLUORESCENCE... 

For water, organic and water-organic metal salts mixtures the dependence of integral and spectral intensities of coherent and non-coherent scattered radiation on the atomic number (Z), density, oscillator layer thickness, chemical composition, and the conditions of the registering of analytical signals (voltage and tube current, tube anode material, crystal-analyzer) was investigated. The dependence obtained was compared to that for the solid probes (metals, alloys, pressed powder probes). 

As a result we propose the technique of Mo, W, and Re determination in production cycle solutions with the use of peak of non-coherent scattered primary radiation in order to take into account the matrix influence on the analytical signal. The accuracy of the results was checked by the input-found technique. 

In conclusion we propose ASR as an efficient computational scheme to study electronic structure of random alloys which allows us to take into account the coherent scattering from more than one site. Consequently ASR can treat effects such as SRO and essential off-diagonal disorder due to lattice distortion arising out of size mismatch of the constituents. 

NES is an elastic and coherent scattering process, i.e., it takes place without energy transfer to electronic or vibronic states and is delocalized over many nuclei. Owing to the temporal and spatial coherence of the radiation field in the sample. 

The spin state of a paramagnetic system with total spin S wiU lift its (25 + l)-fold degeneracy under the influence of ligand fields (zero-field interaction) and applied fields (Zeeman interaction). The magnetic hyperfine field sensed by the iron nuclei is different for the 25 + 1 spin states in magnitude and direction. Therefore, the absorption pattern of a particular iron nucleus for the incoming synchrotron radiation and consequently, the coherently scattered forward radiation depends on how the electronic states are occupied at a certain temperature. 

The bond fluctuation model not only provides a good description of the diffusion of polymer chains as a whole, but also the internal dynamics of chains on length scales in between the coil size and the length of effective bonds. This is seen from an analysis of the normalized intermediate coherent scattering function S(q,t)/S(q,0) of single chains ... 

Projectors often arise in attempts to describe experiments within the structure of Quantum Mechanics. For example, in the case of the coherent scattering of X-rays by crystals the ideal measured intensities are given by the square of the structure factors... 

The prerequisite for an experimental test of a molecular model by quasi-elastic neutron scattering is the calculation of the dynamic structure factors resulting from it. As outlined in Section 2 two different correlation functions may be determined by means of neutron scattering. In the case of coherent scattering, all partial waves emanating from different scattering centers are capable of interference the Fourier transform of the pair-correlation function is measured Eq. (4a). In contrast, incoherent scattering, where the interferences from partial waves of different scatterers are destructive, measures the self-correlation function [Eq. (4b)]. 

In the case of coherent scattering, which observes the pair-correlation function, interference from scattering waves emanating from various segments complicates the scattering function. Here, we shall explicitly calculate S(Q,t) for the Rouse model for the limiting cases (1) QRe -4 1 and (2) QRe > 1 where R2 = /2N is the end-to-end distance of the polymer chain. 

From Fig. 35, where the normalized coherent scattering laws S(Q, t)/S(Q,0) are plotted as a function of 2 (Q)t for Zimm as well as for Rouse relaxation, one sees that hydrodynamic interaction results in a much faster decay of the dynamic structure factor. 

Using the random phase approximation (RPA), the coherent scattering intensity Icoh(Q, t) of a polymer blend/solvent or a diblock copolymer/solvent system can... 

The scattering of neutrons by any molecular system can be elastic or inelastic, coherent or incoherent. The elastic coherent scattering of a labeled polymer in a background matrix can be extracted from the data in a properly designed experiment. 

The Fourier transform of this quantity, the dynamic structure factor S(q, ffi), is measured directly by experiment. The structural relaxation time, or a-relaxation time, of a liquid is generally defined as the time required for the intermediate coherent scattering function at the momentum transfer of the amorphous halo to decay to about 30% i.e., S( ah,xa) = 0.3. 

Figure 12 Test of the factorization theorem of MCT for the intermediate coherent scattering function for the bead-spring model and a range of -values indicated in the Figure. Data taken from Ref. 132 with permission.

Structural relaxation in glass-forming polymers has been studied for many years using chemically realistic simulations. Most of the early work that examined incoherent, as well as coherent scattering functions, is more of a qualitative nature because of the unsatisfactory quality of the force fields employed and the severe limitations on the length of the MD simulations performed. Roe studied the slowdown of structural relaxation in a PE-like model140,141 as well as for polystyrene.142 More recently Okada et al.143,144... 

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