Dynamical scattering

RHEED intensities cannot be explained using the kinematic theory. Dynamical scattering models of RHEED intensities are being developed. With them one will be able to obtain positions of the surface atoms within the surface unit cell. At this writing, such modeling has been done primarily for LEED. 

Thermotropic cholesterics have several practical applications, some of which are very widespread. Most of the liquid crystal displays produced use either the twisted nematic (see Figure 7.3) or the supertwisted nematic electrooptical effects.6 The liquid crystal materials used in these cells contain a chiral component (effectively a cholesteric phase) which determines the twisting direction. Cholesteric LCs can also be used for storage displays utilizing the dynamic scattering mode.7 Short-pitch cholesterics with temperature-dependent selective reflection in the visible region show different colors at different temperatures and are used for popular digital thermometers.8... 

Dynamic recovery, 2 330 Dynamic reversibility of noncovalent interactions, 24 61 Dynamic scattering device, 15 115 Dynamic sealing, for pumps, 21 81-82 Dynamic SIMS method, 24 107-108 Dynamic uncertainties, 26 1019, 1021-1023... 

The decay of the structural correlations measured by the static structure factor can be studied by dynamic scattering techniques. From the simulations, the decay of structural correlations is determined most directly by calculating the coherent intermediate scattering function, which differs from Eq. [1] by a time shift in one of the particle positions as defined in Eq. [2] ... 

The method of strueture analysis developed by the Soviet group was based on the kinematieal approximation that ED intensity is directly related (proportional) to the square of structure factor amplitudes. The same method had also been applied by Cowley in Melbourne for solving a few structures. In 1957 Cowley and Moodie introdueed the -beam dynamical diffraction theory to the seattering of eleetrons by atoms and crystals. This theory provided the basis of multi-sliee ealeulations whieh enabled the simulation of dynamieal intensities of eleetron diffraetion patterns, and later electron microscope images. The theory showed that if dynamical scattering is signifieant, intensities of eleetron diffraetion are usually not related to strueture faetors in a simple way. Sinee that day, the fear of dynamical effects has hampered efforts to analyze struetures by eleetron diffraction. 

Structure refinement based on dynamical scattering was developed by Zandbergen and Jansen (Zandbergen et al, 1997 Jansen et al, 1998), known as the MSLS software. Electron diffraction from crystal regions with relatively homogenous thicknesses was used. Both the crystal orientation, crystal thickness and the atomic coordinates could be refined simultaneously. 

The most important question for the calculation of the structure amplitudes from the intensities is that for the validity of the kinematical approximation. Due to the strong interaction of fast electrons with matter the effects of dynamical scattering become more pronounced with increasing size of the microcrystallites in the film. In order to justify application of the kinematical equations it is necessary that the diffracted intensity is much less... 

Electron dynamic scattering must be considered for the interpretation of experimental diffraction intensities because of the strong electron interaction with matter for a crystal of more than 10 nm thick. For a perfect crystal with a relatively small unit cell, the Bloch wave method is the preferred way to calculate dynamic electron diffraction intensities and exit-wave functions because of its flexibility and accuracy. The multi-slice method or other similar methods are best in case of diffraction from crystals containing defects. A recent description of the multislice method can be found in [8]. 

Large differences between experiment and theory are often the indication of systematic errors, such, deficiency in theoretical model (as in the case kinematics approximation for dynamically scattered electrons) an measurement artifacts (such as uncorrected distortions). 

These uncertain atoms remain to be verified by a careful structure refinement. For a structure refinement, as many reflections as possible should be included. The phases are not needed at the refinement stage, but if possible complete 3D data out to 1 A resolution should be used. Strong and weak reflections are equally important. Such data can be obtained by electron diffraction, which is not affected by the contrast transfer function of the electron microscope, but suffers from dynamical scattering. The higher the accuracy of the amplitudes, the more accurate will the atomic positions become. 

One of the advantages of dynamical scattering we have already seen. It is rather easy to determine the positions of Ce, Cu and P without prior knowledge on them. A similar example is a ZnCuAl-alloy of which to crystal structures were proposed, of which the occupancies of the positions were the only differences. MSLS was able to give an answer which of the two was the one in the sample [7]. 

According to Ref. [11], the dynamical scattering effect was reduced by forcing the integral amplitudes of reflections to be equal to the corresponding structure factor amplitudes of the corresponding perfect... 

It has been demonstrated that the dynamical scattering effect correction technique is also effective in image deconvolution for restoring the atomic configuration for crystals with interface when the elliptical windows are applied. The technique is essential in improving the quality of deconvoluted images so that the available crystal thickness extends to 10 nm or even bigger for Si. 

Z.G.PINSKER Dynamical scattering of X-rays in crystals (Springer, Berlin, 1977). 

Z.G.PINSKER, Dynamical scattering of X-rays (Springer-Verlag, Berlin, 1978). 

The scattering from a distorted surface region is no longer governed by the dynamical scattering in the bulk of the crystal. In the bulk, due to multiple scattering processes, the refractive index is not quite unity and the result is that... 

A variant of the zero average contrast method has been applied on a solution of a symmetric diblock copolymer of dPS and hPS in benzene [331]. The dynamic scattering of multicomponent solutions in the framework of the RPA approximation [324] yields the sum of two decay modes, which are represented by exponentials valid in the short time limit. For a symmetric diblock the results for the observable scattering intensity yields conditions for the cancellation of either of these modes. In particular the zero average contrast condition, i.e. a solvent scattering length density that equals the average of both... 

MSA. Static and dynamic scattering are reported on a nematic phase with a smooth texture, and the... 

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