Crystal reflection

A similar effect occurs in highly chiral nematic Hquid crystals. In a narrow temperature range (seldom wider than 1°C) between the chiral nematic phase and the isotropic Hquid phase, up to three phases are stable in which a cubic lattice of defects (where the director is not defined) exist in a compHcated, orientationaHy ordered twisted stmcture (11). Again, the introduction of these defects allows the bulk of the Hquid crystal to adopt a chiral stmcture which is energetically more favorable than both the chiral nematic and isotropic phases. The distance between defects is hundreds of nanometers, so these phases reflect light just as crystals reflect x-rays. They are called the blue phases because the first phases of this type observed reflected light in the blue part of the spectmm. The arrangement of defects possesses body-centered cubic symmetry for one blue phase, simple cubic symmetry for another blue phase, and seems to be amorphous for a third blue phase. 

Crystal broadening of monochromatic beams, 115, 116, 118 Crystal reflection of x-rays, efficiency, 116... 

The diffraction pattern of the sample of chlorine hydrate consisted of powder lines on which were superimposed a large number of more intense single-crystal reflections for some planes only the latter were visible. The intensities of the lines were estimated by comparison with a previously calibrated powder photograph, and were averaged for several films pre-... 

An X-ray powder photograph taken with a focusing camera and X rays monochromatized by crystal reflection would probably show more than 100 powder lines, providing a more rigorous text of the proposed structure. Accurate values of predicted intensities of the lines will become available only after coordinates have been assigned to all of the atoms, a formidable task with such a complicated structure. This task is now being attempted (S. Samson, personal communication). 

Translation, i.e.- from one plane to another Rotation about an axis of the crystal Reflection across a plane Inversion through a point... 

Fig. 3.1-12. Single crystal reflectivities R of the alkali metals Rb, Cs and some of their suboxides (points) together with the Drude-Lorentz fits (lines).

The glass transition temperature of amorphous PET is in the range of 65-75 °C, and this can increase to 125 C after being drawn and partially crystallized, reflecting the reduced rotational mobility of the chain segments. The crystallite... 

With the right sample, it is even possible to solve structures from electron powder data. Weirich et al. [18] have collected such data on anastase (Ti02) to get a data set comprising 20 unique reflections which also solved with SIR97 by using the data as single crystal reflections. 

If the second crystal is the specimen rather than a beam conditioner element, we shall have got close to the aim of measiuing the plane wave reflectivity of a material. The narrow rocking curve peaks permit us to separate closely matched layer and substrate reflections and complex interference details, as already seen in Figure 1.6. The sensitivity limit depends on the thickness of the layer but for a 1 micrometre layer it is about 50 ppm in the 004 symmetric geometry with GaAs and CuK radiation. This method has been used extensively to study narrow crystal reflections since the invention of the technique. 

As has already been emphasised, it is very difficult to approach a plane wave with the laboratory sources, which are properly described as spherical-wave sources. A single-crystal reflectivity profile from such a source will be dominated by the source profile rather than by the above formulae the integrated intensity expressions will be multiplied by the source profile function. 

The width of the image can be deduced using this simple idea of contrast being formed when the misorientation around the defect exceeds the perfect crystal reflecting range. We consider the case of a screw dislocation nmning normal to the Bragg planes, where the line direction / coincides with the diffraction vector g. The effective misorientation at distance r from the core is =bH r (8.41)... 

Estimation of diffusion distance or diffusion time is one of the most common applications of diffusion. For example, if the diffusion distance of a species (such as °Ar in hornblende or Pb in monazite) is negligible compared to the size of a crystal, it would mean that diffusive loss or gain of the species is negligible and the isotopic age of the crystal reflects the formation age. Otherwise, the calculated age from parent and daughter nuclide concentrations would be an apparent age, which is not the formation age, but is defined as the closure age. This has important implications in geochronology. Another example is to evaluate whether equilibrium between two mineral phases (or mineral and melt) is reached if the diffusion distances in the two phases are larger than the size of the respective phases, then equilibrium is likely reached. 

The optical properties of amorphous solids are interesting. These solids are optically isotropic. Furthermore, the sharp features present in crystal spectra are absent in the spectra of amorphous solids even at low temperatures. The overall features in the electronic spectra of amorphous solids (broad band maxima) are, however, not unlike those of crystals, reflecting the importance of short-range order in determining these characteristics. The optical absorption edges of amorphous materials are not sharp and there is an exponential tail in the absorption coefficient (Fig. 7.13) associated with the intrinsic disorder. 

Diffractometers have been designed for completely automatic operation (Bond, 1955 Benedict, 1955 Furnas and Harker, 1955). The most accurate measurements of single crystal reflections are obtained in this way. 

The intensities of crystal reflections are in some circumstances reduced by effects known as primary and secondary extinction. If the crystal is not ideally imperfect but consists of rather large lattice blocks, the intensities of the reflections are proportional to a power of F between 1 and 2 this is primary extinction . Secondary extinction affects only the strongest reflections and is due to the fact that the top layer of a crystal (the part nearest the primary beam) reflects away an appreciable proportion of the primary beam, thus in effect partially shielding the lower layers of the crystal the strongest reflections are therefore experimentally less strong than they should be in comparison with the weaker reflections. The relation between the actual intensity p and the intensity p which would be obtained if there were no secondary extinction is, for reflection at a large face,... 

Both primary and secondary extinction effects may usually be avoided by powrdering a crystal. For this and other reasons the intensities of the arcs on powder photographs are likely to be more reliable than those of other types of photograph but in practice, in structure determination it is only possible to use powder intensities alone for very simple structures for complex crystals reflections from different planes overlap seriously. 

One way of solving the structure of a crystal composed of molecules of known configuration, one to the unit cell, is to calculate the molecular transform and then to consider what orientation of the transform with respect to the reciprocal lattice gives correct structure amplitudes at the reciprocal lattice points. One of the limitations of this method is that the calculation of transforms in sufficient detail to be useful is very laborious. The amplitude O of the transform is given by essentially the same expression as that for the structure amplitude F of a crystal reflection ... 

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