Extinction mosaic

Fig. 8a-c. r rotation photographs of H. marismortui SOS crystals at 0 "C and at cryotemperature (obtained at XI1/EMBL/DESY and at SSRL/Stanford U.) a The hkO-orientation of a nearly perfectly aligned (although split) crystal reveals the mirror symmetry of the C-centred lattice plane. The severe overlap problem in this orientation caused by the large mosaic spread is obvious from this picture, b The Okl-orientation shows the extinctions of the twofold screw axis, c The best crystals have a Bragg resolution limit of about 6 A, which decreases to about 9 A in the course of a hundred exposures... 

Each sphere has a lamellar structure and a single preferred orientation but shows systematic variations in the optical extinction patterns, which indicate some variation from a strictly lamellar arrangement this is most noticeable at the poles of spheres. As they grow and meet obstructions to their enlargement in particular directions, their extinction behavior becomes increasingly complex, especially when the pitch nears solidification and the complete mosaic structure is formed. 

S4 Moderately shocked Weak mosaicism, planar fractures Undulutory extinction, partially isotropic, planar deformation features 30-35... 

Extinction An effect of dynamical diffraction whereby the incident beam is weakened as it passes through the crystal. If the crystal is perfect there may be multiple reflection of the incident beam, which then is out of phase with the main beam and therefore reduces its intensity (primary extinction). If the crystal is mosaic, one block may diffract the beam, and is not then available to a second block similarly aligned (secondary extinction). Both effects result in a diminution of the intensities so that the most intense Bragg reflections are systematically smaller than those calculated from the crystal structure. The effect can be reduced by dipping the crystal in liquid nitrogen, thereby increaising its mosaicity. 

Mosaic blocks (mosaic spread) Tiny blocks within a crystal structure that are slightly misoriented with respect to each other. As a result of such mosaic spread, Bragg reflections have a finite width. Extinction is weaker in a mosaic crystal than in a perfect crystal, and therefore the intensities can be predicted by the rules of kinematical diffraction. 

Extinction effects, which are dynamical in nature, may be noticeable in diffraction from nearly perfect and/or large mosaic crystals. Two types of extinction are generally recognized primary, which occurs within the same crystallite, and secondary, which originates from multiple crystallites. Primary extinction is caused by back-reflection of the scattered wave into the crystal and it decreases the measured scattered intensity Figure 2.51, left). Furthermore, the re-reflected wave is usually out of phase with the incident wave and thus, the intensity of the latter is lowered due to destructive interference. Therefore, primary extinction lowers the observed intensity of very strong reflections from perfect crystals. Especially in powder diffraction, primary extinction effects are often smaller than experimental errors however, when necessary they may be included in Eq. 2.65 as ... 

Figure 2.51. The illustration of primary (left) and secondary (right) extinction effects, which reduce intensity of strong reflections from perfect crystals and ideally mosaic crystals, respectively. The solid lines indicate actual reflections paths. The dashed lines indicate the expected paths, which are partially suppressed by dynamical effects. The shaded rectangles on the right indicate two different blocks of mosaic with identical orientations.

Secondary extinction Figure 2.51, right) occurs in a mosaic crystal when the beam, reflected from a crystallite, is re-reflected by a different block of the mosaic, which happens to be in the diffracting position with respect to the scattered beam. This dynamical effect is observed in relatively large, nearly perfect mosaic crystals it reduces measured intensities of strong Bragg reflections, similar to the primary extinction. It is not detected in diffraction from polycrystalline materials and therefore, is always neglected. 

These different contrast mechanisms can all be used to reveal the scale of liquid crystalline polymer microstructures. In specimens that exhibit a mosaic texture, and in those that contain predominantly planar defects, domain size is easily defined in terms of areas that uniformly show extinction between crossed polars. However, if the defects are predominantly linear, as in specimens that exhibit schlieren textures, such simple characterization of microstructural scale is no longer possible. Here it is more convenient to look at the length of disclination line per unit volume, which is equivalent to the number of lines intersecting unit area, and analogous to the dislocation density as defined for crystalline solids. Good contrast is essential in order to obtain an accurate count. Technologically, microstructural scale is of growing interest because of its relevance to processability, mechanical properties and optical transparency. 

Absorption means diminution of coherent x-ray intensity in the crystal through inelastic processes such as atomic absorption and fluorescence, photoelectron emission, and Compton effect extinction means intensity diminution due to loss through diffraction by fortuitously oriented mosaic blocks. The simple extinction expression due to Darwin, given in Eq. (18), is only a rough approximation more accurate treatments will be mentioned in what follows. In Eq. (17) the absorption factor is expressed in terms of the linear absorption coefficient /inn (calculated from tabulated values of the elemental atomic or mass absorption coefficients, updated values of which will appear in Vol. IV of International Tables,2 the path length f, of the incident ray from the crystal surface to the point of diffraction r, and the path length t2 of the diffracted ray from that point to the crystal surface. 

Figure 20. Cross section showing dis- Figure 21. Pinhole pores in an extinct layers of sulfur with a feathered terior surface with mosaic texture edge...

At faster rates, the previously reported aL-mosaic formed. Figure 3 shows a field with both forms cocrystallized. The a L-mosaic and airspherulite were identical in DTA and DLI behavior to the solvent-recrystallized crystals. Figure 4 shows the transformation of aL-spherulites into dull ft l-spherulites. On further heating, the (3l phase forms and the crystals brighten somewhat. The extinctions of these crystals correspond to those... 

From the model for takii account of the secondary extinction of mosaic crystals [7], it can be established that the reflection intensity from a crystal exhibiting both primary and secondary extinctions is determined by the following relationship ... 

L is the average size of the mosaic blocks ]/ 2n(p is the average angle of disorientation of the blocks Q <=/Q is the reflectivity of the crystal when account is taken of primary extinction. 

The maximum reflection intensity for a given focus width will be higher, the greater the reflectivity of the crystal. This means that Q should be equal to Q, the reflectivity of an ideally mosaic crystal. Consequently, to obtain the greatest intensity Im, crystals must be selected which have no appreciable primary extinction, i.e., the size of the mosaic blocks should not exceed 10" cm. Crystals with relatively high dislocation densities satisfy this condition. 

By studying paramorphotic patterns and the way that they appear in focal-conics, phase identification can be accomplished and information on mesophase structure can be obtained. However, the problems of phase identification are greatly cased when the focal-conic texture is accompanied by a homeotropically oriented texture. For example, the smectic A phase can exhibit the unbroken focal-conic and optically extinct homeotropic textures together, whereas the smectic C phase exhibits broken focal-conic and schlieren textures, and the E phase exhibits banded focal-conic and mosaic textures. Thus, the... 

Mosaics can be observed for a number of phases, for example, smectics F and hexatic B, and crystals B, E, G, J, K, and H, all exhibit mosaics of one form or another (see Figure 10). It is very difficult to identify these phases from their mosaic textures as they all look very similar. Two exceptions are worthy of note the E phase, because it is biaxial, has a very characteristic mosaic pattern where the domains tend to overlap to give a ghost-like appearance and the B phases, where the mosaic texture is often accompanied by a homeotropic texture that remains optically extinct on rotation of the microscope stage. Figure 11 shows a variety of mosaic textures where the molecules are either tilted or perpendicular with respect to the layer planes. 

E is the extinction coefficient. It depends on the mosaic structure of the crystal and has two components. The secondary extinction (the most important) takes into account that a fraction of the incident beam is reflected by the planes. The primary extinction takes into account the loss of intensity due to multiple reflections from different lattice planes. 

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