Mosaic blocks

Fig. 4. Model of local plastic deformation of lamellae beneath the stress field of the indenter. The mosaic block structure introduces a weakness element allowing faster slip at block boundaries leading to fracture (right)...

This equation arises because both of these extrinsic defects affect the energy of the crystal. We can also have grain boundaries which may be clustering of line defects or mosaic blocks. The latter may be regarded as very large grains in a crystallite. 

This is the most useful quantitative intensity formula that may be derived from kinematical theory, since it is applicable to thin layers and mosaic blocks. We add up the scattering from each unit cell in the same way that we added up the scattering from each atom to obtain the stractme factor, or the scattering power of the unit cell. That is, we make allowance for the phase difference r, . Q between waves scattered from unit cells located at different vectors ri from the origin. Quantitatively, this results in an interference function J, describing the interference of waves scattered from all the unit cells in the crystal, where... 

Keywords Ni films, hydrogen permeation, microtensions, mosaic blocks, porosity, electrolyte temperature... 

Crystallite a small crystal where the only defect is the existence of the external surface. The lattice may be deemed to be distorted but it is not dislocated. Crystallites may further be associated into a mosaic block. 

Kinematical diffraction Diffraction theory in which it is assumed that the incident beam only undergoes simple diffraction on its passage through the crystal. No further diffraction occurs that would change the beam direction after the first diffraction event. This type of diffraction is assumed in most crystal structure determinations by X-ray diffraction. Kinematical theory is well applicable to highly imperfect crystals made up of small mosaic blocks. 

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. 

Diffraction by an ideal mosaic crystal is best described by a kinematical theory of diffraction, whereas diffraction by an ideal crystal is dynamical and can be described by a much more complex theory of dynamical diffraction. The latter is used in electron diffraction, where kinematical theory does not apply. X-ray diffraction by an ideal mosaic crystal is kinematical, and therefore, this relatively simple theory is used in this book. The word "mosaie" describes a crystal that consists of many small, ideally ordered blocks, which are slightly misaligned with respect to one another. "Ideal mosaic" means that all blocks have the same size and degree of misalignment with respect to other mosaic blocks. Most of this chapter is dedicated to conventional crystallographic symmetry, where three-dimensional periodicity is implicitly assumed. 

For a typical slit with / = 10 cm and s = 0.025 cm, a = 0.3°. But further divergence is produced by the mosaic structure of the analyzing crystal this divergence is related to the extent of disorientation of the mosaic blocks, and has a value of about 0.2° for the crystals normally used. The line width B is the sum of these two effects and is typically of the order of 0.5°. The line width can be decreased by increasing the degree of collimation, but the intensity will also be decreased. Conversely, if the problem at hand does not require fine resolution, a more open collimator is used in order to increase intensity. Normally, the collimation is designed to produce a line width of about 0.5°, which will provide adequate resolution for most work. 

The Aral Sea is positioned in the zone where geological structures of the Urals join those of Tien-Shan. The Aral depression is bordered on the west by Precambrian crystalline basement, and on the northeast - by the Central Kazakhstan massif [9]. Pre-Mesozoic rocks are highly metamorphosed, heavily distorted and broken by faults into mosaic block systems of varying altitudes. 

As a preface to a simple mathematical description of the model, let us review with a few equations the relation between the crystal structure and the diffraction experiment. The crystal structure is defined in terms of direct space, while the diffraction experiment is basically concerned with reciprocal space. In the equations below, applicable to a single tiny perfect crystallite (i.e., one mosaic block isolated from the real crystal), the equations concerned with direct space (for which the positional vector is r, expressed in Eq. (la) with base vectors a, b, c and... 

The intensity of diffraction by the single tiny crystallite depends on the square of the magnitude of Fxti, the Fourier transform of the crystallite density function pxti. This is shown schematically in Figure 2. The peak shape at each reciprocal lattice point depends on the square of the magnitude of T, the Fourier transform of the crystal shape function S. The width of the peak decreases, and the ratios of the heights of the ripples to that of the main peak also decrease, as the crystallite size increases. In the mosaic model of the real crystal the individual perfect crystallites scatter incoherently (i.e., with random phase) with respect to each other, and their intensities are additive owing to the tilts of the mosaic blocks with respect to one another, however, the maxima of the various blocks may appear at slightly different places so that the... 

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. 

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