Crystal imperfections mosaic

In order for the dynamical theory of X-ray diffraction to hold, successive reflecting planes would have to be parallel to each other to within a few seconds of arc. This is the case within the mosaic blocks which comprise the crystal. Imperfections produce a warping of the lattice which causes different mosaic blocks to have a misorientation of the order of minutes of arc. The boundaries of these mosaic blocks can be interpreted as consisting of arrays of dislocations. The various ways in which arrays of dislocations can form boundaries are illustrated in the article by Hirsch. The average thickness of the mosaic blocks measured in a particular direction is referred to as the coherently diffracting domain size. 

Diffraction properties of crystals are determined by X-ray analysis which is covered in Chapters 4 and 5. Imperfections within the crystal are indicated by high mosaicity exhibited by broadening of diffraction spots and diffuse scattering. Prolonged exposure of protein and protein-DNA crystals to X-rays causes loss of diffraction due to radiation damage. 

As early as 1829, the observation of grain boundaries was reported. But it was more than one hundred years later that the structure of dislocations in crystals was understood. Early ideas on strain-figures that move in elastic bodies date back to the turn of this century. Although the mathematical theory of dislocations in an elastic continuum was summarized by [V. Volterra (1907)], it did not really influence the theory of crystal plasticity. X-ray intensity measurements [C.G. Darwin (1914)] with single crystals indicated their mosaic structure (j.e., subgrain boundaries) formed by dislocation arrays. Prandtl, Masing, and Polanyi, and in particular [U. Dehlinger (1929)] came close to the modern concept of line imperfections, which can move in a crystal lattice and induce plastic deformation. 

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. 

In this section we shall describe the crystal structures of ideal crystals, that is, the structures which would extend without interruption throughout ideal crystals but which in the normal material, with a mosaic and moreover a polycrystalline structure, persist only over comparatively small volumes. In the case of metals and alloys the imperfections in the crystals are of the utmost importance in determining the properties of the material, and it is necessary to remember that the properties... 

The simple model implies an infinite perfect crystal. The crystal specimen studied is necessarily finite (rarely more than 0.5 mm in size) and, if perfect by conventional criteria, would be utterly unsuitable for collection of intensity data of the kind required for ordinary structure determination and refinement. What is needed is an ideally imperfect crystal shot through with dislocations and intergrain boundaries so that it behaves, so far as diffraction is concerned, like a mosaic of perfect crystal blocks of the order of micrometers or tenths of micrometers in size, tilted with respect to one another by angles of the order of a few seconds of arc and scattering independently (incoherently) with respect to one another. The assumption of an ideally imperfect ... 

The idea that a crystal possesses a mosaic structure was introduced soon after the discovery of X-ray diffraction. It is only in recent years, however, that the nature of the imperfections giving rise to this structure has become known, chiefly as a result of investigations into the mechanical properties of metal crystals. 

For an imperfect crystal, a would be cos220M- Azaroff et al (1974) discussed the possibility of an intermediate power of n in cos"20M between 1 and 2 for intermediate monochromator crystal states. This would apply if graphite is used, for instance, when tests for the mosaic character of the monochromator crystal would be needed. 

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