Crystallites mosaic block structure

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... 

Even if one solves the indexing problem and then proceeds with the analysis by an evaluation of measured reflection intensities, one cannot expect to achieve an accuracy in the crystal structure data which would be comparable to those of low molar mass compounds. This is not only a result of the lack of single crystals, but represents also a principal property In small crystallites, as they are found in partially crystalline polymers, lattice constants can be affected by their size. In many cases crystallites are not only limited in chain direction by the finite thickness of the crystalline lamellae but also laterally since polymer crystallites are often composed of mosaic blocks. Existence of these blocks is indicated in electron microscopic investigations on... 

Photo-micrographs may illustrate both the mosaic structure of metals, and a concentration of impurity between crystal blocks. If diffusion occurs mainly down these boundaries, the permeability of a metal would be governed by their number and nature. The mere fact that oxide is found concentrated in these boundaries does not, however, necessarily imply that diffusion of oxygen occurs along them, since the oxide may be formed within the lattice and then be thrown out of solution in the zones between crystallites. That grain-boundary diffusion plays an important part in diffusion processes such... 

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