Implications of texture on powder diffraction - Three-dimensional powder diffraction

Diffraction in poly crystalline samples is described by an intensity distribution function in the three-dimensional reciprocal space. For ideal crystals the structure factors \F-(hkl)\(2) are distributed continuously over pole spheres with the radii \r((hkl))*\ known as "pole figures". For crystallites with lattice distortions also peak shift and peak broadening pole figures are to be considered. Pole spheres for different (hkl) are often abundantly overlapped in the Bragg angle upsilon. The may, however, be distinguished by their different distributions over the sample angles {alpha beta}. Intensity, measurements in the three-dimensional reciprocal space r = {upsilon alpha beta} of textured samples are the basis for the solution of four "inverse problems" i.e. the calculation of the orientation disribution function f(g), structure factors \F-(hkl)\, distortion functions D-(hkl)(r*)(g), as well as volume fractions V-i of phases. This is illustrated with three examples concerning structure factor separating, indexing, as well as orientation dependent lattice distortion. The most serious problem is the finite (low) number of crystallites which must be taken into consideration independently of the texture. With increasing angular and/or location resolution a "polycrystal" breakes down into "multicrystals" the crystallites of which can be individually distinguished. This requires other than powder diffraction techniques.