A polycrystalline powder can be represented in reciprocal space as a set of nested spherical shells positioned with their centers at the origin (Warren 1990) (Fig. 11). These shells each arise from a reciprocal lattice point from the myriad (e.g. ~109 mm−3 for 1μm crystallites) of small crystals, ideally with random orientation, in the sample. These shells each have some thickness or broadening from both instrumental effects and the characteristics of the crystalline grains themselves. Their magnitude is related to the crystalline structure factors (in this instance for neutron scattering) as well as the...

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