Electron microscopy
 
Friedel (or Bijvoet) Pair & Friedel's Law
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Two centrosymmetric reciprocal lattice points (hkl) and (-h-k-l) are called Friedel (or Bijvoet) pair. The pair of Bragg reflections F(hkl) and F(-h-k-l) arise from the same set of crystal planes but they are the scattering from the opposite sides. Friedel's Law describes the relationship between the structure amplitude of the two centrosymmetric reciprocal lattice points. According to the Friedel's law, regardless of whether the crystal structure is centrosymmetric or not, if there is no anomalous scattering the reciprocal space is always centrosymmetric, given by,
         |F(hkl)| = |F(-h-k-l)| ------------------------ [1626]
where,
         F -- The structure factor.

The square of |F| represents the intensity of the peak of the corresponding reciprocal lattice point. In general, it is difficult to distinguish whether the space group of a material is centrosymmetric or non-centrosymmetric even though there is X-ray anomalous absorption. However, the |F| of F(hkl) and F(-h-k-l) may not be the same if the crystal structure is non-centrosymmetric and there is obvious resonant scattering from some of the atoms.

Note that, the Friedel's Law, presenting centrosymmetric characteristics of crystals, usually gives a good approximation even for non-centrosymmetric crystals.

XRD obeys Friedel's Law because it can be approximately described by kinematical scattering. This limits the number of the space groups of crystals that can be determined by XRD to fifty. For electron diffraction, multiple (dynamical) scattering of the incident electrons in the TEM specimen occurs so that the Friedel's law is broken down, and thus the crystals with all the 230 space groups can be identified.

 

 

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