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International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 6.3, pp. 599-600
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Because Rayleigh scattering is elastic, the scattering from different atoms may combine coherently, giving rise to interference, and hence to Bragg reflection from crystals.
For a crystal oriented so that there is no Bragg reflection, the interference reduces the scattered intensity far below the sum of the intensities that would be scattered by the atoms individually. For a strong Bragg reflection, on the other hand, the atomic scattering amplitudes add approximately in phase. The reduction in incident-beam intensity is many times larger than the sum of the squares of the individual atomic scattering powers.
An extreme case occurs in a perfect crystal, for which total reflection is possible. There is destructive interference with the incident beam producing a marked change in the index of refraction from its normal value of ![[n=1-{\lambda{^2}e{^2} \over 2\pi mc^2}\; \sum_a\; N_a\;f_a(0), \eqno (6.3.1.4)]](/teximages/cbch6o3/cbch6o3fd4.svg)
where e and m are the charge and mass of the electron. ![[f_a(0)]](/teximages/cbch6o3/cbch6o3fi7.svg)
is the scattering factor in the forward direction for an atom of type a and ![[N_a]](/teximages/cbch6o3/cbch6o3fi8.svg)
is the number of atoms of that type per unit volume.
Thus, for strong reflections in near-perfect crystals, the Rayleigh scattering is affected by both crystal texture and beam direction. This reduction of primary-beam intensity due to the Rayleigh scattering is usually included, along with other specimen-dependent factors affecting diffracted-beam intensity, in the analysis of extinction.
