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Understanding Structure Factors in X-ray, Neutron, and Electron Diffraction

This text delves into the relationship between reflection intensity and structural factors in diffraction processes for X-rays, neutrons, and electrons. It discusses how structure factors are formulated, detailing the atom coordinates within a crystal unit cell and their influence on diffraction patterns. The concepts are illustrated with examples from face-centered cubic (fcc) and body-centered cubic (bcc) structures, including conditions for allowed and forbidden reflections. The mathematical representation of scattering factors enhances comprehension of these phenomena.

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Understanding Structure Factors in X-ray, Neutron, and Electron Diffraction

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  1. z wjc rj c a b vjb uja The intensity of a reflection is proportional to: y x Structure factors X-ray: The structure factors for x-ray, neutron and electron diffraction are similar. For neutrons and electrons we need only to replace by fj(n) or fj(e) . The coordinate of atom j within the crystal unit cell is given rj=uja+vjb+wjc. h, k and l are the miller indices of the Bragg reflection g. N is the number of atoms within the crystal unit cell. fj(n) is the x-ray scattering factor, or x-ray scattering amplitude, for atom j. MENA3100

  2. eiφ = cosφ + isinφ enπi = (-1)n eix + e-ix = 2cosx Example: Cu, fcc Atomic positions in the unit cell: [000], [½ ½ 0], [½ 0 ½ ], [0 ½ ½ ] Fhkl= f (1+ eπi(h+k) + eπi(h+l) + eπi(k+l)) What is the general condition for reflections for fcc? If h, k, l are all odd then: Fhkl= f(1+1+1+1)=4f What is the general condition for reflections for bcc? If h, k, l are mixed integers (exs 112) then Fhkl=f(1+1-1-1)=0 (forbidden) MENA3100

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