Phys560Notes-5 - X-Ray Diffraction A method to determine...

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X-Ray Diffraction A method to determine crystal structure. Assumption: ignoring thermal vibrations of lattice (including zero-point vibrations) for now. A charged particle of charge q in an EM field:        2 2 22 2 11 qq q q HV p A V mc m c c c pA r A p p A r Interaction:  2 2 2 1 2 q HA c c Ap , usually treated as a perturbation.  1 H m Rough estimates: 2 2 Scattering prob. for protons 1 Scattering prob. for electrons 1840 e p m m X-ray scattering is dominated by electrons (nuclei can be ignored). Still, x-ray interaction with electrons is weak, and so one can use single-scattering theory (kinematic theory) in most cases. For comparison, electron scattering involves a strong interaction; one must consider multiple scattering (dynamical theory) - complicated. For example: double scattering Consider elastic scattering only; kk   . Inelastic scattering by phonons will be considered later when we discuss neutron scattering. Huygens principle: A = total scattering amplitude at r' (detector) (amplitude of incident plane wave) x (number of electrons in d 3 r ) x (amplitude of scattered spherical wave at r' ) r k k' O r' polarization
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     |' | 3 , ik i V e Ae n d r f rr kr r , where , f = angular distribution factor, determined by || fi H . Assume the crystal dimensions << r' (far field approximation),   , f , k' , r' , and ~ r are approximately constants.
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This note was uploaded on 03/21/2012 for the course PHYS 560 taught by Professor Flynn during the Spring '08 term at University of Illinois, Urbana Champaign.

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Phys560Notes-5 - X-Ray Diffraction A method to determine...

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