anomal_hand1_rev - Anomalous Scattering When the incident...

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Unformatted text preview: Anomalous Scattering When the incident radiation has sufficient energy to promote an electronic transition in atoms contained in the crystal, we observe anomalous scattering in non-centrosymmetric crystals. E.g. Selenium C ourtesy of Michael R. Sawaya. Used with permission. Anomalous Scattering When the incident radiation has sufficient energy to promote an electronic transition in atoms contained in the crystal, we observe anomalous scattering in non-centrosymmetric crystals. .g. Selenium h ν<∆ E No transition possible, Insufficient energy usual case h ν=∆ E Excites a transition from the “K” shell For Se: λ = 0.9795 Å C ourtesy of Michael R. Sawaya. Used with permission. ∆ E is a function of the periodic table. ∆ E is near 8keV for most heavy and some light elements, so anomalous signal can be measured on a home X-ray source with CuKa radiation ( 8kev λ =1.54Å). At a synchrotron, the energy of the incident radiation can be tuned to match ∆ E (accurately). Importantly, ∆ Es for C,N,O are out of the X-ray range. K shell transitions L shell transitions C ourtesy of Michael R. Sawaya. Used with permission. Anomalous Scattering Anomalous scattering causes small but measurable differences in intensity between the reflections hkl and -h-k-l not normally present. That means for non-centrosymmetric crystals in the presence of atoms heavier than sulfur, Friedel’s law is not strictly true. Under normal conditions, electron distributions within atoms are centrosymmetric: C ourtesy of Michael R. Sawaya. Used with permission. The centrosymmetry in the scattering atoms is reflected in the centrosymmetry in the pattern of scattered X-ray intensities. The positions of the reflections hkl and -h-k-l on the reciprocal lattice are related by a center of symmetry through the reciprocal lattice origin ( 0,0,0 ). airs of reflections hkl and -h-k-l are called Friedel pairs. They share the same intensity by Friedel’s law. I ( hkl ) = I (- h- k- l ) and φ ( hkl ) = - φ (- h- k- l ) (15,0,-6) (-15,0,6) · (0,0,0) C ourtesy of Michael R. Sawaya. Used with permission. On an Argand diagram, F (hkl) and F (-h-k-l) appear to be reflected across the real axis. real imaginary φ hkl | F h , k , l | imaginary φ-h-k-l | F- h ,- k ,- l | F h , k , l F- h ,- k ,- l I ( hkl ) = I (- h- k-l) and φ ( hkl ) = - φ (- h- k- l ) (-h,-k,-l) (h,k,l) real C ourtesy of Michael R. Sawaya. Used with permission. On an Argand diagram, F (hkl) and F (-h-k-l) appear to be reflected across the real axis....
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

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anomal_hand1_rev - Anomalous Scattering When the incident...

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