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Diffraction Small Features (   ) Reciprocal Space: k x = 2/x Ordered Array

Microscopy Large Features ( »  ) Real Space: x Single Object . Diffraction Small Features (   ) Reciprocal Space: k x = 2/x Ordered Array. versus. Real space versus reciprocal space.  y. k y. k x = 2/x x = row spacing k x  rows. Reciprocal space: k x , k y , k z.

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Diffraction Small Features (   ) Reciprocal Space: k x = 2/x Ordered Array

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  1. MicroscopyLarge Features (»)Real Space:x Single Object DiffractionSmall Features ()Reciprocal Space:kx = 2/xOrdered Array versus

  2. Real space versus reciprocal space y ky kx = 2/xx = row spacingkx rows Reciprocal space: kx,ky,kz Real space: x,y,z

  3. Test patterns for simulating diffraction from DNA Single helix Double helix

  4. Rosalind Franklin’s x-ray diffraction pattern of DNA, which led to the double-helix model(Linus Pauling’s copy)

  5. X-ray diffraction pattern of DNA  Diffraction pattern The double helix of DNA 2 b 2 p p b  p = period of one turn b = base pair spacing = slope of the helix

  6. X-ray diffraction image of the protein myoglobin • This image contains about 3000 diffraction spots. All that information is needed to determine the positions of thousands of atoms in myoglobin. • Protein crystallography has become essential for biochemistry, because the structure of a protein determines its function.

  7. Real space versus reciprocal space • Diffraction patterns live in reciprocal space, which corresponds to the projection screen. A direction of a beam in real space becomes a point on the screen in reciprocal space. • Everything is backwards in reciprocal space: A large distance x in real space becomes a small k-vector kx in reciprocal space and vice versa. • Even physicists have a hard time thinking in reciprocal space. But it is used widely for characterizing waves, particularly electron waves in solids and nanostructures.

  8. Low Energy Electron Diffraction (LEED) at surfaces K= 2/d k= 2/D D d 1D chain structure 2D planar structure

  9. a Rg P Q1/2  1/Rg Q Neutron Diffraction: Small Angle Neutron Scattering (SANS) Good for light elements (hydrogen, deuterium, polymers) and for magnetic materials (magnetic moment of the neutron). Model of a polymer: Rg = radius of gyration a persistence length (see Lecture 2 on length scales) Diffracted neutron intensity P plotted versus the k-vector Q

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