Microscopy versus Diffraction Large Features Small Features Real

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Microscopy versus Diffraction Large Features ( » ) Small Features ( ) Real Space:

Microscopy versus Diffraction Large Features ( » ) Small Features ( ) Real Space: x Reciprocal Space: kx = 2 / x Single Object Ordered Array Mon. Feb 26, 2006 Phy 107 Lecture 15 1

Real space versus reciprocal space kx = 2 / x x = row spacing

Real space versus reciprocal space kx = 2 / x x = row spacing kx rows y ky Mon. Feb 26, 2006 Real space: x, y, z Reciprocal space: kx, ky, kz Phy 107 Lecture 15 2

Test patterns for simulating diffraction from DNA Single helix Mon. Feb 26, 2006 Double

Test patterns for simulating diffraction from DNA Single helix Mon. Feb 26, 2006 Double helix Phy 107 Lecture 15 3

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

Rosalind Franklin’s x-ray diffraction pattern of DNA, which led to the double-helix model (Linus Pauling’s copy) Mon. Feb 26, 2006 Phy 107 Lecture 15 4

X-ray diffraction pattern of DNA Diffraction pattern The double helix of DNA 2 b

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 Mon. Feb 26, 2006 Phy 107 Lecture 15 5

X-ray diffraction image of the protein myoglobin • This image contains about 3000 diffraction

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. Mon. Feb 26, 2006 Phy 107 Lecture 15 6

Real space versus reciprocal space • Diffraction patterns live in reciprocal space, which corresponds

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. Mon. Feb 26, 2006 Phy 107 Lecture 15 7

Low Energy Electron Diffraction (LEED) at surfaces K= 2 /d k = 2 /D

Low Energy Electron Diffraction (LEED) at surfaces K= 2 /d k = 2 /D D d Mon. Feb 26, 2006 1 D chain structure Phy 107 Lecture 15 2 D planar structure 8

Neutron Diffraction: Small Angle Neutron Scattering (SANS) Good for light elements (hydrogen, deuterium, polymers)

Neutron Diffraction: Small Angle Neutron Scattering (SANS) Good for light elements (hydrogen, deuterium, polymers) and for magnetic materials (magnetic moment of the neutron). a Rg P Model of a polymer: Rg = radius of gyration a persistence length Mon. Lecture Feb 26, 2006 (see 2 on length scales) Q 1/2 1/Rg Q Phy 107 Lecture 15 Diffracted neutron intensity P plotted versus the k-vector Q 9

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