1. Microscopy Large Features ( »  ) Real Space: x Single Object
Diffraction Small Features (   ) Reciprocal Space: kx = 2/x Ordered Array
versus

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

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. Neutron Diffraction: Small Angle Neutron Scattering (SANS)
Good for light elements (hydrogen, deuterium, polymers) and for magnetic materials (magnetic moment of the neutron).
Q1/2  1/Rg P Q Rg a
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