Diffraction Interference of waves creates a diffraction pattern. Diffraction becomes important when the size of the object is comparable to the wavelength. X-rays have much shorter wavelength than visible light. Therefore, one can observe diffraction from much smaller objects (e.g. nanostructures). In protein crystallography, one uses the interference between x-ray waves originating from different atoms in the protein molecule.

Diffraction patterns reveal small structures X-Ray Diffraction Optical 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 all the atoms in myoglobin. Protein crystallography has become essential for biochemistry, because the structure of a protein determines its function.

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

Test patterns Single helix Double helix

X-ray diffraction of DNA Diffraction pattern The double helix of DNA p = period of one turn b = base spacing  = slope of the helix  1 p b p  1 b

Real space and reciprocal space

Real space versus reciprocal space Diffraction patterns “live” in reciprocal space (which corresponds to the projection screen). Everything is backwards in reciprocal space: Large distances in real space become small in reciprocal space and vice versa. The direction of a wave in real space becomes a point in reciprocal space (where the wave hits the screen). Even physicists have a hard time thinking in reciprocal space. But they use it heavily to describe waves (x-ray diffraction, electrons in solids, collisions of elementary particles).

Resolution limit /2 ( Microscopy, Patterning ) Large object: Optical Ruler /2 limit Smaller objects need shorter 