Transcript Lecture09 - UW-Madison Department of Physics

Microscopy
versus
Diffraction
Large Features ( »  )
Small Features (   )
Real Space:
x
Reciprocal Space:
kx = 2/x
Single Object
Ordered Array
Real space versus reciprocal space
kx = 2/x
x = row spacing
kx  rows
y
ky
Real space:
x,y,z
Reciprocal space:
kx, ky, kz
Test patterns for simulating diffraction from DNA
Single helix
Double helix
Rosalind Franklin’s x-ray diffraction pattern
of DNA, which led to the double-helix model
(Linus Pauling’s copy)
X-ray diffraction pattern of DNA
Diffraction pattern
The double helix of DNA

2
b
2
p
p = period of one turn
b = base pair spacing
 = slope of the helix
p b

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 .
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.
Low Energy Electron Diffraction (LEED)
at surfaces
K=
2/d
k = 2/D
D
d
1D chain structure
2D planar structure
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
(see Lecture 2 on length scales)
Q1/2  1/Rg
Q
Diffracted neutron intensity P
plotted versus the k-vector Q