X-ray Diffraction- Electron Density Map Flashcards
What does the structure factor show?
Gives the resultant amplitude and phase of the wave scattered by all the atoms of the unit cell. Each atoms in a unit cell scatters a wave with its own amplitude and phase. Amplitude given by atomic form factor fn. phase given by complex exponential term exp(i2π(hu+kv+lw)).
What is the structure factor?
The sum of the individual amplitude and phase components from each atom in the unit cell. It is also the Fourier transform of the electron density map
Electron density map notation
ρ(uvw). Electron density at position (x,y,z) = (au,bv,cw)
Alternative form of structure factor
Fhkl= triple integral of normal term but fn replaced by ρ(uvw) with respect to dudvdw. All integrals from 0 to 1
What can any periodic function be expressed as?
An addition of a series of sinusoidal curves with the periodicity of each equal to the original periodicity multiplied by an integer number
Electron density Fourier series
ρ(uvw)=ΣFhklexp(-i2π(hu+kv+lw))
Underneath Σ is hkl
What does each Fourier term of the electron density tell you?
Each corresponds to a diffraction peak with indices hkl. Amplitude of each term is structure factor Fhkl
What can’t be determined from the diffraction intensity?
The phase of structure factor Ihkl=KvLp|Fhkl|^2 This is for intensity K is scale factor v is volume of crystal L is Lorentz factor p is polarisation factor
Patterson function
P(uvw)=Σ|Fhkl|^2exp(-i2π(hu+kv+lw)) Has hkl under Σ It is equivalent to the electron density convoluted with its inverse (self-convolution) Always centro-symmetric P(r bar)=ρ(r bar)*ρ(-r bar)
How many peaks does a Patterson map of a unit cell have?
For unit cell with N atoms has N(N-1) peaks
What are the peaks in the Patterson function?
The inter-atomic distances weighted by the product of the number of electrons in the atoms concerned.
Isomorphous replacement
What is true when ρ(uvw) is centro-symmetric?
ρ(uvw)=ρ(-u,-v,-w)
Fhkl is always real
φhkl is 0 or π
Phase problem is much simplified and trial and error approach becomes possible
What does number of peaks from powder X-ray diffraction pattern for 1D structure give?
The number of Fourier terms for the electron density map
How to build up 3D structure from electron density maps
Can see the electron density at different z values (depth) to find positions of atoms and molecules in all layers
Self-assembled supramolecular dendrimers
Large molecules of certain shapes can combine to make 3D shapes like cylinders or spheres. These 3D shapes can combine like atoms to make a larger structure like a unit cell. Cylinders can form hexagonal structure. Spheres can act like atoms and form structures like bcc.
