X ray crystallography

X ray microscope

• Impossible due to two reasons

– No x ray lens

– Low resolutions (interatomic distance)

X ray diffraction

• Light strike object and diffracted in various direction

• Collect diffracted rays and resemble to form an image of the object

Why x ray?

• which has a wavelength of 1.5418Å

• This is very similar to the distance between bonded carbon atoms

Electron density map

• The electrons are mostly tightly localised around the nuclei, the electron density map gives us a pretty good picture of the molecule

• electromagnetic radiation (including X-rays) interacts with matter through its fluctuating electric field

• Intensity of scattered radiation is proportional to the square of the charge/mass ratio

Why crystals

• To detect above the noise level

• Raise the signal (amplifier)

• Problem?

• When the little waves add up, they interfere with one another: they can add up in phase, out of phase, or something in between

• they do depends on the direction of the incoming and outgoing waves and the positions of the electrons relative to each other

• The total path from the source to the detector will determine what happens

• In electronic signaling, phase is a definition of the position of a point in time (instant) on a waveform cycle.

• When two signals differ in phase by -90 or +90 degrees, they are said to be in phase quadrature

• When two waves differ inphase by 180 degrees (-180 is technically the same as +180), the waves are said to be inphase opposition

• Diffraction is observed when waves scatter and interfere

• amplitudes will add up

• Amplitudes will cancel off

• Or mixed

Bragg’s law

• The relationship between scattering angle and the interplanar spacing is given by Bragg's law

• The position of the peaks in the wave that results from the interference of scattering from two atoms depends on their relative position. The position of the peak in a wave is described by its phase.

Structure Factor

• The vector (amplitude and phase) representing the overall scattering from a particular set of Bragg planes is termed the structure factor

Direct methods

• Use number of tricks

• Try all possible combinations of each spots and find combination that best fit the overall data to solve structure

• Or

• Use the phase information for each atom inherent in the intensity data to retrieve some information concerning the relative positions of atoms in the crystal (Patterson)

Patterson function

• if we carry out an inverse Fourier transform of the structure factors (amplitudes and phases), we get a picture of the electron density

• Instead, fourier transformation of the intensities (amplitudes squared) give Patterson map (only measured data)

• Patterson function gives us a map of the vectors between atoms

• The information provided by the maxima of the Patterson Function corresponds to a map of position vectors (relative positions) between each pair of atoms in the structure

• The value of the function at these maxima is proportional to the product of the implied atomic numbers, which provides a clear advantage for detecting vectors between "heavy" atoms, ie atoms with a large number of electrons

• Rotational and translational functions

• u = x1 - x2 ; v= y1 - y2 ; w = z1 - z2

isomorphous replacement

• get a crystal that is nearly identical to the one you're studying, except that a few atoms have been replaced or added

• If these atoms are "heavy", i.e. they have a large atomic number, they will perturb the diffraction pattern. It is possible to deduce the positions of the few heavy atoms and from that to deduce possible values for the phase angles

anomalous scatterering

• which contains atoms called anomalous scatterers

• By changing the wavelength of the X-rays, you can change the degree to which the anomalous scatterers perturb the diffraction pattern

• MAD SAD