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Considering that I have a diffraction pattern of a crystal, how would I calculate the resolution of a structure in Angstroms? How does that value differ from the information that I would get from the beta-factor?

I'm aware that the resolution can be calculated by Bragg's law but how does that provide details for the entire structure?

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Excellent question for the upcoming Chemistry beta. This should be moved once the proposal reaches beta. – CHM Apr 3 '12 at 2:47
I guess the answer is very different for NMR then. Time for a new question. – bobthejoe May 17 '12 at 5:39
up vote 5 down vote accepted

Hi sorry i missed this one - not too hard for "biology"

If you look at a protein crystal (or any crystal really) in an x-ray beam, it scatters lots of spots (diffraction reflections). If you look at a picture of crystalline diffraction, at larger angles from the center of the x-ray beam, the reflections get weaker and weaker and basically just stop, if the wavelength is short enough (in all crystallography labs its plenty short - from 1.5 to 0.9 Angstroms).

The resolution is marked by the angle of scattering to the last measurable spot (aesthetics can vary here, but there is little variance from personal judgement here). Once you have the angle of scattering, you can calculate the resolution from the Bragg scattering equation:

lambda = 2d sin(theta)

which is rearranged to solve for 'd'

d = lambda / 2 * sin (theta)

where lambda is the wavelength of the incident radiation and theta is the scattering angle.
d = the apparent width of the 'slit' which caused this highest resolution reflection is called the 'resolution' of the X-ray scattering experiment.

There is one part that's a bit tricky as in the typical diagram, depicting Bragg reflection/scattering, you would take the incident x-ray beam as first beam and the scattered angle as the beam of the high resolution scattering, which is more easily measured as 180 - 2* theta.

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Does this mean that the resolution is an ensemble average? – bobthejoe May 16 '12 at 17:36
Yes- The resolution is a result of the mean coherence of the crystal; if its disordered on the 2 angstroms, then the resolution peters out at that diffraction angle. There are cases where diffraction in one direction is stronger or weaker than in other directions. Such anisotropic resolution is not unusual and is described pretty literally "crystal diffracts to 4Angstroms along the a axis and 3Angstoms otherwise. – shigeta May 16 '12 at 18:07
Resolution is a general metric, the quality of the x-ray structure, describing the amount of data collected for the structure. The quality of the structure depends on how well the structure reproduces the data collected. – shigeta May 16 '12 at 18:13

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