Dear Jacob, Measurement of the reciprocal space maps at reflections with triple axis diffractometry allows experimental separation of mosaicity and strain (variation in unit cell parameter) effects. See eg Boggon et al 2000 Acta Cryst D56, 868-880 http://dx.doi.org/10.1107/S0907444900005837 for such studies on protein crystals at NSLS.
In terms of diffuse scattering the above effects do get mixed in with molecular disorders correlated over many unit cells, and thus a 'diffuse scattering correction to measured Bragg intensities' is done in the most accurate work.But the above effects are separate from molecular disorders over a few unit cells ie which cause the diffraction streaks between Bragg peaks. Then there are the long range and short range temporal vibrations, optic and acoustic modes, in the crystal........ ************************************ A workshop held at ALS on diffuse scattering recently suggests a systematic effort is on hand to analyse diffuse X-ray scattering information in MX data sets for improved descriptions of macromolecular structure and dynamics. Archiving of raw diffraction data images would also assist such important objectives. Best wishes, John Prof John R Helliwell DSc On 12 Mar 2014, at 21:15, "Keller, Jacob" <kell...@janelia.hhmi.org> wrote: >> For any sample, crystalline or not, a generally valid description of >> diffraction intensity is it being a Fourier transform of electron density >> autocorrelation function. > > I thought for non-crystalline samples diffraction intensity is simply the > Fourier transform of the electron density, not its autocorrelation function. > Is that wrong? > > > > Anyway, regarding spot streaking, perhaps there is a different, simpler > formulation for how they arise, based on the two phenomena: > > (1) Crystal lattice convoluted with periodic contents, e.g., protein > structure in exactly the same orientation > (2) Crystal lattice convoluted with aperiodic contents, e.g. n different > conformations of a protein loop, randomly sprinkled in the lattice. > > Option (1) makes normal spots. If there is a lot of scattering material doing > (2), then streaks arise due to many "super-cells" occurring, each with an > integral number of unit cells, and following a Poisson distribution with > regard to frequency according to the number of distinct conformations. > Anyway, I thought of this because it might be related to scattering from > aperiodic crystals, in which there is no concept of unit cell as far as I > know (just frequent distances), which makes them really interesting for > thinking about diffraction. > > See the images here of an aperiodic lattice and its Fourier transform, if > interested: > > http://postimg.org/gallery/1fowdm00/ > >> Mosaicity is a very different phenomenon. It describes a range of angular >> alignments of microcrystals with the same unit cell within the sample. It >> broadens diffraction peaks by the same angle irrespective of the data >> resolution, but it cannot change the length of diffraction vector for each >> Bragg reflection. For this reason, the elongation of the spot on the >> detector resulting from mosaicity will be always perpendicular to the >> diffraction vector. This is distinct from the statistical disorder, where >> spot elongation will be aligned with the crystal lattice and not the >> detector plane. > > I have been convinced by some elegant, carefully-thought-out papers that this > "microcrystal" conception of the data-processing constant "mosaicity" is > basically wrong, and that the primary factor responsible for observed > mosaicity is discrepancies in unit cell constants, and not the "microcrystal" > picture. I think maybe you are referring here to theoretical mosaicity and > not the fitting parameter, so I am not contradicting you. I have seen > recently an EM study of protein microcrystals which seems to show actual > tilted mosaic domains just as you describe, and can find the reference if > desired. > >> Presence of multiple, similar unit cells in the sample is completely >> different and unrelated condition to statistical disorder. > > Agreed! > > Jacob
