It’s also important to keep in mind that, in this equation, u is the component of the displacement *in the direction of the diffraction vector*. If you assume isotropic displacements and you know the mean-squared value of the overall xyz vector displacement, you have to divide that mean-squared value by 3 to get the variance in any particular direction. This is a source of considerable confusion in crystallography textbooks!
Best wishes, Randy Read > On 28 May 2021, at 11:09, Ian Tickle <ianj...@gmail.com> wrote: > > > Hi Jonathan > > On Thu, 27 May 2021 at 18:34, Hughes, Jonathan > <jon.hug...@bot3.bio.uni-giessen.de> wrote: > > "B = 8π2<u2> where u is the r.m.s. displacement of a scattering center, and > <...> denotes time averaging" > > Neither of those statements is necessarily correct: u is the _instantaneous_ > displacement which of course is constantly changing (on a timescale of the > order of femtoseconds) and cannot be measured. So u2 is the squared > instantaneous displacement, <u2> is the mean-squared displacement, and so > the root-mean-squared displacement (which of course is amenable to > measurement) is sqrt(<u2>), not the same thing at all as u. > > Incidentally, the 8π2 constant factor comes from Fourier-transforming the > Debye-Waller factor expression I mentioned earlier. > > Also for crystals at least, the averaging is not only over time, it's over > all unit cells, i.e. the displacements are not only thermal in origin but > also due to spatial static disorder (instantaneous differences between unit > cells). > > it would seem to me that we would be able to interpret things MUCH more > easily with u rather than anything derived from u². > > So then I think what you mean is sqrt(<u2>) rather than <u2>, which seems not > unreasonable. > > Cheers > > -- Ian > > > > > > > To unsubscribe from the CCP4BB list, click the following link: > https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 > ----- Randy J. Read Department of Haematology, University of Cambridge Cambridge Institute for Medical Research Tel: +44 1223 336500 The Keith Peters Building Fax: +44 1223 336827 Hills Road E-mail: rj...@cam.ac.uk Cambridge CB2 0XY, U.K. www-structmed.cimr.cam.ac.uk ######################################################################## To unsubscribe from the CCP4BB list, click the following link: https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1 This message was issued to members of www.jiscmail.ac.uk/CCP4BB, a mailing list hosted by www.jiscmail.ac.uk, terms & conditions are available at https://www.jiscmail.ac.uk/policyandsecurity/
