Hi Phil My understanding is that when the B factor was devised it was believed that it wouldn't represent any physical reality and was initially at least widely regarded as a "garbage dump" for errors. So it made no difference whether or not it was related to the natural length in reciprocal space, it was just a number, a "fudge factor" used to fit the data. Bs^2 is simplest to calculate from theta (which can be measured directly from the film or diffractometer setting), lambda (which is fixed of course) and B - particularly if you don't have a computer! Also a significant point may be that the scattering factors were tabulated as a function of s=sin(theta)/lambda (but you could equally well ask why 2sin(theta)/lambda wasn't used there). So it's more convenient to have B multiplying s^2 since you can simply add B to the constant part of the Gaussian scattering factor function. Of course they could have absorbed the extra factor of 2 into lambda (i.e. use lambda/2 instead of lambda) but maybe no-one thought of that!
U, the mean square displacement, is the quantity which is directly related to the physics so if it's realism you're after, use U, not B (or beta). Cheers -- Ian On Wed, Oct 12, 2011 at 2:55 PM, Phil Evans <p...@mrc-lmb.cam.ac.uk> wrote: > I've been struggling a bit to understand the definition of B-factors, > particularly anisotropic Bs, and I think I've finally more-or-less got my > head around the various definitions of B, U, beta etc, but one thing puzzles > me. > > It seems to me that the natural measure of length in reciprocal space is d* = > 1/d = 2 sin theta/lambda > > but the "conventional" term for B-factor in the structure factor expression > is exp(-B s^2) where s = sin theta/lambda = d*/2 ie exp(-B (d*/2)^2) > > Why not exp (-B' d*^2) which would seem more sensible? (B' = B/4) Why the > factor of 4? > > Or should we just get used to U instead? > > My guess is that it is a historical accident (or relic), ie that is the > definition because that's the way it is > > Does anyone understand where this comes from? > > Phil
