This may answer some of your questions or at least give pointers:

Grosse-Kunstleve RW, Adams PD:
On the handling of atomic anisotropic displacement parameters.
Journal of Applied Crystallography 2002, 35, 477-480.

http://cci.lbl.gov/~rwgk/my_papers/iucr/ks0128_reprint.pdf

Pavel

On Wed, Oct 12, 2011 at 6:55 AM, 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

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