On 6/28/2013 5:13 PM, Douglas Theobald wrote:
> I admittedly don't understand TDS well. But I thought it was generally
> assumed that TDS contributes rather little to the conventional
> background measurement outside of the spot (so Stout and Jensen tells
> me :). So I was not even really considering TDS, which I see as a
> different problem from measuring background (am I mistaken here?). I
> thought the background we measure (in the area surrounding the spot)
> mostly came from diffuse solvent scatter, air scatter, loop scatter,
> etc. If so, then we can just consider Itrue = Ibragg + Itds, and worry
> about modeling the different components of Itrue at a different stage.
> And then it would make sense to think about blocking a reflection
> (say, with a minuscule, precisely positioned beam stop very near the
> crystal) and measuring the background in the spot where the reflection
> would hit. That background should be approximated pretty well by
> Iback, the background around the spot (especially if we move far
> enough away from the spot so that TDS is negligible there).

Actually, almost by definition, the resolution at which the disorder in
the crystal is enough to make the Bragg peaks fade away is also the
"resolution" where the background due to diffuse scatter is maximized.
Basically, it's conservation of scattered photons. The interaction
cross section is fixed, and the photons that don't go into Bragg peaks
have to go somewhere. For those who like equations, the Bragg peaks
fade with:

Ibragg = I0 * exp(-2*B*s^2)

where "B" is the average atomic B factor (aka "Wilson B"), "s" is
sin(theta)/lambda (0.5/d), and "I0" is the spot intensity you would see
if the B factor was zero (perfect crystal).

The background however, goes as:

Ibg = Igas * (1 - exp(-2*B*s^2))

Where Igas is the background intensity you would see if all the atoms in
the crystal were converted into a gas (infinite B factor) but still
somehow remained contained within the x-ray beam. At the so-called
"resolution limit", the 1-exp() thing is pretty much equal to 1.

In the diffuse scattering field this 1-exp() thing is called the
"centrosymmetric term", and the first step of data processing is to
"subtract it out". What is left over is signatures of correlated
motions, like "TDS", although strictly speaking TDS is the component due
to thermally-induced motions only. At 100K, there is not much "TDS"
left, but there is still plenty of "diffuse scattering" (DS) due to a
myriad of other things.

As long as the path the incident x-ray beam takes through "loop"
(solvent, nylon, etc) is less than the path through the crystal itself,
and the "air path" (exposed to incident beam and visible from the
detector) is less than 1000x the path through the crystal, then most of
the background is actually coming from the crystal "lattice" itself.
You could put a little spot-specific beamstop up, but all that would do
is make what we beamline scientists call a "shadow". Best possible case
would be to mask off everything coming from the crystal, but since most
of the background you need to subtract is coming from the crystal itself
anyway, the "spot specific beamstop" experiment is not really going to
tell you much. Unless, of course, you are trying to study the diffuse
scattering. for these experiments spots are annoying because they are
thousands of times brighter than the effect you are trying to measure.
Some DS studies have actually taken great pains to avoid putting any
Bragg peaks on the Ewald sphere. You can read all about it in T. R.
Welberry's Oxford University Press book: "Diffuse Scattering and Models
of Disorder". Apparently, urea is a classic model system for DS.

A common misconception, however, is that "TDS" can somehow "build up
under the spot" and give it some "extra" intensity that doesn't have
anything to do with the average electron density in a unit cell. This is
absolutely impossible. Anything that contributes intensity to the
regions of reciprocal space "under the spots" must have a repeat that is
identical to the unit cell repeat, and it must also repeat many times in
a row to make the feature "sharp" enough to hide itself "under the
spot". That sounds like a unit cell repeat to me. Yes, there is such a
thing as modulated lattices, and also something called "Huang
scattering" where long-range correlations (cracks and other mechanical
effects) can give Bragg spots "tails", but where the "tails" end and the
"unit cell" begins is really just a matter of semantics. The molecules
don't actually care what you think the "unit cell" is.

-James Holton
MAD Scientist