From: "Radaelli, PG (Paolo) " [P.G.Radaelli@rl.ac.uk] To: "'rietveld_l@ill.fr'" [rietveld_l@ill.fr] Subject: RE: Riet_L: Scale factor in Rietveld (with a question for Bob and Juan) Date: Fri, 15 Sep 2000 13:56:20 +0100 Reply-To: rietveld_l@ill.fr Hi everybody: Here is a useful couple of formulas for you neutron lot. They can be used to predict in advance the Rietveld scale factor S for a TOF powder pattern. I remind you that the profile intensity Y is defined as Y=S|F|^2*H(T-Thkl)*L*A*E*O/Vo (see old GSAS manual, page 122). The profile H(T-Thkl) is normalised so that its TOF integral (in mmsec) is 1. The following formula defines the scale factor S of a TOF powder pattern normalised to an equivalent amount of vanadium (corrected for attenuation): [1] S=K*Ltot*f/Vo [mmsec/Angstrom/barns], where K = 1365 [Angstrom^2*mmsec/barns/m] Vo = Unit cell volume [Angstrom^3] Ltot = Total flightpath [m] f = Fractional density [dimensionless] = mass/volume/theoretical density For the more curious, K=252.8*(2Vv/sigmaV/Zv), where Vv = Vanadium unit cell volume=27.54 A^3 SigmaV = Vanadium total neutron cross section = 5.1 barns Zv = Number of vanadium atoms in a unit cell = 2 252.8 = wavelength-velocity conversion constant for neutrons. >From this, it is easy to deduce the second formula: [2] S=505.56*Ltot*Sinf/sigmas, where Sinf = Q->infinity limit of the scattered intensity S(Q) sigmas = Total neutron cross section for a unit cell of the sample (Just the sum of the individual sigmas of the atoms). For the novices, I remind you that the scattered intensity flatens out at high Q (or it should if all the corrections are done propertly). I verified both formulas using my diffractometer GEM, which has detectors from 15 degrees to 170 degrees 2th. Needless to say that the refined scale factors for the different banks are equal with an uncertaintly of about 3%. [2] is extremely accurate, better than 1% at high angle. [1] is slightly less accurate at the moment (~10%), but I plan to improve my corrections to reach a 1-2% level. If these levels of accuracy can be reached, these formulas could be valuable to obtain absolute |F|^2 for problems with multi-site substitutions/vacancies. I'll leave to the reactor people as an exercise to derive the equivalent of this formulas. Note that, for CW data, you rearly if ever to S(Q) saturation. Finally, here is a question for Bob and Juan. To me, it would be much more natural to remove Vo from the scale factor, that is to redefine a new S' so that Y=S'*L*A*E*|F|^2/Vo^2 and S'=K*Ltot*f This way, the scale factor will only depend on the sample effective density and not its crystal structure. This is very useful in phase transitions involving a change in the size of the unit cell, as you can imagine. Is there any rationale in doing it the way it's currently done? Best Paolo |
Date: Fri, 15 Sep 2000 08:43:33 -0600 To: rietveld_l@ill.fr From: vondreele@lanl.gov (Bob Von Dreele) Subject: RE: Riet_L: Scale factor in Rietveld (with a question for Bob and Juan) Reply-To: rietveld_l@ill.fr Dear Paolo ( others)At 01:56 PM 9/15/00 +0100, you wrote: You wrote: >Finally, here is a question for Bob and Juan. To me, it would be much more >natural to remove Vo from the scale factor, that is to redefine a new S' so >that > > >Y=S'*L*A*E*|F|^2/Vo^2 and S'=K*Ltot*f > >This way, the scale factor will only depend on the sample effective density >and not its crystal structure. This is very useful in phase transitions >involving a change in the size of the unit cell, as you can imagine. Is >there any rationale in doing it the way it's currently done? To me it made more sense for the scale factors to be proportional to the "mole fraction unit cells"; so that's what was chosen for GSAS. Considering that there is frequently a change of density associated with many phase changes, tying the scales to density makes construction of constraints between the scales more difficult than having the scales tied to the number of unit cells. Bob Von Dreele |
Date: Fri, 15 Sep 2000 16:07:25 +0100 (BST)
From: Jon Wright [jpw22@cus.cam.ac.uk]
To: "'rietveld_l@ill.fr'" [rietveld_l@ill.fr]
Subject: RE: Riet_L: Scale factor in Rietveld (with a question for Bob and Juan)
Paolo,
On Fri, 15 Sep 2000, Radaelli, PG (Paolo) wrote:
.....
> Finally, here is a question for Bob and Juan. To me, it would be much more
> natural to remove Vo from the scale factor, that is to redefine a new S' so
> that
>
> Y=S'*L*A*E*|F|^2/Vo^2 and S'=K*Ltot*f
>
> This way, the scale factor will only depend on the sample effective density
> and not its crystal structure. This is very useful in phase transitions
> involving a change in the size of the unit cell, as you can imagine.
> Is there any rationale in doing it the way it's currently done?
[Admittedly it wasn't a question for me, so sorry for butting in.]
Here are two unit cells and scale factors fitted to the same (x-ray)
dataset using PRODD. I'm assuming this is what was meant? The cell doubles
and the scale stays the same (roughly). I'd be pretty confident it does
the same with TOF and CN data provided it's a recent version.
C 8.392690 8.392690 16.775499 89.83088 89.83088 89.80757
L SCAL 91322.
C 8.392508 8.392508 8.387020 89.83144 89.83144 89.80786
L SCAL 91479.
Suffice to say the use of cell volume in scale factors within CCSL was
rather vague until we tried to quantify a multiphase sample. I think a
factor was in for lab x-ray data which still doesn't work anyway, but not
for TOF or CW neutrons. The rationale for doing it this way was that I
weighed the multiphase sample myself and this was the only way to get
sensible numbers out. GSAS got the weight fractions right as well, so the
volume factor must be in there somewhere...
Does this mean GEM now produces data where histogram scale factors may be
constrained to be equal across all banks? An impressive achievement, but
it opens a can of worms with sample absorbtion and attenuation. It has
been suggested that absorbtion corrections are something which belong
firmly with the data, as they depend on the geometry, size and packing
density of the sample (packing density can be measured). As such the A*
values could be supplied to the program, and applied to the model. Bruce
was sorting this out for PRODD. Any comments on this idea? It has been
rumoured that absorbtion (for neutrons at least) is not a refinable
quantity, but something that ought to be known(!)
Best wishes,
Jon
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