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
