Indeed you missed something. I presume you have the paper.
Then, take a look to the formula (15a). This is the size
profile for lognormal.
There is the function PHI - bar of argument 2*pi*s*R.
Replace this function PHI - bar from (15a) by the _expression
(21a) with the argument x=2*pi*s*R.
You get it? So, not only c but also R.
Dear Nicolae,
This arithmetic is clear, thanks, but since you did not specify this
exact way of R calculation in the paper it was not evident. There are
several other ways of deriving R, for instance: to calculate Dv from
the inverse integral breadth and then use eq. (12) or (17) etc.
Besides, you did not refine R for simulated data in chapter 6 - it
was fixed. When you apply this formalism to real data you refine both
R and c, they may correlate and the result of such correlation is not
apparent.
But the most important disadvantage is the necessity to choose the
exact type of size distribution. For Sample 1 (which, obviously, have
certain distribution with certain R and c) you got quite different
values of R and c for lognorm and gamma models, but the values of Dv
and Da were nearly the same. Don't you feel that Dv and Da values
contain more reliable information about R and c than those
elaborate approximations described in chapter 6?
In new version of DDM (see the following message) I included some
estimations of average crystallite diameter D and its dispersion
sigmaD based on empirical approximations derived from fitting TCH-pV
function to simulated profiles for the model of spherical
crystallites with different size distribution dispersions. For
simulated data (which are supplied with the DDM package) these magic
expressions:
D = Da + 0.25(DaDv)^0.5 and sigmaD = D(Dv/Da - 1/2)/2
allowed reproducing D and sigmaD with less than 10% deviation in
the interval of relative dispersions 0.05 c 0.4 for both gamma and
lognorm distributions. Of course, I don't think that these expressions
are perfect and I would be glad to see better estimations.
Best regards,
Leonid
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