Dear Nicolae,
I will comment only upon your last statement because the limitations of
your modeling are clear.
> Well, I don't know where from you taken these formulae
> but I observe that for spheres of equal radius, then zero dispersion,
> you have:
> sigma(D)=5<D>/4, different from zero!
First of all, for spheres of equal radius and IDEAL definition
of Dv and Da:
sigma<D> = <D>(Dv/Da - 1/2)/2 = <D>(9/8 - 1/2)/2 = 5<D>/16
Yes it is not zero, but the expressions I derived work only for
0.05 < c < 0.4 and I derived them not for IDEAL Dv and Da. If you
perform WEIGHTED least-squares fitting of TCH p-V function to a profile
simulated for spherical crystal and added by ~10% background level (to
be closer to real Rietveld refinement) you will obtain the ratio of
Dv/Da~3/4 not 9/8! This ratio is wrong but this is what we have from
WEIGHTED least-squares fitting of TCH p-V to simulated data. In this
case
sigma<D> = <D>(Dv/Da - 1/2)/2 = <D>(3/4 - 1/2)/2 = <D>/8,
different from zero again, sorry, this world is not IDEAL.
Best wishes,
Leonid
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