Dear Maxim,
The formulae
Dv=3mu_4/2mu_3
Da=4mu_3/3mu_2
are valid for spherical crystallites only.
Accordingly, in the expression
mu_i=Int[0, Infinity]{x^i*p(x)dx}
x should be the radius of spherical crystallite, but not “particle size”.
Best regards,
Leonid
*******************************************************
Leonid A. Solovyov
Institute of Chemistry and Chemical Technology
660049, K. Marx 42, Krasnoyarsk, Russia
www.icct.ru/eng/content/persons/Sol_LA
www.geocities.com/l_solovyov
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--- On Mon, 12/8/08, Максим В. Лобанов <[EMAIL PROTECTED]> wrote:
> From: Максим В. Лобанов <[EMAIL PROTECTED]>
> Subject: calculation of VWDS and SWDS from distributions?
> To: "rietveld_l@ill.fr" <rietveld_l@ill.fr>
> Date: Monday, December 8, 2008, 2:04 PM
> Dear colleagues,
>
> I am facing a problem of correlating laser scattering (DLS)
> and X-ray diffraction data.
> For correct comparison, I need either to calculate some
> model distribution from X-ray data (this is feasible
> assuming lognormal distribution - there are ready software
> solutions for that) or typical "X-ray sizes" (Dv
> and/or Da) from given distributions.
> The inverse task (calculating Dv and/or Da from given
> distributions) appears to be very simple, but it seems there
> is no ready software solution, and I need to manually
> integrate the data. But before doing that I would like just
> to be sure that I use correct formulae.
> I read the paper dealing with that in great detail (JAC,
> 35, 338 by Popa & Balzar, Ref. 1), but it is too
> mathematical, and I am not completely confident if I
> understood everything correctly.
>
> If we denote distribution (normalized to unity) as p(x),
> x=particle size
> then, according to Ref.1:
> Dv=3mu_4/2mu_3 (1)
> and
> Da=4mu_3/3mu_2 (2)
>
> Do I understand correctly, that moments mu_i are just:
>
> mu_i=Int[0, Infinity]{x^i*p(x)dx}
>
> Or there are some missing factors somewhere?
>
> Sincerely,
> Maxim.
>
> -------------------------------------------
> Dr. Maxim Lobanov
> R&D Director
> Huntsman-NMG
> mailto: [EMAIL PROTECTED]
>
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