Right.
Nevertheless they can be "phenomenological" extended (with some precautions)
to other crystallite shapes like ellipsoids or cylinders -
see JAC(2008)41, 615-627, sections 2 and 4.3.
In principle Dv & Da can be rigorously calculated for much complex shapes
and distributions if the user is able to 'run' through the three steps
described in section 4.2.
but he must be very careful when comparing experimental data with these
calculations.
Best wishes,
Nicolae Popa
----- Original Message -----
From: "Leonid Solovyov" <[EMAIL PROTECTED]>
To: <rietveld_l@ill.fr>
Sent: Tuesday, December 09, 2008 6:59 AM
Subject: Re: calculation of VWDS and SWDS from distributions?
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
*******************************************************
--- 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]
*********************************
If you encounter any difficulties
sending e-mails to the addresses in huntsman-nmg.com
domain,
this could be due to the our spam filter malfunction.
In case of such an event please send a message to
[EMAIL PROTECTED]
Please note that the old domain nmg.com.ru does not exist
anymore -
please update your address book accordingly
__________ NOD32 3671 (20081208) Information __________
This message was checked by NOD32 antivirus system.
http://www.eset.com
