Right, but specially for students- beginners we must be much, let say,
didactic
LP means (Lorentz) * (Polarisation)
What is important in Rietveld refinement when a lot of mirrors &
monochromators are present is how they change (Polarization)
because (Lorentz) is changed by adding factors independent on hkl, then
entering in the scaling factor
Presuming the same scattering plane for all "scatterers" the polarization
factor is:
pol = SIN(PSI)**2 + COS(PSI)**2*COS(2*TET1)**2*COS(2*TET2)**2
*.....*COS(2*TETm)**2*COS(2*TETb)**2
where TET1, TET2, ....., TETm are the Bragg angles at monochromator 1,
2, ....,m
and where TETb is the Bragg angle at sample (depending on hkl)
and where PSI is the angle between polarization vector of the incident
beam - IF it is TOTALLY POLARIZED!!! - and the scattering plane;
If the incident beam is NOT POLARIZED the averages of both SIN(PSI)**2 and
COS(PSI)**2 result in 1/2.
If the incident beam is partially polarized one replace for example
SIN(PSI)**2 by P0 , consequently COS(PSI)**2 = 1 - P0 and one refine P0
If the geometry is much complicated (different scattering planes for
different monochromators) "pol" should be calculated for the given
geometry by applying successively the known formula (see a book of
electrodynamics, e.g.. Landau)
Ej+1 = (Ej X u)Xu and taking at the END: |E(last)|**2 / |E0|**2 (X
means vectorial product)
where Ej is the electric field vector in the beam scattered j times and u
is the unit vector along the scattered beam j+1
Best wishes,
Nicolae Popa
----- Original Message -----
From: "Leonid Solovyov" <l_solov...@yahoo.com>
To: <rietveld_l@ill.fr>
Sent: Sunday, July 26, 2009 9:05 AM
Subject: RE: LP factor in the Rietveld refinement
In principle, the LP correction for a multi-bounce monochromator is similar
to that for a single-crystal one with the same crystal type and reflection
indexes (or diffraction angle).
The exact LP value depends, as well, on the crystal perfection (mosaicity)
and for supremely precise measurements one might consider refining the LP
value as was mentioned by Kurt and Peter. Besides the angular range, the
correlation with thermal parameters, and the instrument alignment, one more
problem of the LP refinement is the correct choice of the atomic scattering
curves in accordance with the oxidation states which might be not quite
obvious in general.
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 Sun, 7/26/09, Peter Y. Zavalij <pzava...@umd.edu> wrote:
From: Peter Y. Zavalij <pzava...@umd.edu>
Subject: RE: LP factor in the Rietveld refinement
To: rietveld_l@ill.fr
Date: Sunday, July 26, 2009, 5:03 AM
That's right. LP refinement works
just fine within TOPAS but angular range
as wide as possible is needed. If it is up to 140-150 deg.
2thteta LP does
not correlate much with thermal parameters. Refined LP is
not exact but very
close.
Peter Zavalij
X-ray Crystallographic Center
University of Maryland
College Park, MD
Office: (301)405-1861
Lab: (301)405-3230
Fax: (301)314-9121
-----Original Message-----
From: Kurt Leinenweber [mailto:ku...@asu.edu]
Sent: Saturday, July 25, 2009 8:53 PM
To: alor...@unex.es;
Leonid Solovyov
Cc: rietveld_l@ill.fr
Subject: RE: LP factor in the Rietveld refinement
Hi all,
I haven't actually DONE this, so maybe I shouldn't put my 2
cents in, but
can't you refine the polarization factor by using a
standard such as Y2O3
and fixing the structure and thermal parameters of the
standard while
refining the polarization angle?
The angle so obtained should agree with what the theory
tells you for your
diffractometer configuration, but it seems more comforting
to verify it by a
measurement.
- Kurt
________________________________
From: alor...@unex.es
[mailto:alor...@unex.es]
Sent: Sat 7/25/2009 1:29 PM
To: Leonid Solovyov
Cc: rietveld_l@ill.fr
Subject: Re: LP factor in the Rietveld refinement
In this context:
What about the LP for a Goebel mirror followed by a
4-bounce or 2-bounce
primary monochromator?
Best regards
angel l. ortiz
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