Thanks, Nicolae, for the didactic comment, but I must add that the expression
pol = SIN(PSI)**2 + COS(PSI)**2*COS(2*TET1)**2*COS(2*TET2)**2
*.....*COS(2*TETm)**2*COS(2*TETb)**2
is an idealization and the real polarization factor may deviate notably from
the idealized one depending on the crystal type (perfection/mosaicity) and
other factors especially for multi-bounce systems. So, regarding the
polarization factor of a real system in use, it is better to either consult the
manufacturer or try determining it experimentally, for example, by measuring
the same standard sample with and without monochromator.
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, 7/27/09, Nicolae Popa <nicp...@infim.ro> wrote:
> From: Nicolae Popa <nicp...@infim.ro>
> Subject: Re: LP factor in the Rietveld refinement
> To: "Leonid Solovyov" <l_solov...@yahoo.com>, rietveld_l@ill.fr
> Date: Monday, July 27, 2009, 11:04 AM
> 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
>
>
