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 > >