Polarization Effects Of X-Ray Monochromators Modeled Using Dynamical Scattering Theory

The difference in the diffracted intensity of the sigma- and pi-polarized components of an X-ray beam in powder diffraction has generally been treated according to equations based on dipole scattering, also known as kinematic X-ray scattering. Although this treatment is correct for powders and post-sample analyzers known to be of high mosaicity, it does not apply to systems configured with nearly perfect crystal incident-beam monochromators. Equations are presented for the polarization effect, based on dynamical diffraction theory applied to the monochromator crystal. The intensity of the pi component relative to the sigma component then becomes approximately proportional to vertical bar cos 2 theta(m)vertical bar rather than to cos(2)2 theta(m), where theta(m) is the Bragg diffraction angle of the monochromator crystal. This changes the predicted intensities of X-ray powder diffraction patterns produced on instruments with incident-beam monochromators, especially in the regions far from 2 theta = 90 degrees in the powder pattern. Experimental data, based on well known standard reference materials, are presented, confirming that the dynamical polarization correction is required when a Ge 111 incident-beam monochromator is used. The dynamical correction is absent as an option in the Rietveld analysis codes with which the authors are familiar.