Polarization effects of X-ray monochromators modeled using dynamical scattering theory

The difference in the diffracted intensity of the σ- and π-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 π component relative to the σ component then becomes approximately proportional to |cos 2θm| rather than to cos22θm, where θm 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 2θ = 90° 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.