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

Area of Science:

• Materials Science
• Crystallography
• Physics

Background:

• Traditional X-ray powder diffraction analysis uses kinematic scattering theory.
• This theory accurately describes polarization effects for highly mosaic samples but not for perfect crystals.

Purpose of the Study:

• To develop and validate equations for X-ray polarization effects based on dynamical diffraction theory.
• To address the limitations of kinematic scattering for systems with perfect crystal monochromators.

Main Methods:

• Derivation of equations for polarization effects using dynamical diffraction theory for monochromator crystals.
• Experimental validation using standard reference materials and a Germanium 111 incident-beam monochromator.

Main Results:

• The intensity ratio of π to σ polarized components is proportional to |cos 2θm| under dynamical diffraction, not cos²2θm.
• This dynamical correction significantly alters predicted X-ray powder diffraction intensities, especially away from 2θ = 90°.
• Experimental data confirm the necessity of the dynamical polarization correction for Ge 111 monochromators.

Conclusions:

• Kinematic scattering approximations are insufficient for accurate X-ray powder diffraction with perfect crystal monochromators.
• Dynamical diffraction theory provides a more accurate model for polarization effects in such systems.
• Current Rietveld analysis software lacks options for this crucial dynamical correction.