Crystal truncation rods in kinematical and dynamical x-ray diffraction theories

TL;DR

This paper compares kinematical and dynamical x-ray diffraction theories for crystal truncation rods, showing they agree quantitatively for most intensities and clarifying the limits of dynamical calculations.

Contribution

It demonstrates the quantitative agreement between kinematical and dynamical theories for crystal truncation rods and specifies the conditions and limitations of this agreement.

Findings

Kinematical and dynamical calculations agree down to ~10^{-7} of peak intensity.

Agreement depends on the choice and number of reflections included.

Dynamical calculations are limited by electron density truncation effects.

Abstract

Crystal truncation rods calculated in the kinematical approximation are shown to quantitatively agree with the sum of the diffracted waves obtained in the two-beam dynamical calculations for different reflections along the rod. The choice and the number of these reflections are specified. The agreement extends down to at least $\sim 10^{-7}$ of the peak intensity. For lower intensities, the accuracy of dynamical calculations is limited by truncation of the electron density at a mathematically planar surface, arising from the Fourier series expansion of the crystal polarizability.