The role of absorption in three-dimensional electron diffraction dynamical structure refinement

TL;DR

This paper investigates the impact of absorption in 3D electron diffraction, deriving theoretical expressions, performing simulations, and applying dynamical refinement to assess its significance in structure analysis.

Contribution

It introduces a two-beam expression for absorbed intensity and demonstrates the conditions under which absorption affects dynamical refinement accuracy.

Findings

Neglecting absorption causes residuals that grow with thickness.

Including absorption improves refinement for high-Z materials at large thicknesses.

Absorption is negligible for routine refinement in most cases.

Abstract

The role of absorption in 3D electron diffraction is established through analytical theory, simulation, and dynamical refinement. A two-beam expression for the absorbed integrated intensity is derived, showing that for $t/\xi_g \ll 1$ reflections follow a uniform exponential decay set by the mean absorptive potential $U_0'$. Many-beam simulations demonstrate that neglecting absorption in dynamical refinement of integrated intensities incurs a residual that increases linearly with thickness and diverges near zone axes. Dynamical refinements were performed on CsPbBr$_3$, quartz, and borane, with the inclusion of absorption yielding an improvement in $R_{\mathrm{obs}}$ from $6.4$ to $5.3$ \% for CsPbBr$_3$ and negligible changes for quartz and borane. Absorption is therefore deemed negligible for routine refinement of integrated intensities except in high-$Z$ materials at thicknesses approaching $\xi_g$.