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

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 in centrosymmetric crystals is derived, showing that for $t/ξ_g \ll 1$ reflections follow a uniform exponential decay set by the mean absorptive potential $U_0'$. Many-beam simulations of both centrosymmetric and non-centrosymmetric crystals reveal additional reflection-specific anomalous absorption beyond the uniform attenuation set by $U_0'$. Neglecting these effects in dynamical refinement of integrated intensities incurs an error that increases approximately linearly with thickness, with this error becoming more severe 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 improvements for quartz and borane. Anomalous absorption may therefore be ignored for routine refinement of integrated intensities except in high-$Z$ materials at thicknesses approaching $ξ_g $.