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 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 $\xi_g$.