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 $t/ξ_g \ll 1$ 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 $ξ_g$.

💡 Research Summary

The paper investigates how absorption influences the intensities measured in three‑dimensional electron diffraction (3D‑ED) and, consequently, the accuracy of dynamical structure refinements. Starting from the Bloch‑wave formalism, the authors introduce a complex scattering potential U = U + iU′, where the imaginary part accounts for the loss of elastic intensity due to thermal diffuse scattering (TDS) and other inelastic processes. In the simplest two‑beam approximation, analytic expressions for the diffracted intensity with and without absorption are derived (Eqs. 2‑5). In the weak‑absorption limit (t/ξg ≪ 1) the integrated intensity takes the form

I_int^abs(t) ≈ e^(−2κ₀t) · I_int^no abs(t) ·