We introduce a new method called kappa refinement for analyzing crystal structures using three-dimensional electron diffraction (3D ED) data. Traditionally, when scientists use 3D ED to determine the arrangement of atoms in a crystal, they assume that each atom is perfectly spherical and does not interact with its neighbors. This approach, known as the Independent Atom Model (IAM), makes it easier to find where atoms are but fails to capture how electrons are shared or transferred between atoms, which is crucial for understanding chemical bonding and the true electronic structure of materials.
Kappa refinement improves on the IAM by allowing the electron cloud around each atom to expand or contract, which reflects changes in the number of valence electrons due to bonding or ionization. This method introduces only two extra parameters per atom but enables the extraction of information about charge transfer and the degree of ionization of atoms in the crystal. We applied kappa refinement to five different inorganic compounds, including quartz, natrolite, borane, lutetium aluminum garnet, and caesium lead bromide. We showed that kappa refinement leads to more accurate structural models and provides direct information about how electrons are distributed and transferred between atoms. The results from kappa refinement were validated by comparing them with theoretical calculations based on density functional theory (DFT), showing good agreement and confirming the reliability of the method.
This work demonstrates that 3D ED data, when processed with kappa refinement, can reveal not just the positions of atoms but also the subtle details of chemical bonding and ionization states, even in very small or complex crystals. This represents a significant step forward in the use of electron diffraction for materials science, chemistry, and physics, as it allows scientists to study charge density and bonding effects in a wider range of materials than before.
