Visualizing Structural Disorder in Submicron Crystals by 3D Electron Diffraction-Maximum Entropy Method

Structural disorder usually plays a decisive role in determining the functional properties of crystalline materials, yet it remains difficult to characterize, particularly at the micro- and nanometer scales. Three-dimensional electron diffraction (3D ED) provides access to crystallographic information from single crystals far smaller than those required for X-ray or neutron diffraction. However, its application has remained largely confined to average structure determination, where subtle and spatially diffuse electron density features associated with disorder are commonly obscured by truncation artifacts, model bias, and limitations inherent to the conventional Fourier method. Here, we develop a maximum entropy method-based electron density reconstruction framework specifically adapted for 3D ED (3D ED-MEM), enabling quantitative, model-independent electron density mapping directly from submicron crystals. By integrating electron diffraction-specific structure factors extraction and transformation procedures, this approach overcomes intrinsic limitations of the Fourier method and extends the capability of 3D ED to high-fidelity electron density analysis. Benchmarking against synchrotron X-ray diffraction using Si demonstrates that 3D ED-MEM yields electron density distributions of comparable accuracy. The generality of this approach is further validated using two archetypical structurally disordered thermoelectric materials, where 3D ED-MEM resolves trace interstitial ions and continuous ionic migration pathways. By enabling high quality electron density reconstruction from submicron crystals, 3D ED-MEM uniquely complements established diffraction techniques and is particularly powerful for materials where large single crystals cannot be grown and phase-pure powders are difficult to obtain, establishing a broadly applicable tool for probing disorder and dynamics in functional materials.