Abstract
Structurally heterogeneous materials present major challenges for characterization due to their complex nanoscale order. Sodium poly(heptazine imide) (NaPHI), a layered carbon nitride photocatalyst, exemplifies this complexity, with its precise structure remaining unresolved. Here, we uncover new structural insights into NaPHI using energy-filtered four-dimensional scanning transmission electron microscopy combined with machine-learning-based diffraction image segmentation, supported by transmission electron microscopy, atomic force microscopy, X-ray diffraction, and Raman spectroscopy. At the mesoscale, NaPHI flakes display bent morphologies, while nanodiffraction patterns reveal features characteristic of stacking disorder. Based on these insights, we modeled a NaPHI-layered structure incorporating out-of-plane undulations (waves) with amplitudes of ∼0.5 Å and wavelengths of 2-3 nm. This model reproduces the observed line features in nanodiffraction patterns and agrees with powder X-ray diffraction data, thereby bridging local and bulk structural information. The introduced approach uses data-driven machine learning to identify statistically significant features, offering a robust framework for structural analysis of semi-crystalline materials.