Nanoscale Phase Identification Using Two-Dimensional Pair Correlation Functions: A Case Study on Hafnium Oxide

Accurate identification of local phases in nanocrystalline materials is essential for understanding their functional properties, but it remains a significant challenge for polymorphic materials to locally differentiate them at nanoscale. This challenge is further compounded in polycrystalline materials with randomly oriented grains and the coexistence of multiple phases. In this report, we present a methodology for phase and orientation identification at the nanoscale by leveraging vector pair correlation functions extracted from atomically resolved scanning transmission electron microscopy (STEM) images. We demonstrate the accuracy of the methodology on both simulated and experimental data from HfO2-based films, a material that exhibits multiple coexisting phases in films with thicknesses ranging from 5 to 20 nm. While demonstrated on HfO2 films, the methodology can be extended to other polymorphic nanocrystalline systems with complex phase coexistence.