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Machine learning has emerged as a powerful tool for the analysis ofmesoscopic and atomically resolved images and spectroscopy in electron andscanning probe microscopy, with the applications ranging from featureextraction to information compression and elucidation of relevant orderparameters to inversion of imaging data to reconstruct structural models.However, the fundamental limitation of machine learning methods is theircorrelative nature, leading to extreme susceptibility to confounding factors.Here, we implement the workflow for causal analysis of structural scanningtransmission electron microscopy (STEM) data and explore the interplay betweenphysical and chemical effects in ferroelectric perovskite across theferroelectric-antiferroelectric phase transitions. The combinatorial library ofthe Sm-doped BiFeO3 is grown to cover the composition range from pureferroelectric BFO to orthorhombic 20% Sm-doped BFO. Atomically resolved STEMimages are acquired for selected compositions and are used to create a set oflocal compositional, structural, and polarization field descriptors. Theinformation-geometric causal inference (IGCI) and additive noise model (ANM)analysis are used to establish the pairwise causal directions between thedescriptors, ordering the data set in the causal direction. The causal chainfor IGCI and ANM across the composition is compared and suggests the presenceof common causal mechanisms across the composition series. Ultimately, webelieve that the causal analysis of the multimodal data will allow exploringthe causal links between multiple competing mechanisms that control theemergence of unique functionalities of morphotropic materials and ferroelectricrelaxors.

Causal analysis of competing atomistic mechanisms in ferroelectric materials from high-resolution Scanning Transmission Electron Microscopy data