Mapping causal patterns in crystalline solids

TL;DR

This study uses advanced microscopy and causal modeling to analyze atomic structure evolution and causal relationships in Sm-substituted BiFeO3 thin films during phase transitions, revealing new local causal interactions.

Contribution

It introduces a novel application of LiNGAM and sliding window methods to map causal relationships in atomic-scale imaging data of complex materials.

Findings

New causal relationships at domain walls and interfaces

Emergence of causal links in nanophase regions

Spatial variability of causal coupling observed

Abstract

The evolution of the atomic structures of the combinatorial library of Sm-substituted thin film BiFeO3 along the phase transition boundary from the ferroelectric rhombohedral phase to the non-ferroelectric orthorhombic phase is explored using scanning transmission electron microscopy (STEM). Localized properties including polarization, lattice parameter, and chemical composition are parameterized from atomic-scale imaging and their causal relationships are reconstructed using a linear non-Gaussian acyclic model (LiNGAM). This approach is further extended toward exploring the spatial variability of the causal coupling using the sliding window transform method, which revealed that new causal relationships emerged both at the expected locations, such as domain walls and interfaces, but also at additional regions forming clusters in the vicinity of the walls or spatially distributed features. While the exact physical origins of these relationships are unclear, they likely represent nanophase separated regions in the morphotropic phase boundaries. Overall, we pose that an in-depth understanding of complex disordered materials away from thermodynamic equilibrium necessitates understanding not only of the generative processes that can lead to observed microscopic states, but also the causal links between multiple interacting subsystems.