Causal analysis of competing atomistic mechanisms in ferroelectric materials from high-resolution scanning transmission electron microscopy data

Abstract

Machine learning has emerged as a powerful tool for the analysis of mesoscopic and atomically resolved images and spectroscopy in electron and scanning probe microscopy, with the applications ranging from feature extraction to information compression and elucidation of relevant order parameters to inversion of imaging data to reconstruct structural models. However, the fundamental limitation of machine learning methods is their correlative nature, leading to extreme susceptibility to confounding factors. Here, we implement the workflow for causal analysis of structural scanning transmission electron microscopy (STEM) data and explore the interplay between physical and chemical effects in a ferroelectric perovskite across the ferroelectric-antiferroelectric phase transitions. The combinatorial library of the Sm-doped BiFeO 3 is grown to cover the composition range from pure ferroelectric BFO to orthorhombic 20% Sm-doped BFO. Atomically resolved STEM images are acquired for selected compositions and are used to create a set of local compositional, structural, and polarization field descriptors. The information-geometric causal inference (IGCI) and additive noise model (ANM) analysis are used to establish the pairwise causal directions between the descriptors, ordering the data set in the causal direction. The causal chain for IGCI and ANM across the composition is compared and suggests the presence of common causal mechanisms across the composition series. Ultimately, we believe that the causal analysis of the multimodal data will allow exploring the causal links between multiple competing mechanisms that control the emergence of unique functionalities of morphotropic materials and ferroelectric relaxors.

Hypothesis Learning in Automated Experiment: Application to Combinatorial Materials Libraries

“…Previously, we have extensively explored the property of this combinatorial library using high-resolution electron microscopy. [45,62] Here, we have explored the mesoscale electromechanical responses in this material system using PFM experiments. [63][64][65][66] This technique is based on the detection of the local electromechanical response induced by application of small amplitude (≈1 V ac ) periodic bias (100-300 kHz) to the scanning probe.…”

“…Previously, we have extensively explored the property of this combinatorial library using high‐resolution electron microscopy. [ 45,62 ]…”

“…The detailed growth conditions and characterization are described in previous publications. [45,62] Band excitation piezoresponse spectroscopy (BEPS) measurements were performed on an Oxford Instrument Asylum Research MFP3D atomic force microscopy system. A National Instruments DAQ card and a LabView framework are equipped for band excitation measurement.…”

A combined theoretical and experimental study of the phase coexistence and morphotropic boundaries in ferroelectric-antiferroelectric-antiferrodistortive multiferroics

“…Bi1-ySmyFeO3 and Bi1-yLayFeO3 solid solutions are known to possess gradual phase transition with the increase of the dopant concentration from the prototypical ferroelectric R-phase of pure BiFeO3 to an Ophase at 20% Sm and La, respectively [62,47,44]. According to aberration corrected scanning transmission electron microscopy measurements, the transition is readily observable in maps of the polar atomic displacement P between the A-site and B-site cation sublattices [62]. For the pure BiFeO3 P is a proxy for the electrical dipole moment and its distribution is polydomain characteristic of a rhombohedral phase ferroelectric including a 109° (vertical) and 180° (inclined) domain walls.…”

“…The causal [62] or/and Bayesian [63] analyses based on Eqs ( 9) and ( 10) can be in order to consider both (or more) hypothesis together, but the applicability of these approaches goes well beyond the used thermodynamic approach.…”