Mapping causal patterns in crystalline solids

Barakati, Kamyar; Nelson, Christopher T.; Morozovska, Anna N.; Ziatdinov, Maxim A.; Eliseev, Eugene A.; Zhang, Xiaohang; Takeuchi, Ichiro; Kalinin, Sergei V.

doi:10.1063/5.0284465

Mapping causal patterns in crystalline solids

Journal Article · Fri Sep 26 00:00:00 EDT 2025 · APL Machine Learning

DOI:https://doi.org/10.1063/5.0284465· OSTI ID:2997119

^[1]; Nelson, Christopher T. ^[2]; ^[3]; ^[4]; ^[3]; ^[5]; ^[5]; ^[6]

University of Tennessee, Knoxville, TN (United States)
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
National Academy of Sciences of Ukraine, Kyiv (Ukraine)
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
University of Maryland, College Park, MD (United States)
University of Tennessee, Knoxville, TN (United States); Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

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. 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. This approach is further extended to explore the spatial variability of the causal coupling using the sliding window transform method, which revealed that new causal relationships emerged at both the expected locations, such as domain walls and interfaces, and 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 posit that an in-depth understanding of complex disordered materials away from thermodynamic equilibrium necessitates understanding not only the generative processes that can lead to observed microscopic states but also the causal links between multiple interacting subsystems.

View Accepted Manuscript (DOE)

Research Organization:: The Pennsylvania State University, University Park, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC05-00OR22725; SC0020145; SC0021118

OSTI ID:: 2997119

Journal Information:: APL Machine Learning, Journal Name: APL Machine Learning Journal Issue: 3 Vol. 3; ISSN 2770-9019

Publisher:: AIP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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