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In materials science, experimental conditions are precisely controlled to ensure high reproducibility. This property is well suited for causal inference in statistics, yet its potential remains unrealized. In this study, we integrate causal inference with structural equation modeling (SEM) to analyze birefringence images of the stress-induced ferroelectric SrTiO 3. Random forest analysis identified retardance at 14.1 K, 𝛿⁡(1⁢4.1⁢𝐾), as a key predictor of the ferroelectric phase transition temperature, 𝑇F. SEM revealed strong correlations between 𝑇F and 𝛿s, although multicollinearity in 𝛿s necessitated sparse principal component analysis to transform 𝛿⁡(1⁢4.1⁢𝐾) and 𝛿⁡(4⁢0.0⁢𝐾) into two independent components, 𝑃𝐶⁢1 and 𝑃𝐶⁢2, for subsequent causal analysis. Directed acyclic graphs (DAG) based on SEM helped infer causal relationships, revealing 𝑃𝐶⁢1‘s predominant influence on 𝑇F in stress/strain-concentrated regions (cluster E12) and 𝑃𝐶⁢2‘s influence in uniform stress/strain regions (cluster E34). Two-model learner (T-Learner) analysis revealed the factors behind the higher 𝑇F in E12 than in E34. Specifically, the difference in magnitude of the piezoelectric effect, which occurs uniformly throughout the substrate, causes 𝑇F to increase by 0.36 K [0.18 K, 0.54 K], while the flexoelectric effect, which occurs only in E12, causes it to increase by an additional 1.49 K [1.23 K, 1.75 K]. These findings demonstrate the utility of causal inference in disentangling piezoelectric and flexoelectric effects in the stress-induced ferroelectric SrTiO 3.

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• Creative Commons BY Attribution 4.0 International
  

Keyword: Causal inference, SEM, DAG, T-Learner, random forest, flexoelectricity, piezoelectricity, birefringence image, stress-induced ferroelectricity, SrTiO3

Date published: 2025-05-16

Publisher: Taylor & Francis

Journal:

• Science and Technology of Advanced Material (ISSN: 14686996) vol. 5 2503698

Funding:

Manuscript type: Author's version (Accepted manuscript)

MDR DOI: https://doi.org/10.48505/nims.5486

First published URL: https://doi.org/10.1080/27660400.2025.2503698

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Updated at: 2025-05-19 16:16:12 +0900

Published on MDR: 2025-05-20 08:18:55 +0900