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Insights into Cation Ordering of Double Perovskite Oxides from Machine Learning and Causal Relations

  • Ayana Ghosh*
    Ayana Ghosh
    Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
    Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
    *Email: [email protected]
    More by Ayana Ghosh
  • Gayathri Palanichamy
    Gayathri Palanichamy
    Department of Physics and Nanotechnology, SRM Institute of Science and Technology, Kattankulathur 603 203, Tamil Nadu, India
  • Dennis P. Trujillo
    Dennis P. Trujillo
    X-Ray Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
  • Monirul Shaikh
    Monirul Shaikh
    Department of Physics and Nanotechnology, SRM Institute of Science and Technology, Kattankulathur 603 203, Tamil Nadu, India
  • , and 
  • Saurabh Ghosh*
    Saurabh Ghosh
    Department of Physics and Nanotechnology, SRM Institute of Science and Technology, Kattankulathur 603 203, Tamil Nadu, India
    *Email: [email protected]
Cite this: Chem. Mater. 2022, 34, 16, 7563–7578
Publication Date (Web):August 5, 2022
https://doi.org/10.1021/acs.chemmater.2c00217
Copyright © 2022 American Chemical Society

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    Abstract

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    This work investigates origins of cation ordering in double perovskites using first-principles theory computations combined with machine learning (ML) and causal relations. We have considered various oxidation states of A, A′, B, and B′ from the family of transition metal ions to construct a diverse compositional space. A conventional framework employing traditional ML classification algorithms such as Random Forest (RF) coupled with appropriate features including geometry-driven and key structural modes leads to accurate prediction (∼98%) of A-site cation ordering. We have evaluated the accuracy of ML models by employing analyses of decision paths, assignments of probabilistic confidence bound, and finally a direct non-Gaussian acyclic structural equation model to investigate causality. Our study suggests that structural modes are crucial for classifying layered, columnar, and rock-salt ordering. The charge difference between A and A′ is the most important feature for predicting clear layered ordering, which in turn depends on the B and B′ charge separation. We have also designed mathematical relationships with these features to derive energy differences to form clear layered ordering. The trilinear coupling between tilt, in-phase rotation, and A-site antiferroelectric displacement in the Landau free-energy expansion becomes the necessary condition behind formation of A-site cation ordering.

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    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.2c00217.

    • Discussion of dependence of cation ordering on magnetic ground state, choice of on-site Coloumb interactions, disorder tendencies at the cation sites, and finite temperatures, as well as details on methods such as the SISSO and LINGAM causal models and quantification of causal ordering; magnetic ground states of the representative systems; approach of U-value selections for various compounds; additional Structural Modes in the validation data set; comparison between the predicted (SISSO equation) and computed ΔE; classification results as described by confusion matrices for the validation sets using Model III; representative decision paths to predict C[0], L[1], and R[2] ordering arrangements using a combination of geometry-driven and structural mode features for one of the trees among the ensemble of trees; tolerance factors and magnetic ground states of 14 representative compounds; calculated local magnetic moments for various BB combinations in AA′BB′O6 as studied in this work within the GGA+ UE framework; list of compounds with corresponding tolerance factors and energy differences between the ordered and the disordered phases, as computed utilizing SQS; list of compounds and respective A-site ordering arrangements (computed by DFT); list of compounds and respective A-site and B-site ordering arrangements as evaluated for the external validation set; list of non-DFT derived descriptors and corresponding brief descriptions as obtained by Automatminer; coefficients quantifying the positive and negative causation effects for the causal network to predict columnar and layered ordering and for the causal network to predict layered and rock-salt/columnar and rock-salt ordering; coefficients quantifying the positive and negative causation effects to predict clear layered ordering; and finite temperature effects (PDF)

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    Cited By

    This article is cited by 4 publications.

    1. Matthew S. Chambers, Jiadong Chen, Robert L. Sacci, Rebecca D. McAuliffe, Wenhao Sun, Gabriel M. Veith. Memory Effect on the Synthesis of Perovskite-Type Li-Ion Conductor LixLa2/3–x/3TiO3 (LLTO). Chemistry of Materials 2024, 36 (3) , 1197-1213. https://doi.org/10.1021/acs.chemmater.3c01928
    2. Palanichamy Gayathri, Saurabh Ghosh, Ayana Ghosh. Predictive Design of Hybrid Improper Ferroelectric Double Perovskite Oxides. Chemistry of Materials 2024, 36 (2) , 682-693. https://doi.org/10.1021/acs.chemmater.3c02067
    3. Palanichamy Gayathri, M. J. Swamynathan, Monirul Shaikh, Ayana Ghosh, Saurabh Ghosh. Switching of Hybrid Improper Ferroelectricity in Oxide Double Perovskites. Chemistry of Materials 2023, 35 (17) , 6612-6624. https://doi.org/10.1021/acs.chemmater.3c00108
    4. Sathiyamoorthy Buvaneswaran, Monirul Shaikh, Rajan Gowsalya, Trilochan Sahoo, Saurabh Ghosh. Design of Ferroelectric Double Perovskite Oxides as Photovoltaic Materials. The Journal of Physical Chemistry C 2023, 127 (31) , 15486-15499. https://doi.org/10.1021/acs.jpcc.3c02094

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