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  • Open Access

Loop-level surrogate modeling of dopant-distribution effects in Ba(Zr,Ti)O3

Heiko Röthl, Elke Kraker, Julien Magnien, Manfred Mücke, and Florian Mayer*

  • *Contact author: florian.mayer@mcl.at
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Phys. Rev. Materials 10, 093803 – Published 10 September, 2026

DOI: https://doi.org/10.1103/67wx-xw5h

Abstract

Barium titanate–based perovskites are important candidates for lead-free dielectric and electromechanical technologies. In Zr-substituted BaTiO3, functional behavior is usually discussed in terms of the average Zr concentration, while the influence of dopant spatial distribution beyond average concentration is less understood and difficult to explore systematically. Here we present an accelerated materials-design workflow that links controlled dopant distributions to full field-driven response curves. We generate a broad set of Zr distributions spanning a continuum of nanoscale arrangements, with layers, rods, dots, and lamellae serving as representative end-member motifs, and encode each configuration using a compact, parametrized descriptor model. Effective-Hamiltonian molecular dynamics is used to compute polarization–electric-field and strain–field hysteresis loops and we train a conditional autoencoder surrogate to predict complete loops directly from the distribution parameters. This surrogate enables rapid screening and dense, property-selective design maps at scales that are not feasible with direct simulations alone and it supports targeted follow-up simulations in regions of interest. Using the predicted loop database, we screen the distribution space for multiple functional targets, including energy-storage performance, electromechanical response, and switching behavior, and identify the corresponding dopant distribution motif families. The resulting design maps show that dopant distribution is an independent tuning parameter that can strongly affect hysteresis behavior and loop-derived figures of merit: layerlike motifs, vertical lamellae, and nanoplatelike inclusions emerge in different performance regimes. More generally, predicting full response curves enables screening of other loop-derived targets and multiobjective design in substituted ferroelectrics.

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Phys. Rev. Materials 10, 093803– Published 10 September, 2026
  • Received 14 April 2026
  • Accepted 18 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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