Loop-level surrogate modeling of dopant-distribution effects in Ba(Zr,Ti)O$_3$

TL;DR

This paper introduces a surrogate modeling approach that links dopant spatial distributions in Ba(Zr,Ti)O$_3$ to their electromechanical response, enabling rapid design and screening of functional properties.

Contribution

It develops a novel accelerated workflow combining distribution encoding, surrogate modeling, and full response prediction for dopant-distribution effects in ferroelectrics.

Findings

Dopant distribution significantly influences hysteresis behavior and performance metrics.

The surrogate model accurately predicts polarization-electric-field loops from distribution parameters.

Design maps reveal how different distribution motifs optimize energy storage and electromechanical response.

Abstract

Barium titanate-based perovskites are important candidates for lead-free dielectric and electromechanical technologies. In Zr-substituted BaTiO$_3$ (BZT), 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: layer-like motifs, vertical lamellae, and nanoplate-like inclusions emerge in different performance regimes. More generally, predicting full response curves enables screening of other loop-derived targets and multi-objective design in substituted ferroelectrics.