Local-phase framework for the BaTi1−𝑥⁢Zr𝑥⁢O3 phase diagram: From ferroelectricity to dipolar glass

Abstract

We apply a first-principles-based atomistic model to investigate the BaTi1−𝑥⁢𝑍⁢𝑟𝑥⁢𝑂3 phase diagram, focusing on both macroscopic and local structural changes. Our approach, which combines molecular dynamics with machine learning techniques, accurately captures the influence of Ti and Zr cations on their local environment and its evolution with composition and temperature. The computed phase diagram shows excellent agreement with existing experimental and theoretical data. Beyond reproducing known results, our analysis reveals that the behavior of the solid solution across different compositions and temperatures can be understood in terms of coexisting Ti cells with different symmetries, whose stability depends on the local B-site configuration. This local-phase-based approach provides a unified description of the distinct regions of the solid solution—including ferroelectric, relaxor, and dipolar glass phases—and captures the continuous evolution from one regime to another. Our findings demonstrate how atomic-level distortions drive the complex macroscopic behavior of the material.