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A Local-Phase Framework for the BaTi_{1-x}Zr_xO_3$ Phase Diagram: From Ferroelectricity to Dipolar Glass

M. Sepliarsky, F. Aquistapace, F. Di Rino, R. Machado, M. G. Stachiotti

TL;DR

This work addresses how BaTi$_{1-x}$Zr$_x$O$_3$ transitions from ferroelectric to relaxor and eventually to a dipolar-glass state as Ti/Zr distribution varies. It introduces a first-principles–based atomistic framework that combines molecular dynamics with a clustering-based local-phase analysis to connect atomic-scale distortions to the macroscopic phase diagram. The study reproduces Vegard's-law volume, maps the composition–temperature phase boundaries, and reveals that local Ti-neighbor statistics govern the stability of R, O, T, and C local phases, providing a unified picture of ferroelectric, relaxor, and glassy behavior. The findings underscore the crucial role of B-site disorder in shaping dielectric response and offer a pathway to rationally design lead-free perovskites with tailored functional properties.

Abstract

We apply a first-principles-based atomistic model to investigate the BaTi(1-x)Zr(x)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.

A Local-Phase Framework for the BaTi_{1-x}Zr_xO_3$ Phase Diagram: From Ferroelectricity to Dipolar Glass

TL;DR

This work addresses how BaTiZrO transitions from ferroelectric to relaxor and eventually to a dipolar-glass state as Ti/Zr distribution varies. It introduces a first-principles–based atomistic framework that combines molecular dynamics with a clustering-based local-phase analysis to connect atomic-scale distortions to the macroscopic phase diagram. The study reproduces Vegard's-law volume, maps the composition–temperature phase boundaries, and reveals that local Ti-neighbor statistics govern the stability of R, O, T, and C local phases, providing a unified picture of ferroelectric, relaxor, and glassy behavior. The findings underscore the crucial role of B-site disorder in shaping dielectric response and offer a pathway to rationally design lead-free perovskites with tailored functional properties.

Abstract

We apply a first-principles-based atomistic model to investigate the BaTi(1-x)Zr(x)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.

Paper Structure

This paper contains 12 sections, 5 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Model and computational details
  3. Results
  4. Zero-temperature properties
  5. Macroscopic properties
  6. Local Structure Analysis
  7. Clustering analysis of local polarization patterns
  8. Finite temperature properties
  9. Phase diagram
  10. Ferroelectric regime
  11. Non-ferroelectric regime
  12. Conclusions

Figures (9)

  • Figure 1: Simulated average cell volume and net polarization of BaZr$_x$Ti$_{1-x}$O$_3$ as a function of composition.
  • Figure 2: Pair distribution function of Ti–O pairs (blue) and corresponding integrated coordination number (red) for different Zr concentrations.
  • Figure 3: Pair distribution function (PDF) obtained from the simulation with the atomistic model for BZT at $x=$ 0.0, 0.1, 0.8 and 1.0
  • Figure 4: Root mean square of local polarization as a function of Zr concentration at T = 0 K for the complete system (red), Ti cells (blue), and Zr cells (yellow).
  • Figure 5: Phase fractions of Ti-centered unit cells in BaZr$_x$Ti$_{1-x}$O$_3$ as a function of Zr composition at $T = 0$ K. Symbols correspond to the clustering analysis, while solid curves represent the fit from the probabilistic model.
  • ...and 4 more figures