The Diffusion Kinetics of Ba Cations in Perovskite BaTiO$_3$: A Combined Tracer Diffusion and Metadynamics Study

TL;DR

The paper tackles the challenge of identifying Ba diffusion mechanisms in cubic BaTiO3 by combining Ba-130 tracer diffusion experiments with metadynamics simulations of Ba-vacancy migration. The experimental data yield slow bulk Ba diffusion with a high activation enthalpy (≈4.1 eV), while MtD simulations reveal that isolated Ba vacancies have much higher barriers and cannot account for the observed diffusivity; diffusion via defect associates, particularly Ba–Ti vacancy associates, provides a more likely path. Ruling out isolated vacancies based on absolute diffusivities, the study advocates defect-associate or cluster-mediated diffusion as the dominant mechanism in the cubic phase, while acknowledging potential variations with Ba/Ti composition. Overall, the work demonstrates the importance of using absolute diffusion coefficients, not just activation enthalpies, to correctly assign diffusion mechanisms in oxide perovskites and offers a framework for analyzing diffusion in BaTiO3 under high-temperature processing conditions.

Abstract

Tracer diffusion experiments and metadynamics (MtD) simulations were used to study the diffusion of Ba cations in the cubic phase of the perovskite oxide BaTiO$_3$. $^{130}$BaTiO$_3$ thin films were used as diffusion sources to introduce barium tracer diffusion profiles into single-crystal samples at temperatures $1348 \leq T/\mathrm{K} \leq 1498$. The $^{130}$Ba profiles were determined by time-of-flight secondary ion mass spectrometry, and then analysed to yield Ba tracer diffusion coefficients ($D_\mathrm{Ba}^\ast$). MtD simulations were performed in order to obtain barium-vacancy diffusion coefficients ($D_\mathrm{v_{Ba}}$) for selected vacancy mechanisms as a function of temperature. $D_\mathrm{v_{Ba}}$ is predicted to be increased significantly by an adjacent oxygen vacancy, and even more, by an adjacent titanium vacancy. From the combined consideration of $D_\mathrm{Ba}^\ast$ and $D_\mathrm{v_{Ba}}$, we conclude that Ba diffusion in these samples occurred most probably by the migration of defect associates, and not by the migration of isolated barium vacancies. More generally, our results draw attention to the dangers of relying solely on activation enthalpies to interpret diffusion data.

Figures (6)

• Figure 1: Experimentally determined activation enthalpies of cation self-diffusion in perovskite BaTiO3. A site refers to studies in which Ba or Sr diffusion was probed; B site, to studies in which Ti or Zr diffusion was probed; and A or B site, to data extracted from sintering, grain-growth or creep studies: a Garcia.1953, b Kitahara.1999, c Koerfer.2008, d Sazinas.2017, e Garcia.1953, f Preis.2006, g Koerfer.2008, h Nomura.1956, i Anderson.1965, j Carry.1986, k Genuist.1988, m Beauchesne.1989, n Xue.1990, p Lin.2000, q Lin.2000, r Kambale.2014, s Park.2015.
• Figure 2: ToF-SIMS depth profile of a ^130BaTiO3 layer on a single-crystal BaTiO3 sample prior to diffusion (symbols, experimental data; line, fit of Eq. \ref{['eqn_diffsoln']} for $t = 0$).
• Figure 3: ^130Ba tracer diffusion profile obtained by ToF-SIMS depth profiling after a diffusion anneal in air at $T = 1448$ K for $t = 95$ h (symbols, experimental data; black line, fit of Eq. \ref{['eqn_diffsoln']} for bulk diffusion; grey line, fit to $\ln n^\ast \propto x^1$ for faster dislocation diffusion).
• Figure 4: ^130Ba tracer diffusion coefficients in single-crystal BaTiO3 obtained experimentally by ToF-SIMS depth profiling as a function of inverse temperature. .
• Figure 5: Diffusion coefficients of barium vacancies in cubic BaTiO3 as a function of inverse temperature obtained by metadynamics simulations for barium-vacancy migration by isolated $\mathrm{v_{Ba}}$, as part of $\mathrm{(v_{Ba}v_{O})}$, or as part of $\mathrm{(v_{Ba}v_{Ti})}$.