Faster grain-boundary diffusion with a higher activation enthalpy than bulk diffusion in ionic space-charge layers

TL;DR

This study uses continuum simulations to show that in acceptor-doped perovskite oxides, grain-boundary diffusion can be faster than bulk diffusion with a higher activation enthalpy, especially when involving specific defect mechanisms.

Contribution

It demonstrates through simulations that grain-boundary diffusion can have a higher activation enthalpy than bulk diffusion, challenging previous assumptions.

Findings

Simulations show r > 1 for grain-boundary to bulk diffusion ratio.

Faster diffusion occurs with neutral defect associates and accumulated isolated vacancies.

Conditions for observing r > 1 are identified and discussed.

Abstract

Faster diffusion of cations along grain boundaries is reported in the literature for a variety of acceptor-doped $AB\mathrm{O}_{3}$ perovskite-type oxides. The ratio $r$ of the activation enthalpy of grain-boundary diffusion ($\Delta H^\mathrm{gb}$) to the activation enthalpy of bulk diffusion ($\Delta H^\mathrm{b}$) is seen experimentally to lie in the range $0.7 < r = \Delta H^\mathrm{gb} / \Delta H^\mathrm{b} < 1.3$, albeit with substantial errors. In a previous publication [Parras and De Souza, Acta Mater. 195 (2020) 383] it was shown through a set of continuum simulations that cation-vacancy accumulation within negative space-charge layers at grain boundaries in acceptor-doped perovskites will give rise to faster grain-boundary diffusion of cations, with the associated values of $r$ approaching but not exceeding unity. In the present study, we demonstrate by means of continuum simulations that $r > 1$ is possible for faster cation diffusion along grain boundaries in an acceptor-doped perovskite. The specific case we consider is cation diffusion occurring by two related mechanisms, by slower (charged) isolated cation vacancies and by faster (neutral) defect associates of cation and anion vacancies. Within the negative space-charge layers, the isolated cation vacancies are strongly accumulated, whereas the neutral associates are unaffected. We calculate diffusion profiles for a two-dimensional bicrystal geometry by solving, first, Poisson's equation, and subsequently, the diffusion equation. We find that, if a small concentration of faster defect associates is responsible for bulk diffusion, and a hugely enhanced concentration of slower isolated vacancies yields faster diffusion along space-charge layers, $r>1$ is obtained. The conditions under which $r > 1$ may be observed are described, and issues with experimental confirmation are discussed.