A Molecular Dynamics study of grain boundaries in YSZ: Structure, energetics and diffusion of oxygen

Abstract

Several physical characteristics of the Σ3, Σ5, Σ11 and Σ13 grain boundaries in model YSZ bicrystals (namely grain boundary energies, radial distribution functions for pairs of ions and diffusion of oxygen along the grain boundaries) are systematically studied as functions of the concentration of yttria and temperature. The concentration of dopants affects the local structure at the grain boundaries; a preferential location of oxygen vacancies around yttrium cations is detected. Regarding the grain boundary energies, they mainly decrease with temperature, although any clear dependence with the amount of yttria was not apparent. Diffusion of oxygen is found to proceed more slowly along the grain boundaries than within the bulk, the differences becoming less important with increasing the temperature. The grain boundary diffusion coefficients for oxygen do not depend much on the concentration of yttria, but the activation energies exhibit a maximum at around 15 mol.% yttria for all the geometries. To the authors' knowledge, this is the first time that such a systematic study has been carried out. It could constitute the basis for a further understanding of the grain boundary structure and diffusion features at atomic scale in the YSZ system.

Introduction

Cubic, fully-stabilized Y₂O₃–ZrO₂ (YSZ) exhibits a set of physical properties (including high thermal stability, low thermal conductivity and high ionic conductivity among others) which make them attractive functional materials and usable as components of oxygen detectors or solid oxide fuel cells [1], [2], [3]. YSZ has the fluorite-type structure, with the cations distributed in an fcc lattice and the oxygen anions occupying all the tetrahedral interstices; Y³⁺ cations incorporate substitutionally to the Zr⁴⁺ sublattice. The additional charges introduced by the aliovalent doping are compensated by the creation of oxygen vacancies, one for each pair of Y³⁺ cations. These vacancies are responsible for the high ionic conductivity of YSZ, which is in part behind its technological importance and justifies the interest aroused by oxygen transport in this system [3].

Many works have dealt with the bulk diffusion of oxygen in single-crystal YSZ from both the experimental and numerical points of view [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. For instance, it is well known that the self-diffusivity of oxygen (and therefore the ionic conductivity) in YSZ depends on the content of yttria, exhibiting a maximum at around 8 mol.% yttria [16], [17]. This behavior is common to several oxide ceramics with the fluorite structure, and is closely related to the trapping of oxygen vacancies at certain lattice sites [18], [19], [20], [21]. Indeed, Yamamura and co-workers [10] have shown that oxygen vacancies become trapped preferentially as second neighbors of cationic sites, and that the number of trapped vacancies increases with the amount of yttria. The balance between both effects (increasing number of vacancies but decrease of the number of mobile ones with the amount of yttria) yields the observed maximum. In a recent work, an alternative analysis in terms of the accessible free space for vacancies has been performed [22]; in this study, the observed maximum of conductivity arises by the balance between the increasing number of vacancies and the decrease of free space accessible to them.

With respect to the activation energy for bulk diffusion of oxygen, it is commonly reported to lie within the range 0.8–1.4 eV, depending on the content of yttria [8], [17], [23], [24]. In this case, however, the dependence on the amount of yttria is much less clear. A pioneer work showed that the activation energy exhibits a minimum at around 5 mol.% yttria [18], although the most commonly reported behavior is a monotonic increase with the concentration of dopant cations [8], [16].

The presence of grain boundaries (GBs) causes additional features to arise in polycrystals, which become especially relevant at the nanoscale. There are not too many references to this matter in literature. Knöner et al. [25] have reported a significant improvement (up to three orders of magnitude) of the GB diffusion rates for oxygen compared to those within the bulk in nanosized zirconia doped with 6.9 mol.% yttria. To the authors' knowledge, this is the only group which claims for such a tendency. Instead, most of the experimental works seem to point out that the grain boundaries actually hinder diffusion of oxygen [24], [26], [27], [28], [29], [30], an effect which has been associated to the existence of space-charge zones surrounding the GBs.

In any case, it is quite difficult to extract accurate microscopic information about GB diffusion from experiments because one does not have a precise control of the crystallographic variables (such as local structure, grain misorientation angle or type of grain boundary). Numerical simulation appears here as a powerful tool to clarify the features of GB diffusion of oxygen in ceramics. This is the context of the present work, which deals with the systematic study by Molecular Dynamics (MD) of several GBs in YSZ depending on the temperature and the yttria content. In particular, the distributions of ions around oxygen anions nearby the boundaries, the GB energies and the characteristics of GB diffusion of oxygen have been examined. To the authors' best knowledge, this is the first time that such a systematic study, with obvious technologic and scientific relevance, has been made.