Segregation to the grain boundaries in YSZ bicrystals: A Molecular Dynamics study

Solid State Ionics 237 (2013) 8–15

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Segregation to the grain boundaries in YSZ bicrystals: A Molecular Dynamics study Robert L. González-Romero a, Juan J. Meléndez b,⁎, D. Gómez-García c, F.L. Cumbrera a, A. Domínguez-Rodríguez a a b c

Departamento de Física de la Materia Condensada, Universidad de Sevilla, Avda. Reina Mercedes, s/n, 41012 Sevilla, Spain Departamento de Física, Universidad de Extremadura, Avda. de Elvas, s/n, 06006 Badajoz, Spain Departamento de Física de la Materia Condensada-ICMSE, Universidad de Sevilla, CSIC, Avda. Reina Mercedes, s/n, 41012 Sevilla, Spain

a r t i c l e

i n f o

Article history: Received 23 October 2012 Received in revised form 23 January 2013 Accepted 2 February 2013 Available online 8 March 2013 Keywords: YSZ Segregation Grain boundaries Molecular dynamics

a b s t r a c t A Molecular Dynamics study about the segregation of yttrium at 1500 K to a Σ5 grain boundary in 8 mol% YSZ has been performed. Segregation has been induced by explicitly taking into account the excess energy associated to the elastic misfit effect for yttrium cations located nearby the grain boundary planes. After an initial transient, a steady regime is reached, in which the number of yttrium cations does not increase with time. Accumulation of yttrium cations is accompanied by that of zirconium ones and oxygen vacancies at some distance of the grain boundary planes. The changes in the radial distribution functions for different ionic pairs are discussed, as also the effect of segregation on oxygen diffusion along the grain boundaries and in volume. Finally, the possibility that segregated yttrium located at available free sites at the grain boundaries is pointed out. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Yttria―zirconia-based ceramics, among others, are widely used as electrolytes in solid-oxide fuel cells (SOFCs) because of their high ionic conductivity which, together with their stability against oxidizing and reducing environments and mechanical integrity make them very attractive functional materials; Refs. [1–4] are perspective papers about the role played by these systems in the development of SOFCs. In addition, they may exhibit superplasticity under certain conditions of temperature and grain morphologies [5], which justifies their use as structural components. This set of physical properties is intimately related to two factors. First, Y2O3–ZrO2 ceramics are non-stoichiometric. Indeed, Y 3+ cations are aliovalent in the Zr4+ sublattice, where they locate substitutionally, and their incorporation yields the formation of oxygen vacancies (one for each pair of dopant cations) to keep the electroneutrality of the system. The transport of oxygen mediated by these vacancies are responsible for the exceptional ionic conductivity of YSZ (yttria-stabilized cubic zirconia), so that understanding and optimizing the characteristics of oxygen diffusion in this system is crucial for its use in SOFCs and other devices [3,4]. Recent studies have shown that diffusion of oxygen in YSZ can be significantly improved under certain stress states, especially at the intermediate temperature range, as well as in layered structures or nanograined samples, which has promising technological applications [4,6–8]. The second key factor is the behavior of the grain boundaries (GBs). For instance, these greatly affect ionic ⁎ Corresponding author. Tel.: +34 924 28 96 55; fax: +34 924 28 96 51. E-mail address: [email protected] (J.J. Meléndez). 0167-2738/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ssi.2013.02.002

conduction in yttria–zirconia, a fact which becomes crucial at the nanoscale [9]; in relation to superplasticity, deformation proceeds by an accommodated-grain boundary sliding mechanism [5,10]. Both factors are actually related to each other, since Y 3+ cations segregate to the GBs in yttria–zirconia ceramics, as has been set forth in many studies [11–26]. Thus, Fisher et al. [26] have reported a decrease in the ionic conductivity of YSZ because of yttrium segregation at the GBs. Regarding the mechanical behavior, it has been demonstrated that dopant cations segregated at the GBs of superplastic YTZ (tetragonal yttria–zirconia) give rise to a threshold stress below which grain boundary sliding does not occur [27,28]. Segregation of yttrium is driven by two main mechanisms. On one hand, the significant elastic misfit effect due to the dissimilarity between the ionic radii of the Zr4+ (0.84 Å) and Y3+ (1.02 Å) cations helps the dopant species to segregate [12]. The elastic driving force for segregation depends upon the distance to the boundaries (see, for instance, Refs. [29,30]). On the other hand, the several defect species in YSZ behave as effective electric charges, and the Coulombic interaction between them partially drives segregation as well [30]. It seems clear then that segregation to the GBs is a phenomenon which needs to be fully characterized and understood for an optimum development and design of yttria–zirconia ceramics for functional or structural applications. Experimental studies have set forth that Y 3+ cations segregate within a layer a few nanometers thick surrounding the GB planes in both YSZ and YTZ [12,13,20,23,25]. However, controversy exists about the local GB structure in presence of segregated species, which is partially caused by the lack of spatial resolution of the spectroscopy techniques used to characterize segregation. In these cases, numerical simulation has been useful, although the number of

R.L. González-Romero et al. / Solid State Ionics 237 (2013) 8–15

studies is much scarcer [14,31–33]. Despite their successes, some of which will be outlined in the discussion below, most of the numerical studies are unable to justify the co-segregation of oxygen vacancies, and have to postulate the formation of binary defects to reproduce the experimental findings. The role played by segregated species on oxygen diffusion in this system (and thence ionic conduction) has not been clarified so far either. An analytical model for equilibrium segregation has been recently published [30]. The model is consistent with most of experimental evidence about segregation in YSZ, but it adopts a continuous approach in which the atomistic details of the phenomenon are not taken explicitly into account. The present work constitutes the logical continuation of this analytical approach; it deals with the study of segregation of yttrium to a symmetric Σ5 (310)/[001] GB in YSZ by Molecular Dynamics (MD), showing that redistribution of oxygen vacancies is concomitant to yttrium segregation for electrical stability of the system. It also shows that segregation to the grain boundaries affects bulk diffusion of oxygen, but not grain boundary diffusion. 2. Methodology A YSZ model bicrystal containing a symmetric tilt Σ5 (310) / [001] GB has been built. This particular GB, which has been extensively studied in the literature [26,31], was chosen because yttrium cations are particularly prone to segregate to Σ5 [20]. The simulation box (Fig. 1) was a parallelepiped with sizes 20.52 Å × 24.33 Å × 64.93 Å, with the longer axis perpendicular to the plane of the boundary. Periodic boundary conditions made then two identical Σ5 GBs to appear; the separation between them, 32.47 Å, is supposed to be large enough to neglect any electrostatic mutual interaction. Two regions were considered in the bicrystal; all the ions within 6 Å at each side of the grain boundaries were regarded as “grain boundary ions”. The elastic force yielding segregation (see below) was applied only to the dopant cations belonging to the GB region; all the other ions were regarded as “bulk” ones. A concentration of 8 mol% was used. In each grain of the bicrystal, the exact number of zirconium cations substituted yttrium ones, and the number of oxygen vacancies required to keep the electrical neutrality of the system was introduced according to: ⋅⋅

Y2 O3 þ ZrO2 →2Y′Zr þ VO :

ð1Þ

All the substitutions were randomly made. Since the characteristics of segregation and diffusion of oxygen are likely to depend on the

9

particular positions of the defect species, five different configurations were considered. All the reported data were calculated as the average over this set of configurations. MD runs were performed using the LAMMPS code described elsewhere [34]. The potential of interaction between ions i and j was modeled as a Buckingham-type one coupled with a long-range Coulombic term: !
 r ij C ij 1 qi qj V r ij ¼ Aij exp – − 6þ ρij r ij 4πε0 r ij

ð2Þ

where ε0 is the dielectric constant of vacuum, rij is the interionic distance and qi holds for the charge of ion i. The parameters Aij, ρij and Cij were taken from the literature [35,36] and are listed in Table 1; this set of parameters (with integer charges for the ionic species) has been demonstrated to be consistent with the static and dynamic behavior of YSZ [37,38]. We accept implicitly here that Eq. (2) is appropriate to describe the atomistic interactions at Σ5, despite it was optimized for bulk properties. The energy of each initial configuration was minimized by lattice statics followed by a short run (10 ps) of MD under NVE conditions with T0 = 0 and P0 = 0 K, corresponding to a system with no spatial constraints. This first step led to changes in the ionic positions nearby the grain boundaries; when ions approached very close to each other, they were removed consistently with the overall electrical neutrality of the system. The so-obtained structure agreed in all cases with the ionic shifts reported elsewhere for Σ5 [26,31,33]. After minimization, the temperature was set to 1500 K and dynamic calculations were subsequently carried out for times up to 14 ps. To simulate GB diffusion of oxygen, temperatures within the range 1500 K–3000 K were set after segregation, and runs were performed during 500 ps. In all cases, the NVE ensemble with P =0 was used. It is important to notice here that the interaction potential (Eq. (2)) was originally developed to study solution mechanisms and defect cluster geometries for several dopant cations into a ceramic matrix. Therefore, it is not expected to yield segregation naturally by itself. In fact, MD results for oxygen diffusion in similar systems did not exhibit any yttrium segregation effect [38] despite the large simulation times used. On the contrary, Monte Carlo simulation studies reported elsewhere point out that segregation must be induced by adding an extra energy to yttrium cations [33]. It seems clear then that the aforementioned MD setup has to be changed to study segregation; in particular, an extra energy accounting for the elastic misfit effect must be added to yttrium cations. As a first approximation, this excess energy for

Fig. 1. Model bicrystal for the Σ5 grain boundary.

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3. Results

Table 1 Parameters for potential Eq. (2) used in this study (from Refs. [35,36]). Ion pair

Aij (eV)

ρij (Å)

Cij (eV Å6)

3.1. Distribution histograms

O2−–O2− Zr4+–O2− Y3+–O2−

9547.96 1502.11 1766.40

0.2192 0.3477 0.33849

32.0 5.1 19.43

Fig. 2a plots the relative number of Y ′ Zr defects (defined as the ratio between the actual number of these at each position and the corresponding number before segregation

cations located at a radial distance r from the center of the grains (supposed to be spherical) may be described by the following law [29]: ΔE0 ðr−R þ lÞ for R−lbrbR l

ΔEðr Þ ¼

ð3Þ

where ΔE0 is the excess (segregation) energy at the grain boundary, R is the grain radius and l is the thickness of the segregation layer, a small fraction of R (typically of the order of 10%, see Ref. [30] for further details). Consequently, we accepted that yttrium cations within the segregation layer (for the geometry considered here, a bin of thickness l in the xy plane) had an excess (segregation) energy given by:

ΔEðzÞ ¼

ΔE0 ðz−Lz þ lÞ l

for Lz −lbzbLz :

ð4Þ

½Y′Zr seg ½Y′Zr non seg )

vs. the reduced

distance zred (i.e., the ratio between the z position and the length of the simulation box normal to the GB plane) for several simulation times. The relative number of Y ′ Zr at the GB planes increases with the simulation time; this increment is significant for short times, but the number of defects saturates for longer ones. This effect is demonstrated in Fig. 2b, where the relative number of Y ′ Zr at the GB planes is plotted as a function of the simulation time. The increasing concentration of Y ′ Zr defects at each GB plane is produced at the expense of a decrease within the GB region, and no significant changes are observed in the grains. The rearrangement of the Y ′ Zr defects within the GB region is accompanied by that of zirconium cations and oxygen vacancies VO⋅ ⋅. Thus, Fig. 3 shows the relative number of × each type of defect (ZrZr , Y ′ Zr and VO⋅ ⋅) vs. the reduced distance after a run of 14 ps, within the steady regime. The relative numbers × of ZrZr and VO⋅ ⋅ decrease exactly at the GB planes, but they both reach a maximum about 3 to 5 Å at each side of them, still within the GB region.

For YSZ, the segregation energy at the GBs has been reported to be about ΔE0 ≈ 0.5 eV at temperatures above 1473 K [29,39]. As for the characteristic length l, unreported to the authors' knowledge, it depends on the grain size, but may be taken roughly as around 0.1 R, with R the grain radius, for d ≲ 60 nm (see Ref. [30] for further details). For simplicity, we took then l ≈ 6 Å. Results of tests performed at increasing values of l (up to 12 Å) did not differ essentially from those reported here; lower values of l, on the other hand, led to excessively small numbers of yttrium cations within the GB regions and, therefore, yielded results without statistical significance. These choices for ΔE0 and l sufficed for yttrium cations to segregate at the GBs, and also allowed us to follow the evolution of the different defect species within the simulation box. The Coulombic contribution to the driving force for segregation was directly included in the interaction potential, Eq. (2). According to Cahn [39], the elastic driving force for segregation predominates over the electrostatic one in most ceramics systems; the latter becomes relevant only when preferential charge accumulation exists (that is, when segregation has already taken place), at least partially. The radial distribution functions (RDFs) and coordination numbers for ion pairs were computed referenced to yttrium cations in the GB regions. The RDF of a pair of ions i and j is defined as: g ij ðr Þ ¼

4π

nij ðr Þ  Ni Nj r 2 Δr V




ð5Þ

where Ni and Nj are the number of ions of the respective type in a reference volume V, nij(r) is the number of pairs i − j within r− Δr 2 and r þ Δr 2 to each other, and Δr = 0.1 Å in this case. The coordination numbers are calculated as the area below the first or second peaks of the RDF. To study GB and bulk diffusion of oxygen, the mean square displacements 〈r2〉 of oxygen anions in the GB and bulk regions were computed throughout each run as functions of the simulation time t. The corresponding diffusion coefficients were calculated from these displacements as [40]:

D ¼ limt →∞

D E r2 6t

:

ð6Þ

Fig. 2. a) Reduced distribution histograms for Y′ Zr defects, for several times, as a function of the reduced distance. b) Relative number of Y′ Zr at the GB planes as a function of time.

R.L. González-Romero et al. / Solid State Ionics 237 (2013) 8–15

× ⋅⋅ Fig. 3. Reduced distribution histograms for Y ′ Zr, ZrZr and VO defects.

Fig. 2 yields a ratio between the number of yttrium ions after and before segregation

½Y′Zr seg ½Y′Zr non seg

≈3 in the steady regime. For comparison,

it is more convenient to compute the enrichment factor for yttrium  ½Y′Zr   ½Cations Segregation cations fY, defined as the ratio ½Y′Zr  . Fig. 4 displays the enrichment ½CationsjNo segregation factor for yttrium as a function of the reduced distance. This factor reaches a maximum of fY ≈1.6 at the GB planes and decreases to virtually zero at each side of these planes, where the concentration of zirconium is the × highest; the enrichment factor for ZrZr is also included in Fig. 4 for comparison.

3.2. Radial distribution functions The structure of a few high-symmetry grain boundaries in YSZ (particularly Σ5) has been recently reported [38]. Segregation modifies the local environment at the GBs, which results to be different to that in the “clean” GBs lacking defects. To elucidate the structures of the grain boundaries containing segregated cations, we have computed the radial distribution functions for several ion pairs. A comparison between the RDFs in bulk YSZ and in the Σ5 model boundary can be found elsewhere × × [38]. On the other hand, the distributions of OO×–OO× and ZrZr –ZrZr pairs

× Fig. 4. Enrichment factors for Y′ Zr (solid line) and ZrZr defects (dashed line) as a function of the reduced distance.

11

in Σ5 do not change appreciably after segregation, and will not be presented here for brevity. × Fig. 5 show the RDFs for Y ′ Zr–OO× (a), Y ′ Zr–Y′ Zr (b) and Y ′ Zr–ZrZr (c) pairs in the Σ5 GB region with and without segregated defects; Table 2 records the numbers of neighbors at the first and second coordination spheres for the same ion pairs. Segregation causes the Y ′ Zr–OO× and Y ′ Zr–Y ′ Zr pairs to locate closer to each other; these shifts of the first maxima of the RDFs produce changes in the coordination numbers at the first coordination sphere. The second maxima of the RDFs shift slightly to higher distances and become wider and shorter after segregation; the coordination numbers at the second coordination sphere result to change more importantly than for the first. All these changes are more significant for Y′ Zr–Y ′ Zr pairs (particularly the increase in the coordination number at the second sphere, which reaches the 87.5%); these RDFs look noisy because of the relatively scarce number of Y′ Zr within the GB region of the simulation box. Note that the number of Y ′ Zr defects increases in the region between the first two maxima after segregation; this suggests that some of these tend to locate inter× stitially nearby the GBs. The RDF for Y ′ Zr–ZrZr pairs does not exhibit the aforementioned shift at the first maximum, and segregation just produces a slight change in the number of first neighbors. However, the second maximum almost disappears after segregation, which indicates that yttrium and zirconium cations no longer locate as second neighbors to each other. 3.3. Effect of segregation on oxygen diffusion For its potential technological relevance, we have investigated the effect of segregation on oxygen diffusion along the Σ5 GB. Previous studies have demonstrated that GBs hinder oxygen diffusion in YSZ, which has been attributed to the presence of space-charge regions surrounding the boundaries [38,41–43], although the role played by segregation remains to be clarified. Fig. 6 shows the Arrhenius plots for the oxygen diffusion coefficients in Σ5 lacking segregated Y ′ Zr defects and when segregation has reached the steady regime. This figure shows that segregation does not have any appreciable effect on the characteristics of oxygen diffusion along this boundary; in particular, it suggests that GB oxygen diffusion is not much sensitive to the particular distribution of Y′ Zr defects. 4. Discussion Experimental values for the enrichment factor of yttrium obtained by Auger electron (AES), X-ray photoelectron (XPS), electron energy-loss (EELS) or energy dispersive X-ray spectroscopies (EDS) or by lowenergy ion scattering (LEIS) in either YSZ or YTZ range between 1.0 and 3.7 [12–17,19–25] (cf. Table 3). The wide range of variation may be ascribed to differences in the spatial resolution of the particular techniques, to differences in composition or to co-segregation of impurities (especially silicon), which has been reported to be concomitant to yttrium segregation in some systems [24]. In any case, the enrichment factor of yttrium at the grain boundaries reported here, fY = 1.6, agrees reasonably with these values, as well as with Monte Carlo simulations [33,44,45]. Experiments almost incontrovertibly evidence that the concentration of yttrium reaches a maximum at the GB plane [12,14,17,18,20,22,24]; to the authors' knowledge, only Lee et al., in their study performed by an hybrid Monte Carlo-MD algorithm, report the highest concentration of yttrium in the third cation layer from the GB [45]. On the other hand, Ikuhara et al. [24] and Matsui et al. [22] used EDS to report a depletion Y′Zr  in the ½Zr ratio within a layer 4–6 nm thick at each side of the GB planes ½ Zr  in YTZP with a grain size d≈0.5 μm, in good agreement with the XPS study by Bernasik et al. [15], who found that the concentration of zirconium reaches a minimum at the GB plane, but increases towards the grain interior. EELS data by Lei et al. [14] also indicate that segregation

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R.L. González-Romero et al. / Solid State Ionics 237 (2013) 8–15 Table 2 Coordination numbers at the first and second coordination spheres in the Σ5 GB region. Ion pairs

3+

2−

Y –O Y3+–Y3+ Y3+–Zr4+

First coordination sphere

Second coordination sphere

No segregation

Segregation

No segregation

Segregation

6.89 1.47 4.64

6.73 2.63 4.95

18.23 0.72 1.49

19.17 1.35 1.38

of yttrium causes a decrease in the concentration of zirconium at the grain boundaries; the authors used a distance–valence least-squares analysis to justify that such configuration must give rise to an accumulation of oxygen vacancies nearby the GB plane for charge compensation. Thus, the findings reported in this work agree, from a semi-quantitative point of view, with the available experimental evidence for the local structures of GBs containing segregated yttrium. × The redistribution of the ZrZr and VO⋅ ⋅ defects accompanying Y ′ Zr segregation can be understood in the light of the above-mentioned contributions to the driving force for segregation. Indeed, each Y ′ Zr defect in YSZ has an effective electric charge qY = −1; segregation produces then a charged layer to appear at the GB and, consequently, a local electric field within the grains. In metals, this electric field can easily be screened because of the presence of nearly-free electrons, which are highly mobile. In insulators, however, the local electric field can only be screened by the accumulation of positive charges (here, oxygen vacancies) at some distance from the GB. The segregation-induced electric field extends from the boundary to within the grain interior up to a typical length, the Debye screening length, which is a function of the concentration of dopants and temperature. A recent paper has dealt with the segregation of yttrium to the GBs under equilibrium conditions [30]; first-principles considerations yield distribution histograms for the various defect species (including binary [Y′ ZrVO⋅⋅]· defects) which agree reasonably with the results reported here. Note also that, in our methodology, the excess elastic energy has been added only to yttrium cations; therefore, the rearrangement of the zirconium cations and oxygen vacancies is electrostatic in nature. As a consequence, our treatment does not require to impose that each yttrium cation segregates together with an oxygen vacancy, as some works do. The fact that oxygen vacancies surround Y ′ Zr defects as these segregate is favorable from the energetic point of view. To evince this we have computed the segregation energy of a defect at a distance D of a GB as: Eseg ðDÞ ¼ EðDÞ−Eð∞Þ

ð7Þ

where E(D) and E(∞) are the lattice energies when the defect is located at D and when it is infinitely separated from the GB, respectively. The segregation energy was computed for isolated Y ′ Zr defects and for [Y′ ZrVO⋅⋅]· binary defects, with the oxygen vacancy located as first neighbor of the yttrium cation; in the latter case, the energy was taken as the average of the values calculated at different compatible positions. For each type of defect, E(∞) was calculated by locating it at the center of one of the grains in the simulation box (D = 1.62 nm). The presence of whichever of the previous defects violates the electroneutrality of the simulation box; however, the energy excess due to the additional charge cancels exactly when one computes the segregation energy according to Eq. (7), since it affects both E(D) and E(∞) in the same amount. Fig. 7 shows the segregation energy as a function of the distance to the grain boundary for both types of defects. This energy is essentially positive for D ≤ 0.7 nm for Y ′ Zr defects, and it increases as the

× × Fig. 5. Radial distribution functions for Y ′ Zr–OO (a), Y ′ Zr–Y ′ Zr (b) and Y ′ Zr–ZrZr (c) pairs, computed within the GB region before (red lines) and after segregation (blue lines). Data for segregated GBs were calculated in the steady regime.

R.L. González-Romero et al. / Solid State Ionics 237 (2013) 8–15

13

⋅⋅ · Fig. 7. Segregation energy for Y′ Zr (open symbols) and [Y ′ ZrVO ] binary defects (filled symbols) as functions of the distance to the GB plane.

Fig. 6. Arrhenius plot for the oxygen diffusion coefficients along the GBs with and without segregation of yttrium.

defect approaches the GB plane. On the contrary, the segregation energy is negative for D ≤0.3 nm for [Y′ ZrVO⋅⋅] · defects, which indicates that they are more stable than the isolated Y ′ Zr ones. These data agree well with previously reported studies [33]. The most striking consequence of our study is perhaps that oxygen diffusion along the GBs is not affected by segregation. The characteristics of oxygen diffusion in YSZ have been the subject of many experimental and simulation studies [46–63]. Most of them evidence that oxygen diffusion is related to the distribution of oxygen vacancies within the lattice, although the actual diffusion mechanism is still controversial. Recent papers have demonstrated that the distribution of defect species within the YSZ structure is clearly affected by vacancy-cation and vacancy–vacancy interactions [51,59–62]. These are related to the local electronic structure, and can only be accounted for by ab initio calculations. Table 3 Summary of experimental data about yttrium segregation in the yttria–zirconia system. Reference

Experimental techniquea

Yttria content (mol%)

Temperature range (K)b

Enrichment factor

Winnubst et al. [13] Lei et al. [14] Bernasik et al. [15] Hughes [16]

AES EELS XPS XPS

8.5 Not reported 8.0 9.5

Dickey et al. [20] de Ridder et al. [21] Hughes et al. [19] Theunissen et al. [12]

EELS LEIS XPS XPS, AES

Matsui et al. [22] Hines et al.d [23] Hughes et al.d [17] Ikuhara et al.d [24] Matsui et al.d [22]

EDS EDS XPS EDS EDS

Stemmer et al.d [25]

EELS

10.0 10.0c 10.0 8.5 13.2 8.0 2.0 3.0 2.5 2.0 3.0 3.0

1273–1673 Not reported 1073–1673 1173 1373 Not reported 1673 1573–1873 1273

≈1.5 ≈2.0 1.0–1.4 ≈1.2 ≈1.4 ≈1.6 ≈3.7 1.3–1.7 2.2–2.6 1.4 1.2 2.3–2.7 1.6–1.9 >2.0 1.9–2.5 1.9 2.0–2.1

a

1573–1773 1773 1473 1723 1573–1773 1573–1773 1723

AES — Auger Electron Spectroscopy; EELS — Electron Energy-Loss Spectroscopy; XPS — X-Ray Photoelectron Spectroscopy; LEIS — Low-Energy Ion Scattering; EDS — Energy Dispersive X-Ray Spectroscopy. b Sintering or annealing temperatures. c Data for Y2O3–94ZrO2. d Data for tetragonal zirconia.

Despite this, Molecular Dynamics has put some light in the distribution of the defects in YSZ and its effect on oxygen diffusion as well. In bulk YSZ, some works suggest that oxygen vacancies locate preferentially as first neighbors of Zr 4+ cations, where they become partially immobile thus inhibiting diffusion [56,63,64]. In some other cases, it is shown instead that oxygen vacancies become trapped when they locate as second neighbors of Y ′ Zr defects [48,51,53,65–67]. Note that, since experiments have not demonstrated any preferential distribution of dopant cations within the cationic sublattice in YSZ [68,69], both locations for the oxygen vacancies may be considered equivalent in average. These facts have been invoked to explain the existence of a maximum of ionic conductivity at around 8 mol% yttria; they have also been invoked for oxygen diffusion along grain boundaries depleted of segregated species, although the diffusion coefficients do not depend appreciably on the amount of yttria in this case [38]. These characteristics change under mechanical stresses, which have been found to improve the diffusion rates under some conditions [6,7]. Our results about the effect of dopant segregation on oxygen diffusion may be also discussed in terms of how the oxygen vacancies distribute and, particularly, how many of them locate as second neighbors of the Y′ Zr defects. Table 4 records the average number of oxygen anions per Y4+ ion located as second neighbors of Y′ Zr defects within the GB and the bulk regions, referenced to the situation in which segregation does not occur (i.e., nsn −n0sn, where the subscript denotes no segregation). The numbers have been calculated at 1500 K just after segregation has taken place (first column) and after the subsequent dynamic run performed to measure diffusion (second column). The results show that the number of oxygen anions as second neighbors of Y′ Zr defects decreases in the GB region after segregation, in good agreement with the distribution histograms. Diffusion produces an additional rearrangement of the oxygen ions; in the GB region, the average number of secondneighbors oxygen ions results to be virtually the same than for the initial configuration before segregation, whereas it drastically decreases within the bulk region.

Table 4 Distribution of oxygen anions as second neighbors of Y′ Zr defects. The numbers in the table have been calculated as nsn − n0sn, where nsn denotes the average number of oxygen anions per Y4+ ion located as second neighbors of Y ′ Zr defects in each region and the subscript refers to the system without segregation.

Bulk Grain boundary

Segregation

Segregation + diffusion

1.2 ± 0.1 −1.3 ± 0.8

−1.2 ± 0.8 −0.1 ± 0.2

14

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These data justify why segregation does not change the oxygen diffusion coefficients within the GB region, and suggest that the main effect should appear in the bulk; particularly, the bulk diffusion coefficients for oxygen should be smaller than before segregation. Indeed, Fig. 8 displays the Arrhenius plots for these coefficients calculated with and without segregation; data for the latter are taken from Ref. [38]. This plot confirms that segregation changes the characteristics of bulk diffusion of oxygen, particularly the corresponding activation energy. The RDF for Y ′ Zr–Y ′ Zr pairs shows that the first coordination number for these increases significantly after segregation. The shift of the × first maximum in this function, as well as that none the Y ′ Zr–ZrZr or × × the ZrZr–ZrZr RDFs show appreciable changes, suggests that some Y ′ Zr defects could locate interstitially at the GBs after segregation. In this context, we call “interstice” to a region with relatively large free volume where some ions (the dopant ones in this case) may locate. Fig. 9 shows snapshots of the ionic evolution during a typical MD run; only part of the GB region is shown for clarity. During the initial steps (Fig. 9a), the structure of the Σ5, with its typical “arrow” configuration, is clearly recognizable. In this figure, the yttrium cations locate in zirconium lattice sites. In Fig. 9b, taken in the steady regime of segregation, two main differences arise; first, the amount of yttrium cations has increased and, second, they locate not only in zirconium sites (as in positions A and A′), but also fill in the interstices of the original Σ5 structure; positions B and B′ correspond actually to a whole row of yttrium cations located interstitially. 5. Conclusions We have performed a Molecular Dynamics study of the segregation of yttrium cations to a Σ5 GB in 8 mol% YSZ bicrystals assuming that they are subjected to the elastic misfit effect. Such effect may be modeled by an excess elastic energy promoting segregation. Segregation proceeds until a steady state is reached, in which the number of segregated cations does not increase in time. Dopant cations accumulate preferentially at the GB planes, with an enrichment factor fY ≈ 1.6 which agrees with available experimental data. Segregation of yttrium causes a local depletion of the number of zirconium cations and oxygen vacancies, which tend to accumulate within the GB region

Fig. 9. Snapshots of the Σ5 GB. a) Minimized boundary before segregation. The black line denotes the position of the GB plane; b) Boundary containing rows of segregated yttrium cations located interstitially (labeled as “B” and “B′”). The snapshot was taken after 14 ps, in the steady regime of segregation.

at some distance of the GB planes. This rearrangement is electrostatic in nature, and may be explained by the necessity to screen the local electric field induced by the segregated species. In addition, it arises naturally from the movement of the yttrium cations. Segregation also affects the structure of the GBs; in particular, a significant increment in the second-sphere coordination numbers for Y ′ Zr − Y ′ Zr pairs has been detected. Surprisingly, segregation of yttrium does not affect GB diffusion of oxygen, but it decreases the rates of oxygen diffusion within the bulk. This effect has been explained in terms of the accumulation of oxygen vacancies as second neighbors of yttrium cations in the grains. Finally, the results show that segregated yttrium cations may locate interstitially at some positions of the Σ5 GB. Acknowledgments This work has been financially supported by the “Ministerio de Ciencia e Innovación”, Spanish Government, through Grant MAT200914351 and “Ministerio de Economía y Competitividad” through Grant MAT2012-38205. RLGR wishes to acknowledge AECID (Agencia Española de Cooperación Internacional y Desarrollo) for financial support through Grant no. 536875. JJM wishes to acknowledge Dr. Carlos J. García Orellana, from the University of Extremadura, for his kind computational help and Dr. Dario Marrocchelli, from the Trinity College, Dublin, for providing him with some nice papers. References

Fig. 8. Arrhenius plot for the diffusion coefficients for bulk diffusion of oxygen calculated with and without segregation of yttrium.

[1] S.C. Singhal, Solid State Ionics 152–153 (2002) 405. [2] V.S. Stubican, G.S. Corman, J.R. Hellman, G. Senft, in: N. Claussen, M. Rühle, A.H. Heuer (Eds.), Science and Technology of Zirconia, 2, The American Ceramic Society, Columbus, 1983. [3] J.A. Kilner, R.J. Brook, Solid State Ionics 6 (1982) 237. [4] A. Chroneos, B. Yildiz, A. Tarancon, D. Parfitt, J.A. Kilner, Energy Environ. Sci. 4 2774. [5] M. Jiménez-Melendo, A. Domínguez-Rodríguez, A. Bravo-León, J. Am. Ceram. Soc. 81 (1998) 2761.

R.L. González-Romero et al. / Solid State Ionics 237 (2013) 8–15 [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38]

W. Araki, Y. Arai, Solid State Ionics 181 (2010) 1534. W. Araki, Y. Arai, Solid State Ionics 181 (2010) 441. A. Kushima, B. Yildiz, J. Mater. Chem. 20 (2010) 4809. P. Heitjans, S. Indris, J. Phys. Condens. Matter 15 (2003) R1257. A. Domínguez-Rodríguez, M. Jiménez-Melendo, Mater. Trans. JIM 40 (1999) 830. S. Primdahl, A. Tholen, T.G. Langdon, Acta Metall. Mater. 43 (1995) 1211. G. Theunissen, A.J.A. Winnubst, A.J. Burggraaf, J. Mater. Sci. 27 (1992) 5057. A.J.A. Winnubst, P.J.M. Kroot, A.J. Burggraaf, J. Phys. Chem. Solids 44 (1983) 955. Y. Lei, Y. Ito, N.D. Browning, T.J. Mazanez, J. Am. Ceram. Soc. 85 (2002) 2359. A. Bernasik, K. Kowalski, A. Sadowski, J. Phys. Chem. Solids 63 (2002) 233. A.E. Hughes, J. Am. Ceram. Soc. 78 (1995) 369. A.E. Hughes, S.P.S. Badwal, Solid State Ionics 40 (41) (1990) 312. A.E. Hughes, S.P.S. Badwal, Solid State Ionics 46 (1991) 265. A.E. Hughes, B.A. Sexton, J. Mater. Sci. 24 (1989) 1057. E.C. Dickey, X. Fan, S.J. Pennycook, J. Am. Ceram. Soc. 84 (2001) 1361. M. de Ridder, R.G. van Welzenis, A.W.D. van der Gon, H.H. Brongersma, J. Appl. Phys. 92 (2002) 3056. K. Matsui, H. Yoshida, Y. Ikuhara, Acta Mater. 56 (2008) 1315. J.A. Hines, Y. Ikuhara, A.H. Chokshi, T. Sakuma, Acta Mater. 46 (1998) 5557. Y. Ikuhara, P. Thavorniti, T. Sakuma, Acta Mater. 45 (1997) 5275. S. Stemmer, J. Vleugels, O. Van Der Biest, J. Eur. Ceram. Soc. 18 (1998) 1565. C.A.J. Fisher, H. Matsubara, Solid State Ionics 113–115 (1998) 311. A. Domínguez-Rodríguez, D. Gómez-García, C. Lorenzo-Martín, A. Muñoz-Bernabé, J. Eur. Ceram. Soc. 23 (2003) 2969. D. Gómez-García, C. Lorenzo-Martín, A. Muñoz-Bernabé, A. Domínguez-Rodríguez, Philos. Mag. A 83 (2003) 93. M.F. Yan, R.M. Cannon, H.K. Bowen, J. Appl. Phys. 54 (1983) 779. D. Gómez-García, J.J. Meléndez, R.L. González-Romero, A. Domínguez-Rodríguez, Acta Mater. 58 (2010) 6404. Z. Mao, S.B. Sinnott, E.C. Dickey, J. Am. Ceram. Soc. 85 (2002) 1594. N. Shibata, F. Oba, T. Yamamoto, Y. Ikuhara, T. Sakuma, Philos. Mag. Lett. 82 (2002) 393. T. Oyama, M. Yoshiya, H. Matsubara, K. Matsunaga, Phys. Rev. B 71 (2005) 224105. S. Plimpton, J. Comp. Physiol. 117 (1995) 1. R.W. Grimes, D.J. Binks, A.B. Lidiard, Philos. Mag. A 72 (1995) 651. R.W. Grimes, G. Busker, M.A. McCoy, A. Chroneos, J.A. Kilner, S.P. Chen, Ber. Bunsenges. Phys. Chem. 101 (1997) 1204. R.L. González-Romero, J.J. Meléndez, D. Gómez-García, F.L. Cumbrera, A. Domínguez-Rodríguez, F. Wakai, Solid State Ionics 204–205 (2011) 1. R.L. González-Romero, J.J. Meléndez, D. Gómez-García, F.L. Cumbrera, A. Domínguez-Rodríguez, Solid State Ionics 219 (2012) 1.

15

[39] J. Cahn, Physical Metallurgy, Elsevier Science, Amsterdam, 1983. [40] H. Mehrer, Diffusion in Solids, Springer Verlag, Berlin, 2007. [41] R.A. De Souza, M.J. Pietrowski, U. Anselmi-Tamburini, S. Kim, Z.A. Munir, M. Martin, Phys. Chem. Chem. Phys. 10 (2008) 2067. [42] X. Guo, Z. Zhang, Acta Mater. 51 (2003) 2539. [43] T. Nakagawa, I. Sakaguchi, N. Shibata, K. Matsunaga, T. Yamamoto, H. Haneda, Y. Ikuhara, J. Mater. Sci. 40 (2005) 3185. [44] A.D. Mayernick, M. Batzill, A.C.T. van Duin, M.J. Janik, Surf. Sci. 604 (2010) 1438. [45] H.B. Lee, F.B. Prinz, W. Cai, Acta Mater. 58 (2010) 2197. [46] K.-S. Chang, Y.-F. Lin, K.-L. Tung, J. Power. Sources 196 (2011) 9322. [47] K. Park, D.R. Olander, J. Electrochem. Soc. 138 (1991) 1154. [48] P.S. Manning, J.D. Sirman, R.A. De Souza, J.A. Kilner, Solid State Ionics 100 (1997) 1. [49] P.S. Manning, J.D. Sirman, J.A. Kilner, Solid State Ionics 93 (1996) 125. [50] T. Suemoto, M. Ishigame, Solid State Ionics 21 (1986) 225. [51] R. Krishnamurthy, Y.-G. Yoon, D.J. Srolovitz, R. Car, J. Am. Ceram. Soc. 87 (2004) 1821. [52] V.V. Kharton, F.M.B. Marques, A. Atkinson, Solid State Ionics 174 (2004) 135. [53] Y. Yamamura, S. Kawasaki, H. Sakai, Solid State Ionics 126 (1999) 181. [54] T. Arima, K. Fukuyo, K. Idemitsu, Y. Inagaki, J. Mol. Liq. 113 (2004) 67. [55] N. Sawaguchi, H. Ogawa, Solid State Ionics 128 (2000) 183. [56] C.R.A. Catlow, A.V. Chadwick, G.N. Greaves, L.M. Moroney, J. Am. Ceram. Soc. 69 (1986) 272. [57] D.W. Stickler, W.G. Carlson, J. Am. Ceram. Soc. 47 (1964) 122. [58] H. Yugami, A. Koike, M. Ishigame, T. Suemoto, Phys. Rev. B 44 (1991) 9214. [59] J.P. Goff, W. Hayes, S. Hull, M.T. Hutchings, K.N. Clausen, Phys. Rev. B 59 (1999) 14202. [60] F. Pietrucci, M. Bernasconi, A. Laio, M. Parrinello, Phys. Rev. B 78 (2008) 094301. [61] D. Marrochelli, P.A. Madden, S.T. Norberg, S. Hull, (2011). [62] S.T. Norberg, S. Hull, I. Ahmed, S.G. Eriksson, D. Marrochelli, P.A. Madden, P. Li, J.T.S. Irvine, Chem. Mater. 23 (2011) 1356. [63] A. Bogicevic, C. Wolverton, G.M. Crosbie, E.B. Stechel, Phys. Rev. B 64 (2001) 014106. [64] P.K. Schelling, S.R. Phillpot, D. Wolf, J. Am. Ceram. Soc. 84 (2001) 1609. [65] K. Kawata, H. Maekawa, T. Nemoto, T. Yamamura, Solid State Ionics 177 (2006) 1687. [66] G. Stapper, M. Bernasconi, N. Nicoloso, M. Parrinello, Phys. Rev. B 59 (1999) 797. [67] M.O. Zacate, L. Minervini, D.J. Bradfield, R.W. Grimes, K.E. Sickafus, Solid State Ionics 128 (2000) 243. [68] M. Morinaga, J.B. Cohen, J. Faber Jr., Acta Crystallogr. A 35 (1979) 789. [69] M. Morinaga, J.B. Cohen, J. Faber Jr., Acta Crystallogr. A 36 (1980) 520.