Atomistic Analyses of Competition between Site-Selective Segregationand Association of Point Defects at Grain Boundary in Y2O3-Doped ZrO2

T. Yokoi1,+, M. Yoshiya1,2 and H. Yasuda1,3

1Department of Adaptive Machine Systems, Osaka University, Suita 565-0871, Japan2Nanostructures Research Laboratory, Japan Fine Ceramics Center, Nagoya 456-8587, Japan3Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8507, Japan

The site-selective occupation of point defects, Y3+ ions (YAZr) and O2¹ vacancies (V €O), and their associations at a symmetric tilt grainboundary (GB) are studied to understand their competitive contribution to energetically favorable atomic arrangements by using atomisticsimulations. It is found that at the GB there are the favorable sites for segregation of an isolated YAZr and V €O. This indicates that the driving forcefor the site-selective segregation is present. Moreover, our results of YAZr-V €O association at the GB show that the lattice energies are verydispersed despite that a second-nearest neighbor (SNN) vacancy to YAZr is favored for bulk Y2O3-doped ZrO2. The result suggests that the site-selective segregation has significant effects on the favorable point defect arrangement at the GB core, competing with the point defectassociations. For more realistic cases, Monte Carlo simulations are performed to reveal favorable atomic arrangements for a high dopantconcentration, where point defects are crowded at the GB. The results show that the region of GB segregation can be classified with respect toO2¹ coordination to cation species; at the GB core the favorable configuration is not necessarily a SNN O2¹ vacancy relative to Y3+. On theother hand, eight-fold O2¹ coordination is sustained for Y3+ ions more than ³3¡ distant from the GB plane. The difference in O2¹ coordinationmay play an important role in O2¹ ionic conductivity at GBs via the energetics for O2¹ migration. [doi:10.2320/matertrans.MA201567]

(Received March 9, 2015; Accepted May 8, 2015; Published August 25, 2015)

Keywords: grain boundary segregation, point defect association, Y2O3-doped ZrO2

1. Introduction

Impurity-doped zirconia (ZrO2) ceramics are suitable fornumerous applications due to its various materials properties,as well as high-temperature mechanical and chemicalstability. An important application impurity-doped ZrO2 is ahigh oxygen-ion conductor that has particularly beenexpected as electrolytes in solid oxide fuel cells.1­3) Ingeneral, M2+ or M3+ cations with larger ionic radii than Zr4+

is introduced as substitutional point defect, and consequentlycharge-compensating O2¹ vacancies are created for main-taining charge neutrality. Using Kröger-Vink notation thesubstitutional cation defect and anion vacancy are describedas MAZr and V €O for trivalent cations, respectively. A dopantconcentration of approximately ³10mol% is required tofully stabilize to the cubic fluorite structure. Needless tosay, vacancy concentration is key to achieve high ionicconductivity and the number of oxygen vacancies increaseslinearly with dopant concentration.

However, for doped ZrO2 the ionic conductivity · is notproportional to vacancy concentration; · exhibits a maximumat a certain dopant concentration of 8­10mol% and decreasesdrastically at higher dopant concentrations above ³10mol%.4­7) According to previous studies, the dependence of· on dopant concentration is ascribed to interactions betweenforeign point defects: cation-vacancy interactions8­10,12­16)

and vacancy-vacancy interactions.12,17­20) Occurrence ofcation-vacancy association were reported,8,9) and X-rayabsorption analyses10,11) showed that O2¹ vacancies arelocated at second-nearest sites relative to Y3+ ions and 8-foldoxygen coordination relative to Y3+ ions is maintained forY2O3-doped ZrO2. Previous atomistic simulations showedthat a second-nearest O2¹ vacancy is energetically preferredfor oversized M3+ ions12­15) and an energy barrier for O2¹

migration can be affected by the combination of cationssurrounding the pathway of O2¹ diffusion.14­16) Meanwhile,other previous studies suggested that vacancy-vacancyinteractions have critical effects on vacancy configurationsand O2¹ migration.12,17­20) The ordered alignment of O2¹

vacancies along ©111ª directions were identified.17) Moleculardynamics simulations18­20) suggested that vacancy-vacancyinteractions are more dominant in · than cation-vacancyinteractions. Although the effect of point defects interactionson · is not yet fully understood, these studies indicate theimportance of understanding the spatial relationship betweenpoint defects.

On the other hand, polycrystalline doped ZrO2 ceramics,rather than single crystals, are generally used in practicalapplications and grain boundaries (GBs) are inevitablycontained. It is well-known that GBs contribute negativelyto the total · of polycrystalline materials.21­25) In earlierstudies, the negative impact of GBs on · had been ascribed toimpurities such as SiO2 and Al2O3 for sintering aid. However,several previous studies with highly pure specimens23­25) andmore recently high-purity bicrystals26,27) reported that GBconductivity is approximately 2­5 orders of magnitude lowerthan bulk conductivity. These results indicate that the impactsof GBs on · are intrinsic effects caused by GB structureitself and/or grain boundary segregation (GBS) of dopantsand O2¹ vacancies at GBs. In general, changes in crystalstructure and chemical composition induced by GB andGBS are confined to within a few nanometers at most, andthus understanding the intrinsic effects in the atomic levelis needed to reveal the relationship between GB and GBSand ·.

Experimental observations with transmission electronmicroscopy (TEM), scanning TEM (STEM) and high-resolution TEM (HRTEM) have verified previously unclearGB structures at the atomic level.28­32) Dickey et al.28) andLei et al.29) predicted the GB core structures of symmetric tilt+Corresponding author, E-mail: tatsuya.yokoi@ams.eng.osaka-u.ac.jp

Materials Transactions, Vol. 56, No. 9 (2015) pp. 1344 to 1349Special Issue on Nanostructured Functional Materials and Their Applications©2015 The Japan Institute of Metals and Materials

GBs in Y2O3-stabilized ZrO2 bicrystals. Shibata et al.30­32)

determined cation configurations at several symmetric tiltGBs and related the number of coordination-deficient cationsites to the Y3+ segregation level. These studies indicatethat GB core regions exhibit different cation arrangementsfrom the intergrain although it is still challenging toidentify experimentally precise positions of dopants andO2¹ vacancies.

In order to reveal detail spatial positions of point defectsat GBs and the energetic of GBS, several atomisticanalyses have also been performed.33­38) Mao et al.35) andMarinopoulos36) showed that the segregation driving forcefor an isolated dopant strongly depends on individual sites ata GB. Oyama et al.33) and Yoshiya et al.34) showed that adopant-vacancy pair at a GB is more energetically favorablethan an isolated dopant or vacancy. Lee et al.37) showed thatthere are several sites occupied by Y3+ ions at a GB and O2¹

vacancies also segregate at the GB for a high dopantconcentration. More recently, our atomistic study showed thatenriched M3+ ions and O2¹ vacancies at a GB are non-randomly distributed within approximately 0.6 nm of the GBplane.38) From these studies, there is the high possibility thatenergetically preferred configurations of point defects areaffected by their mutual interactions, as well as interactionsbetween point defects and GBs. To the best knowledge of theauthor, however, there is no study that focuses on point defectinteractions and their spatial relationship at GBs despite of anumber of previous studies for their interactions in bulk. Sofar, it remains unclear whether point defects configurationsat GBs are determined in the same manner for bulk. Asdiscussed later, not only point defect interactions but alsoGB- and GBS-related factors can affect significantly theenergetically favorable atomic arrangement.

In this study, we perform atomistic analyses to examine thefollowing three factors: (1) site-selective occupation of pointdefects at a GB, (2) enrichment of them at the GB and (3)point defect interactions. We examine Y2O3-doped ZrO2 thathave been the most widely studied in all trivalent cations dueto practical applications. The present paper focuses mainly oncation-vacancy interactions since there are several exper-imental and theoretical studies for bulk Y2O3-doped ZrO2

mentioned above and thus it is possible to compare ourresults with previous studies.

2. Computational Methodology

A ­5 (310)/[001] symmetric tilt GB model is shown inFig. 1. In the undoped case the computational cell has 472Zr4+ ions and 944 O2¹ ions. The cell size is 97 © ¡ 8 © ¡21¡ in length and the x axis is the longest perpendicular tothe GB planes. A separation of the GB planes introducedperiodically is sufficient enough (³48.5¡) that the separationdoes not affect the trend of favorable positions for pointdefects. The A and B sites in Fig. 1 are half-filled since thefull-filled columns exhibit large energy penalty, which hasbeen validated in our previous studies.33,34,38)

To reveal effects of the GB on energetically favorableconfigurations, particularly the relative position between YAZrand V €O, we examine the following three cases: (1) an isolatedYAZr and V €O, (2) a defect pair ðYAZr � V €OÞ•, ð2YAZr � V €OÞ�, and

2ð2YAZr � V €OÞ�, and (3) crowded point defects at the GBfor high dopant concentrations. In this study, we define“dilute” dopant concentration as the first and second cases.The first one is that either of one YAZr or one V €O is introducedinto the computational cell at a time to examine site-selectiveoccupation at the GB. For the second case we introduceðYAZr � V €OÞ• into the computational cell and examine howthe GB affect the preferred relative position between YAZr andV €O. For this purpose, the YAZr position is fixed and a V €O islocated as second-nearest neighbor (SNN) vacancy to theYAZr. The calculation is performed varying the distancebetween the YAZr and the GB plane. For more realistic cases,we examine the favorable configurations of ð2YAZr � V €OÞ�and 2ð2YAZr � V €OÞ�. However, there are a large number ofthe combination of arrangement for two (four) YAZr and one(two) V €O and it is difficult for computational time to calculateall combinations. Therefore, we carry out Monte Carlo (MC)simulations based on Metropolis algorithm39) to obtainminimum-energy configuration at the GB. Detail descriptionsare given elsewhere.34,38) In the calculations, no constraint isimposed with respect to the positions of point defects andthus they are allowed to move for minimizing the total latticeenergy. The third is that for a high dopant concentration 42Y3+ ions and 21 O2¹ vacancies are introduced, and theirfavorable arrangements are obtained by MC simulations.Based on the result, O2¹ coordination environments to cationspecies at the GB are examined to understand thecontributions of the local structural change to the favorableatomic arrangement.

The energy of a system is evaluated by static latticemethods implemented in the GULP code.41) Total latticeenergy E total is given by the sum of short-range interactionenergy E short and long-range interaction energy ECoulomb.E short is evaluated by using the Buckingham-type potentialwith empirical parameters. Table 1 lists the parameters for thecubic fluorite structure.40) Although the monoclinic and thetetragonal crystal structure cannot be reproduced, previousstudies33,34,37,38) confirmed that the cation arrangement atthe symmetric tilt GB agrees with experimental observa-tions.28­30) The energy cutoff for E short is set to 20¡ foroptimizing crystal structures and 15¡ for MC simulations.To understand the site dependence of segregation energetics,

Fig. 1 (a) Schematic diagram of a ­5 (310)/[001] symmetric tile grainboundary model and (b) atomic arrangement near the GB plane along the[001] direction. The x, y and z directions correspond to the [310], ½�130�and [001] directions, respectively. Red and blue balls represent O2¹ andZr4+ ions, respectively.

Atomistic Analyses of Competition between Site-Selective Segregation and Association of Point Defects at Grain Boundary 1345

we evaluate the driving force for GBS, �EGBSdilute, expressed

as

�EGBSdilute ¼ EðrÞ � Eð1Þ ð1Þ

where E(r) is the total lattice energy as a function of distancebetween a point defect and the GB plane, r, and E(¨) is thereference energy for which a point defect is infinite distantfrom the GB. We assume that E(¨) equals the total latticeenergy when a point defect is located as the midpointbetween two GBs in the computational cell.

3. Results and Discussion

3.1 Site-dependent occupation of isolated point defectFirst of all, we evaluate�EGBS

dilute for an isolated point defectto show the dependence of �EGBS

dilute on the sites near the GBplane. Under this condition, point defect interactions areabsent. Figure 2 shows �EGBS

dilute as a function of two-dimensional location of YAZr (Fig. 2(a)) and V €O (Fig. 2(b)).This figure indicates that �EGBS

dilute decreases with the decreasein distance between a point defect and the GB for both YAZrand V €O, although for V €O the trend is much clearer than YAZr.The energy deviation at the GB from that in the grain interioris confined to the region within ³10­12¡ on either side ofthe GB plane and �EGBS

dilute is in the range within ¹1.0­1.0 eVfor YAZr and ¹1.3­0.5 eV for V €O. These trends, including thequantitative value of �EGBS

dilute, is in agreement with previousstudies.33­36)

For YAZr, there are both the energetically favorable andunfavorable sites at the GB (Fig. 2(a)). For example, the C-site occupation exhibits the largest positive value of �EGBS

dilute

and thus the C site is energetically unfavorable. On the otherhand, the D-site occupation exhibits the minimum and the Dsite is the most energetically favorable for minimization ofthe total lattice energy. Therefore, we can conclude that YAZrtends to occupy selectively the cation sites at the GB, ratherthan randomly distribute, even for an isolated YAZr. It is notedthat the A site is not a favorable site for a dilute segregationlevel while is a favorable site for a high segregation level.The different trend V €O also tends to segregate at the GB asshown in Fig. 2(b). There are several energetically favorablesites for V €O segregation and V €O occupy preferentially themost of anion sites within ³5¡ of the GB plane. Althoughthis trend may not be called as “site-selective occupation”, weconclude that an isolated V €O also has the significant drivingforce for segregation at the GB. The reason that there areseveral segregation sites for V €O may be related to O2¹

displacement. In the undoped model (Fig. 1(b)), for example,the O2¹ positions at the GB deviate from those in the graininterior compared with the cations. This implies that O2¹ ionsare energetically allowed to displace during energy mini-

mization. Therefore, the energy penalty generated by V €O canbe relieved by O2¹ displacement at the GB to lower E total.

3.2 Dilute-concentration defect arrangement at grainboundary

In this section, we discuss how favorable atomic arrange-ments at the GB are affected by the competition between site-selective segregation and point defect association. This studyfocuses on three cases for defect associates: ðYAZr � V €OÞ•,ð2YAZr � V €OÞ� and 2ð2YAZr � V €OÞ�. First, for ðYAZr � V €OÞ•,�EGBS

dilute as a function of distance between YAZr and the GB isshown in Fig. 3. V €O is assumed to be located at a SNNoxygen site to YAZr. This geometric relation is based on thatin the grain interior. A negative value indicates that theposition of ðYAZr � V €OÞ• is more favorable than in the graininterior for E total. There is a trend that �EGBS

dilute decreases withdecrease in distance. However, the values are very dispersedas the distance decreases, particularly in the vicinity of theGB, despite that V €O is located at a SNN site to YAZr for allcalculations. At the same distance, a certain SNN vacancy

Fig. 2 GBS energy for dilute point defect concentrations �EGBSdilute in the

case of (a) an isolated YAZr and (b) V €O. The horizontal and vertical axesrepresent distance between the point defects and the GB plane and Ycoordinate, respectively. The colorbar shows the degree of �EGBS

dilute. Thedashed line represents the GB plane.

Fig. 3 GBS energy for dilute dopant concentrations, �EGBSdilute, as a function

of distance between YAZr and the GB. All SNN anion sites surrounding tothe Y3+ are considered to evaluate the average of �EGBS

dilute.

Table 1 Empirical parameters for Buckingham-type potentials.40)

Ion pair A (eV) µ (¡) C (eV/¡)

Zr4+­O2¹ 1502.11 0.34770 5.100

Y3+­O2¹ 1766.40 0.33849 19.43

O2¹­O2¹ 9547.96 0.21920 32.00

T. Yokoi, M. Yoshiya and H. Yasuda1346

exhibits the lowest value of �EGBSdilute in the other SNN ones.

The considerable variation in �EGBSdilute suggests that at the

SNN O2¹ sites relative to YAZr at the GB is energeticallyinequivalent and their energetics depends strongly on thelocal atomic arrangement of the GB. Therefore, there is thehigh possibility that point defects occupy selectively specificsites at the GB sustaining the SNN position between V €O andYAZr.

In order to understand the effect of doping level onfavorable atomic arrangements, MC simulations are per-formed for ðYAZr � V €OÞ•, ð2YAZr � V €OÞ� and 2ð2YAZr � V €OÞ�.In MC simulations, there is no constraint on the geometricposition of point defects and they are allowed to interchangewith Zr4+ and O2¹ ions to lower E total. The results for threecases are shown in Fig. 4. and the YAZr-V €O distances are listedin Table 2. The configurations and distances were obtainedfrom the atomic arrangements before relaxing structures sincestructural optimization causes large distortion of the O2¹

columns and thus it is difficult to specify the precise positionsfor V €O.

For ðYAZr � V €OÞ• (Fig. 4(a)), the YAZr occupies the A sitethat is by 2¡ distant from the GB plane. The site correspondsto the B site in Fig. 2 and the A site in Fig. 3. This indicatesthat YAZr occupy dominantly the specific cation site that isthe same site as the case of an isolated YAZr. The YAZr-V €O

distance is 4.02¡ close to that in the grain interior (4.24¡).The geometric relation between the YAZr and V €O suggests thatthe favorable configuration for the grain interior also have acritical effect on determining the favorable atomic arrange-ment at the GB. However, the SNN V €O exhibits the lowest

value for �EGBSdilute in the other SNN V €O and is energetically

inequivalent with the other ones. Therefore, V €O segregation isalso affected by the local GB structure and exhibit the site-selective trend. For ð2YAZr � V €OÞ� (Fig. 4(b)), the SNNrelation is violated by the other YAZr. The dopant occupy theC site that is favorable for an isolated YAZr. The dopant-V €O

distance is 7.25¡ longer than the Y2-V1 distance. Based onthe result of an isolated YAZr, the violation indicates that thedriving force for Y3+ segregation at the C site is moredominant than that for point defect association to the SNNrelation.

Figure 4(c) shows the favorable atomic arrangement for2ð2YAZr � V €OÞ�. Several segregation sites are the same asðYAZr � V €OÞ• and ð2YAZr � V €OÞ�, but new segregation sites(the C and D sites) appear. This result indicates that the newsegregation sites are created due to the increase in dopinglevel. The increase in the number of point defects may berelated to large displacement of ions distinct from that in theintergrain. As is listed in Table 1, the variation in YAZr-V €O

distance becomes much clear; although the SNN position ispartly sustained, there are various YAZr-V €O distances bothlonger and shorter than the SNN distance. Therefore, it isconcluded that the SNN relationship between YAZr and V €O aremodified significantly by site-selective occupation of pointdefects as doping levels increase. At higher doping levels, thechange in geometric relation between point defects at the GBcore becomes more significant as is discussed below.

3.3 High-concentration defect arrangement at grainboundary

In Sec. 3.1 and 3.2, we discussed the cases of dilutedoping levels. However, in more realistic cases, dopantconcentrations are rather high (8­10mol%Y2O3) and pointdefects are expected to concentrate in the GB. Therefore, inorder to understand point defect structures for high dopinglevels, we perform MC simulations, where 42 Y3+ ions 21O2¹ vacancies are introduced. At the doping level, pointdefects occupy all energetically favorable sites at the GB,particularly the GB core, and are saturated. Additional pointdefects do not affect the GB atomic configuration. Theobtained atomic arrangement within 10¡ of the GB isdisplayed in Fig. 5. The cation column positions agree withprevious studies.28,33,34) Since detail analyses have beencarried out in our previous studies,38) the main feature ismentioned briefly. The result indicates that the favorableatomic configuration is very different from random distribu-tion with enrichment alone; Y3+ ions occupy the A sites

Fig. 4 Atomic arrangement obtained by MC simulations in the case of (a) ðYAZr � V €OÞ•, (b) ð2YAZr � V €OÞ� and (c) 2ð2YAZr � V €OÞ�.

Table 2 Distance between YAZr and V €O in the energetically favorableconfiguration obtained by MC simulations. The cases of ðYAZr � V €OÞ•,ð2YAZr � V €OÞ� and 2ð2YAZr � V €OÞ� are listed. The YAZr-V €O distances areevaluated before relax atomic positions.

Defect type Y ionDistance against vacancy (¡)

V1 V2

ðYAZr � V €OÞ• Y1 4.02

ð2YAZr � V €OÞ� Y1 7.25

Y2 4.02

2ð2YAZr � V €OÞ� Y1 4.12 8.72

Y2 9.72 7.25

Y3 4.04 2.20

Y4 5.38 4.02

Atomistic Analyses of Competition between Site-Selective Segregation and Association of Point Defects at Grain Boundary 1347

while do not occupy at the B and C sites. The result indicatesthat there are several specific cation sites at the GB core andY3+ ions occupy selectively these sites to lower the totallattice energy. The other Y3+-segregation sites also have atrend that Y3+ occupy the half sites at the cation column inthe [001] direction. Figures 5(b)­(d) show the two-dimen-sional Y3+, Zr4+ and O2¹ distributions, respectively. Theintensity of the O2¹ distribution is weak at the GB, whichindicates that GBS of O2¹ vacancies also occur. In addition,O2¹ vacancies also occupy the specific anion sites, ratherthan random distribution, particularly at the GB core. Forinstance, the O2¹ intensity at the A and B columns (Fig. 5(d))is much weaker than those at the other columns.

Based on the atomic arrangement in Fig. 5, the O2¹

coordination environment to cation species is evaluated.Figures 6(a) and 6(b) show the O2¹ coordination number,CNY­O for Y3+ and CNZr­O for Zr4+. There is the differenttrend in O2¹ coordination between the GB core and theoutside region; at the GB core, both CNY­O and CNZr­O rangefrom 6 to 7. According to previous studies of point defectassociations, SNN vacancies are energetically favorable forY3+. At the GB core, however, this geometric relationshipbetween Y3+ ions and O2¹ vacancies is not necessarily acritical factor to minimize the total lattice energy. Instead,

site-selective occupation is more dominant in determiningthe energetically favorable configuration at the GB core.The trend is also shown for dilute dopant concentrations asdiscussed above.

One may think that the enrichment of O2¹ vacancies at theGB simply cause the decrease in the number of O2¹ ions andthe resultant decrease in CNY­O and CNZr­O. The thought canbe applied for random distributions of point defects butcannot for the non-uniform distribution, since O2¹ coordina-tion number is changed by how point defects are distributedin space.

On the other hand, at the outside region CNY­O is entirely8 while CNZr­O decreases to 7. In addition, 7-fold coordinatedZr4+ and 8-fold coordinated Y3+ are located at the samecolumns along the [001] direction. At the outside region,therefore, O2¹ vacancies are located at the FNN sites relativeto Zr4+ ions and at the SNN sites relative to Y3+ ions at thesame time. The trend in vacancy-cation geometric position issimilar to that in intergrain reported in previous studies.10,13)

Therefore, it is concluded that at the outside regioninteractions between Y3+ and O2¹ vacancy have significanteffects on their favorable configurations.

4. Conclusions

To reveal the competitive effect between site-selectivesegregation and association of YAZr and V €O vacancies on theirconfigurations at GBs, local atomic arrangements at a tiltsymmetric GB inY2O3-doped ZrO2 have been evaluatedusing atomistic analyses. Three cases were addressed: anisolated point defect, ðYAZr � V €OÞ• pairs, and high-concen-tration atomic arrangements. Consequently, we reach thefollowing conclusions: (1) Several favorable and unfavorablesites is present at the GB for both YAZr and V €O, which agreeswith previous studies, indicating that the driving force forsite-selective occupation exists. (2) For ðYAZr � V €OÞ•, �EGBS

dilute

is very dispersed at the GB despite that V €O is located at aSNN site to YAZr, which is favorable in the grain interior forY2O3-doped ZrO2. A certain SNN vacancy is more favorablethan the other SNN ones. The difference in �EGBS

dilute betweenanion sites lead to site-selective segregation. (3) For highdopant concentrations, at the GB core the O2¹ coordinationnumber is around 6 to 7 for both Y3+ and Zr4+. This indicates

Fig. 5 (a) Atomic arrangement obtained by MC simulations, and the two-dimensional ion distribution for (b) Y3+, (c) Zr4+, and (d) O2¹

ions. For eyes aid, the discrete patterns of atoms are broadened by the Gaussian function with FWHM of 0.4.

Fig. 6 O2¹ coordination number to (a) Y3+ ions (the colored octagons) and(b) Zr4+ ions (the colored tetragons) at the GB plane. The open circlesrepresent the positions of the cation columns. The dashed line representsthe GB plane.

T. Yokoi, M. Yoshiya and H. Yasuda1348

that site-selective segregation is more dominant in thefavorable atomic arrangement than point defect association,whereas O2¹ ions are located as 8-fold coordination for Y3+

and 7-fold coordination for Zr4+ at the region more than 3¡distant from the GB. Thus, point defect association isdominant on determining the favorable atomic arrangementat the region. The low coordination environment at the GBcore indicates that the binding energy between the GB andpoint defects is greater than that between point defects. Theeffect at the GB core would affect the energetics of O2¹

migration for polycrystalline Y2O3-doped ZrO2.

Acknowledgements

This study was supported by a Grant-in-Aid for ScientificResearch on Innovative Areas “Nano Informatics” (GrantNo. 25106005) from Japan Society for the Promotion ofScience (JSPS).

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