# Fileset

[ZrO2_Arai_eJSSNT_2025.pdf](https://mdr.nims.go.jp/filesets/47552aba-3200-4f99-b80e-ab638657a096/download)

## Creator

Shungo Arai, Koji Shimizu, [Anh Khoa Augustin Lu](https://orcid.org/0000-0003-4702-0933), Hiroshi Masuda, Hidehiro Yoshida, Satoshi Watanabe

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Charge States of Ions around Σ5(310)/[001] Grain Boundary in Cubic-ZrO<sub>2</sub> Revealed by First-principles Calculations](https://mdr.nims.go.jp/datasets/a8721321-58be-44f2-b974-00536cea93fc)

## Fulltext

Charge States of Ions around Σ5(310)/[001] Grain Boundary in Cubic-ZrO2 Revealed by First-principles Calculationse-Journal of Surface Science and Nanotechnology 23, 323–327 (2025)Charge States of Ions around Σ5(310)/[001] GrainBoundary in Cubic-ZrO2 Revealed by First-principlesCalculationsShungo Arai,a Koji Shimizu,a, b Anh Khoa Augustin Lu,a, c, d Hiroshi Masuda,a Hidehiro Yoshida,aSatoshi Watanabe a, †a Department of Materials Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japanb Materials DX Research Center, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki305-8568, Japanc Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki305-0044, JapandMathematics for Advanced Materials Open Innovation Laboratory, National Institute of Advanced Industrial Science and Technology (AIST),2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan† Corresponding author: watanabe@cello.t.u-tokyo.ac.jpReceived: 14 February, 2025; Accepted: 10 July, 2025; J-STAGE Advance Publication: 23 August, 2025; Published: 23 August, 2025Understanding ion behavior is crucial for advancing theprocessing of ceramic materials. Given that ion transport pre-dominantly occurs at grain boundaries (GBs) in ceramics, in-vestigating the electronic states in their vicinity is essential. Inthis study, we perform electronic structure and Born effectivecharge (BEC) calculations from first principles based on densityfunctional (perturbation) theory, focusing specifically on theΣ5(310)/[001] GB in cubic-ZrO2. Our results reveal the emer-gence of acceptor states just above the top of the valence bandnear the GB region. Furthermore, we observe significant devia-tions in the BECs of both Zr and O near the GB regioncompared to those in the bulk. These findings suggest thepossibility of peculiar ion behavior near GB regions, particularly under applied electric fields.Keywords ZrO2; Grain boundary; Density functional theory; Density functional perturbation theory; Born effective chargeI. INTRODUCTIONCeramic materials are widely employed across diverseindustries owing to their outstanding physical properties,including high heat resistance, wear resistance, and corrosionresistance. Nonetheless, their consolidation process requirescompaction of raw powder and subsequent sintering at hightemperatures exceeding 1000°C, primarily due to the brittlenature of ceramic materials. This poses significant technical,economic, and environmental challenges. To address theseissues, numerous studies have been undertaken to developmore efficient and sustainable processing technologies [1, 2].To enhance the densification of ceramic powder compacts,various experimental approaches have been explored, includ-ing the application of direct or alternating electric fieldsduring sintering [3]. Among these methods, the phenomenonof flash sintering, wherein rapid densification occurs at rel-atively low temperatures under the influence of strong elec-tric fields, has been observed [4]. Additionally, this phenome-non has been found to facilitate ceramic processing such ashigh temperature plastic deformation [5] and joining [6].Although these phenomena are considered to involve en-hanced ion transport in the vicinity of grain boundaries(GBs), the fundamental aspects related to them remain elu-sive, necessitating further elaborate studies using systemsthat include GBs.Regular Papere-J. Surf. Sci. Nanotechnol. 23, 323–327 (2025) | DOI: 10.1380/ejssnt.2025-044 323mailto:watanabe@cello.t.u-tokyo.ac.jphttps://doi.org/10.1380/ejssnt.2025-044One possible factor that promotes ion transport is theformation of a substantial number of defects in the vicinityof GBs induced by applied electric fields. Several experi-mental findings support this hypothesis. For instance, it isknown that temperature and field strength conditions re-quired for onset of flash event in high-purity alumina canbe lowered by doping divalent cations, which would produceoxygen defects [7]. In addition, flash events can enhancefluorescence emission and anelasticity in yttria-stabilizedzirconia (YSZ) [8, 9]. These phenomena are explained interms of the introduction of excessive oxygen vacancies.As for theoretical study, the ionic behavior at theΣ5(310)/[001] GB in 8mol% yttria-stabilized zirconia(8YSZ) was examined using classical molecular dynamics(MD) simulations [10]. This study demonstrated an increasein ion diffusivity in response to applied electric fields, influ-enced by external forces originating from nominal chargestates of ions. This phenomenon was ascribed to the forma-tion of vacancies, which led to a reduction in electrostaticpotential and space charge near the GB. However, the studydid not account for the impacts of polarization resulting fromion displacements and the non-unique allocation of chargedensity in covalent orbitals. On the other hand, a precedingstudy by some of the present authors assessed Born effectivecharges (BECs), which capture the response to externalelectric fields, in lithium phosphate using density functionalperturbation theory (DFPT) [11]. Note that one definition ofthe BECs, Z���, is based on the induced atomic forces inresponse to applied electric fields, which can be calculatedusing the following formula:Z��� ¼@F�@E�;where e is the elementary charge, Fα and Eβ are the atomicforces and the electric field, respectively, and the subscripts αand β denote the X, Y, or Z direction. The preceding studyrevealed significant variations in charge states of ions de-pending on their local atomic environment. Notably, anom-alous charge states were observed, particularly in the pres-ence of defects, suggesting their possible occurrence nearGBs due to the distinct atomic environment compared to thebulk. To the best of our knowledge, BECs at GBs have notbeen previously investigated. Moreover, ions at GBs areexpected to exhibit behaviors distinct from those in bulkcrystals under applied electric fields, potentially due to polar-ization effects arising from atomic misalignment and elemen-tal segregation in the structurally disordered GB region.Alternatively, deviations in charge states from nominal val-ues may lead to enhanced external forces. In the presentstudy, we focused particularly on the latter effect and inves-tigated the electronic states and BECs of GBs in ZrO2.II. METHODWe considered two models. In constructing the first model,we initially modeled a coincidence site lattice GB using theaimsgb software [12], based on the cubic-ZrO2 structureobtained from the Materials Project database (mp-1565)[13, 14] with lattice constants optimized in this study.Given the considerable computational costs associated withDFPT calculations, we focused on a minimal GB model ofΣ5(310)/[001] with a short period of coincidence site lattice.Note that our model contained 120 atoms (40 Zr and 80 O)per supercell in its pristine state. The constructed bi-crystalGB model is depicted in Figure 1, where the GB planes arepositioned at the middle and edge of the cell perpendicular tothe Z-axis. The second model shown in Figure 2 is takenfrom a previous density functional theory (DFT) study [19].This model, after structure relaxation, has the lowest energyamong the models studied in Ref. 15 and is consistent with atransmission electron microscope observation [16]. Thismodel can be constructed by removing a Zr and two O atomsfrom a GB (i.e., two Zr and four O atoms in a supercell). TheFigure 1: Schematic representations of the first model Σ5(310)/[001] GB in cubic-ZrO2 viewed along (a) YZ-plane and (b) XZ-planes.Figure 2: Schematic representations of the second model ofΣ5(310)/[001] GB in cubic-ZrO2 viewed along (a) YZ-plane and(b) XZ-planes.Regular Papere-J. Surf. Sci. Nanotechnol. 23, 323–327 (2025) | DOI: 10.1380/ejssnt.2025-044 324https://doi.org/10.1380/ejssnt.2025-044GB energies of the first and second models calculated withthe following computational conditions were 0.0934 and0.0431 eVÅ−2, respectively, that is, the second model ismore stable. Therefore, we will show and discuss the resultson the second model, while those on the first one are in-cluded in Supplementary Material.All DFT and DFPT calculations were performed using theVienna Ab initio Simulation Package (VASP) [17–19]. Inthese calculations, we used a generalized gradient approx-imation with the Perdew-Burke-Ernzerhof functional [20], aplane-wave basis set with a 520-eV cutoff energy, self-con-sistent field convergence criterion of 10−5 and 10−6 eV forDFT and DFPT calculations, respectively, and k-point sam-pling mesh of 3 × 4 × 2. Geometry relaxation was performeduntil the maximum force on atoms fell below 0.02 eVÅ−1.We optimized the GB structures by adjusting the latticeconstant in the Z-direction to relieve external pressure. Forthis purpose, we modified the source code of VASP 6.2.1 toallow geometry relaxation with some lattice parameters fixed.Note that the previous study [15] did not account for suchchange in the lattice constant in the Z-direction.III. RESULTS AND DISCUSSIONThe optimized structure after relaxation with fixed latticeconstants in the X- and Y-directions and free lattice constantsin the Z-direction is illustrated in Figure 3, with the corre-sponding atomic coordinates provided in Table S1 in Sup-plementary Material. During structural optimization, Zratoms in the partially depleted Zr columns exhibited dis-placements toward the GB plane. Although in the previousstudy, these atoms appeared to lie more directly above theGB plane, the overall displacement trends are qualitativelyconsistent. The atomic configuration near the GB largelypreserves its initial structure; however, noticeable distortionsare observed particularly in the oxygen sublattice, whichis consistent with the previous report. It should be notedthat the method of removing oxygen atoms in our modeldiffers slightly from that inferred from the schematic in theprevious study. Nonetheless, our configuration was found tobe slightly more energetically favorable and was thereforeadopted. As illustrated in Figure S1 (Supplementary Materi-al), the first model exhibits sliding at the GB plane, resultingin more pronounced structural changes at the boundary com-pared to the second model. Despite this, atomic displace-ments in regions far from the GB remain minimal.Additionally, we also present the calculated density ofstates (DOS) for the optimized GB structure in Figure 3.The color map visualizes the projected DOS along the Z-axis, with the energy reference set to the highest occupiedstate. The obtained DOS shows the emergence of uniqueelectronic states near the GB region, distinguishing themfrom those in areas farther from the GB. Specifically, accep-tor energy levels appear just above the valence band aroundthe GB, while no distinct changes are seen in the conductionband. The analysis of the local DOS indicated that thecontributions to the valence band top and conduction bandbottom were predominantly from O and Zr orbitals, respec-tively. O orbitals also mainly contribute to the acceptor levelsaround the GB.Subsequently, DFPT calculations were conducted to assessthe BECs of the optimized GB structure. Figure 4 displaysthe BEC values of the respective tensor components for theions along the Z-axis. Note that the horizontal dotted lines inthe figure denote the BECs of bulk cubic-ZrO2 (with Zr at+5.77e and O at −2.88e). Interestingly, our findings revealedsignificant deviations in the diagonal components of BECs(Z�xx, Z�yy, and Z�zz) from their bulk values, as depicted inFigure 4(a, e, i). The maximum and minimum BEC values ofZr (O) in the GB structure were +6.49e (−1.91e) and +3.75e(−3.28e), respectively, as summarized in Table 1. In partic-ular, the Z�yy and Z�zz components exhibit the most pro-nounced deviations from the bulk values among the diagonalelements. Additionally, the non-diagonal components of theBEC tensor attain finite and non-negligible values, which isespecially evident for oxygen atoms. Zirconium atoms alsoshow finite off-diagonal components.In cubic crystalline bulk, the off-diagonal components ofthe BECs were typically zero for both Zr and O ions. How-ever, our calculations revealed finite values for these compo-nents. In the vicinity of the GB, this can be attributed to thereduced symmetry, which induces structural anisotropy andresults in anomalous off-diagonal BEC values. As shown inFigure 2, atomic displacements are observed throughout thestructure, suggesting that the system may have undergone atransition from the ideal cubic phase to a monoclinic-likeconfiguration during structural relaxation. This is plausible,as cubic-ZrO2 is thermodynamically stable only at hightemperatures. The monoclinic phase, being inherently ani-Figure 3: Schematic representation of the optimized Σ5(310)/[001]GB structure in cubic-ZrO2, along with the corresponding DOS andprojected DOS along the Z-direction, perpendicular to the GB. Theenergy reference is set to the highest occupied state.Regular Papere-J. Surf. Sci. Nanotechnol. 23, 323–327 (2025) | DOI: 10.1380/ejssnt.2025-044 325https://doi.org/10.1380/ejssnt.2025-044sotropic, naturally exhibits non-zero off-diagonal BEC com-ponents. Correspondingly, even the diagonal components ofthe BEC tensor are expected to differ from those of the cubicphase, given that monoclinic-ZrO2 contains two distinct Zrsites and four distinct O sites. Additionally, the monoclinicphase typically has a lower density than the cubic phase,implying that tensile strain may be introduced in the GBmodel. Such strain could further amplify the variation andmagnitude of the BEC values. It is noteworthy that in thecase of our first model, significant deviations from the bulkvalues were observed mostly in the vicinity of the GB (seeSupplementary Material for details). This difference betweenthe first and second models may be attributed to the differ-ence in thickness perpendicular to the GB; the thickness ofthe second model is only about half of the first model. Sinceour preliminary calculation on the structural relaxation of theenlarged second model where the thickness perpendicular tothe GB was almost doubled exhibited considerable structuralchange even in the regions far from the GB, which may bedue to the fact that the monoclinic phase is the most stable,we remain detailed analysis on the effects of GB on theregion far from the GB as a future task. Furthermore, asdemonstrated in Ref. 11, under applied electric fields, suchnon-zero off-diagonal components of the BECs generateexternal forces perpendicular to the electric field, therebycontributing to enhanced ionic mobilities. Note that thesefeatures of the BECs in the GB model are expected to appearregardless of the functional employed, judging from the BECcalculations on monoclinic-ZrO2 (for details, see Supplemen-tary Material). It is also noteworthy that the Bader chargeswere insensitive to change in local environment compared tothe BECs as can be seen in Table 1.In this way, this study highlights the anomalous variationof BEC values, which depends on the surrounding atomicenvironment near GBs. Furthermore, under an applied elec-tric field, ions positioned near the GB region are anticipatedto experience heightened external forces compared to thoseFigure 4: Calculated BECs Z� for each ion in the Σ5(310)/[001] GB model of cubic-ZrO2. Each tensor component is depicted along the Z-direction. Green and red circles denote values of Zr and O, respectively. The vertical dotted lines indicate the boundary between two grains,while the horizontal dotted lines represent the Z� values of bulk cubic-ZrO2.Table 1: Maximum and minimum BECs. Parentheses indicate thecomponents of BECs.Diagonal Z� (e) Off-diagonal Z� (e) Bader (e)Max. Min. Max. Min. Max. Min.Zr+6.49(zz)+3.75(yy)+0.929(zx)−0.929(zx)+2.60 +2.53O−1.91(zz)−3.28(yy)1.58(xy)−1.58(xy)−1.23 −1.32Regular Papere-J. Surf. Sci. Nanotechnol. 23, 323–327 (2025) | DOI: 10.1380/ejssnt.2025-044 326https://doi.org/10.1380/ejssnt.2025-044in bulk. Therefore, we shall extend the simulation methodsproposed, e.g., in Refs. 11 and 21 to be applicable to GBmodels in future work, thereby elucidating ion behaviorunder applied electric fields.IV. CONCLUSIONSIn this study, we performed electronic structure and BECcalculations from first principles based on density functional(perturbation) theory, focusing specifically on the Σ5(310)/[001] GB in cubic-ZrO2. Our findings unveil the emergenceof acceptor states just above the top of the valence band nearthe GB region. Furthermore, notable deviations in the BECsof both Zr and O near the GB region compared to those in thebulk were observed. Especially, the off-diagonal componentsof BECs took finite values for ions near the GB, suggestingthe occurrence of forces under applied electric fields in thedirections perpendicular to the fields. These findings high-light the distinctive behavior of ions near GB regions, partic-ularly under applied electric fields.AcknowledgmentsThis study was supported by JST CREST Program ‘Strong fieldnanodynamics at grain boundaries and interfaces in ceramics’(JPMJCR1996) and JSPS KAKENHI Grant Numbers (19H02544,21H05552, 23H04100). Some of the calculations used in this studywere performed using the computer facilities at ISSP Supercom-puter Center and Information Technology Center, The University ofTokyo.AppendixThe atomic coordinate of the optimized pristine GB model, thecharge density distributions along the Z-axis, and the BECs of VO2+models are available in Supplementary Material at https://doi.org/10.1380/ejssnt.2025-044.NoteThis paper was presented at the 10th International Symposiumon Surface Science, Kitakyushu International Conference Center,Fukuoka, Japan, 20–24 October, 2024.References[1] M. Yu, S. Grasso, R. Mckinnon, T. Saunders, and M. J. Reece,Adv. Appl. Ceramics 116, 24 (2017).[2] C. E. J. Dancer, Mater. Res. Express 3, 102001 (2016).[3] R. Raj, M. Cologna, and J. S. C. Francis, J. Am. Ceram. Soc. 94,1941 (2011).[4] M. Cologna, B. Rashkova, and R. Raj, J. Am. Ceram. Soc. 93,3556 (2010).[5] H. Motomura, D. Tamao, K. Nambu, H. Masuda, and H.Yoshida, J. Eur. Ceram. Soc. 42, 5045 (2022).[6] K. Nambu, T. Kitaoka, K. Morita, K. Soga, T. Tokunaga, T.Yamamoto, H. Masuda, and H. Yoshida, J. Am. Ceram. Soc. 106,2073 (2023).[7] M. Cologna, J. S. C. Francis, and R. Raj, J. Eur. Ceram. Soc. 31,2827 (2011).[8] Y. Yamashita, T. Kurachi, T. Tokunaga, H. Yoshida, and T.Yamamoto, J. Eur. Ceram. Soc. 40, 2072 (2020).[9] H. Masuda, K. Morita, T. Tokunaga, T. Yamamoto, and H.Yoshida, Acta Mater. 227, 117704 (2022).[10] W. Xu, A. Maksymenko, S. Hasan, J. J. Meléndez, and E.Olevsky, Acta Mater. 206, 116596 (2021).[11] K. Shimizu, R. Otsuka, M. Hara, E. Minamitani, and S.Watanabe, Sci. Technol. Adv. Mater. 3, 2253135 (2023).[12] J. Cheng, J. Luo, and K. Yang, Comput. Mater. Sci. 155, 92(2018).[13] The Materials Project provides open web-based access tocomputed information on various materials properties. http://www.materialsproject.org.[14] A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S.Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A.Persson, APL Mater. 1, 011002 (2013).[15] Z. Mao, S. B. Sinnott, and E. C. Dickey, J. Am. Ceram. Soc.85, 1594 (2002).[16] E. C. Dickey, X. Fan and S. J. Pennycook, J. Am. Ceram. Soc.84, 1361 (2001).[17] G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996).[18] G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).[19] X. Gonze and C. Lee, Phys. Rev. B 55, 10355 (1997).[20] J. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77,3865 (1996).[21] A.-M. El-Sayed, M. B. Watkins, T. Grasser, and A. L. Shluger,Phys. Rev. B 98, 064102 (2018).All articles published on e-J. Surf. Sci. Nanotechnol. are licensedunder the Creative Commons Attribution 4.0 International (CC BY4.0). You are free to copy and redistribute articles in any medium orformat and also free to remix, transform, and build upon articles forany purpose (including a commercial use) as long as you giveappropriate credit to the original source and provide a link to theCreative Commons (CC) license. If you modify the material, youmust indicate changes in a proper way.Copyright: ©2025 The author(s)Published by The Japan Society of Vacuum and Surface ScienceRegular Papere-J. Surf. Sci. Nanotechnol. 23, 323–327 (2025) | DOI: 10.1380/ejssnt.2025-044 327https://doi.org/10.1380/ejssnt.2025-044https://doi.org/10.1380/ejssnt.2025-044https://doi.org/10.1080/17436753.2016.1251051https://doi.org/10.1088/2053-1591/3/10/102001https://doi.org/10.1111/j.1551-2916.2011.04652.xhttps://doi.org/10.1111/j.1551-2916.2011.04652.xhttps://doi.org/10.1111/j.1551-2916.2010.04089.xhttps://doi.org/10.1111/j.1551-2916.2010.04089.xhttps://doi.org/10.1016/j.jeurceramsoc.2022.04.055https://doi.org/10.1111/jace.18889https://doi.org/10.1111/jace.18889https://doi.org/10.1016/j.jeurceramsoc.2011.07.004https://doi.org/10.1016/j.jeurceramsoc.2011.07.004https://doi.org/10.1016/j.jeurceramsoc.2019.12.060https://doi.org/10.1016/j.actamat.2022.117704https://doi.org/10.1016/j.actamat.2020.116596https://doi.org/10.1080/27660400.2023.2253135https://doi.org/10.1016/j.commatsci.2018.08.029https://doi.org/10.1016/j.commatsci.2018.08.029http://www.materialsproject.orghttp://www.materialsproject.orghttps://doi.org/10.1063/1.4812323https://doi.org/10.1111/j.1151-2916.2002.tb00317.xhttps://doi.org/10.1111/j.1151-2916.2002.tb00317.xhttps://doi.org/10.1111/j.1151-2916.2001.tb00842.xhttps://doi.org/10.1111/j.1151-2916.2001.tb00842.xhttps://doi.org/10.1016/0927-0256(96)00008-0https://doi.org/10.1103/PhysRevB.54.11169https://doi.org/10.1103/PhysRevB.55.10355https://doi.org/10.1103/PhysRevLett.77.3865https://doi.org/10.1103/PhysRevLett.77.3865https://doi.org/10.1103/PhysRevB.98.064102https://doi.org/10.1380/ejssnt.2025-044