Strain-Induced Phase and Oxygen-Vacancy Stability in Ionic Interfaces

Article pubs.acs.org/JPCC

Strain-Induced Phase and Oxygen-Vacancy Stability in Ionic Interfaces from First-Principles Calculations Dilpuneet S. Aidhy,*,† Bin Liu,† Yanwen Zhang,†,‡ and William J. Weber‡,† †

Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States

‡

S Supporting Information *

ABSTRACT: Understanding interfacial chemistry is becoming crucial in materials design for heterointerfaces. Using density functional theory, we elucidate the effect of strained interfaces on phase and oxygen-vacancy stability for CeO2|ZrO2, ThO2|ZrO2 and CeO2|ThO2 interfaces. The calculations show that ZrO2 transforms from cubic fluorite to the orthorhombic columbite under tensile strain providing evidence of a previous experimental speculation of an unrecognized ZrO2 phase. We also show oxygen vacancy formation energy decreases in the presence of tensile strain. As a result, the interfacial strain could be used as a knob to stabilize oxygen vacancies on either side of the interface, and control their concentration for fast-ion conductor applications.

■

INTRODUCTION Over the past 15 years, the push in materials’ research has been exceedingly driven by materials interfaces.1−11 The manipulation of properties by controlling materials interfaces demonstrated in systems such as LaAlO3|SrTiO3,11 BaF2| CaF2,10 and YSZ|SrTiO39 has opened up new avenues in materials design where the relative fraction of bulk and interface material is roughly equal. These types of structures are usually far from equilibrium, and understanding of materials chemistry in such structures is only beginning to develop. In recent years, the YSZ|SrTiO3 interface has remained under wide discussion,9,12−16 primarily driven by a study that revealed 8 orders of magnitude increase in oxygen conductivity originating at the interface.9 While the quantitative results have yet to be satisfactorily reproduced by other researchers,13,17−19 the underlying theme of enhancing oxygen conductivity by inducing tensile strain in one material (e.g., YSZ) through interfacing with another (e.g., SrTiO3) has now been demonstrated in various other systems.17,20−26 Studies to understand oxygen diffusion mechanisms in such strained interfaces are now at the forefront, and recent modeling efforts have shown that tensile strains lower migration barriers significantly.27−31 In parallel, the stability of the fluorite structure of ZrO2 under nanoscale and strained conditions is gaining interest, triggered by recent postulations on the existence of a different phase at the interface.12,32,33 Previous studies on the monoclinic phase have revealed a rich polymorphism of ZrO2 under both compressive34−37 and tensile conditions.32,38 In the context of the interface structures, similar understanding of fluorite-ZrO2 under tensile conditions needs to be fully developed. © XXXX American Chemical Society

Besides the indispensability of oxygen vacancies in solid-state ionics applications, there is a growing appreciation of their critical role39−41 in the physics of interface/thin-film structures based on transition-metal oxides for magnetic and electronic applications. While current efforts are focused on understanding/probing oxygen vacancy distributions near the interfaces,7 gaining traction to affect their desired distribution would be widely useful. With strain being a common denominator in these structures, understanding its effect on the stability of oxygen vacancies such that it could be used as a controlling “knob” to preferably stabilize vacancies on either side of the interface would be of wide interest to materials’ design. Some recent reports have shown that tensile strain can lower the formation energy of oxygen vacancy, opening a possibility to enhance their concentration. However, in a structure with interfaces, particularly in multilayers, whether the lowering of formation energy is a sufficient criterion to stabilize the vacancy within a material is not well understood. In this work, we show that the lower vacancy formation energy induced by tensile strain does not always lead to high oxygen vacancy concentration. Using density functional theory (DFT) calculations, we focus on two aspects of interfaces in this work: (1) on the straininduced phase transformation of fluorite-ZrO2, and (2) on the effect of strained-interfaces on the stability of oxygen vacancies. This work allows probing phases possibly stable only under strained conditions, and the stability of oxygen vacancies that may form during thin-film synthesis. We create two interface Received: August 4, 2014 Revised: November 23, 2014

A

dx.doi.org/10.1021/jp507876m | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

two materials is done on the x × y plane. Considering the bulk lattice parameters, the interface area of bulk-ZrO2 is 26.01 Å2, that of CeO2 is 29.91 Å2, and that of ThO2 is 31.18 Å2. Due to the lattice mismatch, ZrO2 is under tensile strain while CeO2 and ThO2 are under compressive strain. The optimized supercell parameters of CeO2|ZrO2 interface structure are x = 5.41 Å, y = 11.06 Å, and z = 63.95 Å, and those of ThO2|ZrO2 interface are x = 5.52 Å, y = 11.30 Å, and z = 64.72 Å. All angles are 90°. In the optimized structures, we find that ZrO2 undergoes a phase transformation from the initial cubic fluorite to the orthorhombic columbite (α-PbO2) structure. While the columbite phase is not a stable phase of ZrO2 under normal conditions, the phase transformation occurs due to the local tensile-strain conditions. A schematic representation of the phase transformed ZrO2 for both interfaces, CeO2|ZrO2 and ThO2|ZrO2, is shown in Figure 2, parts a and b, respectively, and the crystallographic information on the phase is given in Table 1.

structures between ZrO2 with CeO2 and ThO2. Both these materials are crystallographically similar but have larger lattice parameters than ZrO2, thereby inducing tensile strain on it. In addition, we also create a third interface between CeO2 and ThO2 and elucidate the preferred stability of the oxygen vacancy among the three structures.

■

METHODOLOGY We use the Vienna Ab Initio Simulation Package (VASP) for DFT calculations.42 The exchange-correlation energy is evaluated by generalized-gradient approximation (GGA) using the Perdew−Burke−Ernzerhof (PBE) function.43 The projector-augmented wave method with plane waves up to the energy cutoff of 450 eV is used. Integrations over the Brillouin zone were carried out using the Monkhorst−Pack scheme44 with a kpoint sampling of 2 × 2 × 1. After the tests for plane-wave energy cutoff and k-point sampling, the numerical error is less than 1 meV/atom. Recent research has demonstrated that the strong on-site Columbic interaction needs to be corrected for CeO2, whereas standard DFT is sufficient for ZrO2 and ThO2.29,45−47 The on-site repulsion in Ce is described by considering the Hubbard-U correction proposed by Dudarev et al.48 In this work, we use Ueff = 5.0 eV for Ce based on previous work.45 The bulk lattice parameters of ZrO2, CeO2, and ThO2 obtained by full relaxation of the 1 × 1 × 1 unit cells are 5.10, 5.48, and 5.60 Å, respectively, which are within 2% of experimentally reported values49−51 as is typical of DFT calculations. The three interface structures, i.e., CeO2|ZrO2, ThO2|ZrO2, and CeO2|ThO2 are created using (100) interfaces. All three materials are in fluorite crystal structures while creating the interfaces. We use a supercell containing 1 × 2 × 12 unit cells (288 atoms) in which 1 × 2 × 4 unit cells of ZrO2 are sandwiched between 1 × 2 × 8 unit cells of CeO2 (or ThO2). A schematic representation is shown in Figure 1. Similarly, the

Figure 2. Initial ZrO2 in fluorite phase transforms to columbite phase upon relaxation: (a) CeO2|ZrO2 interface and (b) ThO2|ZrO2 interface.

Table 1. Space Group Parameters of Columbite-ZrO2 space group a b c vol (Å3) α, β, γ

Figure 1. A 1 × 2 × 12 supercell CeO2|ZrO2 interface structure. atom

CeO2|ThO2 interface is created by sandwiching ThO2 in CeO2. These structures are fully relaxed without applying any constraint on atomic positions. All relaxations were done until the forces are smaller than 0.01 eV/Å. The oxygen vacancy formation energy (ΔEf) as a function of strain is calculated using the following expression: ΔE f = Ev − Ep + μo

Zr O

(1)

Wyckoff position 4c 8d

y = −0.3164 x = −0.2749 y = 0.1055 z = −0.4246

Pbcn, 60 5.76 5.26 5.00 151.49 90° occupancy 1.0 1.0

To put this phase into perspective with the other stable phases of ZrO2, Figure 3 shows the energy vs volume plot with monoclinic, tetragonal, and fluorite phases. The energy ordering of the three phases is correctly predicted by DFT and in agreement with previous work.53 The noticeable feature is that the columbite phase is an expanded phase having much larger volume than the fluorite phase. To verify that the phase transformation occurs only due to the tensile strain, we applied exactly the same two-dimensional strain experienced by the sandwiched ZrO2 on bulk-ZrO2, i.e., in the absence of interfaces. Here, again we found the transformation of the fluorite phase to the columbite phase.

Here, Ev is the system energy with a vacancy, Ep is the pure system energy, and μo is the oxygen chemical potential with reference to oxygen gas. The O2 gas reference state is taken as the total energy for the ground state of a spin-polarized optimized oxygen molecule in the gas phase, plus a correction of 1.36 eV for known errors in the O2 energy.46,52

■

RESULTS ZrO2 Phase Stability. We first consider the CeO2|ZrO2 and ThO2|ZrO2 structures to elucidate the instability of the fluorite phase of ZrO2 under tensile strain. The interfacing between the B

dx.doi.org/10.1021/jp507876m | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Figure 4. (a) Oxygen vacancy formation energy (ΔEf) in CeO2. (b) Equation-of-state for bulk system (circles) and containing oxygen vacancy (squares). The energies are calculated with reference to the fully relaxed CeO2 bulk structure.

Figure 3. Energy vs volume plot for the monoclinic, tetragonal, and fluorite phases of ZrO2, and the columbite phase obtained from tensile strained interfaces in Figure 2.

ceria are shown in open circles, while those for the system containing the vacancy are shown in solid squares. We find that the minimum in the parabola lies at zero strain for the pure system representing the equilibrium lattice parameter, while that of the vacancy system lies under tensile strain. This shows that oxygen vacancy prefers to occupy a larger volume, thereby leading to lattice expansion. With relation to interface structures, tensile strain provides the larger volume required by the oxygen vacancy thus stabilizing it under tensile strained conditions. These results show that tensile strain lowers the formation energy and provides the larger volume required by the oxygen vacancy. However, calculating only the formation energy may not predict whether the oxygen vacancy would be stable and available for transport in the interfacial materials. For illustration, we take the DFT-relaxed CeO2−ZrO2 interface structure from Figure 2a and calculate the relative stability of oxygen vacancy across the interface by placing it at three different locations, as shown in Figure 5a.58 Three separate calculations are performed to calculate the system energy for each site. Furthermore, to calculate the stability as a function of applied strain, we also strain the system in the x and y directions that form the interfacial plane. Figure 5b shows the stability of the oxygen vacancy with reference to the interface (set to zero and shown with black diamonds); the results for ZrO2 and in CeO2 are shown with blue circles and gray squares, respectively. In the unstrained case, the vacancy is stable inside ceria by 0.25 eV. However, upon tensile straining, the stability starts to decrease gradually, and by 3% strain, the vacancy is only stable by 0.16 eV. Such high strains are not unrealistic in these materials, as illustrated by previous experiments.9,15 From the trend, further straining would lead to the vacancy becoming unstable within ceria but stabilized at the interface. A similar trend is also observed on the compressive side, where the vacancy becomes equally stable inside ceria and at the interface. The plot also shows that oxygen vacancy is never stable in zirconia within the applied strain range. We carry out similar calculations in the ZrO2− ThO2 interface structure, and the results are shown in Figure 5c. At zero strain, the oxygen vacancy is most stable in ZrO2 by 0.44 eV followed by that at the interface, and is least stable in ThO2 (red diamonds). However, similar to CeO2 in Figure 5b, the stability of the oxygen vacancy in ZrO2 gradually decreases upon tensile strain. By 3% strain, the vacancy is only stable by 0.2 eV in ZrO2. In addition, the stability trend changes, i.e., between ThO2 and interface, the vacancy is now more stable in ThO2. Further strain would completely reverse the trend, and

Similar phase transformation was also previously observed in nanocrystalline UO2 via classical molecular-dynamics simulations.54 It was shown that under the influence of tensile stress, the fluorite phase in columnar-grained UO2 transformed to the columbite phase. The stability of the columbite phase was also validated by DFT calculations in the same work. In a recent YSZ|STO interface study using interatomic pair potentials and a genetic algorithm methodology,32 phases such as rutile, columbite, pyrite, and anatase were observed in strained, bulkYSZ. The stability of these phases was then evaluated from DFT calculations, and for a certain range of tensile strain, the columbite phase was found to be one of the lowest-energy phases. Hence, from these three theoretical studies, a general consensus emerges that the fluorite-to-columbite phase transformation under tensile strain could be inherent to fluorite phase and fluorite-based materials. These calculations thus provide insights on such phases possibly stable only under tensile conditions. Oxygen Vacancy Stability. The effect of strain on kinetics of oxygen diffusion has recently been illustrated from atomistic modeling27,28,30 where it has been shown that tensile strain could be used to lower oxygen migration barriers. This understanding has provided a tailoring mechanism in the design of better oxygen conducting materials. From the vacancy stability viewpoint, it would be equally interesting to understand whether thermodynamics could be altered such that one could preferably stabilize oxygen vacancies on either side of the interface structure. Recently, it was shown that the formation energy of the oxygen vacancy decreases under tensile strain in CaMnO3,55 indicating that a larger concentration of oxygen vacancies could be achieved via tensile strain. The oxygen vacancy formation energy as a function of strain in ceria is calculated using eq 1. At zero strain, the formation energy is 4.94 eV, which is in fair agreement with experimental values (4.72 eV).45,56 Upon applying tensile strain, the formation energy decreases, as shown in Figure 4a. The electronic structure details, i.e., density of states and charge distribution on the neighboring Ce atoms due to oxygen vacancy is given in the Supporting Information, section S1. Our results are consistent with previous DFT calculations.45,57 The stability of the oxygen vacancy under tensile strain can be explained using the equation-of-state analysis. The equationof-state of pure ceria, and that containing an oxygen vacancy are plotted in Figure 4b. The plots are obtained by using a 2 × 2 × 2 bulk single crystal strained hydrostatically. The data for pure C

dx.doi.org/10.1021/jp507876m | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

diverge, and the stability in CeO2 continuously increases with increasing tensile strain. This difference shows that the stability trends are rather complex, and likely to be dependent on specific material compositions comprising the interface. The complex stability dependency is revealed even further in the stability analysis for charged vacancies. Similar to the above results for neutral vacancies, we plot the relative stability of charged vacancies in Figure 6 for all three interface systems,

Figure 5. (a) Part of the CeO2−ZrO2 DFT relaxed interface structure showing the location of oxygen vacancy placed to calculate system energy calculations. (b, c) Oxygen vacancy relative stability (with reference to interface (black diamonds) as a function of twodimensional interfacial strain applied in x and y directions in (b) CeO2−ZrO2 and (c) ThO2−ZrO2. (d) Oxygen vacancy stability in the CeO2−ThO2 interface in CeO2 with reference to that in ThO2.

Figure 6. Charged oxygen vacancy relative stability as a function of two-dimensional interfacial strain (with reference to interface (black diamonds)) in (a) CeO2−ZrO2 and (b) ThO2−ZrO2. (c) Charged oxygen vacancy stability in the CeO2−ThO2 interface in CeO2 with reference to that in ThO2.

where panels a, b, and c of Figure 6 correspond to CeO2−ZrO2, ZrO2−ThO2, and CeO2−ThO2 structures, respectively. The charged vacancies are created by removing two electrons from the system as implemented in the code. In Figure 6a, the charged vacancy is unstable inside CeO2. This is in contrast to the neutral vacancy in Figure 5b, which is primarily stable inside CeO2. In addition, while the charged vacancy is stable at the interface across the strain range, its relative stability in ZrO2 increases with decreasing tensile strain, and by −1% strain, it is almost equally stable at the interface and inside ZrO2. In the ZrO2−ThO2 structure, the charged vacancy is stable only at the interface across the entire strain range (see Figure 6b). In contrast, in the CeO2−ThO2 structure, the charged vacancy is stable only inside CeO2, similar to its neutral counterpart (see Figures 6c and 5d). These results highlight the significance of understanding the relative stabilities of oxygen vacancies across the interfaces in addition to the vacancy formation energies.

the vacancy would become most stable in ThO2, and least in ZrO2. These results show that predicting the stability of the oxygen vacancy across the interface is strain dependent. In addition to the lowering of the formation energy by tensile strain, the relative stability of the oxygen vacancy across the interface is also important. The above two interface structure calculations show that, albeit the lower formation energies, one could actually switch the stabilities via strain. The significance of studying the relative energies is highlighted even more in the case of the CeO2−ThO2 interface. The relative stability of the oxygen vacancy across the CeO2−ThO2 interface is shown in Figure 5d. Here, we have plotted the oxygen vacancy stability with reference to ThO2, as we found that the oxygen vacancy is highly unstable at the interface. When it is placed at the interface, upon relaxation, it jumps back into CeO2. The results show that, across the applied strain range, the vacancy is stable only inside CeO2, and both ThO2 and the interface are always relatively less preferable. A comparison of the three interfaces shows that the oxygen vacancy stability trends are very different. Under tensile strain, the vacancy stabilities for the CeO2−ZrO2 and ZrO2−ThO2 interfaces gradually converge as shown in Figure 5b,c. However, for the CeO2−ThO2 interface, the vacancy stabilities instead

■

DISCUSSION Lowering of the oxygen vacancy formation energy via tensile strain is an important emerging concept. However, the above calculations show that gaining control over the thermodynamic stability (or location) of oxygen vacancies via tensile strain may not be easily achievable. The concentration of vacancies in a given material appears to depend on the relative stability of D

dx.doi.org/10.1021/jp507876m | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

(6) Rohrer, G. S.; Affatigato, M.; Backhaus, M.; Bordia, R. K.; Chan, H. M.; Curtarolo, S.; Demkov, A.; Eckstein, J. N.; Faber, K. T.; Garay, J. E.; et al. Challenges in Ceramic Science: A Report from the Workshop on Emerging Research Areas in Ceramic Science. J. Am. Ceram. Soc. 2012, 95, 3699−3712. (7) Kim, Y.-M.; He, J.; Beigalski, M. D.; Ambaye, H.; Lauter, V.; Christen, H. M.; Pantelides, S. T.; Pennycook, S. J.; Kalinin, S. V.; Borisevich, A. Y. Probing Oxygen Vacancy Concentration and Homogeneity in Solid-Oxide Fuel-Cell Cathode Materials on Subunit-Cell Level. Nat. Mater. 2012, 11, 888−894. (8) Yu, P.; Chu, Y.-H.; Ramesh, R. Oxide Interfaces: Pathways to Novel Phenomena. Mater. Today 2012, 15, 320−327. (9) Garcia-Barriocanal, J.; Rivera-Calzada, A.; Varela, M.; Sefrioui, Z.; Iborra, E.; Leon, C.; Pennycook, S. J.; Santamaria, J. Colossal Ionic Conductivity at Interfaces of Epitaxial ZrO2: Y2O3/SrTiO3 Heterostructures. Science 2008, 321, 676−680. (10) Sata, N.; Eberman, K.; Eberl, K.; Maier, J. Mesoscopic Fast Ion Conduction in Nanometer-Scale Planar Heterostructures. Nature 2000, 408, 946−949. (11) Ohtomo, A.; Hwang, H. Y. A High-Mobility Electron Gas at the LaAlO3/SrTiO3 Heterointerface. Nature 2004, 427, 423−426. (12) Pennycook, T. J.; Beck, M. J.; Varga, K.; Varela, M.; Pennycook, S. J.; Pantelides, S. T. Origin of Colossal Ionic Conductivity in Oxide Multilayers: Interface Induced Sublattice Disorder. Phys. Rev. Lett. 2010, 104. (13) Guo, X. Can We Achieve Significantly Higher Ionic Conductivity in Nanostructured Zirconia? Scr. Mater. 2011, 65, 96− 101. (14) Korte, C.; Peters, A.; Janek, J.; Hesse, D.; Zakharov, N. Ionic Conductivity and Activation Energy for Oxygen Ion Transport in Superlattices–the Semicoherent Multilayer System YSZ (ZrO2 + 9.5 Mol % Y2O3)/Y2O3. Phys. Chem. Chem. Phys. 2008, 10, 4623−35. (15) Schichtel, N.; Korte, C.; Hesse, D.; Janek, J. Elastic Strain at Interfaces and Its Influence on Ionic Conductivity in Nanoscaled Solid Electrolyte Thin Films - Theoretical Considerations and Experimental Studies. Phys. Chem. Chem. Phys. 2009, 11, 3043−3048. (16) Fronzi, M.; Cereda, S.; Tateyama, Y.; De Vita, A.; Traversa, E. Ab Initio Investigation of Defect Formation at ZrO2-CeO2 Interfaces. Phys. Rev. B 2012, 86, 085407 (1)−(5). (17) Aydin, H.; Korte, C.; Janek, J. 18O-Tracer Diffusion Along Nanoscaled Sc2O3/Yttria Stabilized Zirconia (YSZ) Multilayers: On the Influence of Strain. Sci. Technol. Adv. Mater. 2013, 14, 035007. (18) Kim, H. R.; Kim, J. C.; Lee, K. R.; Ji, H. I.; Lee, H. W.; Lee, J. H.; Son, J. W. ’Illusional’ Nano-Size Effect Due to Artifacts of in-Plane Conductivity Measurements of Ultra-Thin Films. Phys. Chem. Chem. Phys. 2011, 13, 6133−7. (19) Cavallaro, A.; Burriel, M.; Roqueta, J.; Apostolidis, A.; Bernardi, A.; Tarancón, A.; Srinivasan, R.; Cook, S. N.; Fraser, H. L.; Kilner, J. A. Electronic Nature of the Enhanced Conductivity in Ysz-Sto Multilayers Deposited by Pld. Solid State Ionics 2010, 181, 592−601. (20) Aydin, H.; Korte, C.; Rohnke, M.; Janek, J. Oxygen Tracer Diffusion Along Interfaces of Strained Y2O3/YSZ Multilayers. Phys. Chem. Chem. Phys. 2013, 15, 1944−55. (21) Jiang, J.; Hu, X.; Shen, W.; Ni, C.; Hertz, J. L. Improved Ionic Conductivity in Strained Yttria-Stabilized Zirconia Thin Films. Appl. Phys. Lett. 2013, 102, 143901. (22) Li, B.; Zhang, J.; Kaspar, T.; Shutthanandan, V.; Ewing, R. C.; Lian, J. Multilayered YSZ/GZO Films with Greatly Enhanced Ionic Conduction for Low Temperature Solid Oxide Fuel Cells. Phys. Chem. Chem. Phys. 2013, 15, 1296−301. (23) Kubicek, M.; Cai, Z.; Ma, W.; Yildiz, B.; Hutter, H.; Fleig, J. Tensile Lattice Strain Acceleraters Oxygen Surface Exchange and Diffusion in La(1−X)Sr(X)CoO(3−X) Thin Films. ACS Nano 2013, 7, 3276−3286. (24) De Souza, R. A.; Ramadan, A. H. Ionic Conduction in the SrTiO3|YSZ|SrTiO3 Heterostructure. Phys. Chem. Chem. Phys. 2013, 15, 4505−9.

oxygen vacancies between the interfacing materials, thus making the studies composition dependent. Therefore, the choice of substrate or applied strain becomes critical in designing interfacing materials with enhanced oxygen vacancy concentration. Simultaneously, with the effect of tensile strain on lowering migration barriers now quite evident from recent works,59 it appears that the approach in designing better iontransport materials might involve optimizing three key straindependent parameters, i.e., migration energy, formation energy, and relative vacancy stability, thus requiring a Materials Genome type database building approach. In conclusion, we show that interfacing of zirconia with other larger lattice parameter materials may transform it from cubic to columbite phase, making it a stable phase under tensile conditions. Stabilizing such phases via strain provides another degree of freedom in the design of materials. Similarly, stabilizing vacancies by strain provides additional control in materials design. While it is shown that tensile strain lowers the oxygen vacancy formation energy, it is not sufficient to predict vacancy stability; the relative stability of the oxygen vacancy with the interfacing materials also needs to be simultaneously understood. From these calculations, it is interesting to note that, while grain boundaries are conventionally considered as sinks for vacancies, the sink strength of interfaces could depend on the interfacial strain, and the segregation of vacancies to interfaces may not be taken trivially.

■

ASSOCIATED CONTENT

S Supporting Information *

Electronic structure details and calculations showing the effect of system size. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel: 865 241 2720. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. The computer simulations were performed at the National Energy Research Scientific Computing Center at Lawrence Berkeley National Laboratory which is supported by the Office of Science, U.S. Department of Energy under Contract No.DEAC02-05CH11231.

■

REFERENCES

(1) Chakhalian, J.; Millis, A. J.; Rondinelli, J. Whither the Oxide Interface. Nat. Mater. 2012, 11, 92−4. (2) Zubko, P.; Gariglio, S.; Gabay, M.; Ghosez, P.; Triscone, J.-M. Interface Physics in Complex Oxide Heterostructures. Annu. Rev. Condens. Matter Phys. 2011, 2, 141−165. (3) Hwang, H. Y.; Iwasa, Y.; Kawasaki, M.; Keimer, B.; Nagaosa, N.; Tokura, Y. Emergent Phenomenon at Oxide Interfaces. Nat. Mater. 2012, 11, 103−113. (4) Nakagawa, N.; Hwang, H. Y.; Muller, D. A. Why Some Interfaces Cannot Be Sharp. Nat. Mater. 2006, 5, 204−209. (5) Kalinin, S. V.; Borisevich, A.; Fong, D. Beyond Condensed Matter Physics on the Nanoscale: The Role of Ionic and Electrochemical Phenomenon in the Physical Functionalities of Oxide Materials. ACS Nano 2012, 6, 10423−10437. E

dx.doi.org/10.1021/jp507876m | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

(47) Lu, Y.; Yang, Y.; Zhang, P. Thermodynamic Properties and Structural Stability of Thorium Dioxide. J. Phys.: Condens. Matter 2012, 24, 225801. (48) Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Electron-Energy-Loss Spectra and the Structureal Stability of Nickel Oxide: An Lsda+U Study. Phys. Rev. B 1998, 57, 1505−1509. (49) Katz, G. X-Ray Diffraction Powder Pattern of Metastable Cubic ZrO2. J. Am. Ceram. Soc. 1971, 54, 531. (50) Bukaemskiy, A. A.; Barrier, D.; Modolo, G. Thermal and Crystallization Behaviour of ThO2−CeO2 System. J. Alloys Compd. 2009, 485, 783−788. (51) Gerward, L.; Staun Olsen, J.; Petit, L.; Vaitheeswaran, G.; Kanchana, V.; Svane, A. Bulk Modulus of CeO2 and PrO2an Experimental and Theoretical Study. J. Alloys Compd. 2005, 400, 56− 61. (52) Wang, L.; Maxisch, T.; Ceder, G. Oxidation Energies of Transition Metal Oxides within the GGA+U Framework. Phys. Rev. B 2006, 73, 195107 (1)−(6). (53) Finnis, M. W.; Paxton, A. T.; Methfessel, M.; Schilfgaarde, M. V. Crystal Structures of Zirconia from First-Principles and SelfConsistent Tight Binding. Phys. Rev. Lett. 1998, 81, 5149−5152. (54) Desai, T. G.; Uberuaga, B. P. Stress-Induced Phase Transformation in Nanocrystalline UO2. Scr. Mater. 2009, 60, 878−881. (55) Aschauer, U.; Pfenninger, R.; Selbach, S. M.; Grande, T.; Spaldin, N. A. Strain-Controlled Oxygen Vacancy Formation and Ordering in CaMnO3. Phys. Rev. B 2013, 88, 054111. (56) Panhans, M. A.; Blumenthal, R. N. A Thermodynamic and Electrical Conductivity Study of Nonstoichiometric Ceriumoxides. Solid State Ionics 1993, 60, 279−298. (57) Castleton, C. W.; Kullgren, J.; Hermansson, K. Tuning LDA+U for Electron Localization and Structure at Oxygen Vacancies in Ceria. J. Chem. Phys. 2007, 127, 244704. (58) While the vacancy images can interact in the “x” direction due to only one unit cell thick supercell, the error is canceled to a large degree as we calculate the relative energy with respect to the vacancy at the interface. See S2 in the Supporting Information. (59) Yildiz, B. “Stretching” the Energy Landscape of OxidesEffects on Electrocatalysis and Diffusion. MRS Bull. 2014, 39, 147−156.

(25) Hinterberg, J.; Zacherle, T.; De Souza, R. A. Activation Volume Tensor for Oxygen-Vacancy Migration in Strained CeO2 Electrolytes. Phys. Rev. Lett. 2013, 110. (26) Aidhy, D. S.; Zhang, Y.; Weber, W. J. Strained Ionic Interfaces: Effect on Oxygen Diffusivity from Atomistic Simulations. J. Phys. Chem. C 2014, 118, 4207−4212. (27) Kushima, A.; Yildiz, B. Oxygen Ion Diffusivity in Strained Yttria Stabilized Zirconia: Where Is the Fastest Strain? J. Mater. Chem. 2010, 20, 4809−4819. (28) Rushton, M. J. D.; Chroneos, A.; Skinner, S. J.; Kilner, J. A.; Grimes, R. W. Effect of Strain on the Oxygen Diffusion in Yttria and Gadolinia Co-Doped Ceria. Solid State Ionics 2013, 230, 37−42. (29) Li, F.; Lu, R.; Wu, H.; Kan, E.; Xiao, C.; Deng, K.; Ellis, D. E. The Strain Effect on Colossal Oxygen Ionic Conductivity in Nanoscale Zirconia Electrolytes: A First-Principles-Based Study. Phys. Chem. Chem. Phys. 2013, 15, 2692−7. (30) De Souza, R. A.; Ramadan, A.; Hörner, S. Modifying the Barriers for Oxygen-Vacancy Migration in Fluorite-Structured CeO2 Electrolytes through Strain: A Computer Simulation Study. Energy Environ. Sci. 2012, 5, 5445−5453. (31) Chroneos, A.; Yildiz, B.; Tarancon, A.; Parfitt, D.; Kilner, J. A. Oxygen Diffusion in Solid Oxide Fuel Cell Cathode and Electrolyte Materials: Mechanistic Insights from Atomistic Simulations. Energy Environ. Sci. 2011, 4, 2774−2789. (32) Cheah, W. L.; Finnis, M. W. Structure of Multilayer ZrO2/ SrTiO3. J. Mater. Sci. 2012, 47, 1631−1640. (33) Korte, C.; Schichtel, N.; Hesse, D.; Janek, J. Influence of Interface Structure on Mass Transport in Phase Boundaries between Different Ionic Materials. Monatsh. Chem.−Chem. Monthly 2009, 140, 1069−1080. (34) Jaffe, J.; Bachorz, R.; Gutowski, M. Low-Temperature Polymorphs of ZrO2 and HfO2: A Density-Functional Theory Study. Phys. Rev. B 2005, 72. (35) Terki, R.; Bertrand, G.; Aourag, H.; Coddet, C. Structural and Electronic Properties of Zirconia Phases: A Fp-Lapw Investigations. Mater. Sci. Semicond. Process. 2006, 9, 1006−1013. (36) Al-Khatatbeh, Y.; Lee, K. K. M.; Kiefer, B. Phase Relations and Hardness Trends of ZrO2 Phases at High Pressure. Phys. Rev. B 2010, 81, 214102(1)−(10). (37) Ö ztürk, H.; Durandurdu, M. Formation of Cotunnite Phase in ZrO2 under Uniaxial Stress: A First Principles Study. J. Am. Ceram. Soc. 2011, 94, 932−937. (38) Durandurdu, M. Expanded Phase of ZrO2: An Ab Initio Constant-Pressure Study. Europhys. Lett. 2009, 88, 66001. (39) Zhong, Z.; Xu, P. X.; Kelly, P. J. Polarity-Induced Oxygen Vacancies at LaAlO3/SrTiO3 Interfaces. Phys. Rev. B 2010, 82, 165127. (40) Jiang, W.; Noman, M.; Lu, Y. M.; Bain, J. A.; Salvador, P. A.; Skowronski, M. Mobility of Oxygen Vacancy in Srtio3 and Its Implications for Oxygen-Migration-Based Resistance Switching. J. Appl. Phys. 2011, 110, 034509. (41) Borisevich, A. Y.; Lupini, A. R.; He, J.; Eliseev, E. A.; Morozovska, A. N.; Svechnikov, G. S.; Yu, P.; Chu, Y.-H.; Ramesh, R.; Pantelides, S. T.; Kalinin, S. V.; Pennycook, S. J. Interface Dipole between Two Metallic Oxides Caused by Localized Oxygen Vacancies. Phys. Rev. B 2012, 86, 140102(R) (1)−(6). (42) Kresse, G.; Furthmuller, J. Efficiency of Ab-Initio Total Energy Calculations for Metels and Semicoonductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (43) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (44) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188−5192. (45) Xiao, H. Y.; Weber, W. J. Oxygen Vacancy Formation and Migration in Ce(X)Th(1−X)O2 Solid Solution. J. Phys. Chem. B 2011, 115, 6524−33. (46) Liu, B.; Xiao, H.; Zhang, Y.; Aidhy, D. S.; Weber, W. J. Investigation of Oxygen Point Defects in Cubic ZrO2 by Density Functional Theory. Comput. Mater. Sci. 2014, 92, 22−27. F

dx.doi.org/10.1021/jp507876m | J. Phys. Chem. C XXXX, XXX, XXX−XXX