Article pubs.acs.org/JPCC
Strained Ionic Interfaces: Effect on Oxygen Diffusivity from Atomistic Simulations Dilpuneet S. Aidhy,†,* Yanwen Zhang,†,‡ and William J. Weber‡,† †
Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996
‡
ABSTRACT: The role of materials’ interfaces/grain boundaries on enhancing anion conductivity is an intensely debated issue that has exposed limited understanding on point-defect energetics at interfaces. Using static atomistic simulations on ZrO2 | CeO2 and ThO2 | CeO2 interfaces, we disentangle key interface issues, i.e., oxygen vacancy migration barriers at interfaces in the absence and presence of dopants, and oxygen vacancy-dopant binding energies at interfaces. The results show that, while pure, strained interfaces indeed possess very low oxygen migration barriers, the segregated dopants counteract and significantly raise the barriers. In addition, the dopants bind oxygen vacancies much more strongly at the interfaces than in the bulk, thereby further lowering oxygen diffusivity at interfaces. From our simulations, we conclude that the concept of strained interfaces to enhance anion conductivity prevails primarily in the absence of segregated dopants, and strategies that prevent dopant segregation need to be considered in the design of anion-conducting interfacial materials.
1. INTRODUCTION Enhancing anion conductivity via material interfacing is increasingly being pursued as a design parameter for fast-ion conductor applications.1−10 In one of the earliest such studies, anion conductivity in the CaF2 | BaF2 interface was shown to increase proportional to the density of interfaces.1 A similar phenomenon was observed in oxide-based YSZ | STO interface2 that showed a significant enhancement in oxygen conductivity, although the reported values have still to be reproduced.5 The enhancement in conductivity was attributed to strained interfaces,7,11,12 and in recent years, this concept has been observed in many other studies.13−17 However, there is also sufficient contradicting results,5,18,19 and therefore, while the strain-enhanced conductivity concept is beginning to gain momentum, the understanding on energetics of oxygen conductivity at materials interfaces has not yet been fully developed. Understanding oxygen energetics at interfaces is a complex issue.13,16 Experimentally, the greatest concerns are the correct evaluation of strain-release during interface synthesis, stability of phases under strain, effect on cation and anion positions leading to change in materials chemistry, and the effect of dopants on oxygen migration barriers under strain, all of which are simultaneously active parameters at interfaces. Recent atomistic modeling has focused on some of these key aspects and has developed strong but separate understanding on the effects of strain15,20−24 and dopants on oxygen migration barriers.21,25−27 Except for a few studies,3,28−31 most research has been performed only on bulk systems where the effect of interface has not yet been fully captured. There is a great need to extend this work to interfaces and to understand oxygen © 2014 American Chemical Society
energetics, where the effects of dopants, strain, and materials chemistry are simultaneously active. In this work, we focus on calculating oxygen migration and binding energies at interfaces with and without dopants using static atomistic simulations. Our results show that oxygen migration barriers are significantly low at strained, pure interfaces, and very high oxygen diffusivities could be achievable, as also evidenced in some of the experimental studies. However, the presence of dopants at interfaces in the vicinity of diffusing oxygen vacancies nullify these low migration barriers, and raise them significantly. In addition, oxygen vacancies bind much more strongly with the dopants at interfaces compared to bulk, thereby further degrading oxygen diffusivity. From the simulations on the given strained systems, we find that, while strained interfaces would enhance oxygen conductivity, the effect may only be practical in sparingly doped systems. For this work, we choose model fluorite-based materials, i.e., ZrO2, CeO2, and ThO2 with calculated lattice parameters of 5.10,32,33 5.41,32,33 and 5.59 Å34, respectively, creating ZrO2 | CeO2 and ThO2 | CeO2 interfaces. These materials are of wide interest for fast-ion conduction and in nuclear applications. While ZrO2 | SrTiO3 would be a more relevant interface for the ongoing discussion on strained-interfaces, our choice is based on elucidating the isolated effect of strain without involving other factors that may originate from crystallographically and chemically dissimilar materials such as ZrO2 and STO. Received: November 16, 2013 Revised: February 7, 2014 Published: February 10, 2014 4207
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Figure 1. (a) The interface structure between ZrO2 | CeO2 and ThO2 | CeO2. (b) A magnified view of the left-vertical interface. The oxygen−oxygen distances at the interface, in ZrO2 and in CeO2 are also shown. Due to smaller lattice parameter of ZrO2 than CeO2, the oxygen−oxygen distances are smaller in ZrO2 than in CeO2. At the interface, the oxygen−oxygen distances are intermediate between those of ZrO2 and CeO2. Color scheme: oxygen atoms in red, Zr in green, Ce in yellow, and vacancy in gray square.
along ⟨100⟩ for pure CeO2 is 0.47 eV compared to 0.46 eV from DFT.36 It is also in fair agreement with the experimental values between 0.49 and 0.76 eV.37 Similarly, the migration energy in ZrO2 is 0.3 eV in fair agreement with DFT.38 A similar migration energy (0.37 eV) was obtained by Khan et al.39 from atomistic calculations. Our calculated energy is also in fair agreement with the 0.44 eV obtained from tracer diffusion experiments by Oishi and Ando.40 However, it is generally found that the computationally predicted values are lower than experimental values. The prime reason is that the experiments are carried out in doped systems that also include dopantoxygen vacancy association energy contributions leading to higher values. It is also noteworthy that higher migration barriers are experimentally observed for ZrO2 compared to CeO2. As pointed out by Marrocchelli et al.,26 the difference originates primarily from the dopant-vacancy association, i.e., there are more dopants that have comparable ionic size of Ce than Zr. A smaller (larger) mismatch with Ce (Zr) leads to smaller (larger) association contribution to migration barrier. The effect of dopants is also well captured by this method as shown in Figure 2, where oxygen migration energies in the vicinity of dopants in CeO2 (see Figure 2a) are compared to a previous DFT study.36 They are found to be in good qualitative and fair quantitative agreement with DFT (Figure 2b).36 Given the large system sizes considered here, this method captures the atomistic energetics fairly well.
Interfacing these materials induces tensile strain on ZrO2 in ZrO2 | CeO2 interface, and compressive on CeO2. Similarly, ThO2 | CeO2 interface imparts tensile strain on CeO2 and compressive in ThO2. Simulating these two interfaces thus allows elucidation of the effect of both types of strains on CeO2.
2. METHODOLOGY The two interface structures are created by embedding CeO2 into ZrO2 and ThO2. A schematic of such embedded structure is shown in Figure 1a. Such structure allows relaxation of the embedded CeO2 in two dimensions (x and z), rather than only one as done conventionally in these types of simulations.29 As a result, while the interface is strained due to lattice mismatch, the materials gradually relax and approach their bulk lattice parameters with increasing distance from the interface, more representative for the practical cases.35 This structure, therefore, allows us to compare the effect of strained interface on oxygen vacancy migration energies to bulk within the same system. A close-up snapshot of the left-vertical interface and oxygen− oxygen distances are shown in Figure 1b. While the oxygen− oxygen distance is 2.64 Å at the interface, it is 2.68 and 2.59 Å in the center of CeO2 and in ZrO2, respectively. The three other interfaces also have similar oxygen−oxygen distances. Due to compressive strain on CeO2, the oxygen−oxygen distance increases with increasing distance from the interface; whereas due to the tensile strain on ZrO2, this oxygen−oxygen distance decreases. Eventually, the oxygen−oxygen distances gradually approach their equilibrium bulk distances of 2.70 Å (CeO2) and 2.55 Å (ZrO2), respectively. Similar relaxations take place in ThO2 | CeO2 structure, but the strains are in opposite directions as mentioned above. The interface is built from a fluorite single crystal of 12 ao × 2 ao × 12 ao in x, y, and z dimensions containing a total of 3456 atoms. Out of 1152 cations, 162 are replaced with Ce, and the rest (990) are Zr (or Th). The structure is then relaxed thereby leading to a (100) interface between ZrO2 | CeO2 or ThO2 | CeO2. Due to large system size, simulations are performed using classical interatomic potentials rather than more accurate but computationally very expensive density functional theory (DFT) calculations. For the energetics calculated in this work, this is a reasonable choice of method, validated by DFT calculations and results from experimental studies. The energy barriers predicted from this method are in good agreement with DFT; for example, the oxygen migration energy calculated
Figure 2. (a) Oxygen vacancy migration under three configurations, namely, 1_2 (between two Ce atoms), 1_3 (between one Ce and one dopant), and 1_4 (between two dopants). (b) The migration energies for the three configurations from the current simulations are compared to that from DFT.36 The results are in fair comparison with DFT. 4208
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The interatomic potentials used to model ZrO2 | CeO2 and ThO2 | CeO2 are taken from Minervini et al.32,33 and Nadeem et al.,34 respectively. The atoms are modeled using a rigid-ion Buckingham-type potential. In addition, we model the effect of +3 dopants, i.e., Sc, Lu, Yb, Y, Gd, Eu, Sm, and La in ZrO2 | CeO2 and Yb, Y, Gd, and La in ThO2 | CeO2 for the dopants whose potentials are available, to capture the effect of ionic radii on oxygen energetics. The static relaxation and migration barrier calculations (obtained from the nudged elastic band (NEB) method)41 are performed using the LAMMPS code.42
This is due to tensile strain on the oxygen sites in the interface structure in ZrO2. Third, the migration barriers increase gradually as moving into ZrO2, while the barriers are at minimum at the interface. The result in Figure 4d shows migration barriers on the other side of the interface, i.e., in CeO2, where the barrier shows a reversed trend. While the barriers at site B (not shown) remain the same as in Figure 4c, that of the bulk-CeO2 is now lower than that at site C in the interface-CeO2 due to the compressive strain. In order to show a gradual effect of compressive strain, barriers at the first layer of CeO2 right next to the interface are also calculated. We find that the barriers are highest at the first layer, as this layer is under the most compressive strain. With increasing distance away from the interface, the barriers decrease as shown in Figure 4d. The bulk structure that is under zero compression shows lowest migration barriers. ThO2 | CeO2 Interface: CeO2 under Tensile Strain. Now we interface CeO2 with ThO2 so as to induce tensile strain in CeO2. Because CeO2 and ThO2 are modeled using a different interatomic potential than the ZrO2 | CeO2 interface, the migration energy in pure CeO2 from this potential is different, i.e., 0.67 eV compared to 0.45 eV. However, this difference in migration barriers from different potentials is routinely observed in interatomic calculations.49 As a result, the migration barriers predicted are higher in this case. Nevertheless, their qualitative trend remains same, and the relative comparison is of the most interest here. The oxygen migration barriers in CeO2 at the interface (circles), in the center (diamonds), and in the bulk (triangles) are shown in Figure 5. Because CeO2 is now under tensile strain, the barrier trend is similar to ZrO2 as in the ZrO2 | CeO2 interface. The barriers at the interface are the lowest, followed by that in the center, and are maximum in the unstrained bulk-CeO2. These barriers are calculated for the oxygen−oxygen distances of 2.72 Å at the interface, 2.71 Å in the center, and 2.70 Å in the bulk-CeO2. 3.2. Oxygen vacancy-dopant binding energetics. Oxygen vacancy-dopant binding is a well-understood phenomenon in bulk materials.32,36,50 The binding adversely affects conductivity due to oxygen vacancy sequestration thus decreasing their mobility. The segregated dopants are also perceived to pin oxygen vacancies at interfaces/grain boundaries;51 it is viewed as the most likely reason for lower oxygen conductivity in nanocrystalline materials.5 While the energetics of binding in bulk have been widely calculated, their strength at interfaces remains unclear. Here, we calculate binding energies at the interfaces. It is calculated as a difference between the energy of a system containing a dopant and oxygen vacancy as nearest neighbors to that of a system when they are kept far apart. The oxygen vacancy-dopant binding energies for the ZrO2 | CeO2 and ThO2 | CeO2 interfaces are compared with that in bulk-CeO2 in Figure 6a,b, respectively. We find that, irrespective of the direction of strain on CeO2, the oxygen vacancy-dopant binding energy is higher at the interface than that in the bulk. This shows that the strain direction has no effect on their binding, and they always bind more strongly at the interface than in the bulk. Hence, these simulations elucidate that dopants segregated at interfaces will have a much larger detrimental effect on oxygen diffusion than if they are distributed in the bulk.
3. RESULTS 3.1. Oxygen Migration Energy Calculations. ZrO2 | CeO2 Interface: CeO2 under Compressive Strain. Using the interface structure shown in Figure 1b, we calculate migration along the ⟨100⟩ direction that has been widely observed to be the most preferable hopping direction in fluorite materials. The oxygen vacancy migration energy at the interface is calculated to be 0.08 eV. This value is significantly lower than the bulk values in ZrO2 (0.3 eV) and CeO2 (0.47 eV), as illustrated in Figure 3. This shows that there occurs a significant drop in the migration barriers at the interface, and interfaces could indeed provide very fast channels for oxygen diffusion.
Figure 3. Oxygen-vacancy migration energy comparison between bulk-ZrO2, bulk-CeO2, and at the ZrO2−CeO2 interface. The migration energy at the interface is only 0.08 eV, which is much smaller than 0.3 and 0.47 eV in bulk-ZrO2 and bulk-CeO2, respectively.
Now we calculate similar migration barriers in the presence of dopants. It has been widely observed both experimentally and theoretically that dopants prefer to segregate at grain boundaries and interfaces.43−48 It is also found from bulk calculations that they alter oxygen migration barriers significantly (see Figure 2).25,36 Therefore, here we calculate their effect on oxygen energetics at interfaces under the influence of strain. Figure 4a shows a schematic configuration of a diffusing oxygen vacancy in the presence of a nearestneighbor dopant. Figure 4b shows three locations where the migration energies are calculated, i.e., in ZrO2 (marked A), at the interface (B) and in CeO2 (C). These oxygen sites are the same as that shown in Figure 1b. Figure 4c shows the oxygen migration barriers in ZrO2 for site A (diamonds), site B (circles), and in a single crystal bulkZrO2 (triangles) as a function of dopant radii. First, we find that oxygen migration barriers increase with increasing dopant radius. This result is consistent with the previous DFT studies (see Figure 2). Second, the migration barriers are higher in bulk-ZrO2 compared to the both sites in the interface structure.
4. DISCUSSION By calculating migration barriers at pure and doped interfaces, a clearer picture emerges that strained interfaces indeed provide 4209
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Figure 4. Oxygen-vacancy migration energy in the presence of dopants. (a) A schematic of oxygen-vacancy diffusion in ⟨100⟩ direction the presence of one dopant. (b) Illustration of the three sites, A, B, and C in the ZrO2 | CeO2 interface structure where oxygen migration energies are calculated as shown in (c) and (d). Also shown is a dopant in the vicinity of diffusing oxygen vacancy identical to crystallographic position as shown in (a). (c) Oxygen-vacancy migration energies at sites A, B and in the bulk-ZrO2 as a function of dopant radii. (d) Oxygen-vacancy migration energies at sites C, in the 1st layer in CeO2 next to interface, and in bulk-CeO2. Due to tensile strain in ZrO2, the migration energies in interface-ZrO2 are smaller than that in the bulk-ZrO2. In contrast, due to the compressive strain on interface-CeO2, the migration energies are higher than bulk-CeO2. For details, see text.
comparable to that in the bulk. Even in the presence of the smallest sized +3 dopant, Sc, the barrier at interface, ∼0.2 eV, is more than twice that of the undoped case. Hence, it is possible that segregation of dopants may degrade the effectiveness of the interfacial properties. It also becomes clear that while the lowest migration barriers are obtained from the smallest dopants, they bind most strongly with the oxygen vacancies at the interfaces. Thus, in the design of interfacial materials, the choice of dopants would require a critical balance between segregation, binding, and migration energies. Previous design strategies for materials primarily involved binding and migration energies;36 however, in the design of interfacial materials, segregation energy would at least play an equally important role. While the tensile strain on one material would enhance oxygen diffusivity, there could be an equally degrading effect from the other side of the interface in the compressed material, as shown by ZrO2 | CeO2 simulation. In case multilayers of such materials were to be used, similar to the work by Sata et al.,1 the size of the material under compression would need to be optimized, such that the desirable tensile strains would be achieved in one material, while the compressive strains would be minimized on the other side. Hence, studies on layer thickness could become prerequisite to the design of interfacial materials. This work has attempted to elucidate key oxygen vacancy energetics at interfaces. This work shows that while strained interfaces indeed provide very low oxygen migration barriers
Figure 5. Oxygen-vacancy migration energy in ThO2 | CeO2 interface at sites B and C (see Figure 4b), and in bulk-CeO2. Due to the tensile strain on CeO2 originating from the larger lattice parameter of ThO2, the migration energies are lower in the interface-CeO2 compared to bulk-CeO2.
very low diffusion paths for oxygen conduction. However, the presence of segregated dopants nullifies that effect, and raises the barriers. In the case of tensile-strained ZrO2, depending upon the choice of dopants, the migration barrier lies between 0.2 and 0.6 eV at the interface, compared to only 0.08 eV in the absence of dopants (see Figure 4c). The dopant effect is so large that the barrier for La-doped interface is almost 4210
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Figure 6. Binding energy between dopant and oxygen vacancy at the interface, and in bulk-CeO2. (a) at ZrO2 | CeO2 interface and (b) at ThO2 | CeO2 interface. In both interfaces, oxygen vacancies bind much more strongly at the interfaces compared to that in the bulk. (6) 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, 6133−6137. (7) Korte, C.; Peters, A.; Janek, J.; Hesse, D.; Zakharov, N. Ionic Conductivity and Activation Energy for Oxygen Ion Transport in SuperlatticesThe Semicoherent Multilayer System Ysz (Zro2 + 9.5 Mol% Y2o3)/Y2o3. Phys. Chem. Chem. Phys. 2008, 10, 4623−4635. (8) Tuller, H. L. Ionic Conduction in Nanocrystalline Materials. Solid State Ionics 2000, 131, 143−157. (9) Tuller, H. L.; Bishop, S. R. Point Defects in Oxides: Tailoring Materials through Defect Engineering. Ann. Rev. Mater. Res. 2011, 41, 369−398. (10) Fabbri, E.; Pergolesi, D.; Traversa, E. Ionic Conductivity in Oxide Heterostructures: The Role of Interfaces. Sci. Technol. Adv. Mater. 2010, 11, 054503. (11) Schichtel, N.; Korte, C.; Hesse, D.; Janek, J. Elastic Strain at Interfaces and Its Influence on Ionic Conductivity in Nanoscaled Solid Electrolyte Thin FilmsTheoretical Considerations and Experimental Studies. Phys. Chem. Chem. Phys. 2009, 11, 3043−3048. (12) Korte, C.; Schichtel, N.; Hesse, D.; Janek, J. Influence of Interface Structure on Mass Transport in Phase Boundaries between Different Ionic Materials. Monat. Chem.−Chem. Monthly 2009, 140, 1069−1080. (13) 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. (14) Aydin, H.; Korte, C.; Rohnke, M.; Janek, J. Oxygen Tracer Diffusion Along Interfaces of Strained Y2o3/Ysz Multilayers. Phys. Chem. Chem. Phys. 2013, 15, 1944−1955. (15) Kushima, A.; Yildiz, B. Oxygen Ion Diffusivity in Strained Yttria Stabilized Zirconia: Where Is the Fastest Strain? J. Mater. Chem. 2010, 20, 4809. (16) Rupp, J. L. M. Ionic Diffusion as a Matter of Lattice-Strain for Electroceramic Thin Films. Solid State Ionics 2012, 207, 1−13. (17) 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. (18) Gerstl, M.; Friedbacher, G.; Kubel, F.; Hutter, H.; Fleig, J. The Relevance of Interfaces for Oxide Ion Transport in Yttria Stabilized Zirconia (Ysz) Thin Films. Phys. Chem. Chem. Phys. 2013, 15, 1097− 1107. (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.
and are promising materials design parameter, the segregation of dopants at interfaces appears to be a big bottleneck and strategies that could prevent dopant segregation need to be investigated.52 This work has been performed on the most ideal interface structures. Various factors, such as effect of strain on cation positions, phase stability of materials at interfaces, dopant segregation energetics, and effect of the (111) interface still need to be carefully understood. Similarly, the effect of segregated dopants on the stability of oxygen vacancies into dimer or trimer complexes at interfaces needs to be investigated in the future.
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AUTHOR INFORMATION
Corresponding Author
*Phone: 865 241 2720; e-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
This work was supported as part of the Materials Science of Actinides, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. The computer simulations were performed at the National Energy Research Scientific Computing Center at Lawrence Berkeley National Laboratory.
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