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Cite This: ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Strain-Induced Tailoring of Oxygen-Ion Transport in Highly Doped CeO2 Electrolyte: Effects of Biaxial Extrinsic and Local Lattice Strain Junsung Ahn,†,‡ Sungjun Choi,† Kyung Joong Yoon,† Ji-Won Son,† Byung-Kook Kim,† Jong-Ho Lee,† Ho Won Jang,‡ and Hyoungchul Kim*,† †
High-Temperature Energy Materials Research Center, Korea Institute of Science and Technology, 5 Hwarang-ro 14-gil, Seongbuk-gu, Seoul 02792, Republic of Korea ‡ Department of Materials Science and Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea S Supporting Information *
ABSTRACT: We explored oxygen-ion transport in highly doped CeO2 through density-functional theory calculations. By applying biaxial strain to 18.75 mol % CeO2:Gd, we predicted the average migration-barrier energy with six different pathways, with results in good agreement with those of experiments. Additionally, we found that the migration-barrier energy could be lowered by increasing the tetrahedron volume, including the space occupied by the oxygen vacancy. Our results indicate that the tetrahedron volume can be expanded by larger codopants, as well as biaxial tensile strain. Thus, the combination of thin-film structure and codoping could offer a new approach to accelerate oxygen-ion transport. KEYWORDS: oxygen-ion transport, strain effects, solid-state ionics, doped CeO2, SOFC
I
bilayers was increased by around 1 order of magnitude, along with enhanced chemical stability of the δ-Bi2O3. Recently, Shi et al.5 demonstrated reliable manipulation of oxygen-ion conduction with strain energy in a free-standing nanoscale membrane of Ce0.8Gd0.2O1.9‑δ, utilizing an optimized Pt microelectrode design. Despite comprehensive studies on the development of fast oxygen-ion conductors using thin-filmbased nanostructures, it has remained unclear how much fast ionic conduction can be achieved by lattice strain, and how to control lattice strain in a material system. These two subjects are linked to the question of reproducibility of many reported experimental studies, and the inconsistency between computational predictions and experimental results.3 The conductivity enhancement reported by Garcia-Barriocanal et al.,2 in particular, has never been achieved in other studies, even those using similar material systems.9 Therefore, it is necessary to develop detailed computational predictions of oxygen-ion migration-barrier energy (Em) that take into consideration the effects of biaxial extrinsic strain under a wide range of strain conditions, and local lattice strain induced by dopants that have different ionic radii from host ions. Such predictions should substantially contribute to the development of superior and fast oxygen-ion conductors.
on-conducting nanostructures have attracted much attention for their applications in a variety of energy-conversion and energy-storage systems such as batteries,1 fuel cells,2−6 and electrolysis cells,7 owing to their improved ion-transport properties. In particular, with the development of vacuumbased deposition processes such as molecular beam epitaxy,8 atomic layer deposition,1 and pulsed laser deposition,3−7 the fabrication of thin-film ionic nanostructures has become an important technology that has led to great innovations. Over the past decade, attempts have been made to enhance ionic conductivity through combinations of such thin-film nanostructures (e.g., ultrathin,2 multicoated,4 and free-standing layers5); these efforts have mainly utilized the effects of strain (ε) resulting from external force or internal stress of thin-film structured materials. A report by Garcia-Barriocanal et al.2 on the colossal oxygen-ion conductivity at the interfaces of ZrO2:Y2O3/SrTiO3 heterostructures, which showed an enhancement of more than 8 orders of magnitude, was the initiator of research in this field. Since then, many researchers have observed various strain-induced enhancements of ion conductivity in nanostructures such as ultrathin, multicoated, and free-standing layers. Fluri et al.6 reported the suppression of oxygen-ion migration energy (−0.05 eV under ε = 0.35%) in an ultrathin Sm-doped CeO2 (SDC) film with thickness of 20 nm, whose tensile strain was induced by a SrTiO3 buffer layer. Sanna et al.4 also reported that the ion conductivity of a multilayer stack consisting of 20 CeO2:Gd/δ-Bi2O3:Er2O3 © XXXX American Chemical Society
Received: September 5, 2017 Accepted: December 1, 2017
A
DOI: 10.1021/acsami.7b13440 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Letter
ACS Applied Materials & Interfaces
listed in Table 1, the predicted elastic properties of a SQS GDC structure were in general agreement with the experimental
In the present study, we used density-functional theory (DFT) to investigate the effects of biaxial extrinsic and local intrinsic lattice strain on oxygen-ion transport in a highly doped CeO2 structure. Taking the thin-film layout into consideration, we examined the effects of strain on oxygen-ion transport under biaxial strain conditions. The effects of local lattice strain induced by the highly doped structure were also analyzed using various atomic configurations and dopant ions with different radii. On the basis of our calculation results, we will propose a strategy to accelerate oxygen-ion transport using the effects of both biaxial extrinsic and local lattice strain. To describe the complex configuration of a highly doped CeO2 structure, we used a special quasi-random structure (SQS) model of 18.75 mol % Gd-doped CeO2 (GDC), which is close to the GDC composition with 20 mol % of Gd that is commonly used in practical applications. This approach generates the atomic structure of a random alloy in a computationally efficient way by reproducing the nearestneighbor (NN) pair and multisite correlation functions of an infinite random alloy.12,13 Even though the SQS model is not the lowest-energy configuration, it adequately preserves and shows the local environment of random alloys. Applying the SQS approach to highly doped CeO2, a SQS unit cell for GDC with 18.75 mol % Gd, as shown in Figure 1, was obtained; the
Table 1. Calculated Thermo-Mechanical Properties, Elastic Constant (Cij), Shear Modulus (G), Young’s Modulus (E), and Poisson’s Ratio (ν) of our SQS Model of CeO2 Doped with 18.75 mol % Gd (18.75 mol % GDC)a Property
This work
Reference
C11 (GPa) C12 (GPa) C44 (GPa) G (GPa) E (GPa) ν
285.6 84.3 48.1 65.0 171.3 0.31
− − − 71.710 187.011 0.3310
a
The materials reported in refs 10 and 11 were 10 mol % GDC and 20 mol % GDC, respectively.
results, indicating that the SQS cell and its DFT treatment effectively reproduced the structural features of GDC. (See the Supporting Information for computational details.) Our quantitative analysis of the oxygen-ion transport phenomenon in highly doped CeO2, i.e., SQS 18.75 mol % GDC, was carried out using the nudged−elastic band (NEB) method for different oxygen sites and migration pathways. Considering the number of Gd ions at the first NN cation sites, four different oxygen sites and six different oxygen−oxygen migration pathways in the out-of-plane ⟨100⟩ direction were observed. Note that only the oxygen ions hopping along the ⟨100⟩ direction were considered in this work, because the migration path in the ⟨100⟩ direction is usually reported as the lowest-energy path, rather than the paths in the ⟨110⟩ and ⟨111⟩ directions.16 Figure 2 shows various atomic configurations and migration pathways, along with the four designated oxygen positions.
Figure 1. Schematic illustration of strain-induced tailoring of oxygenion transport in highly doped CeO2. The image in the inset shows a SQS unit cell for CeO2 doped with 18.75 mol % Gd (18.75 mol % GDC) as used in this study.
Gd ions substitute for cations in six octahedral cation sites among the 32 cation sites, and thus three oxygen vacancies are placed under the electroneutrality condition as follows: × Gd 2O3 → 2Gd′Ce + 3OO + V″O
(1)
Hence, it seems reasonable to investigate the effect of strain on the SQSs for 18.75 mol % GDC to account for the effect of a complex configuration of random alloys that has yet to be covered in DFT calculations. To investigate the effect of strain on oxygen-ion migration, we performed DFT calculations, applying anisotropic strain ranging from −3.78% to +2.14% along the lateral (x-y) and longitudinal (z) directions, with Poisson’s ratio (ν) defined as ν = εzz/(εzz − 2εxx) = εzz/(εzz − 2εyy), where εxx, εyy, and εzz are the strains in the x, y, and z directions, respectively. Because the epitaxial strain is experimentally limited within 1% by introducing dislocation above the critical thickness of a thin film,14,15 we believe it is reasonable to carry out extensive analysis in such a wide range of biaxial extrinsic strain. In addition, based on the predicted thermo-mechanical properties
Figure 2. Variety of oxygen-ion migration paths in the out-of-plane direction of SQS 18.75 mol % GDC. Pathi‑j indicates the migration path between Oi and the adjacent Oj site.
To derive the averaged migration-barrier energy (Em,a) from different values of Em,ij, which is the migration-barrier energy of Pathi‑j, we assumed that the SQS GDC cell had N parallel migration paths with the same migration length (L). In a consecutive migration step, we also assumed that the migration step with the highest Em,ij determined the migration-barrier energy of the path (see Figure S1). Then, the total conductivity (σ) of the parallel circuit can be expressed as B
DOI: 10.1021/acsami.7b13440 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Letter
ACS Applied Materials & Interfaces
Figure 3. (a) Em as a function of the biaxial extrinsic strain. The solid lines represent computational and experimental results obtained from the literature.6,18,19 The shaded area corresponds to the range of Em for bulk 20 mol % GDC reported previously.20−22 The dashed and dash-dotted lines are the guidelines of the symmetric and asymmetric paths, respectively. (b) Em as a function of tetrahedron volume of the initial state, including the space occupied by the oxygen vacancy. Same-color symbols indicate migration paths with the same number of dopant atoms at their first NN sites.
σ=
1 R total
L = A
∑
1 L = R ij A
∑ σij
Aij A
18.75 mol % GDC indeed describes the nature of a highly doped material with a complex configuration. From these results of migration-energy calculations in a SQS, we found two novel tendencies for oxygen-ion transport in a strained GDC structure. First, the change in slope of the plot of Em versus strain according to the structural symmetry was confirmed. As shown in Figure 2, the structural symmetry indicates whether the dopant configuration of the tetrahedron (including an oxygen vacancy) that makes up the start and end points of the path is the same. In our SQS GDC structure, one group has a symmetric dopant configuration on the initial−final state (Path0‑0, PathI‑I, PathII‑II), whereas the other has an asymmetric dopant configuration (Path0‑I, PathI‑II, PathII‑III). The slope of Em versus strain was higher in the asymmetric state, indicating that the Em of the asymmetric path was more affected by the biaxial extrinsic strain. Second, Em and the tetrahedron volume (Vi) consisting of an oxygen vacancy and the first NN cations are inversely proportional to each other (see Figure 3b). This tendency can be easily understood, because oxygen-ion transport can be allowed by distorting the three-dimensional cation sublattice.16,18,19,23 Thus, the larger tetrahedron volume leads to a smaller lattice distortion. As is well-known, the critical-radius (rcrit) models reported in literature16,19,23 describe the migration process of oxygen ions to be in close correlation with the oxygen-ion radius and the two-dimensional aperture size formed by the edge cations. To consider the threedimensional factors (e.g., atomic configuration including nonedge NN cations and oxygen-ion transport pathway) governing oxygen-ion migration; however, we suggest a new descriptor: a “tetrahedron-volume” model. This model is an extension of the existing two-dimensional critical-radius model (see the linear correlation of Vi and rcrit in Figure S2), but enables more accurate prediction of the oxygen-ion migrationbarrier energy including complex biaxial extrinsic and local multidopant strain conditions. Consequently, it seems reasonable to suppose that variations in tetrahedron volume would be a key parameter in the modification of the barrier energy of oxygen-ion migration. In general, the tetrahedron volume seems to be modified by biaxial extrinsic tensile or compressive strain, which is generally induced by lattice mismatch at an interface between heterophases. Here, we would like to emphasize that the tetrahedron volume also varies with the effects of local lattice
(2)
where R and A indicate resistance and area, respectively, and the subscript ij denotes the properties of the migration path with Em,ij. Because we only consider the ⟨001⟩ path in the cubic oxygen-ion sublattice, the area of each migration path can be assumed to be same for all paths; thus, the area fraction (Aij/A) can be determined by the fraction of a migration path which has Em,ij in the total migration paths, nij/N (N = 16 in this work). From the Arrhenius relation, the total conductivity can be expressed as σT =
∑ fij ·σijT = ∑ fij γijexp(−Em,ij /kT )
(3)
where k is the Boltzmann constant, T is the temperature, and γij is a pre-exponential factor related to the average jump distance, the total charge-carrier concentration, and the jump frequency prefactor.17 Because the jump frequency prefactor only depends on lattice vibration frequency and the migration entropy term, γij can be assumed to be equal for all migration paths. Finally, expressing the total conductivity in Arrhenius form with one single Em, Em,a can be derived as Em,a = −kT ln ∑ fi exp( −Em, i /kT )
(4)
The value of Em predicted by the DFT-NEB method is plotted as a function of the biaxial extrinsic strain, εxx (= εyy) in Figure 3a. We observed general monotonic behavior for all migration paths: the biaxial tensile strain decreased Em, whereas the biaxial compressive strain increased Em. This result is highly consistent with those of previous computational and experimental studies.6,18,19 In particular, Fluri et al.6 reported that a tensile strain of 0.35% in the thin-film structure of 15 mol % SDC decreased Em by ∼0.05 eV (∼5.9%), which is consistent with the result of this work (in which Em decreased by ∼0.03 eV (∼5.3%) at εxx = 0.35%). Using eq 4, we also calculated the value of Em,a, which is shown in Figure 3a. Interestingly, Em,a seemed to converge on the two most frequent migration-path energies (Em,0−0 and Em,I−I), i.e., Em,a = 0.65 eV at εxx = 0%; this was predictable, as oxygen ions might detour to avoid crossing a high Em. Furthermore, for the unstrained state, the Em,a value of 0.65 eV lay within the range reported in the literature for 20 mol % bulk GDC (0.55−0.76 eV).20−22 Therefore, the SQS of C
DOI: 10.1021/acsami.7b13440 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Letter
ACS Applied Materials & Interfaces
Figure 4. (a) Schematic illustration of local lattice strain of GDC (in PathII‑III) with large La3+ or small Sc3+ codopant under biaxial extrinsic tensile stress. (b) Em as a function of ionic radius of dopant in doped CeO2; the solid symbols represent Em of singly doped CeO2, and the half-filled symbols represent Em of codoped CeO2. For [28] (olive symbol), Em of the codoping system is plotted as a function of average ionic radius, because the two dopant atoms are substituted by the same amount. (c) Predicted change in Em in PathII‑III of GDC after application of biaxial extrinsic tensile strain (1%; orange arrow) and codopant substitution (with La3+ or Sc3+ ion; blue arrow).
agreement with those of the experiments. More specifically, Kahlaoui et al.28 reported that Ce0.8Sm0.1La0.1O1.9 has higher oxygen-ion conductivity and lower activation energy than singly doped CeO2, which is similar to the findings of the current work. Finally, the extent to which the Em can be reduced by applying both biaxial extrinsic and local lattice tensile strain is shown in Figure 4c. Given that the limitation of biaxial extrinsic tensile strain is 1%, which reduces Em by 9%, a further 26% reduction can be attained by codoping of Gd and La ions. In summary, we investigated the effect of strain on various migration paths in highly doped CeO2 produced by the SQS approach. It is worth noting that the calculated thermomechanical properties and oxygen-ion Em of highly doped CeO2 are comparable with values reported in the literature, which indicate that the SQS structure adequately describes the nature of highly doped materials. With a computationally efficient description of the complex atomic configuration, we found that the Em of oxygen-ion can be controlled by modifying not only the biaxial extrinsic strain but also the local lattice strain, for example, by changing the dopant configuration and number of dopants. Consequently, we propose that the limitation of the biaxial extrinsic strain below ε < 1% can be overcome by applying local tensile strain with large codopants, which would expand the tetrahedron space of the oxygen ions without changing the mobile-carrier concentration. Consequently, this work sheds light on a new approach to control strain in nanostructured oxygen-ion-conducting materials by considering both the external strain at the heterophase interface and the local strain induced by codoping.
strain, e.g., the number of dopants (ndopant). This indicates that the barrier energy of oxygen-ion migration can be further modified by the local lattice strain induced by ndopant. This effect of dopants on the Em has mostly been attributed to two main factors: first, a lattice distortion caused by the difference between the ionic radii (r) of host and dopant cations; second, attractive columbic interaction between a negatively charged dopant (e.g., Gd′Ce) and a positively charged oxygen vacancy (VO·· ).16 Notably, Nakayama et al.16 reported that the Coulombic interaction between charged point defects became more pronounced as the coordination number of dopants around the oxygen vacancy increased, which is consistent with our work (e.g., PathII‑II). Thus, it has been suggested that lattice distortion, which is demonstrated by coupling of different ionic radii and the Coulombic interaction, affects the Em.24,25 Consequently, the tetrahedron shrinkage and increase of Em with increasing number of Gd ions at first NN sites (Figure 3b) could be attributed to the more prominent attractive columbic interactions between Gd′Ce and V··O. On the basis of the above conclusions, we propose a new strategy to tailor the barrier energy of oxygen-ion migration by employing biaxial extrinsic strain as well as local lattice strain. As shown in Figure 4a, combining cosubstitution with a dopant that is larger than a Gd ion and biaxial extrinsic strain in an epitaxial thin-film structure offers a good solution to expand the tetrahedron volume and lower the Em without any deterioration in oxygen-ion concentration. For example, we considered the unstrained PathII‑III, which led to the highest Em for all strain states, and the remaining Ce site (rCe = 0.94 Å) at the initial state of PathII‑III was replaced with a large La ion (rLa = 1.16 Å) or a small Sc ion (rSc = 0.87 Å).26 The predicted Em under the unstrained state (εxx = 0%) is plotted in Figure 4b as a function of the ionic radius of the dopant to show the effect of codoping on the Em in the SQS GDC structure; experimental results of codopants reported in the literature are also included for comparison.27−30 Interestingly, we found that cosubstitution of larger dopants effectively lowers the Em of oxygen ions. The value of Em in PathII‑III was reduced by ∼26% when a La ion substituted the Ce ion, whereas Em was increased when a Sc ion substituted the Ce ion. This result is consistent with our tetrahedron-volume model (see Figure S3), and is in general
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.7b13440. Computational details and further analysis on oxygen-ion migration in a highly doped CeO2 structure (PDF)
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AUTHOR INFORMATION
Corresponding Author
*H. Kim. E-mail:
[email protected]. D
DOI: 10.1021/acsami.7b13440 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Letter
ACS Applied Materials & Interfaces ORCID
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Kyung Joong Yoon: 0000-0002-4161-5111 Ji-Won Son: 0000-0002-5310-0633 Jong-Ho Lee: 0000-0003-4481-6258 Ho Won Jang: 0000-0003-4074-4277 Hyoungchul Kim: 0000-0003-3109-660X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was financially supported by the New & Renewable Energy Core Technology Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) funded by the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20143030031430). This work also supported in part by the Energy Efficiency & Resources Core Technology Program of the KETEP granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20152020106100).
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DOI: 10.1021/acsami.7b13440 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
