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Structure and segregation of dopant–defect complexes at grain boundaries in nanocrystalline doped ceria Pratik P. Dholabhai,*a Jeffery A. Aguiar,b Longjia Wu,c Terry G. Holesinger,d Toshihiro Aoki,e Ricardo H. R. Castroc and Blas P. Uberuagaa Grain boundaries (GBs) dictate vital properties of nanocrystalline doped ceria. Thus, to understand and predict its properties, knowledge of the interaction between dopant–defect complexes and GBs is crucial. Here, we report atomistic simulations, corroborated with first principles calculations, elucidating the fundamental dopant–defect interactions at model GBs in gadolinium-doped and manganese-doped ceria. Gadolinium and manganese are aliovalent dopants, accommodated in ceria via a dopant–defect complex. While the behavior of isolated dopants and vacancies is expected to depend on the local atomic structure at GBs, the added structural complexity associated with dopant–defect complexes is found to have key implications on GB segregation. Compared to the grain interior, energies of different dopant–defect arrangements vary significantly at the GBs. As opposed to bulk, the stability of oxygen vacancy is found to be sensitive to the dopant arrangement at GBs. Manganese exhibits a stronger propensity for segregation to GBs than gadolinium, revealing that accommodation of dopant–defect clusters depends on the nature of dopants. Segregation strength is found to depend on the GB character, a result qualitatively supported

Received 15th April 2015, Accepted 7th May 2015

by our experimental observations based on scanning transmission electron microscopy. The present

DOI: 10.1039/c5cp02200b

dopant–defect complexes would influence ionic conductivity across GBs in nanocrystalline doped ceria.

results indicate that segregation energies, availability of favorable sites, and overall stronger binding of Our comprehensive investigation emphasizes the critical role of dopant–defect interactions at GBs in gov-

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erning functional properties in fluorite-structured ionic conductors.

1. Introduction Fluorite-structured (CaF2) ceria-based oxide nanoceramics have several technological applications including solid oxide fuel cells (SOFCs),1,2 catalytic converters,3–6 and oxygen separation membranes,7 as well as serving as a model system for studying radiation response in ceramics.8 As grain boundaries (GBs) are ubiquitous in nanocrystalline materials, most of the aforementioned applications are influenced in part by the local atomic structure at the GBs. Since transport in nanocrystalline materials is dominated

a

Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. E-mail: [email protected] b Microscopy and Imaging Group, National Renewable Energy Laboratory, Golden, CO 80401, USA c Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616, USA d Materials Physics and Application Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA e LeRoy Eyring Center for Solid State Science, Arizona State University, Tempe, AZ 85287, USA

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by GBs, GB engineering has been suggested as a viable means to boost transport along and across GBs.9 Structural anomalies at GBs in ceramic oxides lead to complex structures. For instance, oxygen vacancies play a critical role in the stable GB structure of ceria10–13 and fluorite-structured yttriastabilized zirconia (YSZ),12,14 suggesting that GB structures in doped ceria would be further complicated due to the presence of both dopants and vacancies. In doped ceria, trivalent dopants that substitute on the cation sublattice introduce oxygen vacancies to maintain charge neutrality. Enhanced vacancy concentrations due to the addition of aliovalent dopants are primarily responsible for higher ionic conductivity in doped ceria, which is reported to be sensitive to the dopant type15–18 and concentration.19,20 The general consensus is that dopants in ceria segregate to GBs,21–31 primarily due to the relative size mismatch between host cations and dopants. In addition, oxygen vacancies are also found to segregate at the GBs.21,23,25 At low temperatures, these species are not independent and would co-segregate. Thus, the interaction of defects and dopants with GBs and their distribution at GBs are critical in governing the functional properties of nanocrystalline doped ceria. Crucially, in doped ceria, dopant segregation to GBs

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and their subsequent influence on ionic conductivity have received conflicting experimental reports. The majority of the experimental studies reveal that dopant segregation to GBs is detrimental for ionic conductivity applications wherein the blocking (increase in GB resistance) effect is due to the formation of space-charge layers.22,24,26–31 Contrastingly, it has been suggested that the segregated dopant-enriched region may have a positive effect on the electrochemical activity of doped ceria. In either case, understanding the defect structuring at boundaries is key to predict and design GBs with high conductivity.21,32,33 From a theoretical perspective, the fundamental aspects of GB segregation were established almost three decades ago,34 yet there is a lack of understanding of the essential role of GBs in doped functional oxides. Due to the inherent structural and chemical complexity at oxide GBs, only few computational studies have tackled this problem. The limited studies that address oxide GBs predominantly utilize molecular dynamics (MD) simulations, as the system size limitations make application of density functional theory (DFT) impractical. MD simulations have shown that oxygen vacancies and dopants segregate to S5 (310)/[001] tilt GBs in doped ceria23,25 and YSZ.25,35 In another context, segregation of fission products to a variety of GBs have been studied in UO2, to unravel the role of charge and ionic radius on segregation.36,37 However, none of these studies considered the segregation behavior of dopant–defect clusters that will dominate the defect chemistry in aliovalent-doped ceria, particularly as a function of GB character. Vitally, as oxygen vacancies in doped ceria can exist at first, second or third nearest neighbor positions relative to the dopant ion,16–20,38 the fundamental dopant–defect cluster structure at the GB will unequivocally influence the dopant and defect segregation at GBs. The dopant–defect cluster is also expected to vary at different GBs due to variances in atomic structure and local strain. Further, the structure of this dopant–defect cluster at GBs might be very different than in the bulk of the material. Finally, as observed in bulk doped ceria,16–20,38 different dopant species are expected to prefer distinct dopant–defect structures at the GBs. Thus, the fundamental interplay between defect complex and GB structure in accommodating aliovalent dopants in nanocrystalline doped ceria necessitates further study. In the present article, we report results based on atomistic simulations that examine a wide range of dopant–defect cluster structures at three model GBs in gadolinium-doped ceria (GDC) and manganese-doped ceria (MDC): S3 (111)/[110] symmetric tilt, S5 (310)/[001] symmetric tilt, and S5 (001) y = 36.87 symmetric twist GBs. Key results and trends were qualitatively validated by first-principles DFT + U calculations. Asymmetry, strain, and the availability of a broad range of nearest neighbor environments between dopants and oxygen vacancies at GBs are responsible for a wide dispersion in energies of a given dopant–defect complex at any of the three GBs. Both smaller segregation energies and the availability of fewer favorable sites at each GB in GDC result in the weaker segregation of Gd3+ as compared to Mn3+. Different GBs exhibit variations in the magnitude of dopant segregation, which was corroborated by experimental observations displaying significant differences in

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the concentration of dopants aggregating at different GBs. Extended dopant–defect structures are stable at GBs, indicating that such complexes would influence ionic conductivity at GBs. However, at the same time, the preference for a particular arrangement of the dopant–defect complex is stronger at the GB than in the bulk, implying a stronger binding of the vacancy to the dopants. Notably, our work sheds light on the significance of understanding fundamental dopant–defect interactions at GBs, and further assists in unraveling the complex role of dopants, oxygen vacancies, and GB structure in influencing the transport properties of nanocrystalline doped ceria.

2. Methods 2.1.

Computational details

Atomistic calculations with three-dimensional periodic boundary conditions (PBC) were performed within the framework of LAMMPS.39 The calculations are based on energy minimization using a classical Born-like description of an ionic solid. Two-body short-range interactions were described using parameterized Buckingham40 pair potentials, whereas interactions due to long-range Coulombic (electrostatic) forces were summed using Ewald’s method.41 Buckingham pair potentials were used for GDC42 and MDC.43 Structures for undoped ceria GBs were obtained by utilizing GB structures studied in UO2,54 which served as starting point for the present study. Optimized structures of stoichiometric undoped ceria GBs were obtained by energy minimization along all three directions and the forces on all atoms were allowed to relax. Application of PBC in all dimensions resulted in two GBs existing within each simulation cell (Fig. 1). This is essential to avoid any electrostatic dipole originating from surface termination. For the S3 tilt (Fig. 1a), S5 tilt (Fig. 1b), and S5 twist GB (Fig. 1c), the size of the respective GB models are 7.31  2.36  3.38 nm3 (4416 atoms), 6.79  3.36  4.28 nm3 (7488 atoms), and 8.61  3.38  3.38 nm3 (7680 atoms). For evaluating the role of MVO M clusters in GDC and MDC, after the inclusion of two dopants and an oxygen vacancy, energy minimization was performed wherein the atomic positions were allowed to fully relax prior to computing the energies quoted in Tables 1–3. To validate atomistic results for select cases, we conducted spin-polarized DFT44,45 calculations using the PBE46 exchange correlation functional as implemented in VASP.47,48 We have employed the rotationally invariant form of DFT + U,49 wherein a Ueff value of 5 eV (ref. 50) was applied to account for strong on-site Coulomb repulsion amid the localized Ce 4f electrons. The stoichiometric 456-atom model of S5 tilt GB for undoped ceria minimized using DFT + U calculations is shown in Fig. 5a. The size of this GB model is 1.11  1.74  3.44 nm.3 Throughout both atomistic simulations and DFT + U calculations for doped ceria, the cell volume was held constant at the undoped ceria cell volume. 2.2.

Experimental details

MDC nanoparticles were synthesized by a co-precipitation method. Cerium nitrate hexahydrate [Ce(NO3)36H2O, 99.99%, Alfa Aesar] and Manganese carbonate [MnCO3, 99.9%, Alfa Aesar] were used as

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Paper Table 2 Energy ranges for various MVO M clusters arrangements in GDC and MDC calculated in the bulk and at the GB plane in the S5 tilt GB. Structures for several select cases for 1NN–1NN arrangement are shown in Fig. 3

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MVO M arrangement E1NN–1NN E1NN–2NN E1NN–3NN E2NN–2NN E2NN–3NN E3NN–3NN

GDC

MDC

Bulk (eV)

GB (eV)

Bulk (eV)

GB (eV)

1.28–1.38 1.16–1.40 1.40–1.59 1.15–1.41 1.42–1.61 1.56–1.77

0.00–1.55 0.58–2.35 0.68–2.34 0.07–1.97 0.61–3.31 0.72–2.73

4.09–4.27 4.23–4.50 4.65–5.03 4.82–5.35 5.02–5.42 5.59–5.95

0.00–1.52 0.35–2.21 0.63–2.60 0.36–2.43 0.74–3.86 1.73–4.15

Table 3 Energy ranges for various MVO M clusters arrangements in GDC and MDC calculated in the bulk and at the GB plane in the S5 twist GB. A few select cases for 1NN–2NN are illustrated in Fig. 4

MVO M arrangement E1NN–1NN E1NN–2NN E1NN–3NN E2NN–2NN E2NN–3NN E3NN–3NN

Fig. 1 Minimum energy structures for (a) S3 tilt, (b) S5 tilt, and (c) S5 twist GBs in ceria obtained using atomistic simulations. For tilt boundaries, the perspective is along the tilt axis, while it is down the rotation axis for the twist boundary. In the case of the two tilt GBs, the orientations of the leftmost grain are provided. For the twist GB, orientation of the top grain is provided. Ce ions and O ions are indicated by red and yellow spheres, respectively.

Table 1 Energy ranges for various MVO M cluster arrangements in GDC and MDC calculated in the bulk and at the GB plane in the S3 tilt GB. A few select cases for 1NN–2NN are illustrated in Fig. 2. The energies presented in Tables 1–4 are shifted so that 0.00 eV corresponds to the most favorable MVO M cluster in GDC and MDC, respectively

MVO M arrangement E1NN–1NN E1NN–2NN E1NN–3NN E2NN–2NN E2NN–3NN E3NN–3NN

GDC

MDC

Bulk (eV)

GB (eV)

Bulk (eV)

GB (eV)

2.54–2.56 2.48–2.68 2.71–2.96 2.57–2.85 2.79–3.01 2.98–3.26

0.86–5.56 0.00–3.66 0.91–2.86 1.45–4.00 1.07–3.72 1.51–3.96

5.64–5.65 5.81–6.02 6.52–6.65 6.87–6.94 7.01–7.31 7.68–7.82

0.67–6.20 0.00–3.39 0.74–4.36 1.32–3.49 2.31–6.17 1.47–5.94

the cationic precursors, and ammonia solution was used as the precipitating agent. In a typical synthesis procedure, 100 mL of a solution containing 98 mol% cerium and 2 mol% manganese ions (0.15 M for total cations) were added drop wise into a 100 mL of ammonia solution (1.5 M), which was kept under

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GDC

MDC

Bulk (eV)

GB (eV)

Bulk (eV)

GB (eV)

7.54–7.56 7.46–7.72 7.67–7.94 7.53–7.74 7.72–7.92 7.95–8.22

2.67–6.19 0.00–6.59 3.38–6.62 2.22–7.84 2.30–7.96 1.19–7.91

10.84–10.87 10.99–11.36 11.72–11.83 11.96–12.23 12.23–12.47 12.75–12.98

2.89–7.39 0.00–7.65 1.23–6.16 2.53–4.90 2.28–6.92 1.12–8.39

constant stirring at room temperature. After homogenizing for 2 h, the resultant suspension (hydroxide) was centrifuged and washed repeatedly with distilled water and ethanol. The precipitate was dried at 90 1C for 24 h and calcined at 600 1C for 8 h under oxygen flow to obtain 2 mol% MDC nanoparticles. X-ray diffraction analysis, performed using a Bruker-AXS D8 Advance diffractometer (Bruker-AXS, Inc.) operated at an accelerating voltage of 40 kV and an emission current of 40 mA, with l = 0.15406 nm, confirmed the powder had a fluorite structure, with absence of second phases, and crystallites sizes of 9.6 nm. The nanoparticles were consolidated in high-pressure spark plasma sintering (SPS model 825S, Syntex, Tokyo, Japan) apparatus, as described by Munir et al.51 5 mm graphite die, inserted into a 19 mm graphite die with SiC plungers and spacers, was used in the sintering with a 150 1C min1 heating rate and an isotherm of 700 1C for 5 min under 600 MPa. Due to reducing environment during SPS, the pellets after sintering required polishing to remove graphite from the surface and annealing at 550 1C for 12 h under oxygen flow for oxidation. The obtained pellets showed relative densities higher than 93%, determined by using Archimedes method, and grain sizes about 19 nm. Analytical TEM was performed on the probe-corrected JEOL ARM 200F. The JEOL ARM is equipped with a field-emission gun that was operated in STEM mode at 200 kV and equipped with a Gatan Enfinium electron energy loss image filter, windowless high solid angle 50 mm2 X-ray detector, and the latest PED system from AppFive. Electron dispersive X-ray spectral (EDS) chemical imaging was utilized to acquire the O–K, Ce–M, and Mn–L edges with the best achievable spatial and energy resolution for the microscope. Given the sensitivity to beam damage, where cubic CeO2 easily transforms to the

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fluorite-derivative bixbyite structure Ce2O3, structural and spectral imaging was performed over reduced beam current conditions and sub-second exposures. Core loss electron energy loss spectroscopy (EELS) was simultaneously performed over the same areas to capture the near edge fine structure for the same edges (O–K, Ce–M, and Mn–L) with beyond 15 mrad collection half angles providing an energy resolution defined by the full-width halfmaximum of the zero-loss peak of 0.95 eV. The acquisition time to resolve both EDS and EELS near edge fine structures was performed over a series of consecutive sub-second exposures. All collected EELS spectra were aligned based on their peak maxima, individually dark count subtracted, and summed to produce the results shown here. The core loss EELS spectra were furthermore processed to reduce effects of plural scattering events using Fourier-log deconvolution. Given the proximity of O–K and Mn–L core-loss near edge onsets, we applied a triple window background subtraction that utilized the known cross-section profiles for each of these transitions. Integrated windows were then applied at these edges, as well the intense Ce–M lines, and processed into elemental maps as discussed elsewhere.52 The point resolved Mn–L and Ce–M lines were further processed to refine the fine structure associated with each of these elements, where the results were scrutinized for the presence of Ce3+, and the details of Ce valence state calculations are given in Aguiar et al. and references therein.53 AppFive PED system was further utilized to report the out-of-plane crystallographic direction for the nanocrystalline material; the domain orientations reported are parallel to the electron beam.

3. Results We have considered three representative low S (where S is the reciprocal of the ratio of coincidence sites to the total number of sites in coincidence site lattice theory) GBs in nanocrystalline ceria: S3 (111)/[110] symmetric tilt, S5 (310)/[001] symmetric tilt, and S5 (001) y = 36.87 symmetric twist GBs, which were previously studied in uranium dioxide.54 The primary reasons to study low S GBs are that they have been reported experimentally,11 are relatively easy to model, and represent simple cases that help in elucidating the fundamental mechanisms responsible for GB properties. Snapshots of minimum energy 0 K structures for S3 tilt, S5 tilt, and S5 twist GBs in ceria are depicted in Fig. 1a, 1b, and 1c, respectively. Stoichiometric GB structures shown in Fig. 1, minimized using atomistic simulations were found to be stable at elevated temperature (900 K). The minimized structure predicted in this study for the S3 tilt GB (Fig. 1a) is similar to the CeO2 S3 GB observed using scanning transmission electron microscopy (STEM) by Ikuhara and coworkers.11 The stable S5 tilt GB structure, depicted in Fig. 1b, has a lower density of coincident sites than the S3 GB, and is one of the most studied fluorite GB structures, both theoretically23,25,54–56 and experimentally.12,57 Fig. 1c portrays the ground state structure for the S5 twist GB. The rationale behind studying the S5 twist boundary is that they are representative of several high-energy GBs in nanocrystalline materials, and have been examined in other materials.54,58–60 While it is impossible to

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study every single GB present in a nanocrystalline material, the assortment of stable GBs exploited in this work provides insight into the fundamental mechanisms at GBs accountable for controlling vital properties of nanocrystalline doped ceria. GBs optimized for nanocrystalline ceria (Fig. 1) were further employed to examine the role of aliovalent dopants and the associated defects (oxygen vacancies) in both nanocrystalline GDC and MDC. GDC was chosen in this study as it is one of the most promising electrolytes used in SOFCs.1,2 It has been reported that Gd can substantially increase GB conductivity in ceria by reducing GB width,61 but the structural impacts leading to this phenomenon are still not well understood.62 Mn3+ doping can also enhance ionic conductivity of ceria,63 and co-doping with Gd3+ has shown a significant decrease in activation energy for boundary ionic conduction, suggesting replacement of Gd3+ by Mn3+ at the boundaries.27 In this work, we propose the rationale behind the different behavior for these two dopants to be linked to the ionic radius differences; the radius of Mn3+ is 0.058 nm and that of Gd3+ is 0.108 nm, both significantly different as compared to the host Ce4+ (0.101 nm) cation, but in opposite directions. Comparatively analyzing GDC and MDC allows us to interpret the role of dopant size on segregation at GBs and on the defect structure profile. Improved oxide ion conductivity in doped ceria is primarily due to higher vacancy concentrations resulting from charge balance after the incorporation of aliovalent dopants. For instance, the defect reaction that governs the addition of trivalent dopants to ¨ger–Vink notation as: ceria can be expressed in Kro CeO2

M2 O3 ! 2M0Ce þ VO þ 3O O

(1)

where M = Gd3+ or Mn3+ and VO represents an oxygen vacancy. This relationship indicates that the substitution of two Ce4+ ions with trivalent dopant ions on the cation sublattice will result in an oxygen vacancy on the anion sublattice. Particularly at low temperatures, this will lead to the formation of dopant–defect   clusters VO 2M0Ce , which will be hereafter denoted as MVO M clusters. Henceforth, the notations 1NN, 2NN, and 3NN will correspond to oxygen vacancies at the first, second, and third nearest neighbors (NN) to the dopant ions, respectively. As described by the defect reaction in eqn (1), upon introduction of aliovalent dopants in bulk ceria, oxygen vacancies are formed on the anion sublattice at 1NN, 2NN, or 3NN to the dopant, forming MVO M clusters.16–18 These MVO M clusters are found to have high binding energies, as a consequence of the strong electrostatic and elastic interactions between the negatively charged dopant and the positively charged vacancy, suggesting that there is a reasonable fraction of such clusters in doped ceria, especially at low temperatures. The preferred position of oxygen vacancies relative to the dopants and the overall binding of the dopant–defect complex are found to be dependent on the ionic radius of the dopants,16,18–20,42 which is well documented for bulk ceria. Consequently, ionic conductivity of trivalentdoped ceria is also found to depend on the ionic radius of dopant ion.64 However, there is a lack of understanding of this fundamental defect reaction and the formation of MVO M

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clusters at GBs in nanocrystalline doped ceria, a knowledge that can enable the design of highly ionic conductive nanoceramics. We address this key issue by studying the energetics of various MVO M clusters (each cluster has two trivalent dopants and an oxygen vacancy) at three different GBs in GDC and MDC. Energies of these clusters influences dopant segregation at GBs, and as a result, vital transport properties of doped ceria. Henceforth, the notation xNN–yNN will correspond to an MVO M cluster wherein the oxygen vacancy is at x (x = 1, 2, 3) NN to dopant 1 and at y (y = 1, 2, 3) NN to dopant 2. For instance, 1NN–2NN indicates that the oxygen vacancy is 1NN to dopant 1 and 2NN to dopant 2. For clarity, we will refer to the family of all possible xNN–yNN clusters for a given x and y as ‘‘arrangements’’ and specific configurations within a given arrangement as ‘‘clusters’’. For the three GBs considered in this study, we have examined several structural variants of MVO M clusters for each xNN–yNN arrangement in the bulk and at the GB within GDC and MDC. We have not considered interactions beyond 3NN, as at larger distances, the interaction between dopants and the oxygen vacancy is expected to diminish. In bulk ceria with lattice parameter a = 0.5411 nm, 9 pffiffiffi > 3a > dðCeOÞ 1NN ¼ ¼ 0:2343 nm > > > 4 > > > > pffiffiffiffiffi = 11a (2) ¼ 0:4487 nm > dðCeOÞ 2NN ¼ 4 > > > > pffiffiffiffiffi > > > 19a > dðCeOÞ 3NN ¼ ¼ 0:5897 nm ; 4 where, d(Ce–O)xNN is the distance between a cerium ion and oxygen ion that are at xNN to each other. Although these distances are fixed in the grain interior, they will vary within GBs, due to their open structures and varied bonding lengths, a consequence of the complicated atomic arrangements at the GB. For the minimized GB structures depicted in Fig. 1, as expected, we found fluctuations in bond lengths, which are greatest at the GB plane. To incorporate this variation in bond length in our search for various xNN–yNN cluster arrangements at each GB, we added a cutoff of 0.015 nm to define the NN distance. For instance, a bond distance is termed 1NN if it ranges between 0.2193 nm o d(Ce–O)1NN o 0.2493 nm. For screening the various xNN–yNN arrangements at the GB, we have considered the GB plane to be a region with a width of B0.68 nm, B0.65 nm, and B0.58 nm for S3 tilt, S5 tilt, and S5 twist GB about the mirror plane of the structure, respectively. While the effect of the GB could extend beyond these distances, the chosen region best represents the GB and its immediate vicinity, and is expected to essentially capture the influence of the GB on the MVO M clusters. 3.1. Dopant–defect clusters at R3 tilt, R5 tilt, and R5 twist boundaries Energy ranges for MVO M clusters in GDC and MDC having different xNN–yNN arrangements encountered in the bulk and at the GB plane of S3 tilt, S5 tilt, and S5 twist boundaries are given in Tables 1–3, respectively. For all data presented in this

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Paper Table 4 First principles results for energies of MVO M clusters considered at the GB in S5 tilt GB in GDC. Corresponding energy for a similar cluster in the bulk is also given. Two select configurations for 1NN–1NN and 1NN–2NN arrangements are shown in Fig. 5b and c, respectively

MVO M arrangement E1NN–1NN E1NN–2NN

GDC Bulk (eV)

GB (eV)

0.72 0.85

0.00–0.81 0.23–0.88

work (Tables 1–4), energies are shifted such that 0 eV corresponds to the most favorable location for the MVO M cluster within each of GDC and MDC for each GB. In both GDC and MDC, 1NN–2NN is found to be the most favorable arrangement at the S3 tilt and S5 twist boundaries (Tables 1 and 3). Contrary to this, in both GDC and MDC, 1NN–1NN is found to be the most favorable arrangement (Table 2) at the S5 tilt boundary. At these GBs, while a particular xNN–yNN arrangement is found to be the most favorable, it is unlikely that they will exist exclusively at the GB, as there are other arrangements that are only slightly higher in energy and thus will coexist. For the most favorable arrangements in GDC and MDC, the energies of other clusters with the same arrangement vary greatly. These are illustrated in Fig. 2–4, which depict the respective GB plane for the S3 tilt, S5 tilt, and S5 twist boundary with several representative MVO M clusters highlighted in different colors. Analogous to the most favorable arrangement within each

Fig. 2 Schematic of several stable MVO M clusters in GDC and MDC, existing in the vicinity of the GB plane at the S3 tilt GB. The view is normal to the GB plane. The most favorable 1NN–2NN arrangement of the MVO M cluster in GDC and MDC is shown. Several different configurations of the cluster are shown, each with a unique color, to highlight the dispersion in energetics for clusters of the same arrangement. Filled spheres of different colors signify two dopant atoms (Gd3+ in GDC and Mn3+ in MDC), whereas the checkered spheres correspond to the oxygen vacancy for the respective MVO M cluster of the same color. The energy (eV) for a particular cluster of the respective color in GDC and MDC is given in the neighboring frames. Ce ions and O ions are indicated by red and yellow spheres, respectively.

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Fig. 3 Schematic of several stable MVO M clusters in GDC and MDC, existing in the vicinity of the GB plane at the S5 tilt GB. The view is normal to the GB plane. The most favorable 1NN–1NN arrangement of the MVO M cluster in GDC and MDC is shown. The color scheme is same as in Fig. 2.

Fig. 4 Schematic of several stable MVO M clusters in GDC and MDC, existing in the vicinity of the GB plane at the S5 twist GB. The view is normal to the GB plane. The most favorable 1NN–2NN arrangement of the MVO M cluster in GDC and MDC is shown. The color scheme is same as in Fig. 2.

material at each GB, all different xNN–yNN arrangements exhibit clusters with a wide range of stability (Tables 1–3); their structures are not shown for brevity. Fig. 2–4 further reveal that the lowest energy MVO M cluster in GDC and MDC at each GB prefer specific and distinct locations at the GB. That is, the lowest energy structure and location of a cluster for a particular xNN–yNN arrangement at a given GB is different in GDC and MDC. For identical MVO M clusters in GDC and MDC at a given GB, (Fig. 2–4), the energies are very different indicating that different trivalent dopants interact differently with a specific GB, and thus will segregate to different sites within the GB plane. Consequently, we find that the energies of clusters within a given arrangement vary significantly and that the lowest energy cluster is different in GDC and MDC. For nearly all clusters for all xNN–yNN arrangements considered at tilt boundaries in GDC (with the exception of the 1NN– 3NN arrangement at the S3 tilt boundary), the GB contains

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neighborhoods that are both energetically favorable and unfavorable (Tables 1 and 2) for cluster accommodation as compared to the bulk, demonstrating that certain locations at the tilt GBs are conducive for Gd3+ dopants but others are not. That is, there are clusters for each arrangement that have a lower energy at the GB than in the bulk, but other clusters that have a higher energy. In contrast, all xNN–yNN arrangements (except the 1NN–1NN arrangement at the S3 tilt boundary) located at the tilt GBs in MDC are energetically more stable than their bulk counterpart, suggesting that most or all of the locations at the tilt GBs are favorable for Mn3+ dopants. In contrast, at the S5 twist boundary (Table 3), nearly all clusters in GDC (except for 2NN–2NN and 2NN–3NN arrangements, wherein a few clusters are less favorable compared to the bulk) and all clusters in MDC are more stable at the GB than in the bulk. This highlights the contrasting behavior at different GBs. Further, for all MVO M clusters studied at the different GBs, the energy differences between the bulk and GBs (Tables 1–3) are consistently larger in MDC than in GDC, indicating that Mn segregation to GBs is always stronger than Gd segregation. In addition, there will be higher fraction of low energy sites present at the three GBs in MDC than GDC, suggesting that dopant segregation at these three GBs in MDC would be more pronounced as compared to GDC. Thus, two factors favor Mn segregation over Gd segregation to GBs in ceria: the higher gain in energy obtained by placing Mn at GBs and the higher density of favorable sites for Mn. Comparing the trends in Tables 1 and 2 indicates that the difference in energy between the MVO M clusters in the bulk and at the GB are consistently larger at the S3 tilt boundary, also referred to as a twin boundary, as compared to S5 tilt boundary. As a result, the propensity for dopant and defect segregation would be stronger at the S3 tilt boundary as compared to the S5 tilt boundary in both GDC and MDC. This is surprising as defect interactions with twin boundaries in simple metals are very weak.65 Given that twins have been reported in ceria nanoparticles,66 our results suggest that there will be a strong coupling between dopant profiles and twin boundary structure and that the amount of dopant segregation will be very sensitive to the density of twin boundaries. Considering all three GBs, the energy differences for MVO M clusters in the bulk and at the GB (Tables 1–3) reveal that the tendency for dopant and defect segregation would be strongest in the S5 twist boundary as compared to the S3 tilt and S5 tilt boundaries in both GDC and MDC. Vitally, in contrast to the two tilt boundaries, S5 twist boundary shows a stronger preference for one specific type of arrangement (1NN–2NN), and the energetics of the other arrangements are significantly higher. This indicates that while segregation of dopants to this boundary is strong, there are only a few sites at which the dopant can be easily accommodated. That is, while almost all sites are lower in energy at the GB than in the bulk, there is still a significant preference for putting the dopant at very specific sites at the S5 twist boundary. While this preference is seen at the two tilt boundaries, it is significantly weaker. An important finding is that the spread in energies

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between different arrangements is smaller in S5 tilt boundary than for the S3 tilt and S5 twist boundaries, indicating that more dopants can be accommodated into this boundary even at lower temperatures. Conversely, the large spread in energies between the different arrangements suggests that more extended structures are somewhat favorable at the S3 tilt and S5 twist boundaries compared to the bulk. This highlights the contrasting stability of dopant–defect clusters at the GBs. While nearly all clusters are more favorable at the GB than in the bulk, the preference for a specific arrangement is greater at the GB. 3.2. Dopant–defect clusters at R5 tilt boundary from firstprinciples calculations First-principles calculations were conducted for selected cases in GDC to validate key results. Fig. 5a displays the minimum energy structure of the S5 tilt GB in undoped ceria obtained using DFT + U calculations. The structure is very similar to that obtained with the potential (Fig. 1b), providing confidence in the quality of the potential. This structure was then used to examine the energetics of MVO M clusters in nanocrystalline GDC. Table 4 provides energies for two MVO M clusters with 1NN–1NN (Fig. 5b) and 1NN–2NN (Fig. 5c) arrangements at the S5 tilt GB in GDC. A single energy for each of these arrangements in the bulk is also given in Table 4. Due to the computational cost, additional arrangements in the bulk and at the GB were not considered. Nonetheless, Table 4 essentially corroborates the primary results and trends discussed above. In both the atomistic simulations (Table 2) and DFT + U calculations (Table 4) for the S5 tilt boundary in GDC, 1NN–1NN is found to be the more favorable arrangement at the GB, implying that results pertaining to the most favorable arrangement in other GBs (S3 tilt and S5 tilt) are credible. Analogous to the trend observed from atomistic simulations for S5 tilt boundary (Table 2), an important finding in Table 4 is that for a respective arrangement (for either 1NN–1NN or 1NN–2NN), there are favorable and unfavorable arrangements at the GB as compared to the bulk. This trend validates that the non-homogeneity in energies of various MVO M clusters is characteristic of the GB and not an artifact of the atomistic simulations. Although the magnitude of the energy difference between various structures within each xNN–yNN arrangement is more pronounced in the atomistic simulations, the qualitative physical trends are comparable. 3.3. Insights from scanning transmission electron microscopy To further support the predictions of the modeling, analytical aberration corrected STEM was used to reveal the details of segregation at GBs in MDC. Nanocrystalline ceria prepared by spark plasma sintering was used in this study. Because the sample is nanoscaled-polycrystalline, a great variety of GBs exists. Though different from the idealized simulation models, the wide variety of GB structures provide for qualitative comparisons with the basic physical trends uncovered by the atomistic calculations. Fig. 6a is an atomic contrast STEM

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Fig. 5 (a) Minimum energy structure for the S5 tilt GB obtained using DFT + U calculations. Illustrations of stable MVO M clusters in GDC within the vicinity of the GB plane in S5 tilt with the cluster arrangements are provided in (b) for the 1NN–1NN arrangement and in (c) for the 1NN– 2NN arrangement. For both cases, the view is normal to the GB plane. Filled spheres of different colors signify two Gd3+ dopants, whereas the checkered spheres indicate the corresponding oxygen vacancy within the respective MVO M cluster of the same color.

Fig. 6 (a) STEM image of nanocrystalline MDC encompassing several grains. (b) PED map of the out-of-plane orientations of the grains near the region imaged in (a). (c) EELS map of the MnL edge in the region highlighted by the green box in (a). Grains A, B, C, and D are labeled in each frame for reference and to highlight the GBs between them in the EELS map in (c).

image from nanocrystalline MDC taken over a region containing several GBs. The precessed electron diffraction (PED) map shown in Fig. 6b reveals that the out-of-plane orientations of the different grains differ, indicating that the GBs have varying

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Table 5 Manganese content for different GBs between grains labeled A, B, C, and D in Fig. 6

Boundary

A/B

A/C

A/D

Average grain interior

Mn (atomic %)

3.80

1.62

2.24

1.21

orientation relationships, as expected in a polycrystal. Using atomically resolved STEM-EELS based spectral imaging, the distribution of Mn was mapped across these GBs, based on the acquired Mn–L edge, as shown in Fig. 6c. According to the PED map, three distinct boundaries are identified between the larger grain A (taken as reference) and grains B, C and D. The relative pixel density qualitatively suggests an anisotropic distribution of Mn, indicating preferential boundaries for segregation, in particular showing higher Mn content at the A/B boundary. The integrated average Mn content for those boundaries close to edge-on orientation was calculated using windowed analytical routines52 and reported in Table 5. These results clearly indicate that Mn content varies by over a factor of two depending on the GB character. Further, there is significantly more Mn present at the GBs than in the grain interior. These experimental observations confirm the basic physical trends predicted by the atomic-scale modeling that Mn segregation to GBs is strong and that the relative amount of segregation depends on the nature of the GB.

4. Discussion The primary results from our study of the dopant–defect cluster behavior at GBs include (a) within a given xNN–yNN arrangement, the energies of diverse clusters vary significantly, (b) the presence of strongly preferred arrangement at each GB, (c) segregation of dopant–defect clusters depends on the character of the GB (sites availability and boundary energy), and (d) Mn segregates more strongly than Gd. Here, we discuss the implications of these results. In the bulk of GDC and MDC (Tables 1–3), the energies of a given type of arrangement do not vary significantly, less than 0.5 eV in all cases and typically much less. In contrast, GBs induce considerable dispersion in energies for all arrangements considered in GDC and MDC demonstrating that there is a wide range of energies for different clusters of the same arrangement at the GB. A key trend found in Tables 1–3 is that 1NN–2NN is the most favorable arrangement at the GBs in S3 tilt and S5 twist boundaries (in both GDC and MDC), whereas 1NN–1NN is the most favorable arrangement at the GB in S5 tilt boundary, suggesting that diverse boundaries will react uniquely to MVO M clusters depending on the specific type of dopant and the structure of the boundary. Another important feature apparent in Tables 1–3 is that favorable MVO M cluster arrangements at the GB do not necessarily resemble those found in the bulk (for instance S3 tilt GB in MDC, S5 tilt GB in GDC, and S5 twist GB in MDC), indicating that evaluating the structure of MVO M clusters in the grain interior is not sufficient to characterize their structure at the GBs. These key findings reveal that not only is the most favorable

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MVO M cluster at a given GB typically different than in the bulk, but it is also characteristic of a particular GB in the material and nature of the dopants. In general, in concentrated solutions, because of the fact that there is a strong binding between the defect and the dopant in these complexes, we expect that they will be bound at the GBs as well. That is, the position of the dopants and defects will not be independent at the GB, just as they are not in the bulk. Therefore, the MVO M clusters examined in this work are essential to comprehend the multifaceted role of GBs in nanocrystalline doped ceria. Another feature that can be seen in comparing the behavior of dopant–defect complexes at the GBs versus bulk is the stronger preference for a specific arrangement at the GB. As mentioned, within the bulk, energy differences between the lowest energy cluster for different arrangements are rather modest, about 0.5 eV for GDC and 1–2 eV for MDC. At the GBs, these differences are significantly higher, particularly at the S5 twist GB, but also at the tilt boundaries. In several cases, the energy differences for the lowest energy cluster for different arrangements are in excess of 1–2 eV for GDC. Given that the energy differences between the different arrangements are related to the binding of the dopant– defect cluster, this implies that the binding of oxygen vacancies to dopants at the GB is stronger than in the bulk. This has ramifications for the mobility of oxygen vacancies, as discussed below. In all cases considered in this work, stronger dopant segregation to GBs is found in MDC than in GDC (Tables 1–3). A potential explanation for this trend is found in the ionic radii of Mn3+ (0.058 nm) and Gd3+ (0.108 nm). The size mismatch between Gd3+ and Ce4+ (ionic radius of host Ce4+ is 0.101 nm) is considerably smaller compared to the size difference between Mn3+ and Ce4+, indicating that the reduction in elastic strain energy at GBs in MDC would be more pronounced if Mn3+ ions aggregate at the GBs than would be found in GDC for Gd3+ segregation. For the majority of MVO M clusters with diverse xNN–yNN arrangements within GDC, the three GBs exhibit locations that are energetically favorable and unfavorable as compared to the grain interior (Tables 1–3). This result critically emphasizes that all locations at a given GB are not conducive for dopant segregation in GDC. In contrast, our results for MDC demonstrate that the vast majority of locations within the three GBs are energetically favorable for dopant segregation. In addition to the fact that stronger segregation will be observed in MDC, it is apparent from this trend that the same location that is unfavorable for Gd3+ ions can be favorable for Mn3+ ions. As discussed previously, the potential reason for this behavior is the significantly smaller ionic radius of Mn3+ ion, which tends to favor compressive sites while the larger Gd3+ ion would favor tensile sites. However, segregation to GBs in oxides is not a simple function of local strain; other factors such as electrostatics could play an important role.55 Overall, this trend elucidates that trivalent dopants with different ionic size and chemical nature will exhibit variations in propensity of segregation at GBs in nanocrystalline doped ceria. As is evident from Tables 1–3, the most favorable arrangement of MVO M cluster at any given GB in GDC and MDC

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has one of the dopant ions at 1NN to the oxygen vacancy. The DFT + U results (Table 4) also exhibit a similar trend. This important finding is analogous to the behavior in bulk in the present calculations, and other theoretical calculations, which report that the most favorable location for oxygen vacancy formation in bulk MDC67 and GDC16,18,19,50 is 1NN to one of the dopant ions. Calorimetric measurements also reported a similar preference of oxygen vacancies to remain at 1NN to trivalent dopants such as Gd, Y, and La.68 However, our calculations further suggest that the location of the second dopant within a MVO M cluster is also critical in determining its energy, especially at the GBs, and further will be contingent on the GB character as well as on the dopant type. Crucially, the large dispersion in energies for a particular xNN– yNN arrangement for clusters at GBs in GDC and MDC would never be observed in the bulk. For instance, in Table 3, the energy range for the various 1NN–2NN arrangements at the S5 twist GB in MDC is 0.0–7.65 eV. Such a notable difference in energy is not expected in the bulk of MDC or other trivalentdoped ceria. That is, the stability of the complex at the GB is much more sensitive to the position of the second dopant than it is in the bulk. As a result, examining the basic MVO dimers or MVO M (trimers) clusters in the bulk, which has been addressed in the past,16–20,38 does not elucidate their behavior at GBs. In addition to the most favorable arrangement of MVO M clusters residing at a given GB (in GDC and MDC), numerous other xNN–yNN cluster arrangements would exist at the GB depending on their energetics and the fraction of accessible sites. This is because almost all clusters are lower in energy at the GB than in the bulk and there are only a few sites with very low energy. Once those are filled, other sites would necessarily be occupied. Likewise, for a given site at a GB (defined as the position of the oxygen vacancy), the energy of the dopant–defect cluster depends greatly on the local arrangement of the dopants. To illustrate this, for the most favorable MVO M cluster (Table 3 and Fig. 4) at the S5 twist boundary in GDC and MDC, we kept the vacancy at the same position, but altered the dopant locations, sampling all xNN–yNN arrangements. For such permutations of dopant arrangements, the energy changes from 0.0–6.43 eV and 0.0–6.66 eV in GDC and MDC, respectively, indicating that the energy of the cluster is dependent on both the location of the vacancy and the arrangement of the dopants around the vacancy, and that the stability of oxygen vacancy is much more sensitive to the dopant arrangement at the GB than in the bulk. This further supports the fact that binding of oxygen vacancies to dopants is very different at the GB than in the bulk and that the landscape for oxygen vacancies (and thus their mobility) is very sensitive to the details of the dopant distribution at the GB. It is important to note that throughout this study, we have only considered one cluster at a given instant, so the influence of other clusters is not accounted for in this scenario. At higher dopant concentrations, there would be several clusters at the GBs due to stronger segregation. For instance, a particular dopant–defect cluster with a 1NN–1NN arrangement could have

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a dopant at 3NN position relative to the vacancy and thus the energetics of that vacancy will be dictated by cluster–cluster interactions. Accordingly, there could be numerous overlapping MVO M clusters existent at a GB, which would complicate the energetics of segregation and the energetic landscape of oxygen vacancies. However, in examining isolated dopant– defect clusters, the present work provides insight into the segregation behavior as a function of dopant type and GB character in nanocrystalline doped ceria. The magnitude of segregation at various GBs is also expected to impact the overall oxide ionic conductivity in nanocrystalline doped ceria. As discussed above, the MVO M clusters are even more strongly bound at the GBs, than they are in the bulk.16,18 As a result, analogous to the behavior observed in the grain interior of doped ceria at higher dopant fractions,17,19,20 the high concentration of trivalent dopants at GBs due to segregation would trap mobile vacancies and lead to a decrease in oxide ion conductivity across GBs. A similar result was found for isolated dopants interacting with oxygen vacancies at the S5 tilt GB.23 That is, even for dopant concentrations that would lead to enhancement of ionic conductivity in the bulk, strong segregation will lead to higher concentration at the GBs, which will decrease conductivity across GBs due to carrier blocking. Further, our results suggest that this behavior would differ depending on the nature of trivalent dopants and their propensity to segregate at GBs. Complicating this picture is the fact that, at GBs, one arrangement is strongly preferred, as compared to the bulk. This suggests an even stronger binding between dopants and oxygen defects at the boundary and possibly an early trapping of vacancies versus dopant concentration than observed in the bulk.19,20 Finally, within a given GB there is a wide distribution of sites with very different energetics, many of which are more costly than placing the dopant in the bulk. This suggests that there are barriers to vacancy diffusion at the GBs that are not present in the bulk, as moving the vacancy away from the dopant complex requires more energy when in the GB than in the bulk. Thus, competing effects would exist. Segregation will lead to higher concentrations of dopants at GBs; and thus provide more carriers (defects) at the boundaries that could lead to higher conductivity. However, the mobility of those carriers may be impeded due to the inhomogeneous atomic structure of the boundary and stronger dopant–vacancy binding at the boundary, decreasing conductivity. These potentially contradictory effects of dopant segregation on ionic conductivity in nanocrystalline ceria may be responsible for the conflicting experimental findings discussed earlier. Fully understanding the role of GBs on ionic conductivity necessitates a more comprehensive modeling effort that is beyond the scope of this paper. Our experimental results qualitatively support the key finding from modeling that the propensity of segregation depends on the nature of GBs. We wish to stress that experimentally, it is nontrivial to identify the precise dopant–defect cluster geometries and characterize each GB present in nanocrystalline doped ceria given the complex three-dimensional arrangements. Consequently,

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although a one-to-one comparison between theoretical results for segregation to specific GB and experimental observations is not possible at this point, our collective study undoubtedly indicates that the tendency for dopant segregation will be altered at diverse GBs in MDC. Similar behavior is expected in GDC or other trivalentdoped ceria. To summarize, our results suggest that aliovalent dopant segregation to GBs in nanocrystalline ceria have competing effects on ionic conductivity:  Large segregation energy - high dopant concentrations at GBs - high carrier concentrations - increased conductivity.  Large segregation energy - high dopant concentrations at GBs - early blocking of carriers - decreased conductivity.  Large binding energy of defect–dopant complexes stronger trapping of carriers - decreased conductivity.

5. Conclusions We have examined the fundamental dopant–defect interactions at three different GBs, namely S3 tilt, S5 tilt, and S5 twist GBs in GDC and MDC. We have demonstrated the existence of numerous geometrically and energetically dissimilar dopant– defect clusters at GBs in GDC and MDC, which are found to exhibit much greater disparities in energetic stability in comparison to similar clusters in the grain interior. Variations in nearest neighbor arrangements at GBs are responsible for the energetics and structure of dopant–defect clusters, which have significant impact on the segregation behavior. Mn3+ exhibits stronger tendencies for segregation as compared to Gd3+ revealing that trivalent dopants with different ionic size and chemical nature would exhibit differences in propensity for segregation at GBs in nanocrystalline doped ceria. Within both GDC and MDC, the magnitude of dopant segregation is found to be different for distinct GBs. This key result is qualitatively supported by our experimental observations, which demonstrate that diverse GBs in MDC have altered dopant content. Existence of somewhat extended dopant–defect structures at GBs and the stronger binding of dopant–defect complexes at GBs have key implications for ionic conductivity. Segregation to GBs will lead to competing effects wherein more carriers at GBs will increase conductivity, but the mobility of carriers will be sluggish due to the inhomogeneous atomic structure of the boundary and stronger dopant–defect binding at the boundary, in turn decreasing conductivity. The present results underpin the importance of understanding fundamental dopant–defect interactions at GBs, and further assists in disentangling the multifaceted role of dopants and defect segregation, which influences key transport properties in nanocrystalline doped ceria.

Acknowledgements This work was supported by UC Lab Fees Research Program 12-LF-239032. BPU acknowledges support by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. Los Alamos

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National Laboratory, an affirmative action equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. DOE under contract DE-AC52-06NA25396. JAA acknowledges the use of facilities at LeRoy Center for Solid State Science, Arizona State University. RC acknowledges U.S. DOE, Office of Science, Basic Energy Sciences, Early Career Program Award ER46795.

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Phys. Chem. Chem. Phys.

Structure and segregation of dopant-defect complexes at grain boundaries in nanocrystalline doped ceria.

Grain boundaries (GBs) dictate vital properties of nanocrystalline doped ceria. Thus, to understand and predict its properties, knowledge of the inter...
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