Influence of Nonstoichiometry on Proton Conductivity in Thin-Film

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Influence of Non-stoichiometry on Proton Conductivity in Thin Film Yttrium-doped Barium Zirconate Jilai Ding, Janakiraman Balachandran, Xiahan Sang, Wei Guo, Gabriel M. Veith, Craig A. Bridges, Christopher M. Rouleau, Jonathan David Poplawsky, Nazanin Bassiri-Gharb, Panchapakesan Ganesh, and Raymond R. Unocic ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b16900 • Publication Date (Web): 11 Jan 2018 Downloaded from http://pubs.acs.org on January 11, 2018

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ACS Applied Materials & Interfaces

Influence of Non-stoichiometry on Proton Conductivity in Thin Film Yttrium-doped Barium Zirconate Jilai Ding1,2#, Janakiraman Balachandran1#, Xiahan Sang1, Wei Guo1, Gabriel M. Veith3, Craig A. Bridges4, Christopher M. Rouleau1, Jonathan D. Poplawsky1, Nazanin Bassiri-Gharb2,5, Panchapakesan Ganesh1* and Raymond R. Unocic1* 1 2

Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831 Department of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332

3

Material Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831

4

Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831

5

The George Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332

# Joint first author contribution *[email protected] and *[email protected] Abstract Proton conducting perovskites have been widely studied due to their potential application as solid electrolytes in intermediate temperature solid oxide fuel cells. Structural and chemical heterogeneities can develop during synthesis, device fabrication or service, which can profoundly affect proton transport. Here, we use time-resolved Kelvin probe force microscopy, scanning transmission electron microscopy, atom probe tomography and density functional theory calculations to intentionally introduce Ba-deficient planar and spherical defects, and link the resultant atomic structure with proton transport behavior in both stoichiometric and non-stoichiometric epitaxial, yttrium doped barium zirconate thin films. The defects were intentionally induced through high temperature annealing treatment, while maintaining the epitaxial single crystalline structure of the films, with an overall relaxation in the atomic structure. The annealed samples showed smaller magnitudes of local lattice distortions, due to formation of proton-polarons, thereby leading to decreased proton trapping effect. This resulted in a decrease in the activation energy for proton transport, leading to faster proton transport. Keywords: Proton Conducting Solid Oxide Fuel Cells, Yttrium-doped Barium Zirconate, Kelvin Probe Force Microscopy, Scanning Transmission Electron Microscopy, Atom Probe Tomography, Density Functional Theory

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Introduction Acceptor doped perovskites have attracted a great deal of attention as solid-electrolytes in proton conducting solid oxide fuel cells (SOFCs).1-4 Among the leading candidate materials is yttrium-doped barium zirconate (Y-BZO), which has been shown to exhibit high proton conductivity at intermediate temperatures as well as excellent chemical stability in water and carbon dioxide environments.3 Most experimental and theoretical studies of proton conduction in Y-BZO have focused on stoichiometric YBZO.5-9 However, structural and chemical heterogeneities (e.g., compositional variations, grain boundaries, or extended defects) can develop during synthesis, device fabrication and service, creating high resistance pathways for proton transport thereby lowering proton conductivity.10-11 In fact, a wide range of measured conductivity values – from 10-6 to 10-1 S/cm – have been reported in literature.5, 10, 12 Moreover, due to the high refractory nature of bulk Y-BZO, high temperature sintering (Tsint>1600°C) is often needed for densification and grain growth.9 Such high temperature heat treatment on polycrystalline samples leads to Ba loss, formation of structural defects such as stacking faults, or in extreme cases emergence of lower conductivity phases (Y2O3).11-14 To date, a fundamental understanding of how these heterogeneities affect proton conduction has yet to be achieved. Many challenges remain in decoupling intrinsic proton conduction mechanisms that occur at the atomic scale from non-proton conducting phases, grain boundaries and structural defects. More specifically, non-stoichiometry has been achievable only in polycrystalline samples, critically coupling the effects of chemical heterogeneity and high density of grain boundaries, precluding a clear understanding of the role of off-stoichiometry on proton conduction. To separate the intrinsic proton conductivity of Y-BZO from these heterogeneities, techniques such as pulsed laser deposition (PLD) have been utilized to fabricate large-grained Y-BZO thin films with significantly enhanced proton conductivity.12,

15-16

Our previous systematic study

on stoichiometric Y-BZO thin films, at Y-

concentrations of 0, 5, 10, 15 and 20%, has systematically shown that with increasing dopant concentrations, there is an increase in the magnitude of lattice distortions due to formation of protonpolarons17 and that this increased distortion adversely affects proton mobility, thereby reducing the overall conductivity. The presence of proton polarons, and adverse effects on intrinsic proton conductivity has been shown to be present across all possible chemistries in cubic perovskites,18 and reducing these distortions has been proposed to be a novel approach to designing new proton-conducting materials. Here, we explore the effect of non-stoichiometry, specifically Ba deficiency and structural defects, on proton conduction in Y-BZO at the atomic scale without the additional complications of increasing grainboundaries in the material, and quantify the degree of non-stoichiometry to local polaronic distortions, and resultant proton mobilities. Epitaxial Y-BZO thin films were prepared by PLD on MgO substrates.


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Small amounts of off-stoichiometry phases were formed through a post-deposition high temperature anneal. The microstructural and (proton) conduction properties were then compared between stoichiometric and non-stoichiometric Y-BZO using scanning transmission electron microscopy (STEM), atom probe tomography (APT) and time resolved Kelvin probe force microscopy (tr-KPFM).19 We find that, after annealing, minor regions with Ba deficiency and high Y concentration form, due to Y atoms occupying the Ba-sites. This in turn results in Y deficiency with respect to the stoichiometry in the remaining major regions. Ba loss is also expected in the major regions, leading to lower activation energy for proton transport, compared to the virgin, stoichiometric Y-BZO. To investigate how Ba deficiency leads to a lower activation energy, density functional theory (DFT) based calculations were performed. We find that the Y-deficient (with respect to the stoichiometry) major regions of the annealed samples have smaller local polaronic structural distortions when hydrated, compared to the Y-rich, Ba-deficient, minor regions, as well as the stoichiometric, virgin material. Because proton transport is expected to be dominated by the major regions, presence of smaller local proton-polaronic distortions can thus be considered to be the origin of the improved proton transport properties in annealed Y-BZO samples. Methods Materials Synthesis Pulsed laser deposition (PLD) was used to deposit thin films of 20 mol% Y doped BaZrO3 (20Y-BZO) on oriented MgO single crystal substrates (Princeton Scientific Corp). A 20Y-BZO target was prepared by mixing stoichiometric amounts of BaCO3 (99.95%), Y2O3 (99.9%) and ZrO2 (99%) powders, followed by sintering at 1500 °C for 24 h. Epitaxial 20Y-BZO films (~500 nm thick) were then deposited on the MgO substrates using a KrF excimer laser (Coherent Lambda Physik GmbH) with a wavelength of 248 nm, and a pulse width of 25 ns that was focused on the pellet target with a spot area of about 2 mm2. The laser energy density was ~1.5 J/cm2 with a repetition rate of 10 Hz. The films were deposited at 750 °C under 40 mTorr O2 with a target-to-substrate distance of 40 mm. The growth rate of the films was ~ 3 Å/s. Thermal contact between sample holder and substrate was achieved by silver paste. The PLD system was equipped with a reflection high-energy electron diffraction (RHEED) system for in situ diagnostics of the deposition process. After each deposition, the sample was sectioned into two pieces. One was used for controlled baseline characterization and transport measurements and the other was subjected to a high temperature annealing treatment (1050ºC for 24hrs) to induce structural and chemical changes. Materials Characterization


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Several characterization techniques were used to determine the crystalline structure and chemical composition of the as deposited and annealed 20Y-BZO thin films. The crystal structure of the 20Y-BZO thin films was determined using a Philips Xpert X-ray diffractometer (Cu Kα=1.5418 Å). An aberration corrected Nion UltraSTEM 100 (operating at 100 kV) was used to obtain atomic resolution images of the Y-BZO specimens. High-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images were acquired with an electron probe convergence semi-angle of 31 mrad, and 86-200 mrad collection semi-angle. The STEM images were frame averaged from 10 individual frames, each recorded with a pixel dwell time of 4 µs and 512x512 frame size. The location of each atom in the STEM images were identified by 2-D Gaussian fitting and a cross-correlation method and then analyzed to quantify local lattice distortions.20 Electron energy loss spectroscopy (EELS) experiments were performed using a Gatan Enfina spectrometer for chemical analysis. For atom probe tomography (APT), an FEI Nova 200 dual-beam focused ion beam (FIB) instrument was used to perform lift-outs and annular milling to fabricate the needle-shaped APT specimens containing the 20Y-BZO layer. A wedge lift-out geometry was used to mount multiple samples on a Si microchip coupon to enable the fabrication of multiple needles from one wedge lift-out. APT was performed with a CAMECA instruments LEAP 4000X HR (~36 % detection efficiency) and a 5000 XS (~80% detection efficiency) local electrode atom probe. APT experiments were performed at a base temperature of 40 K, applying 355 nm wavelength, 10 ps laser pulses of 50 pJ at a repetition rate of 200 kHz. The datasets were reconstructed and analyzed using the IVAS 3.6.12 software (CAMECA Instruments). Proton Transport Measurements Transport measurements were performed via time-resolved Kelvin probe force microscopy (tr-KPFM) on a Bruker multimode AFM equipped with a Nanonis controller. Conductive, Cr/Pt-coated cantilevers (Budget Sensors, Co.; resonance frequency ≈75 kHz) were used for the tr-KPFM measurements. Lateral Cr/Pt electrodes (20 nm/80 nm thick) were created on the Y-BZO thin films by evaporation and photolithographic lift-off. The electrodes were 10 µm wide with an inter-electrode distance of 70 µm. Measurements were performed under 15 V DC bias and 1 V AC bias (ω = 44 kHz), applied through the cantilever. An external function generator (DS345, Stanford Research) was used to generate the AC waveform, and an external lock-in amplifier (SR844, Stanford Research) was used for signal processing. For tr-KPFM measurements, the tip is scanned over spatially defined grid points virtually overlaid on the sample, without physically touching the surface. The surface potential variation as a function of time at each point was then recorded.21 A time-resolved, two-step measurement was performed at each point. For the first t seconds (t ranges from 2 s to 100 s, the choice of t value varies, depending on the time constant, or the potential changing rate at a certain temperature) a 30 V DC bias was applied through one electrode


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(biased electrode), driving electrochemical reactions that generate movable charge carriers, while the other electrode was grounded (grounded electrode). For the following t seconds, both electrodes were grounded to allow the accumulated charge carriers to relax. tr-KPFM experiments were performed in a temperature range from 300 to 450 K, and relative humidity of 90 % (as measured at room temperature) using a gas cell. At each temperature, the surface potential variation was measured on at least 16 points (on a 4 along electrodes × 4 between electrodes grid) on a 6 µm × 6 µm region in proximity to the biased electrode. First Principle Calculations The ab initio calculations were performed using density functional theory based methods employing VASP, wherein we use density gradient based exchange-correlation functional (PBE) and projector augmented (PAW) pseudopotentials. All the calculations were performed on a 3x3x3 supercell, with an experimental lattice constant of 4.197 Å. We employed a 2x2x2 k-point mesh for all calculations. Only the internal atomic coordinates were relaxed upon introduction of defects, and the calculations were converged until the forces were lower than 0.01 eV/atom. Results and Discussion The crystal structure of the PLD prepared 20Y-BZO films before and after annealing was characterized by X-ray diffraction (XRD), as shown in Figure 1. Both patterns are in agreement with the perovskitetype structure of BaZrO3 (JCPDS 00-006-0399), and only peaks corresponding to 100 orientation were observed, indicating that the deposited films are epitaxial along the 100 direction. No secondary phase peaks were observed, either before or after annealing. The rocking curve of the 100 reflection was measured for each sample (Figure 1 insets), with the full-width at half-maximum (FWHM) being 0.12° for virgin films and 0.13° for annealed films. Similar FWHM values suggest that the mosaicity is not greatly affected by annealing.


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Figure 1. (a) XRD patterns from the as-deposited and annealed 20Y-BZO films deposited on 100 MgO single crystal substrates. (b) Enlarged rocking curve of the 100 peak for the annealed and as deposited 20Y-BZO films. To examine the microstructural differences between the virgin and annealed thin films, HAADF-STEM imaging was performed, as shown in Figures 2a-d. For the virgin samples (Figure 2a-b), the STEM images confirm that the film is well oriented along 100 without any detectable defects or secondary phases. The STEM image in Figure 2b shows the atomic structure of the cubic perovskite Y-BZO structure with Ba atomic columns occupying corner positions and Y/Zr atomic columns occupying body centered positions in a unit cell as viewed along the [100] direction as see in the inset in Figure 2b. Following the annealing treatment (Figure 2c,d), the existence of spherical and planar defects planar become visible. The darker regions in these Z-contrast STEM images are locally depleted of high atomic number atoms, such as Ba (atomic number 56). The EELS spectrum imaging (Figure 2e), acquired using the Ba-M4,5 edge, provides direct evidence of Ba depletion within the planar defects. Furthermore, the atomically resolved image in Figure 2d shows that the darker contrast region has slightly different orientation than the rest of the Y-BZO lattice, which suggests that a localized change in composition may result in a local lattice distortions. Hereafter, we refer to the thermal annealing-induced, Ba-deficient regions as the “secondary” phase, in order to distinguish this from the primary Y-BZO phase.


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Figure 2. HAADF-STEM images of the (a,b) virgin and (c,d) annealed 20Y-BZO films. (e) Atomic resolution STEM image of the planar defect region and the corresponding EEL spectrum image mapping from the Ba M4,5-edge, showing localized Ba deficiency. APT was performed to detect chemical heterogeneities in the annealed samples. We note that evaporating oxide species can be disassociated and deionized after evaporation, causing certain evaporation events to be undetected.22 This might lead to larger error in the elemental quantification than reported by the error bars in Figure 3c. However, the overall trends in the elemental quantification provide semi-quantitative concentrations at the sub-nanometer scale. The virgin samples have a homogeneous distribution of each element, as shown in supplementary information Figure S1. The annealed sample’s tomographic reconstruction includes a yttrium cluster region (Figure 3a) that is similar in size to the dark spheroidal features observed via STEM. Ba deficiency is observed within the same cluster, as identified by the isoconcentration surface in Figure 3b. A proximity histogram (Figure 3c) of the isosurface from Figure 3a displays the concentration profile of each element within and outside of the Y-rich cluster: Y and Zr concentrations increase and Ba concentration significantly decreases within the cluster. Moreover, the Y:Zr ratio increases within the same region. A nearest neighbor distribution (NND) analysis was also performed to statistically analyze heterogeneous Ba and Y distributions. The distances were calculated by the Y-Y and Ba-Ba 10th nearest neighbor (10NN) within the matrix (the Y-cluster was extracted from the dataset) and within the entire APT-analyzed sample (shown in Figure 3d-g). The deviation of the experimentally-measured distribution from the binomial one (which represents a random solid solution)


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can be quantified by means of χ2 statistics. The Pearson coefficient (µ-value), which is χ normalized to the sample size, is used to quantify the degree of fit between the binomial distribution and the observed data. The µ-value ranges from 0 to 1, with 0 indicating a complete random solid solution and 1 representing a complete association of the elements. Detailed explanation is shown in SI. The Y-Y distribution within the extracted matrix is the same as the random distribution from a statistical point-ofview, with µ=0.04, indicating that Y is homogeneously distributed in the matrix. However, the Y-Y NND deviates from the random distribution when only the atoms surrounding the cluster are considered, with µ=0.17. In addition to the statistical deviation, a visual deviation can be seen between the curves in Figure 3e. The same calculation was performed for the Ba atoms, i.e. Ba-Ba distribution, within the cluster, where we found that µ=0.15. The observed 10NN Ba-Ba NND distribution is slightly shifted as compared to the random distribution, confirming a heterogeneous barium distribution within the APT dataset.

Figure 3. APT analysis of the annealed 20Y-BZO sample: (a) a reconstructed volume showing the distribution of yttrium atoms with two clusters envisioned by 5 at.% isoconcentration surfaces; (b) a reconstructed volume showing the distribution of barium atoms with a cluster envisioned by 20 at.% isoconcentration surfaces; (c) the concentration of Ba, Zr and Y atoms in matrix and cluster area, as shown dotted line in (a); and the distribution of normalized count for 10th nearest neighbor (10NN) of YY distance at (d) matrix and (e) cluster region; the distribution of normalized count for 10th nearest neighbor (10NN) of Ba-Ba distance at (f) matrix and (g) cluster region.


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From the STEM and APT characterization results, it is clear that high temperature annealing introduces structural and chemical defects in the Y-BZO thin films. To further analyze these defects, we quantify the local lattice distortion from atomically resolved STEM images by focusing on the B-site coordination polyhedra. As illustrated in Figure 4a, two types of distortion measurements were performed. The bond angle deviation, labeled as α, is the difference between 90° (cubic) and the actual B-site bond angle with regard to the nearest B-site neighbors. The displacement, labeled as d, is a measure of the distance between the actual B-site atom location and the geometrical center of its four nearest A-site atoms. These two distortions are indicators of how the local lattice structures deviate from the prototypical cubic perovskite structure. While a single measured lattice distortion might not be meaningful by itself, a frequency-distribution obtained from hundreds of such distortions in an STEM image offers a statistical measure of the distortion, both meaningful and comparable across samples. For the annealed sample, the minor region is small and not continuous: thus, the corresponding lattice distortion analysis has relatively large error. Therefore, only the major region distortion analysis was performed in the annealed sample, since it is the major region that will dominate proton transport. The normalized frequency histogram for the distortions were fitted with half-normal distribution and normal distribution, shown in Figure 4b and 4c, respectively. The representative STEM images with overlaid distortion maps are shown in the supplementary information Figure S2. Compared with virgin 20Y-BZO, the major phase of the annealed sample shows a smaller bond angle deviation, as well as a smaller displacement, indicative of a smaller distortion after annealing. The distortion value of virgin 0Y-BZO and 10Y-BZO are also shown in the figure as a reference. The distortion in annealed 20Y-BZO is comparable with that of virgin 10Y-BZO sample. Recently, it has been demonstrate using hard X-ray photoelectron spectroscopy that A-site cation substitution can exist which can have a positive influence of proton transport; however, due to the spatial and energy resolution limits in our STEM-EELS results we cannot determine if A-site Y cation substitution exist in our materials.23 As will be detailed in the following part, the decrease of distortion in the annealed sample should affect the proton conductivity in the lattice, given that lattice distortion plays a crucial role in proton trapping and thus determines the activation energy for proton transport, as discovered in our earlier study.17


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Figure 4. (a) The representative perovskite structure of Y-BZO and schematic representations showing the B-site bond angle deviation and B-site displacement used for quantitative lattice distortion measurements. (b, c) Half-normal distribution fitting of B-site bond angle deviation and normal distribution fitting of B-site displacement of the annealed 20Y-BZO sample as compared with virgin, BZO, 10Y-BZO, and 20Y-BZO. To further understand the influence of microstructural features appearing after annealing on proton transport, tr-KPFM was performed, and activation energy for proton transport was calculated. Figure 5a shows a schematic representation of microfabricated devices for tr-KPFM measurements. Driven by an externally applied DC bias (30 V), ambient water adsorbed on the Y-BZO thin films is expected to decompose at the electrode, as shown in Equation 1. Protons are generated and transported towards the grounded electrode, resulting in an increase in the surface potential.17 2 ⇄ 4 4

(1)

An applied 30 V bias has been demonstrated to provide sufficient power to drive electrochemical processes while minimizing irreversible damage to the material.17,

19, 21

When the proton distribution

stabilizes and the surface potential reaches saturation, both electrodes are grounded, allowing the


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accumulated protons to dissipate and redistribute. The changes in surface potential are recorded by trKPFM, and a representative potential curve over time at 100 ºC for both annealed and virgin samples are plotted in Figure 5b. The surface potential evolution is fitted to an exponential model: ∙ /

(2)

Where is the surface potential, A is the saturation potential, B is the total potential change from beginning to saturation, t is time and τ is the time constant, which is indicative of how fast the potential changes. The time constant (τ) for the annealed sample is calculated to be 0.25±0.01 s, substantially smaller than that of the virgin sample (1.90±0.03 s), which thereby indicates faster proton diffusivity in annealed samples. Since the time constant is inversely proportional to the transport process of ions, it is used to determine energy barriers and conductivity for proton transport according to the following equation:

!

(3)

where is the pre-exponential factor, " is Boltzmann constant, and #$ is the activation energy for proton transport along the sample. The time constant is obtained for a range of temperatures (from 300 to 450 K), and the Arrhenius plot for both virgin and annealed 20Y-BZO thin films is shown in Figure 5c. The activation energy for proton transport is calculated to be 0.55±0.01 eV, which is lower than that of the virgin sample (≈0.65±0.01 eV).

Figure 5. (a) A schematic representation of the microfabricated platforms for tr-KPFM experiments. (b) A representative surface potential change for virgin and annealed samples as a function of time, during


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bias-on (the first 5s) and bias-off (the following 5s) steps, at 100 ºC and in proximity to the biased Pt electrode. (c) Arrhenius plot of time constant for both annealed and virgin 20Y-BZO samples at 300-450 K. Ab-initio Modeling Recent work by Han et.al employing X-ray diffraction from synchrotron sources has shown that 10% Badeficient 20Y-BZO polycrystalline samples exhibit two intra-grain phases, in addition to a slight amount of Y2O3.11 The authors identified both the primary phase and the secondary phase to be barium deficient. The primary phase contained higher Zr concentration and lower Y concentration compared to stoichiometry, where the Y dopants mostly substituted the B-site Zr ions. On the other hand, the secondary phase showed much lower Ba and Zr concentration and higher Y concentration, where Y substituted both the B-site (Zr) and A-site (Ba) ions. The STEM, EELS and APT measurements performed in our work on epitaxial films are consistent with these findings. There is no direct and quantified evidence of barium loss in the primary region of the annealed samples. However, Ba loss is expected from high temperature annealing, due to the volatility of Ba. Ba vacancies essentially act as acceptor dopants, creating compensating oxygen vacancies, as shown in Equation 4.

) ) 55 Ba)'( Zr, 3O)0 → Zr, 223 V'( V0∙∙ BaO ↑

(4)

As suggested by both EELS analysis and APT results, the barium deficiency is stronger in the minor region with respect to the major region. The high Ba vacancy concentration can lead to a relatively unstable lattice structure. Although the perovskite phase is retained, the Ba vacancies may be occupied by Zr or Y, as suggested by previous studies22. Occupancy of A-sites with Y and Zr atoms leads to donor doping: 55 ∙∙ 5555 Zr,- V'( 323 → Zr'( V, 323

(5)

′ ′′ ∙ ′′′′ Y, V'( 323 → Y'( V, 323

(6)


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Similarly, the generation of Zr vacancies in presence of Ba deficiency will also consume oxygen vacancies, according to Equation 7, in order to maintain charge balance:

5555 55 V, V'( 3V0∙∙ → nil

(7)

Most of the previous studies have used polycrystalline samples for proton transport measurements in YBZO. The presence of extended defects such as grain boundaries and stacking faults in such samples result in substantial challenges in attempting to isolate the effects of Ba vacancy formation on proton transport properties. However, in the present study, the epitaxial films have limited grain boundaries, and do not suffer from such extended defects. Since the primary phase dominates proton transport, systematically modeling this phase and comparing the results to experiments can help us to resolve the influence of Ba vacancy on proton transport. We create atomistic models with the hypothesis that the secondary phase have both Ba-vacancies as well as Y-dopants occupying both the Ba/Zr-sites, while the primary phase has Ba-vacancies and Y-dopants predominantly in the Zr-site. To compare the degree of local distortions between virgin, primary and secondary phase models quantitatively, we create three different charge neutral model systems of protonated Y-BZO keeping the same concentration of protons, as shown in Figure 6. Positions of protons are randomly determined. The models to describe the stoichiometric, primary and secondary phases are: > (a) Stoichiometric phase: Model ; the stoichiometric Y-BZO, as shown in Fig. 6a (labeled Model ; (b) Primary phase: Model ; > (c) Secondary phase: Model ; > doping the B-site 4; , as shown in Fig. 6c (labeled Model (4; @"$ − ;"$ in Figure 6d). This model thus consists of Ba-vacancies, and Y-dopants occupying

both the Ba and Zr-sites.


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(d)

> > Figure 6. Schematic lattice representation of (a) Model ; > phase of the annealed Y-BZO, exhibits the lowest distortion, and model ;

Influence of Nonstoichiometry on Proton Conductivity in Thin-Film

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