# Real-Time Observation of Oxygen Diffusion in CGO Thin Films Using Spatially Resolved Isotope Exchange Raman Spectroscopy

Alexander Stangl, Nicolas Nuns, Caroline Pirovano, Kosova Kreka, Francesco

Chiabrera, Albert Tarancón, Mónica Burriel

► To cite this version:

Alexander Stangl, Nicolas Nuns, Caroline Pirovano, Kosova Kreka, Francesco Chiabrera, et al.. Real-Time Observation of Oxygen Diffusion in CGO Thin Films Using Spatially Resolved Isotope Exchange Raman Spectroscopy. Small Structures, 2024, 5 (11), 10.1002/sstr.202400237. [https://doi.org/10.1002/sstr.202400237](https://doi.org/10.1002/sstr.202400237)

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# Real-Time Observation of Oxygen Diffusion in CGO Thin Films Using Spatially Resolved Isotope Exchange Raman Spectroscopy

Alexander Stangl,* Nicolas Nuns, Caroline Pirovano, Kosova Kreka, Francesco Chiabrera, Albert Tarancón, and Mónica Burriel*

The exploitation of advanced materials for novel energy, health, and computing applications requires deep insight and fundamental understanding of physico-chemical mechanisms, such as ionic and electronic conductivity, defect formation processes, and reaction kinetics. Therefore, access to the underlying constants of the functional materials via advanced but accessible and straightforward experimental techniques is key. Herein, a novel, cheap, fast, and widely applicable approach is presented to analyze oxygen tracer diffusion in thin films with unprecedented time resolution based on the novel in situ isotope exchange Raman spectroscopy (IERS) methodology. IERS utilizes the sensitivity of micro-Raman spectroscopy to changes in the local isotopic composition. In-plane tracer diffusion gradients are established by partially blocking the exchange at the surface followed by an isotope exchange. The isotope exchange and diffusion processes are followed via consecutive spatial and time-resolved in situ Raman line scans. These isotopic gradients are analyzed to obtain mass transport coefficients, with an additional time component, not accessible by conventional destructive techniques. Diffusion coefficients of gadolinium-doped ceria (CGO) thin films are reported within the range of interest for intermediate-temperature emerging applications and confirm the validity of the measurement procedure and extracted parameters by comparison with the finite-element method simulations and literature results.

and conversion devices, neuromorphic computing, gas sensors, and membranes and have attained significant attention among diverse disciplines in science and industry, while meaningful, cheap, and widely available analysis techniques are still scarce, especially under in situ and operando conditions.[2] One of the most extensively used approaches to study diffusion phenomena is based on the replacement of a chemical element with an isotope of low natural abundance (such as ¹⁸O or ⁶Li, so-called tracer isotopes) and analyzes the tracer distribution within the sample via time-of-flight secondary-ion mass spectrometry (ToF-SIMS).[3] ToF-SIMS is highly sensitive and accurate and commonly used to perform depth profiling to study out-of-plane transport properties in thin films[4–6] or along different directions in single crystal[7] or polycrystalline or polycrystalline bulk samples.[8] Its 3D spatial resolution has previously also enabled the study of in-plane oxygen tracer gradients in thin films,[9] wherefore the top surface was blocked utilizing metallic capping layers, and subsequent isotope exchange was limited

to a lateral surface reopened by trenching. Postexchange analysis allowed to obtain in-plane diffusion and surface exchange coefficients for the first time in epitaxial thin films. However, ToF-SIMS is costly, time-consuming, and destructive

## 1. Introduction

Ionic transport processes at the nano- and microscale play a key role in various emerging fields,[1] such as energy storage

A. Stangl, M. Burriel
CNRS
Grenoble-INP
LMGP
Université Grenoble Alpes
38000 Grenoble, France
E-mail: alexander.stangl@gmail.com; monica.burriel@grenoble-inp.fr

N. Nuns, C. Pirovano
CNRS
Centrale Lille
Université d'Artois
UMR 8181—UCCS—Unité de Catalyse et Chimie du Solide
Université de Lille
F-59000 Lille, France

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/sstr.202400237.

K. Kreka, F. Chiabrera, A. Tarancón
Department of Advanced Materials for Energy
Catalonia Institute for Energy Research (IREC)
08930 Barcelona, Spain

© 2024 The Author(s). Small Structures published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

A. Tarancón
ICREA
23 Passeig Lluis Companys, 08010 Barcelona, Spain

DOI: 10.1002/sstr.202400237
and thus limiting its general availability and the reuse of specimens.

To overcome these drawbacks, we take advantage of the non-destructive and cost-effective nature of the recently introduced isotope exchange Raman spectroscopy (IERS) methodology, which is a novel tool to study physicochemical processes in real time.[10] IERS utilizes the sensitivity of micro-Raman spectroscopy to study changes in the local isotopic composition, manifested by a frequency shift of the oxygen Raman modes.[11–14] Raman spectroscopy thus can be used to map the surface of a thin-film sample to investigate the in-plane isotopic distribution in a fast and nondestructive manner. Compared to conventional techniques, IERS is performed in situ, which gives access to time-resolved measurements of the diffusion coefficient with the potential to evaluate the time evolution of transport properties under operation conditions. This can help to identify possible degradation mechanisms and enhance material durability.

To establish an in-plane oxygen tracer gradient, thin-film samples are coated with a Raman-transparent thin capping layer, limiting surface exchange to a lateral surface opened via trenching and annealed in a gas atmosphere of controlled isotopic composition using a temperature cell between 300 and 500 °C. In this work, we study gadolinium-doped ceria (CGO) thin films capped with thin Si₃N₄ or Al₂O₃ blocking layers and map tracer oxygen in-plane gradients in situ using IERS. We report self-diffusion coefficients and analyze the robustness of the outlined methodology to obtain meaningful results. IERS can be applied to a large number of promising mixed-ionic electronic conducting oxides to study their ionic transport kinetics, for example, for solid oxide fuel cell applications. Beneficially however, it is not limited to oxygen ions as tracers and therefore can be deployed as well to other material families, including electrode and electrolyte materials for solid-state Li-ion batteries[15] by deploying Li tracer isotopes.[16]

# 2. Methods

## 2.1. Isotopic Sensitivity of Raman Spectroscopy and Isotope Exchange Raman Spectroscopy

Raman spectroscopy is based on the inelastic scattering of monochromatic light and used to investigate the vibrational modes of a molecule or crystal. The Raman wavenumber, $\omega$, of the vibration of two crystal atoms, depends within the harmonic approximation on their reduced mass, $\mu$, via $\omega \propto \mu^{-1/2}$.[17] Upon isotopic changes in the oxygen sublattice, a continuous frequency shift of the oxygen modes is observed rather than a linear combination of two or three modes for oxygen-cation ($^{16}$O-X, $^{18}$O-X) or oxygen-oxygen ($^{16}$O-$^{16}$O, $^{18}$O-$^{18}$O, $^{16}$O-$^{18}$O) vibrations, respectively. This single-mode behavior is understood within the virtual crystal approximation (VCA), where the masses of the constituting isotopes can be replaced by their weighted average mass, with respect to their relative abundances.[18] The isotopic fraction, $^{18}$C, can therefore be determined by measuring the Raman frequency, $\omega$($^{18}$C). For the case of a diatomic vibration only involving oxygen,[19] $^{18}$C can be expressed as (for details Note 1, Supporting Information)

$$^{18}\text{C} = \frac{[^{18}\text{O}]}{[^{18}\text{O}] + [^{16}\text{O}]} = \frac{\left(\frac{\omega_{\text{ref}}}{\omega_{^{18}\text{C}}}\right)^2 - 1}{\left(\frac{m_{^{18}\text{O}}}{m_{^{16}\text{O}}}\right) - 1} \quad (1)$$

with the wavenumber of the oxygen mode, $\omega_{\text{ref}}$, corresponding to natural abundance and the atomic weights $m_{^{18}\text{O}} = 17.999$ and $m_{^{16}\text{O}} = 15.995$ u of $^{18}$O and $^{16}$O, respectively.

IERS utilizes the mass sensitivity of Raman spectroscopy to directly follow changes in the isotopic composition of a sample in situ with time and spatial resolution.[10] Therefore, the specimen is annealed in a temperature cell under the microscope and brought in contact with a media of different isotopic concentration (e.g., via the atmosphere) under isothermal conditions to activate isotopic exchange. An optical image of the setup is shown in Figure S1a, Supporting Information. For example, for surface-limited exchange reactions, such as in thin films or (nano-)powders, the analysis of the time evolution of the frequency shift is equivalent to transients obtained by other in situ probes such as electrical conductivity relaxation (ECR).[3,21] However, the spatial resolution of IERS allows additionally to monitor in-plane tracer gradients for diffusion-limited processes in thin films and bulk to extract diffusion coefficients, as outlined in the following section, not achievable by means of any other direct in situ technique.

## 2.2. Solution of the 2D Cross Section Diffusion in Thin Films

For the study of the in-plane diffusion coefficient, we need to establish a tracer gradient within the thin film. Therefore, a Raman-transparent, inert, and oxygen-exchange blocking layer is conformally deposited on top of the sample and oxygen exchange is only permitted laterally along one well-defined line by cutting a trench through the capping layer and the thin film before performing an isotopic (back-)exchange annealing.[22] The sample cross section is depicted in Figure 1a, with the thickness, $d_f$, and the sample width, $w_f$. $x=0$ is throughout this work defined at the interface of the trench with the thin film, while $z=0$ corresponds to the interface with the substrate.

The in-plane tracer concentration gradients are analyzed in the framework of Fick's diffusion equations. We assume a homogeneous distribution along the direction of the trench ($\gamma$), which reduces the diffusion model to the 2D cross section along $x$ and $z$

$$\frac{\partial^2 c}{\partial x^2} + \frac{\partial^2 c}{\partial z^2} = \frac{1}{D^*} \frac{\partial c}{\partial t} \quad (2)$$

with the oxygen tracer concentration, $c = {}^{18}c(x, z, t)$, and the tracer self-diffusion coefficient $D^*$. In the following, we consider oxygen exchange along the trenched out-of-plane surface at $x=0$ and the possibility of a small leakage exchange through the capped in-plane surface. Therefore, the boundary conditions are given by

$$-D^* \frac{\partial c}{\partial x} = k_{\text{CGO}}^* (c_{\infty} - c), \quad x = 0, 0 < z < d_f \quad (3)$$

$$-D^* \frac{\partial c}{\partial z} = k_{\text{leak}}^* (c_{\infty} - c), \quad 0 < x < w_f, \quad z = d_f \quad (4)$$
<figure><img src="image_2.png" /><figcaption>**Figure 1.** a) Schematic of IERS methodology to study oxygen diffusion in thin films. b) Measurement and data treatment procedure to obtain in-plane diffusion profiles in thin films by IERS: 1) isotope exchange in ¹⁸O-enriched atmosphere; 2) low-temperature deposition of capping layer followed by 3) mechanical trenching; 4) spatially resolved in situ Raman measurements during the isotopic back exchange; and 5) Data interpolation, discretization, and conversion give tracer profiles, which can be analyzed within the framework of Fick's diffusion equation.</figcaption></figure>

$$ -D^* \frac{\partial c}{\partial x} = 0, \quad x = w_f, \quad 0 < z < d_f \qquad (5) $$

$$ -D^* \frac{\partial c}{\partial z} = 0, \quad 0 < x < w_f, \quad z = 0 \qquad (6) $$

with the surface exchange coefficient, $k_{CGO}^*$, at the open lateral surface at $x=0$, and $k_{leak}^*$ accounts for the leakage exchange through the capping layer and the initial and equilibrium concentrations, $c_0$ and $c_\infty$, whereas the latter corresponds to the ¹⁸O concentration of the annealing atmosphere. We neglect any exchange at the interface with the substrate and any contribution from the second lateral side at $x=w_f$. This can be experimentally guaranteed by ensuring that $w_f$ is much larger than the diffusion length (i.e., semi-infinite diffusion problem). However, we will use the more general (and numerically more stable) solution for the plane sheet model, which is equivalent to the solution of the semi-infinite model for diffusion profiles shorter than $w_f$. In addition, we assume $c_0$ and $c_\infty$ to be homogeneous.

The solution to Equation (2) can be expressed as the product of the separated solutions for 1D diffusion problems in $x$ and $z$ direction, $c(x,z,t) = c_x \times c_z$. [23] Due to the low film thickness, $d_f$, and high $D^*$ of CGO, we assume a homogeneous tracer concentration along $z$ ($D^* \gg d_f k_{leak}^*$, see discussion and verification in Figure S3, Supporting Information). Thus, the diffusion problem in out-of-plane direction reduces to the surface-limited case, while $c_x$ is given as the solution to the plane sheet model.[24] The normalized isotopic fraction, $C'$, varying between 0 and 1, thus can be written as

$$ \begin{aligned} C'(x, z, t) &= \frac{c(x, z, t) - c_0}{c_\infty - c_0} \\ &= 1 - \underbrace{\left[ \sum_{n=1}^{\infty} \frac{2\delta \cos(\beta_n (w_f - x)/w_f)}{(\beta_n^2 + \delta^2 + \delta) \cos \beta_n} \exp\left[\frac{-\beta_n^2 Dt}{w_f}\right] \right]}_{C'_x} \quad (7) \\ &\quad \times \underbrace{\exp\left[\frac{-t k_{leak}^*}{d_f}\right]}_{C'_z} \end{aligned} $$

with $\beta_n$ being the n'th positive root of the transcendental equation $\beta \tan(\beta) = w_f k_{CGO}^* / D^*$ and $\delta = d_f k^* / D^*$. As shown in Equation (7), $C'_z$ reduces to unity for a perfect capping layer with $k_{leak}^* = 0$.

## 2.3. Monitoring of the Lateral Oxygen Diffusion Using IERS

A graphical description of the sample preparation steps, IERS measurement procedure, and data analysis is given in Figure 1b. Small pieces of a thin-film sample (≈2 mm side length) are annealed in an ¹⁸O-enriched atmosphere to reach a high homogeneous initial tracer concentration: 1) Next, the samples are capped with a Raman-transparent, inert, and conformal oxygen-exchange blocking layer; 2) Low-temperature deposition techniques are favored to limit the loss of tracer oxygen during this step. Here, Al₂O₃ and Si₃N₄ coatings were employed using atomic layer deposition (ALD) and plasma-enhanced chemical vapor deposition (PECVD), respectively, with deposition temperatures between 200 and 280 °C. A trench of ≈3 µm is cut through the capping and thin-film layer using a precision diamond scriber in order to enable oxygen exchange at the lateral side of the CGO thin film; 3) Mechanical scratching was selected to avoid thermal or chemical modifications of the CGO surface, as may occur using focused ion beam or chemical etching techniques. The following back-exchange in dry air is monitored using continuous Raman line scans perpendicular to the direction of the trench; and 4) using a motorized linear stage. The movement of the oxygen tracer becomes directly visible via the time- and spatial-dependent frequency shift of the oxygen Raman mode, which is obtained via line fitting.

The line scan parameters (scanning length and point spacing) have to be adopted to expected $D^*$ and $k^*$ parameters, for example, via prior finite-element method (FEM) simulations using literature values. To improve time resolution, a variable point spacing has been used, for example, increasing spacing with increasing distance from the trench. Raman acquisition times have to be reasonably short, while laser-induced heating has to be avoided by restricting the laser power to a material-dependent maximum.
At small times, $t$, and fast kinetics, there may be large changes in $\omega$ between two spectra measured at the same location (e.g., after one completed line scan) and changes between the first spectrum and the last in one single line scan may be significant. To obtain meaningful diffusion profiles at the same discrete time, $t_i$, the transients for each position, $\omega_{max}(x_i)$, are interpolated using an analytical function and discretized at the same discrete times, $t_i$ (step 5 in Figure 1b, see Figure S8, Supporting Information).

The isotopic fraction, ¹⁸C, and consequently the ¹⁸O-normalized isotopic fraction, C', are determined using the VCA model and Equation (1) (step 6 in Figure 1b). The reference values, $\omega_{ref}(T)$, are determined by temperature calibration of the frequency shift of a sample with natural ¹⁸O abundance. The resulting in-plane diffusion profiles at different discrete times are fit to the solution of the diffusion equation (Equation (7)) to obtain the transport coefficients.

Note, in this work, in situ experiments were performed during back-exchange, as this allows to exchange various samples at the same time and thus significantly reduces the consumption of tracer oxygen gas, while the described approach is equally valid to study the initial exchange.

Further details can be found in the Experimental Section at the end of the manuscript.

# 3. Results and Discussion

## 3.1. Structural Characterization and Isotope Profiling

We have selected to study CGO, as it is a highly relevant material for various advanced energy applications due to its high oxygen mobility and its well-defined Raman spectrum, required for this study. Polycrystalline 120 nm-thick dense Ce<sub>0.8</sub>Gd<sub>0.2</sub>O<sub>2-δ</sub> films were deposited by pulsed laser deposition (PLD) on platinized Si substrates (see Experimental Section for more details). The obtained films are of low roughness ($R_q = 1.6$ nm) with nanometric grains of about 48 ± 23 nm. An overview of their structural and chemical characteristics is shown in Figure S2, Supporting Information. The cubic fluorite structure (O<sub>5</sub>H<sub>8</sub> (Fm-3m) space group) of cerium oxide leads to one Raman-active phonon mode of $T_{2g}$ symmetry. It results from the symmetric stretching vibrations of the cation-oxygen O-Ce-O units and therefore only involves the motion of oxygen atoms. A representative Raman spectrum of an as-deposited CGO thin film with natural ¹⁸O isotopic abundance (0.2%) is shown in Figure S2a, Supporting Information. The wavenumber of the main mode (I) is about 465 cm<sup>-1</sup>, as observed for undoped ceria. The long tail on the left shoulder of the main band and additionally observed modes at slightly higher frequencies (II & III) are caused by Gd doping, which reduces the symmetry of the crystal lattice.[25] The metallic Pt buffer layer blocks any signal coming from the Si substrate.

The CGO films were filled with oxygen tracers by annealing in ¹⁸O-enriched atmosphere and subsequently capped with an oxygen-exchange blocking layer. Using low-temperature deposition techniques, we minimized changes in ¹⁸C during the capping process as verified via Raman measurements before and after the deposition. ToF-SIMS analysis revealed a homogeneous

and isotropic tracer distribution in plane as well as out of plane, see Figure S3a,b, Supporting Information. The flat ¹⁸C depth profile indicates that the overall exchange process is limited by a surface reaction (in the uncapped sample) and out-of-plane diffusion is comparably fast. This, together with a homogeneous, initial in-plane distribution, is a requirement for further analysis. The isotopic-induced redshift of the $T_{2g}$ peak and the two defect modes are shown in Figure S4, Supporting Information, which confirm that all three modes only involve the motion of oxygen atoms.

To show the continuous shift of the Raman mode with the isotopic fraction, we have mapped the same area of a sample with an in-plane isotopic gradient using Raman spectroscopy and ToF-SIMS. The inset of **Figure 2** shows the *x* distribution of ¹⁸C as obtained by SIMS measurement, as well as the corresponding Raman-mode position. Both datasets were averaged along *y* to reduce the error arising from the uncertainty in selecting the same sample area. Combining both measurements for each *x* position, as displayed in the main panel, shows a very good correlation between the frequency shift and the isotopic fraction, as expected within the VCA. Fitting this data to Equation (1) (dashed line) gives $\omega_{ref} = 463$ cm<sup>-1</sup>, which serves as room-temperature calibration reference to directly assess the isotopic concentration, ¹⁸C, from Raman measurements with high accuracy.

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Raman frequency shift as a function of the ¹⁸O isotopic fraction. The dashed line corresponds to the best fit to the VCA. This continuous calibration curve is obtained by mapping the same sample area with an ¹⁸C in-plane profile using ToF-SIMS and Raman spectroscopy, as shown in the inset, and correlating the two measurements via the x-axis. Note, that shown data for both techniques is integrated along the y-axis. *x* = 0 corresponds to the edge of the trench.</figcaption></figure>

## 3.2. Impact of Leakages in the Blocking Layer

We have tested Al<sub>2</sub>O<sub>3</sub> and Si<sub>3</sub>N<sub>4</sub> thin films, deposited by ALD and PECVD, respectively, as blocking layers on top of ¹⁸O-filled CGO samples, as these materials are thought to be inert to oxygen exchange, Raman transparent, compatible with CGO, and available and widely used in science and industry. The layer thicknesses were varied between 20 and 100 nm. Higher thicknesses were avoided to minimize any detrimental influence on
the Raman signal, such as increased background and decreased signal-to-noise ratio. A cross-sectional transmission electron microscopy (TEM) image of the sample architecture is shown in Figure S2d, Supporting Information and a SEM/energy-dispersive X-ray spectroscopy (EDX) top-view analysis of the trench cut into the sample is shown in Figure S5, Supporting Information, confirming that the trench cuts through the full multilayer structure and reaches the Si substrate.

The layer tightness was tested using in situ IERS measure-
ments at 400 °C in dry air (natural ¹⁸O abundance), as shown
in Figure S6a, Supporting Information. If the capping layer per-
fectly blocks the exchange with the atmosphere, one would expect
no changes in the Raman-mode position with time at constant
temperature. However, for all tested materials, we find a slow
increase of ω_max, which corresponds to the loss of ¹⁸O and thus
imperfect capping. Assuming a simple surface-limited reaction,
one can estimate the leakage rate through the blocking layer (see
Supporting Information for details). The resulting surface
exchange coefficients for the leakage processes, k_leak*, are in
the range of 1 × 10⁻¹¹–10 × 10¹¹ cm s⁻¹, with no significant dif-
ferences between Al₂O₃ and Si₃N₄ deposited by different techni-
ques (the lowest value corresponds to a 40 nm Al₂O₃ capping
layer by ALD at 200 °C). In comparison, this is significantly
slower than the uncovered CGO surface with k* ≈ 1 × 10⁻⁹.
Still, this leakage needs to be considered when analyzing in-plane
diffusion profiles.

An exemplary ToF-SIMS tracer gradient after back-exchange at 400 °C is shown in Figure S6b, Supporting Information. x=0 corresponds to the trench position. The measurement was cut off after around 240 µm, while the sample width was ≈2 mm. The profile can be separated into two regions. First, for x < 150 µm, the curve follows the shape of a classic diffusion profile. For larger distances from the open surface, the profile is flat, but nonzero. This behavior cannot be explained with a simple 1D diffusion process, with oxygen exchange occurring only at the lateral side surface at x = 0, but is well described via a mechanism taking into account a small leakage through the capped surface, as shown via fitting of the diffusion Equation (7) for the case of leakage with a reduced surface exchange coefficient, k\_leak, compared to perfect capping with C'z = 1. The first solution matches well the experimental data along the full profile, with k\_leak ≈ 3 × 10⁻¹¹ (D* = 3 × 10⁻¹⁰ and k* = 8 × 10⁻⁷ cm s⁻¹). This value is similar to the leakage rates observed above by in situ IERS and confirms that the employed capping layers are not fully tight. However, it is clearly visible that the exchange within the top surface is strongly reduced, leading to an ¹⁸O in-plane gradient, which can be successfully fit to obtain the oxygen transport coefficients.

Note that we have observed the formation of blisters in the
capping layer during heating to the annealing temperature,
which locally enabled faster oxygen exchange. These may have
been caused by impurities on the sample surface, which resisted
the cleaning procedure before the deposition of the capping layer
or by trapped gas during the deposition. For details, see Figure
S7, Supporting Information. As these defects are easily visible by
the optical microscope of the Raman setup, they can be avoided
when selecting the region for the in situ IERS measurements, as
described next.

**3.3. In Situ IERS Measurements and Calculation of the Mass Transport Properties**

IERS measurements were performed as described in the Experimental Section using a temperature cell mounted to the Raman stage under flowing dry air. A spatially and time-resolved in situ IERS measurement is shown in **Figure 3a** for a trenched SiN/CGO sample at 350 °C during a back-exchange experiment. Each line scan consists of 15–25 spectra, with variable spacing (1 µm close to the trench, 5–20 µm at the right end), a scanning length of 100 µm, and a total duration of about 10 min. The time evolution of the T₂g mode for one specific distance from the surface (x = 10 µm) is depicted in the inset, showing a clear shift to higher wavenumbers with time. The Raman-mode frequency, ω_max(xᵢ,t), is obtained by line fitting, as shown in the Figure S8a, Supporting Information, using a single-Voigt profile. Starting at the opened lateral surface at x = 0, a diffusion profile starts building up with time as the ¹⁸O concentration reduces in the film due to annealing in an ¹⁶O atmosphere.

The transients are normalized with respect to the initial tracer
concentration in the sample before the back-exchange and the
saturation value, which corresponds to the ¹⁶O reference position
and is then converted to the normalized isotopic fraction C', as
shown in Figure 3b, for some selected discrete times. The solu-
tion of the 2D diffusion equation (Equation (7)) is used for fitting
the in-plane tracer gradients. As shown, generally experimental
data can be well reproduced over the whole time range of the
experiment, as shown with solid lines. At the end of the in situ
experiment, the same sample area was mapped at room temper-
ature using Raman spectroscopy and the resulting C' profile is
shown with black open diamonds (RT). The remarkable
resemblance to the final high-temperature data validates the in
situ approach presented here.

One of the main advantages of any in situ methodology is its
time resolution, while postmortem analysis is restricted to a sin-
gle time frame and reveals only an averaged picture of the trans-
port processes over the whole annealing time. In situ IERS allows
to study the evolution of transport properties with time, as shown
in Figure 3c, for k*, k\*_{leak}, and D* over about 19 h. The diffusion
coefficient remains constant, while we observe some variations
with time for the fitted surface exchange coefficients. Notably,
for all three coefficients, the final parameters at high
temperature match well ex situ values from the room tempera-
ture analysis.

The exchange rate through the capping layer is ≈10⁻¹¹ cm s⁻¹ at 350 °C, which is slightly lower than the values found above at 400 °C and therefore plausible. On the other hand, the lateral surface exchange coefficient is very large with about 10⁻⁶ cm s⁻¹. Values reported for CGO in literature were found in the range of 10⁻⁹–10⁻⁸ cm s⁻¹ around 350 °C[¹⁰,²⁶] and thus, more than two orders of magnitude smaller. As shown in the Arrhenius plot of the surface exchange coefficients in Figure S9, Supporting Information, this trend persists within the whole analyzed temperature range between 300 and 500 °C. To exclude possible catalytic influences of the Pt buffer layer, we have reproduced the experiment with a twin CGO thin film sample grown on MgO single-crystal substrate with similar results. As the samples are polycrystalline, intrinsic differences between the lateral
<figure><img src="image_4.png" /><figcaption>**Figure 3.** In situ in-plane IERS measurements: a) Spatially and time-resolved Raman frequency shift of T<sub>2g</sub> mode during a back-exchange of trenched SiN/CGO thin film at 350 °C obtained by repeated line scans. Inset shows the time evolution of the Raman spectrum for x = 10, marked with a red rectangle. b) In-plane diffusion profiles of oxygen tracer for various times, determined from (a). Solid lines are best fits to the diffusion equation. Black symbols/line are obtained ex situ at room temperature after back-exchange. c) Time evolution of the fit transport coefficients at 350 °C from in situ Raman measurements and comparison with ex situ values from room-temperature mapping. d) Temperature dependence of D* values from SIMS, in, and ex situ Raman measurements. Solid line is an Arrhenius fit to the in situ data (x). Dashed lines correspond to data found in literature for 10%[31] (extrapolated to lower temperatures) and 20%[26] doped CGO bulk.</figcaption></figure>

and the top surfaces are not expected; however, the fact that the trench was opened just before the back-exchange may play a possible role. The detrimental influence of surface contamination on exchange rates is well documented in literature and pristine surfaces were found to be significantly more active than their aged counterparts due to the exposure to different atmospheres, annealing conditions, or contaminants.[27–29] We have observed previously that alumina deposited by ALD is strongly reduced and may therefore lower the total oxygen content of the CGO layer as well, which would result in an additional chemical driving force, with a chemical surface exchange coefficient, *k*⁸, and thus lead to faster overall kinetics. However, this is not expected for Si₃N₄, while the obtained exchange coefficients do not differ significantly between the different capping materials.

Also the triple-phase boundary between the capping layer, the CGO thin film, and the atmosphere at the trench may enhance the exchange rate but this remains beyond the scope of this work. Additionally, as will be discussed in the next section, the extraction of the lateral surface exchange coefficient based on the described approach is error prone due to uncertainties in the definition of the origin and possible chipping off of the coating close to the trench due to the mechanical trenching process and bad adhesion.

But first, we focus on the analysis of the diffusion coefficient. At 350 °C D* is ≈1 × 10⁻¹⁰ cm² s⁻¹, which is close to literature values for bulk CGO. A comparison for in situ and ex situ measurements and literature over the full measured temperature range is shown in Figure 3d. We find thermally activated behavior of D* and striking agreement between in situ and ex situ values obtained by either Raman or SIMS mapping. Reported values for CGO bulk (dashed and dashed dotted lines) are similar to the values obtained here for polycrystalline thin films. Notably, previously reported diffusion coefficients for oriented CGO thin-film samples (not shown) are 3–5 orders slower.[30] This strong deviation from the behavior observed of ceramic samples was explained by halide impurities, the specific oriented nanocrystalline structure, and the formation of space-charge layers at the grain boundary level.[30] These factors do not apply for the herein studied CGO films, and we therefore expect values close to the bulk, as it is observed.

The solid line is an Arrhenius fit to the in situ data with an activation energy of ≈0.7 eV, compared to 0.9–1.2 eV found in literature for CGO bulk samples.[26,31,32] These small differences likely originate in the different material types studied (single crystal and ceramics vs. thin film) and small variations in Gd doping, which are known to impact the process of oxygen transport.
The diffusion coefficients obtained within this work for polycrystalline thin films are 3–5 orders of magnitude faster than recently reported values for oriented thin films.[30]

Overall, we find excellent agreement between SIMS and IERS results, reasonably close to reported values, which underlines the validity of this novel approach. While we show that the diffusion coefficient of CGO is constant and does not suffer from degradation processes within the studied temporal frame, we demonstrate that in-plane IERS is the first direct in situ tool to study temporal effects on the bulk transport properties, which are of relevance to a large number of applications, including batteries.

### 3.4. Factors Fuel Cells and Affecting the Determination of the Mass Transport Properties

We found very good correlation between SIMS, in situ, and ex situ Raman measurements and literature values for the diffusion coefficient, $D^*$, and matching values for $k_{leak}$ for different types of experiments. However, the lateral surface exchange coefficient of CGO, $k^*$, was significantly larger than expected. We have identified two potential factors which may affect the accuracy of the obtained transport properties. First, the blocking layer may partially chip off close to the trench due to weakened adhesion, the brittle structure of the capping, etc. during the mechanical trenching process and thereby reopen the top surface of the CGO layer, as schematically shown in the inset of Figure 4. Second, uncertainties in defining the origin, that is, the position of the trench, may arise due to small movements of the sample during the measurement due to thermal expansion of the sample and the heater or precision errors in the repeated positioning of the stage. While movements toward the trench are easily detected by the loss of the Raman signal of the material and the appearance of the substrate peak, shifts toward the sample are not trivially identified.

To analyze the influence of these issues and verify the robustness of the method and the validity of the obtained results, we have performed FEM simulations using COMSOL. A schematic of the employed 2D model is shown in the inset of Figure 4, which approximates the real sample geometry. The width of the unblocked surface area is given by $\Delta w$ and was varied

between 0 and 10 µm. We have tested various combinations for the input parameters $k^*$, $D^*$, and $k_{leak}^*$, matching experimental results at different temperatures. The input values for the simulated data displayed in Figure 4 correspond to about 350 °C and are given in the table of Figure 4. Note that we used the same exchange coefficient, $k^*$, for the unblocked top and the opened lateral surface for the simulation, as the studied thin films are of polycrystalline structure.

Upon partially uncovering the top surface (increasing $\Delta w$ from the ideal case 0 to larger values), the isotopic fraction inside the thin film drastically increases (simulations #1, #2, and #3). This is expected as the film thickness is just 120 nm and already in scenario #2 ($\Delta w$ = µm), the uncovered surface (the sum of the lateral surface plus the partially reopened top surface) is about 10× larger. Subsequently we fit the simulated data to Equation (7). For scenario #1–#3, the origin corresponds to the beginning of the capping, $x_0$, while it is shifted toward the trench position, $x'_0$, or toward the inside of the sample, $x''_0$, for the simulations #4 and #5. We determine the accuracy of the evaluation method by comparing input and fitting values for $k^*$, $D^*$, and $k_{leak}^*$, as given in the table of Figure 4. The apparent (fitted) $k^*$ is strongly affected by partially reopening the top surface and fitted values deviate from the input value up to two orders of magnitude. On the other hand, fitting values for $D^*$ and $k_{leak}^*$ match very well with the input values for all simulation scenarios at all temperatures. Thus, the determination of $D^*$ and $k_{leak}^*$ is robust and uncertainties and imperfections in the sample geometry have only minor impact on the extracted values. On the other hand, precautions must be taken to preserve the integrity of the capping layer and high spatial resolution is required for accurate determination of the trench position to obtain meaningful $k^*$ values. Ideally, the measurement is started at the immediate boundary to avoid redundant spectra recorded on top of the trench. However, experimentally under in situ conditions, this is challenging to be achieved (optical precision, thermal movement, etc.). Therefore, we propose to start the in situ line scan a few µm shifted onto the trench, rather than just at the sample edge, at the cost of time resolution but benefiting the determination of the boundary position and thus reducing the uncertainties in the calculation of the surface exchange coefficient using in-plane IERS measurements. We also note that surface

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Finite-element model simulations to analyze the influence of a partially uncovered top surface and the resulting uncertainty in defining the origin for five different scenarios varying the width of the uncovered top surface $\Delta w$ between 0 and 10 µm and the origin for the fit. Solid lines are fits of the diffusion equation to the simulated data. Input and fitted values for $k^*$, $D^*$, and $k_{leak}^*$ are given in the table on the right ($\Delta w$ is varied for the different simulations, while the origin is shifted for the fittings #4 and #5). The simulated annealing time is 67800 s.</figcaption></figure>

<table><thead><tr><th>Origin</th><th>Δw<br>μm</th><th>k*<br>cm s<sup>-1</sup></th><th>D*<br>cm<sup>2</sup> s<sup>-1</sup></th><th>k*<sub>leak</sub><br>cm s<sup>-1</sup></th></tr></thead><tbody><tr><td>Input:</td><td></td><td>1 · 10<sup>-9</sup></td><td>10 · 10<sup>-11</sup></td><td>1 · 10<sup>-11</sup></td></tr><tr><td colspan="5"><strong>Fit:</strong></td></tr><tr><td>#1</td><td>x<sub>0</sub></td><td>0</td><td>1 · 10<sup>-9</sup></td><td>9.9 · 10<sup>-11</sup></td><td>1 · 10<sup>-11</sup></td></tr><tr><td>#2</td><td>x<sub>0</sub></td><td>1</td><td>8 · 10<sup>-9</sup></td><td>9.8 · 10<sup>-11</sup></td><td>1 · 10<sup>-11</sup></td></tr><tr><td>#3</td><td>x<sub>0</sub></td><td>10</td><td>54 · 10<sup>-9</sup></td><td>9.0 · 10<sup>-11</sup></td><td>1 · 10<sup>-11</sup></td></tr><tr><td>#4</td><td>x'<sub>0</sub></td><td>10</td><td>140 · 10<sup>-9</sup></td><td>11.0 · 10<sup>-11</sup></td><td>0.9 · 10<sup>-11</sup></td></tr><tr><td>#5</td><td>x''<sub>0</sub></td><td>10</td><td>36 · 10<sup>-9</sup></td><td>8.4 · 10<sup>-11</sup></td><td>1.0 · 10<sup>-11</sup></td></tr></tbody></table>
exchange coefficients can be obtained straightforward for a surface-limited reaction in thin films via direct IERS measurements without the need for a blocking layer, as demonstrated recently by our group.[10]

While EDX top-view mapping did not indicate any large areas where the signal intensity of Al and Ce did not coincide (compare Figure S5, Supporting Information), any alteration of the capping layer close to the trench, such as chipping, could not be excluded to contribute to the observed higher k*. As mentioned above, the fact that a purely pristine surface was used during the back-exchange could also add to the observation of apparent faster kinetics.

However, we want to emphasize that the determination of the diffusion coefficient is little affected by any of these factors, and in-plane IERS measurements allow to obtain reliable D* values in a fast, cheap, and rather straightforward manner.

## 4. Conclusion

We have described a new in situ approach to study the in-plane self-diffusion coefficient as a function of time using IERS in thin-film samples. We report D* coefficients of Gd-doped ceria thin films and validate them via comparison with conventional ex situ measurements and literature data. FEM simulations confirm the robustness of the described method, while IERS is cheaper, faster, and more versatile compared to the standard isotope exchange-SIMS approach. This will accelerate the ongoing efforts in establishing a materials catalogue of transport properties of functional materials for energy applications, computing, etc. Additionally, IERS grants access to time-resolved D* measurements, which is expected to deepen our understanding of physicochemical processes in functional materials with the ultimate goal to improve their performance and enhance their durability.

## 5. Experimental Section

Polycrystalline 120 nm-thick Ce₁₋ₓGd₂O₂ (x = 0.2) films were fabricated by large-area pulsed laser deposition (PVD Systems, PLD 5000) equipped with a 248 nm KrF excimer laser (Lambda Physics, COMPex PRO 205) under the following conditions: temperature 700 °C, oxygen pressure 7 × 10⁻³ mbar, target-to-substrate distance 90 mm, laser fluency ≈1.2 cm⁻², and 10 Hz repetition rate. The films were deposited on top of 10 × 10 mm² MgO (100)-polished single-crystal substrates (CrysTec GmbH, Germany) and Si (111) wafers, coated with a Pt (150 nm)/TiO₂ (40 nm)/SiO₂ (500 nm) multilayer (LETI, Grenoble, France) and cut into several pieces using a water-cooled diamond saw. Conformal surface blocking layers with thicknesses between 40 and 100 nm were deposited by ALD between 180 and 250 °C and PECVD at 280 °C on top of the ¹⁸O-enriched CGO samples. Trenches were opened at the center of each sample with a precision diamond scriber.

The isotope exchange was performed in a tubular furnace at 640 °C for 0.5 h using a sealed quartz tube filled with ¹⁸O-enriched oxygen gas (c(¹⁸O) = 98%, p = 0.2 atm, CK Isotopes, UK) and fast heating (100 °C min⁻¹) and cooling (quenching by rolling off) ramps. If not stated otherwise, pre-equilibration steps in natural oxygen, as commonly performed for tracer diffusion experiments, were omitted, as a high ¹⁸O isotopic fraction was desired. For CGO, the oxygen vacancy concentration within the studied temperature window was fixed by the amount of Gd doping.[33,34] A temperature difference between the initial exchange and the subsequent back-exchange was therefore not expected to cause an additional chemical driving force.

The chemical and isotopic composition was obtained by SIMS analysis, which was performed using a ToF-SIMS V instrument (ION-TOF GmbH Germany) equipped with a Bi liquid metal ion gun for analysis and a cesium (Cs⁺) gun for sputtering. Negative secondary ions were collected and data was obtained in burst mode operation (6 pulses), applying Poisson correction. Charge effects were compensated by means of a 20 eV pulsed electron flood gun. Depth profiling was performed by alternating sputtering of a 300 × 300 mm² surface area with the Cs⁺-ion beam (2 keV, 110 nA) and chemical analysis with the Bi³⁺ primary ion beam (25 keV, 0.25 pA, rasterized surface area: 50 × 50 µm²). Generally, two SIMS profiles per sample were recorded to confirm its homogeneity.

Raman spectroscopy measurements were performed using the blue excitation wavelength (488 nm) of a Renishaw inVia Qontor spectrometer, with a focused spot size of ≈1 µm². A 50× (long working distance) and a 100× objective were used for in situ studies and room-temperature measurements, respectively. The maximum laser power on the sample surface did not exceed 1 mW. Raman measurements were performed using Renishaw's LiveTrack option to ensure sample focus at all times. The spectrometer was calibrated at room temperature using a silicon reference sample with a theoretical position of 520.7 cm⁻¹.

For in situ back-exchange measurements, a temperature cell (Linkam THMS 600 and Nextron MPS-CHH) was mounted onto the motorized Raman stage. The cells were equipped with a ceramic heater (diameter of 1" Linkam, 0.5" Nextron) and a sapphire window for Raman measurements. Fast heating ramps between 20 and 100 °C min⁻¹ were used to minimize any isotopic exchange during heating, while at the same time avoid cracking of the multilayer sample. Automatic Raman acquisition was typically started within 30–60 s after reaching the exchange temperature, with acquisition times of 30–60 s. Isotopic back-exchanges were performed under flowing dry air (<100 mL min⁻¹) of natural ¹⁸O composition at atmospheric pressure.

## Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

## Acknowledgements

This work received funding from the European Union's Horizon 2020 research and innovation program under grant agreement no. 824072 (Harvestore). The authors acknowledge Florence Robaut and Laetitia Rapenne for focused ion beam lamella preparation and TEM analysis. This research benefited from characterization equipment of the Grenoble INP—CMTC platform supported by the Centre of Excellence of Multifunctional Architectured Materials “CEMAM” n°ANR-10-LABX-44-01 funded by the “Investments for the Future” Program. In addition, this work was performed with the help of the “Plateforme Technologique Amont” de Grenoble, with the financial support of the “Nanosciences aux limites de la Nanoélectronique” Fundation and CNRS Renatech network. Chevreul institute (FR 2638), the French ministry of research, the Région Hauts de France, and FEDER are acknowledged for supporting and funding the surface analysis platform (ToF-SIMS). F.C. acknowledges funding from a Marie Skłodowska Curie Actions Postdoctoral Fellowship grant (101107093).

## Conflict of Interest

The authors declare no conflict of interest.

## Author Contributions

**Alexander Stangl**: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Resources (lead);
Software (lead); Validation (lead); Visualization (lead); Writing—original draft (lead); Writing—review & editing (lead). **Nicolas Nuns**: Investigation (supporting). **Caroline Pirovano**: Investigation (supporting). **Kosova Kreka**: Investigation (supporting); Writing—review & editing (equal). **Francesco Chiabrera**: Investigation (supporting); Writing—review & editing (equal). **Albert Tarancón**: Writing—review & editing (equal). **Mónica Burriel**: Funding acquisition (lead); Writing—review & editing (equal).

## Data Availability Statement

The data that support the findings of this study are openly available in zenodo at https://doi.org/10.5281/zenodo.11028322, reference number [1].

## Keywords

functional thin films, in situ characterizations, ionic conducting oxides, oxygen tracer diffusions, time-resolved kinetic coefficients

Received: May 14, 2024

Revised: July 30, 2024

Published online:

[1] J. Maier, *Nat. Mater.* **2005**, *4*, 805.

[2] A. Stangl, D. Muñoz-Rojas, M. Burriel, *J. Phys. Energy* **2021**, *3*, 012001.

[3] J. A. Kilner, S. J. Skinner, H. H. Brongersma, *J. Solid State Electrochem.* **2011**, *15*, 861.

[4] E. Navickas, Y. Chen, Q. Lu, W. Wallisch, T. M. Huber, J. Bernardi, M. Stöger-Pollach, G. Friedbacher, H. Hutter, B. Yildiz, J. Fleig, *ACS Nano* **2017**, *11*, 11475.

[5] G. Kim, S. Wang, A. J. Jacobson, Z. Yuan, W. Donner, C. L. Chen, L. Reimus, P. Brodersen, C. A. Mims, *Appl. Phys. Lett.* **2006**, *88*, 024103.

[6] Y. Chen, H. Téllez, M. Burriel, F. Yang, N. Tsvetkov, Z. Cai, D. W. McComb, J. A. Kilner, B. Yildiz, *Chem. Mater.* **2015**, *27*, 5436.

[7] J. M. Bassat, M. Burriel, O. Wahyudi, R. Castaing, M. Ceretti, P. Veber, I. Weill, A. Villesuzanne, J. C. Grenier, W. Paulus, J. A. Kilner, *J. Phys. Chem. C* **2013**, *117*, 26466.

[8] M. Burriel, J. Peña-Martínez, R. J. Chater, S. Fearn, A. V. Berenov, S. J. Skinner, J. A. Kilner, *Chem. Mater.* **2012**, *24*, 613.

[9] M. Burriel, G. Garcia, J. Santiso, J. A. Kilner, R. J. Chater, S. J. Skinner, *J. Mater. Chem.* **2008**, *18*, 416.

[10] A. Stangl, D. Pla, C. Pirovano, O. Chaix-Pluchery, F. Baiutti, F. Chiabrera, A. Tarancón, C. Jiménez, M. Mermoux, M. Burriel, *Adv. Mater.* **2023**, *35*, 2303259.

[11] M. Guerain, M. Mermoux, C. Duriez, *Corros. Sci.* **2015**, *98*, 140.

[12] B. Kim, S. J. Park, H. Hamaguchi, *J. Am. Ceram. Soc.* **1994**, *77*, 2648.

[13] D. Stender, S. Heiroth, T. Lippert, A. Wokaun, *Solid State Ionics* **2013**, *253*, 185.

[14] G. Mestl, P. Ruiz, B. Delmon, H. Knözinger, *J. Phys. Chem.* **1994**, *98*, 11283.

[15] Y. Zhu, J. C. Gonzalez-Rosillo, M. Balaish, Z. D. Hood, K. J. Kim, J. L. M. Rupp, *Nat. Rev. Mater.* **2020**, *6*, 313.

[16] D. Uxa, H. J. Holmes, K. Meyer, L. Dörrer, H. Schmidt, *Phys. Chem. Chem. Phys.* **2021**, *23*, 5992.

[17] N. B. Colthup, L. H. Daly, S. E. Wiberley, *Introduction to Infrared and Raman Spectroscopy*, Elsevier **1975**. https://www.sciencedirect.com/book/9780121825546/introduction-to-infrared-and-raman-spectroscopy.

[18] M. Cardona, M. L. Thewalt, *Rev. Mod. Phys.* **2005**, *77*, 1173.

[19] B. K. Kim, H. O. Hamaguchi, *Phys. Status Solidi B* **1997**, *203*, 557.

[20] L. Chen, C. Chen, A. Jacobson, *IEEE Trans. Appl. Supercond.* **2003**, *13*, 2882.

[21] P. Cayado, C. F. Sánchez-Valdés, A. Stangl, M. Coll, P. Roura, A. Palau, T. Puig, X. Obradors, *Phys. Chem. Chem. Phys.* **2017**, *19*, 14129.

[22] We use the term exchange to describe the initial annealing in an ¹⁸O enriched atmosphere to fill the material with the tracer isotope, while back-exchange corresponds to a second, subsequent annealing in an atmosphere of natural ¹⁸O abundance to deplete the tracer within the sample.

[23] H. S. Carlsow, J. C. Jaeger, *Conduction of Heat in Solids*. Oxford Press **1959**. https://www.scribd.com/doc/63559781/Carslaw-and-Jaeger-Conduction-of-Heat-in-Solids-1959-ISBN-0198533683.

[24] J. Crank, *The Mathematics of Diffusion*, 2nd ed., Clarendon Press, Oxford **1979**.

[25] J. R. McBride, K. C. Hass, B. D. Poindexter, W. H. Weber, *J. Appl. Phys.* **1994**, *76*, 2435.

[26] K. Kowalski, *Defect Diffus. Forum* **2009**, 289–292, 769.

[27] M. Acosta, F. Baiutti, X. Wang, A. Cavallaro, J. Wu, W. Li, S. C. Parker, A. Aguadero, H. Wang, A. Tarancón, J. L. MacManus-Driscoll, *J. Power Sources* **2022**, *523*, 230983.

[28] G. M. Rupp, A. Optiz, A. Nenning, A. Limbeck, J. Fleig, *Nat. Mater.* **2017**, *16*, 640.

[29] M. Siebenhofer, T. M. Huber, G. Friedbacher, W. Artner, J. Fleig, M. Kubicek, *J. Mater. Chem. A* **2020**, *8*, 7968.

[30] S. P. Waldow, B. J. Statham, H. F. Wardenga, T. E. Weirich, A. Klein, R. A. De Souza, *ACS Appl. Mater. Interfaces* **2020**, *12*, 36768.

[31] P. S. Manning, J. D. Sirman, J. A. Kilner, *Solid State Ionics* **1996**, *93*, 125.

[32] E. Ruiz-Trejo, J. D. Sirman, Y. M. Baikov, J. A. Kilner, *Solid State Ionics* **1998**, *113–115*, 565.

[33] K. Yashiro, S. Onuma, A. Kaimai, Y. Nigara, T. Kawada, J. Mizusaki, K. Kawamura, T. Horita, H. Yokokawa, *Solid State Ionics* **2002**, *152–153*, 469.

[34] S. Wang, H. Inaba, H. Tagawa, M. Dokiya, T. Hashimoto, *Solid State Ionics* **1998**, *107*, 73.