V Tezyk

C Rossignol

N Sergent

Elisabeth Djurado

Jérôme Laurencin

Elisabeth Siebert
email: elisabeth.siebert@lepmi.grenoble-inp.fr

Cyclic voltammetry and high-frequency series resistance of La0.6Sr0.4Co0.2Fe0.8O3-δ electrode deposited on GDC : effect of the electrode microstructure and the oxygen partial pressure

Keywords: LSCF/GDC interface, cyclic voltammetry, high-frequency series resistance, microstructure, oxygen partial pressure

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Introduction

La1-xSrxCoyFe1-yO3-δ perovskite oxides are good candidates for oxygen electrode materials in Solid Oxide Fuel Cells (SOFC) and Solid Oxide Electrolysis Cells (SOEC) operating at intermediate temperatures (500-800°C) [START_REF] Skinner | Recent advances in Perovskite-type materials for solid oxide fuel cell cathodes[END_REF]. In particular, the composition La0.6Sr0.4Co0.2Fe0.8O3-δ (LSCF) in contact with Gadolinium Doped Ceria (GDC) is widely accepted as the oxygen electrode material with a good trade-off between electrochemical performances and long-term stability.

Indeed, this compound exhibits suitable electronic and ionic conductivity [START_REF] Tai | Structure and electrical properties of La1 -xSrxCo1 -yFeyO3. Part 2. The system La1 -xSrxCo0.2Fe0.8O3[END_REF][START_REF] Fan | The ionic conductivity, thermal expansion behavior, and chemical compatibility of La0.54Sr0.44Co0.2Fe0.8O3-δ as SOFC cathode material[END_REF][START_REF] Jiang | A comparison of O2 reduction reactions on porous (La,Sr)MnO3 and (La,Sr)(Co,Fe)O3 electrodes[END_REF][START_REF] Murata | Morphology control of La(Sr)Fe(Co)O3-δ cathodes for IT-SOFCs[END_REF] leading to good electrochemical performances [START_REF] Baqué | High performance nanostructured IT-SOFC cathodes prepared by novel chemical method[END_REF][START_REF] Çelikbilek | Influence of sintering temperature on morphology and electrochemical performance of LSCF/GDC composite films as efficient cathode for SOFC[END_REF][START_REF] Marinha | Microstructure-Electrical Properties of Original LSCF Films Deposited by ESD for IT-SOFCs[END_REF][START_REF] Hwang | Electrochemical performance of LSCF-based composite cathodes for intermediate temperature SOFCs[END_REF][START_REF] Marinha | Microstructural 3D reconstruction and performance evaluation of LSCF cathodes obtained by electrostatic spray deposition[END_REF]. Concerning the electrolyte, GDC is preferred to the standard Yttria Stabilized Zirconia (YSZ) electrolyte in order to avoid the reactivity of LSCF at high temperature with YSZ, which results in the formation of insulating phases at the interface [START_REF] Tu | Ln0.4Sr0.6Co0.8Fe0.2O3-δ (Ln=La, Pr, Nd, Sm, Gd) for the electrode in solid oxide fuel cells[END_REF].

Kharton et al. [START_REF] Kharton | Ceria-based materials for solid oxide fuel cells[END_REF] reported the best stability for 10 mol. % Gd-doped ceria (Ce0.9Gd0.1O2-δ) in reducing atmospheres and at temperatures below 1000 K, which makes Ce0.9Gd0.1O2-δ the most appropriate electrolyte material for IT-SOCs. In addition, the linear thermal expansion coefficient of Ce0.9Gd0.1O2-δ in the temperature range of 30 to 800 °C is equal to αGDC = 13.4•10 -6 K -1 which is close to LSCF [START_REF] Tai | Structure and electrical properties of La1 -xSrxCo1 -yFeyO3. Part 2. The system La1 -xSrxCo0.2Fe0.8O3[END_REF]. This good compatibility improves the long-term stability of solid oxide cells [START_REF] Kiebach | Stability of La0.6Sr0.4Co0.2Fe0.8O3/Ce0.9Gd0.1O2 cathodes during sintering and solid oxide fuel cell operation[END_REF].

The electrochemical properties of the LSCF/GDC electrode are related to the degree of the oxygen deficiency within LSCF which is strongly dependent on the B site ion oxidation state within perovskite type ABO3 metal oxides at high temperature [START_REF] Bucher | Defect equilibria and partial molar properties of (La,Sr)(Co,Fe)O3-δ[END_REF]. High concentration of oxygen vacancies leads to high oxygen reduction rate, thus increasing the performance of LSCF as cathode.

However, high oxygen vacancy content can affect the structural stability of LSCF [START_REF] Kivi | Oxygen Stoichiometry in La0.6Sr0.4CoO3-δ and La0.6Sr0.4Co0.2Fe0.8O3-δ Cathodes under Applied Potential as a Function of Temperature and Oxygen Partial Pressure, Measured by Electrochemical in Situ High-Temperature XRD Method[END_REF] and its thermochemical stability [START_REF] Hashimoto | Oxygen nonstoichiometry and thermo-chemical stability of La 0.6Sr0.4Co1-yFeyO 3-δ (y = 0.2[END_REF]. Those properties are also highly dependent on the redox properties of the B site [START_REF] Kuhn | Oxygen nonstoichiometry and thermo-chemical stability of perovskite-type La0.6Sr0.4Co1-yFeyO 3-δ (y = 0, 0.2, 0.4, 0.5, 0.6, 0.8, 1) materials[END_REF].

Cyclic voltammetry has already been used to characterize the reducibility of the B site and formation of oxygen vacancies [START_REF] Chen | Cyclic voltammetry of (La,Sr)MnO3 electrode on YSZ substrate[END_REF][START_REF] Roche | Physicochemical origins of electrochemical promotion of LSM/YSZ[END_REF][START_REF] Van Herle | Electrochemical characterisation of oxygen nonstoichiometry and transport in mixed conducting oxidesApplication to La0.4Ba0.6Fe0.8Co0.2O3-δ[END_REF]. Previous studies of the porous Co-rich compound, La0.7Sr0.3Co0.8Fe0.2O3-δ, deposited on GDC have been carried out by cyclic voltammetry [START_REF] Siebert | Oxido-reduction properties of La0.7Sr0.3Co0.8Fe0.2O3-δ perovskite oxide catalyst[END_REF] and Raman spectroscopy measurements, from 300 to 500 °C, under applied dc voltage [START_REF] Siebert | Electrochemical and Raman study of La0.7Sr0.3Co0.8Fe0.2O3-δ reduction[END_REF]. A reversible phase transition from perovskite (ABO3) towards the brownmillerite (ABO2.5 or A2B2O5) was observed under cathodic polarization leading to the existence of two cathodic peaks on the voltammograms under air. The cathodic peaks were tentatively attributed to the reduction of Co 4+ to Co 2+ in tetrahedral environment. On the contrary, for the porous Fe-rich La0.8Sr0.2Co0..2Fe0.8O3-δ compound, Kournoutis et al. [START_REF] Kournoutis | Cyclic voltammetry characterization of a La0.8Sr 0.2Co0.2Fe0.8O3 -δ electrode interfaced to CGO/YSZ[END_REF] have concluded that no peak was observed under air in the temperature range of 600 to 800 °C. However, when the oxygen partial pressure was decreased, current peaks appeared both in the forward and backward scans.

In the present work, LSCF deposited on GDC was studied by cyclic voltammetry and dc bias impedance measurements over a wide range of temperatures and oxygen partial pressures. LSCF was deposited with two different microstructures: (i) porous 10 μm thick film prepared by Screen-Printing (SP) and (ii) almost dense 2 μm thin film deposited by Electrostatic Spray Deposition (ESD) [START_REF] Marinha | Microstructural 3D reconstruction and performance evaluation of LSCF cathodes obtained by electrostatic spray deposition[END_REF]. The purpose of the study was to understand the role of the microstructure and the oxygen partial pressure on the shape of the voltammograms and the variation of the series resistance, Rs, deduced from the high-frequency axis intercept on the impedance diagrams as a function of the dc bias.

Experimental

Sample preparation

The dense Ce0.9Gd0.1O2-δ substrate, ≈ 1 mm in thickness, was prepared by isostatically pressing of GDC powder (Praxair, 99.9 %, 20.5 m².g -1 ) at 300 MPa, followed by sintering at 1200 °C for 2 h in air. The substrates were polished with abrasive disc P400, on MECAPOL P 200 machine, in order to obtain a flat and uniform surface, allowing a well-defined and reproducible surface for further deposits.

The starting La0.6Sr0.4Co0.2Fe0.8O3-δ commercial powder was provided from Marion Technologies with particle size distribution d50 = 0.27 μm. Porous LSCF electrodes were deposited by screen-printing. The ink was made-up by mixing LSCF powder with a commercial solvent "Product KD2921" (ZSCHIMMER & SCHWARZ) 50/50 wt. % and 2 % total weight polymer PVB (Polyvinyl butyral) as binder. A printing screen with a very fine mesh (INOX MESH SD 95/46) was used. The screen-printed sample was pre-annealed at 450 °C (heating rate 1 °C.min -1 ) to burn out binders and ink solvents. Then, it was fired at 900 °C for 2 hours in air (heating rate 2 °C.min -1 ) to get good adhesion on GDC. It is worth mentioning that this heat treatment takes place at a lower temperature than that conventionally used for the deposit of LSCF by SP [START_REF] Kournoutis | Cyclic voltammetry characterization of a La0.8Sr 0.2Co0.2Fe0.8O3 -δ electrode interfaced to CGO/YSZ[END_REF]. Consequently, possible changes in the electrode microstructure cannot be excluded because the electrode is likely to be less stable than the conventional electrode.

An almost dense electrode was deposited by ESD as described in [START_REF] Marinha | Microstructural 3D reconstruction and performance evaluation of LSCF cathodes obtained by electrostatic spray deposition[END_REF]. It will be denoted "dense" throughout the text. A precursor salt solution was prepared by weighing La(NO3)3.6H2O (Prolabo, 99.99%), SrCl2.6H2O (Strem Chemicals, 99%), Co(NO3)2.6H2O (Sigma-Aldrich, 99.999%) and Fe(NO3)2.9H2O (Sigma-Aldrich, 99.99%) salts in adequate amounts, as to obtain the La0.6Sr0.4Co0.2Fe0.8O3-δ composition. The solution was obtained by mixing salts in ethanol (C2H5OH, 99.9%; Prolabo) and diethylene glycol monobutyl ether, also known as butyl carbitol CH3(CH2)3OCH2CH2OCH2CH2OH (Acros Organics, 99+%) with a 1:2 volume ratio. Depositions were made at 30 mm nozzle-to-substrate distance and 1.59 mL h -1 solution flow rate, using a model A-99 Bioblock Scientific flowmeter. Deposition time was equal to 3 h. The substrate temperature was 300 °C with a value referring to the surface of the substrate facing the solution spray, obtained after temperature calibration. A positive voltage ranging from 8 to 10 kV was selected and applied between the nozzle and the grounded substrate for aerosol generation and spray stabilization. The sample was annealed at 900 °C in air for 2 h. ESD was also used to prepare a porous sample with a columnar microstructure. The sample was deposited in the conditions depicted in [START_REF] Marinha | Microstructural 3D reconstruction and performance evaluation of LSCF cathodes obtained by electrostatic spray deposition[END_REF] but with a deposition time equal to 6 h. For all the films, X-ray diffraction showed that the LSCF exhibited a single rhombohedral phase with R 3c space group.

Microstructure characterization

The characterization of the LSCF microstructure was performed by Scanning Electron Microscopy (SEM) with a field emission gun equipment (ZEISS Ultra 55), operating at 3-10 kV voltage and 6.4-7 mm working distance. The samples were coated with Pt to avoid electron charging. The samples were analyzed on the surface as well as on a fresh fractured section. For the porous sample, the average grain and pore sizes, as well as the porosity, were estimated using the ImageJ software. This analysis was performed on a polished LSCF surface.

Electrochemical measurements

The electrochemical measurements were performed with a three-electrode set-up. The geometry and nature of the electrodes are depicted in Fig. 1. For characterization of porous SP layer, both working and counter electrodes, WE and CE respectively, were deposited symmetrically on each side of the electrolyte (surface area ≈ 1.1 cm²). For characterization of dense and thin LSCF, the counter electrode consisted of a silver paste (Ferro L-200N) deposited symmetrically with the LSCF working electrode (surface area ≈ 0.5 cm 2 ). In both set-ups, the reference electrode (RE) consisted of an Ag wire applied on the periphery of the GDC pellet, in the middle of the cylinder height. This geometry ensured a rather uniform current density through the cell, thus solving the problem in solid-state electrochemistry with the position of the reference electrode [START_REF] Rutman | Reference electrodes for thin-film solid-state ionic devices[END_REF].

Ag was used instead of Pt because it is a better oxygen reference electrode at low temperature. Indeed, the Nernst law is well verified for the reference electrode by using this material even at T<500°C. Gold grids with a surface area equal to that of LSCF electrodes were used as current collectors (fine 52 mesh woven from 0.102 Alfa Aesar). The electrical contact between gold grids and the sample was ensured by mechanical pressure. The electrochemical measurements were performed from 300 to 700 °C for the porous sample, in order to be as close as possible to the conditions of SOFC and/or SOEC. For the dense sample, only two temperatures were characterized, i.e. 300 and 500°C. The gas flow was synthetic O2 + N2 gas mixture or Ar, with 3 L.h -1 flow rate.

The oxygen partial pressure within the gas was measured with an oxygen gauge located at the exit of the furnace. The oxygen gauge was a home-made potentiometric sensor based on yttria stabilized zirconia. It used ambient air as reference atmosphere and was operating at 700°C. The electrochemical measurements were performed with a Solartron SI 1280B electrochemical equipment. Electrochemical impedance measurements at Open-Circuit Voltage (OCV) were first measured as a function of temperature, in order to check the reproducibility of the electrode and evaluate the precision of the measurement. They were carried out with an ac signal amplitude of 50 mV, over a frequency range of 20 kHz to 0.5 Hz. Impedance spectra were fitted with electrical circuits using the EC-Lab ® software (V11.01) as described in our previous work [START_REF] Federico Monaco | Experimental validation of a La0.6Sr0.4Co0.2Fe0.8O3-δ electrode model operated in electrolysis mode: Understanding the reaction pathway under anodic polarization[END_REF]. This allowed the determination of the ohmic series resistance, Rs, corresponding to the highfrequency intercept with the real axis, the electrode polarization resistance, Rpol, determined from the low-frequency intercept, and the top impedance diagram frequency, f0, as defined in Fig. 2a.

This figure shows a typical impedance spectrum recorded at OCV. As expected from our previous work [START_REF] Federico Monaco | Experimental validation of a La0.6Sr0.4Co0.2Fe0.8O3-δ electrode model operated in electrolysis mode: Understanding the reaction pathway under anodic polarization[END_REF] and from literature data [START_REF] Adler | Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes[END_REF], the classical Gerischer impedance is obtained at 500°C, for the porous film. As a consequence, the frequency, f0, can be linked to the characteristic time constant, tchem, defined by ALS model [START_REF] Adler | Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes[END_REF] according to:

= √3 2 (1)
with tchem ∝ 1/SMIEC/gas, where SMIEC/gas is the LSCF specific surface area. It is worth mentioning that the impedance diagram shape changes from the Gerischer-type element (Ge), corresponding to a semi-infinite medium, to the finite-length Gerischer element (FLGe) when the thickness of the electrode decreases and/or the gas exposed surface area decreases [START_REF] Nielsen | Impedance of porous IT-SOFC LSCF:CGO composite cathodes[END_REF]. The finite-length-Gerischer impedance starts with the Warburg impedance at high frequencies and turns into a semi-circle at low frequencies. In that case, the relationship between f0 and tchem must diverge from Eq. (1).

However, whatever the Ge or LFGe behavior, the value of the characteristic frequency f0, defined as the maximum absolute value of the imaginary part of the impedance, exhibits the same dependence with the gas/LSCF interfacial specific surface area.

The error on Rs, Rpol and f0 was estimated from measurements on 4 similar porous samples.

The Arrhenius plot of Rs (Fig. 2b) shows that the error was small (less than ±0.05) at low temperature while it increased at high temperature (T > 490 °C). It was estimated to be ±0.07 on a logarithmic scale. This larger error could be explained by the decrease of ohmic resistance of the cell with increasing the temperature so that the contribution of the contact resistance (roughly independent of T) induced the scattering in Rs. Moreover, the identification error on Rs became more important as the temperature increased due both to the smaller value of Rs and the more pronounced high-frequency artifacts. For log (Rpol) (Fig. 2c), the error was constant on the whole temperature range. It was equal to ±0.11. This dispersion was mainly attributed to difference in porous film reproducibility during the synthesis process. By assuming that the error at OCV was the same as under dc polarization, it could be suggested that the error on the logarithm of the faradaic current would be equal to ±0.11. This value will be used on the polarization curve Tafel plot. In the same way as Rpol, the error on log (f0) (Fig. 2d) was found to be independent of the temperature and equal to ±0.1. This led to ∆f0/ f0 = ±0.1 corresponding to an error of ±10% on f0. Thereafter, f0 will be used to compare SMIEC/gas for the different samples tested. Therefore, samples will be considered to have a specific surface area variation if the difference between f0 is greater than 20%.

Then, the polarization curves, as well as the impedance diagrams under polarization, were recorded using the up-face as the working electrode. The polarization curve was measured in a potentiostatic mode with a potential step of 50 mV. The applied potential, denoted E, varied in the range of 0.3 to -0.7 V. The equilibration time was equal to 600 s as shown by the corresponding chronoamperometric curves (I vs t), which were recorded to check the stationarity of the current.

The dc impedance spectra were recorded at each applied potential with the same ac signal amplitude than the one used at OCV. In the present work, we were interested in the variation of Rs with dc potential, denoted Rs(E). The Rpol dependence on the polarization was reported in a recent previous work [START_REF] Federico Monaco | Experimental validation of a La0.6Sr0.4Co0.2Fe0.8O3-δ electrode model operated in electrolysis mode: Understanding the reaction pathway under anodic polarization[END_REF]. In the present work, the polarization curves were presented as log (j) vs η,

where η was the overvoltage, corresponding to the applied potential corrected from the ohmic drop according to:

η = E -Rs E . j E (2)
In Eq. ( 2), j(E) was the current density calculated from the geometric surface area of the LSCF layer and Rs(E) was the potential dependent series resistance.

The linear sweep cyclic voltammetry experiments were performed by varying linearly the electrode potential with scan rates, v, in the range from 0.5 mV.s -1 to 500 mV.s -1 . An anodic pretreatment, 0.1 V/air during 20 min, was applied to stabilize the same oxidation state of the electrodes corresponding to a low oxygen vacancy concentration within LSCF (δ → 0). In the present paper, the potential on the voltammograms was the potential uncorrected from the ohmic drops. As it corresponded to the applied potential, it was denoted E by analogy with the terminology of Eq. ( 2). The peak potential, ηp, was determined from E by correction from the ohmic drop and calculated with respect to 1 atm of oxygen according to the Nernst equation expressed as:

η V / = η V /! + RT 4ℱ ln x (3)
where x was the corresponding pO2 atmosphere. This was done in order to keep the same potential scale and to be able to compare the results obtained under different pO2.

The open-circuit potential was measured before each experiment and, as expected, was practically zero.

Results

Role of the microstructure

The study on the role of the microstructure on electrochemical properties was performed under pO2 = 0.21 atm, by comparing the response of a porous and a dense film. Fig. 3 presents surface and cross-sectional SEM images for the different electrode microstructures tested in the present work. The micrograph in Fig. 3b shows that the porous film prepared by SP was 10 μm thick. It was homogeneous and uniform over the whole section. The average particle and pore sizes were almost the same (see Table 1) and around 90 nm, which corresponded to a rather fine microstructure. This result could be related to the low sintering temperature [START_REF] Nielsen | Impedance of porous IT-SOFC LSCF:CGO composite cathodes[END_REF][START_REF] Nielsen | Effect of low temperature in-situ sintering on the impedance and the performance of intermediate temperature solid oxide fuel cell cathodes[END_REF]. The porosity was equal to 43 ± 2%. A good adherence between the electrode and the electrolyte was obtained. It can be noticed that the so-called dense film could be rather considered as nanoporous in comparison with dense films deposited by Pulsed Laser Deposition (PLD) [START_REF] Hildenbrand | Improved cathode/electrolyte interface of SOFC[END_REF]. Taking into account the values of f0 given in Table 1, it can be proposed that the dense film has a very small specific surface area compared to the porous film. 4a shows the typical voltammetry response corresponding to the porous LSCF electrode. No peaks were evidenced and the cyclic voltammetry corresponded to the steady-state polarization curve. This shape was obtained whatever the scan rate, v, from 0.5 to 500 mV.s -1 in the whole temperature range (from 300 to 700 °C). This result is in good agreement with the study of Kournoutis et al. [START_REF] Kournoutis | Cyclic voltammetry characterization of a La0.8Sr 0.2Co0.2Fe0.8O3 -δ electrode interfaced to CGO/YSZ[END_REF], who have not detected any peak under air. However, no reverse hysteresis was observed in the backward scan in our work, while Kournoutis et al. [START_REF] Kournoutis | Cyclic voltammetry characterization of a La0.8Sr 0.2Co0.2Fe0.8O3 -δ electrode interfaced to CGO/YSZ[END_REF] have highlighted this phenomenon, corresponding to higher currents in the backward scan than in the forward scan. Fig. 4b represents the Rs vs E curve measured at different temperatures. The upper limit of 550°C, chosen to present the results was due to the fact that, above 600°C, impedance diagrams under dc bias may have high-frequency artifacts, that make it difficult to determine Rs accurately. However, despite the dispersion of the experimental points, the results obtained at 600 and 700°C on one sample confirm the evolution trend observed from 300 to 550°C on all the samples. Based on this comment and on the results in Fig. 4a, it can be concluded that Rs was independent on the applied potential whatever the temperature from 300 to 700°C. The series resistance, Rs, is commonly associated with the migration of O 2-ions through the electrolyte. Comparison with literature data and, in particular, Rs GDC calculated from the GDC conductivity reported by Steele [START_REF] Steele | Appraisal of Ce 1-y Gd y O 2-y / 2 electrolytes for IT-SOFC operation at 500C[END_REF], shows that the measured Rs was slightly higher than the theoretical resistance Rs GDC , roughly estimated from a 1D geometry with a thickness equal to half that of the GDC pellet and a surface area equal to that of LSCF. Moreover, the activation energy for OCV conditions measured from all tested samples was between 0.5 and 0.55 eV. This value was lower than the value of 0.64 eV given by Steele [START_REF] Steele | Appraisal of Ce 1-y Gd y O 2-y / 2 electrolytes for IT-SOFC operation at 500C[END_REF] for T > 400°C. The difference between Rs and Rs GDC increased when the temperature was increased.

This phenomenon was already observed in our previous work [START_REF] Siebert | Oxido-reduction properties of La0.7Sr0.3Co0.8Fe0.2O3-δ perovskite oxide catalyst[END_REF]. The difference between both sets of data might be attributed to small differences in sample composition and/or bad current collector properties due to an electrical sheet resistance of the porous LSCF electrode [START_REF] Kleitz | Optimized SOFC electrode microstructure[END_REF]. This effect could be reinforced at high temperature as the electrical conductivity of LSCF decreases with increasing the temperature above 500°C [START_REF] Tai | Structure and electrical properties of La1 -xSrxCo1 -yFeyO3. Part 2. The system La1 -xSrxCo0.2Fe0.8O3[END_REF]. Moreover, as already stated in the experimental section, additional contact resistance due to the experimental set-up may also lead to an error on the value of Rs measured at high temperature.

Fig. 5a shows the typical voltammetry response for dense LSCF obtained at 500 °C. One cathodic peak corresponding to the forward scan (from 0.1 to -1 V) and a reverse anodic peak corresponding to the backward scan (from -1 to 0.1 V) were observed. The cathodic and anodic peaks were almost of the same shape from 2 to 160 mV.s -1 , with approximately the same surface area at 300°C. As expected, the peak intensities were increasing with the scan rate. Indeed, the ratio between the current and the scan rate (I/v) corresponds to the capacitance in a charge/discharge process. The Rs vs E curve is given in Fig. 5b. Contrary to the porous sample, Rs was found to rise with the applied cathodic potential. The polarization threshold at which Rs started to increase was shifted toward more cathodic overpotential when temperature was decreased. Indeed, the overpotential threshold was calculated and found to be equal to -0.28 V / and -0.11 V / at 300 and 500°C, respectively. For example, such Rs shift to higher values for larger cathodic dc bias have already been observed by Baumann et al. [START_REF] Baumann | Impedance spectroscopic study on welldefined (La,Sr)(Co,Fe)O3-δ model electrodes[END_REF] on microelectrodes of the Co-rich LSCF deposited by PLD. This phenomenon was explained by decreasing of LSCF conductivity and increasing of oxygen vacancies concentration under cathodic polarization as described in [START_REF] Niedrig | Characterization of oxygendependent stability of selected mixed-conducting perovskite oxides[END_REF]. As before, the value of Rs was compared to Rs GDC calculated from GDC conductivity reported by

Steele [START_REF] Steele | Appraisal of Ce 1-y Gd y O 2-y / 2 electrolytes for IT-SOFC operation at 500C[END_REF]. At 300°C, the relative difference between both sets of data was practically the same for both the porous and dense samples. However at 500°C, Rs near OCV was greatly higher than Rs GDC , contrary to the porous thick film. This could be attributed to constriction phenomenon as the film thickness was only 2 μm and not thick enough for good current collecting with grids [START_REF] Fleig | The Influence of Current Constriction on the Impedance of Polarizable Electrodes[END_REF][START_REF] Kenjo | Influence of the local variation of the polarization resistance on SOFC cathodes[END_REF][START_REF] Celikbilek | State-of-the-Art La0.6Sr0.4Co0.2Fe0.8O3-δ Cathode for SOFC: Microstructural and Electrochemical Properties[END_REF].

Actually, the LSCF electronic conductivity decreases when the concentration of oxygen vacancies V * •• increases. So, constriction phenomenon due to in-plane resistance becomes more important under reducing conditions thus leading to Rs >> Rs GDC under cathodic polarization.

The effect of the sweep rate on the voltammograms was addressed by determining the variation of the peak potential, ηp, and the peak current, Ip (or peak current density, jp). The peak potentials Epc and Epa were determined as represented in Fig. 6a. The cathodic peak current, Ipc, corresponded to the current measured at the minimum of the voltammetry response, as classically defined in electrochemistry [START_REF] Bard | Electrochemical Methods: Fundamentals and Applications[END_REF][START_REF] Diard | Cinetique électrochimique[END_REF]. On the other hand, the determination of the reverse anodic peak current, Ipa, required a baseline correction as it may depend on the return potential. The baseline for Ipa measurement in the cathodic zone was determined as proposed by Bard and Faulkner [START_REF] Bard | Electrochemical Methods: Fundamentals and Applications[END_REF], by extrapolating the limiting current in the voltammograms . It is worth mentioning that there is no solid theory behind baseline correction. In the anodic part, it was taken as the stationary current corresponding to the oxygen evolution. Indeed, this one corresponds to the surface path that takes place in parallel as shown in [START_REF] Hubert | Role of microstructure on electrode operating mechanisms for mixed ionic electronic conductors: From synchrotron-based 3D reconstruction to electrochemical modeling[END_REF]. It should be noted that, by doing so, the baseline and dc polarization curve were almost the same. Moreover, baseline correction was necessary only for small Ipa or high Epa values. The peak potential, ηp, was calculated from Ep, by ohmic correction according to Eq. ( 2), using either Rs (OCV) as it was done in our previous work [START_REF] Siebert | Oxido-reduction properties of La0.7Sr0.3Co0.8Fe0.2O3-δ perovskite oxide catalyst[END_REF] or Rs (Ep), i.e. Rs value corresponding to E = Ep. Fig. 6b shows an example of a result for the cathodic peak potential. The representation mode as a function of log (v 1/2 ) is the one proposed by Diard et al. [START_REF] Diard | Cinetique électrochimique[END_REF]. Note that the usual scale using log (v) is obtained simply by setting log (v 1/2 ) = ½ log (v). The determination of ηpc using the ohmic drop measured at OCV led to a variation curve as a function of the scan rate similar to that observed in our previous work [START_REF] Siebert | Oxido-reduction properties of La0.7Sr0.3Co0.8Fe0.2O3-δ perovskite oxide catalyst[END_REF]. Indeed, ηpc was constant at a low scan rate and found to decrease as log (v) at the high scan rate. On the contrary, the correction by Rs (Ep) led to a strong increase of ηp at high scan rate. This huge enhancement was meaningless due to excess ohmic drop correction. This result clearly indicates that, when ηp is located in a potential zone where Rs may vary, any variation of ηp with the scan rate is rather an artifact due to the fact that the Rs value necessary for ohmic drop correction is between Rs (OCV)

and Rs (Ep). In other words, the electrode series resistance Rs obtained at steady-state potential equal to the peak potential is different from the value determined at the same potential under the transient conditions of the voltammetric scan, the latter being lower but higher than the Rs under OCV. In addition, it must be emphasized that this Rs value may vary throughout the scan, especially under cathodic potentials. For these reasons, the variation in peak potential with scan rate, given in our previous work [START_REF] Siebert | Oxido-reduction properties of La0.7Sr0.3Co0.8Fe0.2O3-δ perovskite oxide catalyst[END_REF], should be reconsidered in the light of the present result. Therefore, unless Rs was proved to be constant, only ηp values obtained for low scan rate were considered relevant.

Indeed, under these conditions, the ohmic drop correction did not change the value of Ep, regardless of the Rs value due to small value of Ip.

Variation of cathodic and anodic peak current, Ip (or current density, jp) with scan rate is illustrated in Fig. 7. The mode of presentation, i.e. log (jp.v -1/2 ) vs log (v 1/2 ), is the one proposed in [START_REF] Diard | Cinetique électrochimique[END_REF] to describe the voltammetry response of an insertion compound with a 1D planar geometry (linear diffusion). In such compounds, a transition from a law of the type Ip ∝ v to the type Ip ∝ v 1/2 is predicted as the scan rate increases. It is due to the transition from homogeneous diffusion to semi-infinite diffusion as discussed in part 4. The results in Fig. 7 show that Ipa was almost equal to Ipc at 300°C. At 500°C, Ipa was almost equal to Ipc only for the high scan rates and lower than Ipc at low scan rates. A more detailed study as a function of the temperature would be required to confirm this change in the relative height of anodic and cathodic peaks with temperature. We also noticed from the results in Fig. 7 that Ipc increased with the temperature. The same was true for Ipa for high scan rate, i.e. log (v 1/2 ) values higher than 0.6. The shape of the variation curve was very similar at both temperatures, i.e. Ip increased more significantly with v at the low scan rate. For example, Ipa obeyed almost a law of the type Ip ∝ v at 500 °C for v < 50 mV.s -1 . As the scan rate increased, Ip deviated from this variation law to tend towards a law of the type Ip ∝ v 1/2 . Typically, at 300 °C, Ip varied almost as Ip ∝ v 1/2 for v > 10 mV.s -1 . This is important to note that this result must be analyzed with caution because the significant ohmic drop at high scan rate may result in a change in the voltammetry response curve. Indeed, lower peak current may be expected due to uncompensated ohmic drop [50]. The peak potentials, ηpc and ηpa, measured at 300 and 500 °C as a function of the scan rate were also studied. As previously discussed, we have determined those points where ohmic drop correction makes sense, which leads only to a small number of experimental points that are not represented. From those few points and taking into account the results of impedance measurements [START_REF] Federico Monaco | Experimental validation of a La0.6Sr0.4Co0.2Fe0.8O3-δ electrode model operated in electrolysis mode: Understanding the reaction pathway under anodic polarization[END_REF], we can tentatively propose that ηp did not vary with the scan rate. Indeed, this is consistent with a fast oxygen ion transfer kinetics at the LSCF/GDC interface as evidenced by impedance spectroscopy [START_REF] Federico Monaco | Experimental validation of a La0.6Sr0.4Co0.2Fe0.8O3-δ electrode model operated in electrolysis mode: Understanding the reaction pathway under anodic polarization[END_REF][START_REF] Nielsen | Impedance of porous IT-SOFC LSCF:CGO composite cathodes[END_REF][START_REF] Hubert | Role of microstructure on electrode operating mechanisms for mixed ionic electronic conductors: From synchrotron-based 3D reconstruction to electrochemical modeling[END_REF]. ηpa was slightly larger than ηpc but located within the same potential range as expected for an intercalation reaction controlled by masstransport [START_REF] Vassiliev | Kinetic analysis of lithium intercalating systems: Cyclic voltammetry[END_REF]. The values of ηpa and ηpc were around -0.35 V / at 300°C and -0.2 V / at 500°C, respectively. As shown in our previous work on the Co-rich LSCF [START_REF] Siebert | Electrochemical and Raman study of La0.7Sr0.3Co0.8Fe0.2O3-δ reduction[END_REF], this result confirms that the peak potential was found to increase with the temperature in agreement with the thermodynamic behavior of LSCF [START_REF] Kuhn | Oxygen nonstoichiometry and thermo-chemical stability of perovskite-type La0.6Sr0.4Co1-yFeyO 3-δ (y = 0, 0.2, 0.4, 0.5, 0.6, 0.8, 1) materials[END_REF].

Role of the oxygen partial pressure

The effect of the oxygen partial pressure was investigated on the porous sample by varying pO2 from 0.21 to 1.8×10 -4 atm. Fig. 8a illustrates the cyclic voltammograms obtained at 500 °C under 1.8×10 -4 atm. Cathodic and reverse anodic peaks were observed similarly to the dense film in air.

However, the shape of the voltammogram was more complex and found to vary with the temperature and the scan rate. For temperature lower than 450 °C, only one cathodic peak was observed whatever the scan rate in the range of 0.5 to 80 mV.s -1 . In the temperature range 450°C≤ -≤ 600°1, two cathodic peaks could be evidenced. Those peaks were mainly visible at low scan rate as shown in the zoom on Fig. 8a. Double cathodic peaks were also observed by Kournoutis et al. [START_REF] Kournoutis | Cyclic voltammetry characterization of a La0.8Sr 0.2Co0.2Fe0.8O3 -δ electrode interfaced to CGO/YSZ[END_REF] under low oxygen partial pressure at high temperature. At high scan rate, double peaks were hard to identify. However, the cathodic peak exhibited a "complex" shape, different from that obtained for the dense thin film under pO2 = 0.21 atm. Moreover, the backward anodic peak was always much lower than the forward "complex" cathodic peak. Indeed, the surface area of the anodic peak was approximately 3 to 4 time lower than that of the cathodic peak. At high temperature (T > 600°C), the peaks were not so well defined. Typically, only one large scan rate dependent plateau was observed at 700°C during the forward scan, with a large hysteresis during the reverse scan. The origin of the complex shape of the voltammograms at high temperature is still an open question. Different explanations may be tentatively proposed such as : (i) reversible structural phase transition in LSCF as proposed in [START_REF] Siebert | Electrochemical and Raman study of La0.7Sr0.3Co0.8Fe0.2O3-δ reduction[END_REF] for the Co-rich compound, (ii) additional peak due to reduction of oxygen adsorbed species.

Fig. 8b shows the Rs vs E curves at different temperatures. Similarly to the dense thin film under air, Rs was found to increase under high cathodic polarization. The higher the temperature, the lower the cathodic polarization necessary to observe Rs enhancement was. In particular at 500 °C, Rs increase was observed even for small cathodic polarization under pO2 = 1.8×10 -4 atm. As already stated, the points above 600°C are not shown in this figure, due to the lack of accurate measurement, which can be seen on the anodic part of the Rs vs E curve at 550°C. However, despite this dispersion, the results obtained at 700°C allowed us to confirm that Rs increase was observed even for small cathodic polarization under pO2 = 1.8×10 -4 atm. In the same way as for the dense film, the overpotential threshold at which Rs was found to increase was calculated. The values obtained were very similar to those obtained with the dense film since we found -0.25 V / and -0.13 V / at 300 and 500°C, respectively. This good agreement between the two data sets could be an indication that the threshold would be rather fixed by the thermodynamic properties of LSCF.

In order, to confirm this interpretation, it would be interesting to examine the effect of changing PO2 on Rs for the dense film.

The peak currents, Ip (or peak current density, jp) and peak potentials variation as a function of the scan rate were studied at 300 and 500 °C (Fig. 9a and9b), for a fixed pO2 of 1.8×10 -4 atm. Ipc and Ipa, were found to increase with the scan rate. At high temperature, the variation law roughly followed the classical Ip ∝ v 1/2 relationship for a semi-infinite linear diffusion as the scan rate increased while it was obtained in all the investigated scan rate range, at 300°C. Indeed, the small deviation at high scan rate observed for Ipa as well as the decreasing observed for Ipc could be attributed to the ohmic drop effect [50]. The absolute value of Ipc was always higher than that of Ipa, which could be in agreement with the highest cathodic peak surface area. This was evidenced at 300 °C. Unfortunately, Ipa was difficult to be extracted from voltammograms at 500 °C, except for 3 mV.s -1 for which jpc = -2.3×10 -3 A.cm -² and jpa = 9×10 -4 A.cm -², which confirms the above interpretation. As explained from the results in Figure 6, it is likely that the peak potential does not vary with the sweep rate in the whole studied temperature range, since the small increase in potential is not significant. The points reported in Fig. 9b allow us to confirm this interpretation.

This result could be in agreement with fast ion transfer at the GDC/LSCF interface as already discussed for the dense film. Anodic peak potential, ηpa, was greater than ηpc at 300 °C. The potentials of anodic and cathodic peaks increased with the temperature as already stated.

Fig. 10 compares the polarization curves of the porous film at 500 °C, under pO2 = 0.21 and pO2 = 1.8×10 -4 atm. A few points corresponding to the dc response of the dense film under pO2 = 0.21 atm at 500°C are also indicated. As expected, the steady-state current on the porous film at low pO2 was lower than at high pO2 under cathodic polarization. A limiting current was evidenced whose origin is still an open question. Under anodic polarization, the polarization curve was less sensitive on the oxygen partial pressure. As stated in [START_REF] Federico Monaco | Experimental validation of a La0.6Sr0.4Co0.2Fe0.8O3-δ electrode model operated in electrolysis mode: Understanding the reaction pathway under anodic polarization[END_REF], it was mainly attributed to oxygen evolution by the surface path mechanism. At low pO2, the low value of oxygen reduction rate enabled the peak current due to oxygen transport within LSCF under transient condition to be evidenced on the cyclic voltammetry. A low dc cathodic current was also measured with the thin film under pO2 = 0.21 atm. In that case, it was mainly related to the low specific surface area of the LSCF electrode as shown in Table 1.

Discussion

At this stage, the theoretical laws describing the voltammetry response of the oxygen electrode reaction as a function of microstructure in a MIEC have not been established yet. We will, therefore, limit the discussion to a qualitative analysis of the results, based on the theoretical laws established in solution electrochemistry. Indeed, from a formal point of view, it can be suggested that the LSCF/GDC electrode behaves like an oxygen intercalation compound in which oxygen can exchange with the gas phase by a chemical reaction, unlike the insertion compound for which the inserted species is stored only. For those reasons, we will use the theoretical treatments established for the insertion reaction [START_REF] Diard | Cinetique électrochimique[END_REF] and the EC type reactions (electrochemical reaction followed by a chemical reaction) [START_REF] Bard | Electrochemical Methods: Fundamentals and Applications[END_REF].

Assignment of peaks

Peaks on the voltammograms can be attributed to de-insertion (cathodic peak) and insertion (anodic peak) of oxygen into LSCF. In terms of defect chemistry, this corresponds to oxygen vacancy transfer at the GDC/LSCF interface and transport by diffusion within LSCF according to the reaction:

O 3 ! LSCF + V 3 •• GDC ↔ O 3 ! GDC + V 3 •• LSCF (4)
In Eq. ( 4), the creation of oxygen vacancies within LSCF according to the forward reaction is responsible for the cathodic peak while the anodic peak may be related to their disappearing by the backward reaction. It is worth underlying that reaction (4) corresponds to an electrochemical reaction as described in [START_REF] Adler | Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes[END_REF][START_REF] Laurencin | Reactive Mechanisms of LSCF Single-Phase and LSCF-CGO Composite Electrodes Operated in Anodic and Cathodic Polarisations[END_REF].

In LSCF, it is assumed that there is no barrier for electron transfer [START_REF] Adler | Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes[END_REF][START_REF] Baumann | Impedance spectroscopic study on welldefined (La,Sr)(Co,Fe)O3-δ model electrodes[END_REF][START_REF] Kawada | Determination of Oxygen Vacancy Concentration in a Thin Film of La0.6Sr0.4CoO3-δ by an Electrochemical Method[END_REF][START_REF] Laurencin | Reactive Mechanisms of LSCF Single-Phase and LSCF-CGO Composite Electrodes Operated in Anodic and Cathodic Polarisations[END_REF].

Consequently, the shape of the voltammograms depends on the kinetics of ion transfer and the ion transport rate only. From the ηp variation as a function of the scan rate observed in the present work and according to impedance measurements reported in [START_REF] Federico Monaco | Experimental validation of a La0.6Sr0.4Co0.2Fe0.8O3-δ electrode model operated in electrolysis mode: Understanding the reaction pathway under anodic polarization[END_REF], the kinetics of oxygen ion transfer at the LSCF/GDC interface can be considered as fast so that the electrode potential can be related to the oxygen vacancy ion concentration within LSCF, or oxygen non-stoichiometry, δ, by the socalled insertion isotherm [START_REF] Diard | Cinetique électrochimique[END_REF][START_REF] Vassiliev | Kinetic analysis of lithium intercalating systems: Cyclic voltammetry[END_REF] or η vs δ curve. According to Nernst's equation, the reversible electrode potential, η, can be translated (formally) into an oxygen partial pressure [START_REF] Van Herle | Electrochemical characterisation of oxygen nonstoichiometry and transport in mixed conducting oxidesApplication to La0.4Ba0.6Fe0.8Co0.2O3-δ[END_REF][START_REF] Baumann | Impedance spectroscopic study on welldefined (La,Sr)(Co,Fe)O3-δ model electrodes[END_REF]. The insertion isotherm is therefore equivalent to the non-stoichiometry curve, δ vs ln pO2, which is fixed by the defect chemistry in the material [START_REF] Hashimoto | Oxygen nonstoichiometry and thermo-chemical stability of La 0.6Sr0.4Co1-yFeyO 3-δ (y = 0.2[END_REF][START_REF] Kuhn | Oxygen nonstoichiometry and thermo-chemical stability of perovskite-type La0.6Sr0.4Co1-yFeyO 3-δ (y = 0, 0.2, 0.4, 0.5, 0.6, 0.8, 1) materials[END_REF]. Consequently, the current responsible for the peak on the voltammetric response, Icv, may be related to the change in oxygen stoichiometry (or oxygen storage capability) according to the relationship [START_REF] Van Herle | Electrochemical characterisation of oxygen nonstoichiometry and transport in mixed conducting oxidesApplication to La0.4Ba0.6Fe0.8Co0.2O3-δ[END_REF][START_REF] Diard | Cinetique électrochimique[END_REF][START_REF] Vassiliev | Kinetic analysis of lithium intercalating systems: Cyclic voltammetry[END_REF]:

I <= ∝ dδ dη = dδ d lnpO A (5)
From an electrical point of view, it is equivalent to a "capacitive" current, which can be related to the so-called "chemical" capacitance, Cchem, determined by impedance spectroscopy. This phenomenon describes the capability of the sample to store chemical energy [START_REF] Baumann | Impedance spectroscopic study on welldefined (La,Sr)(Co,Fe)O3-δ model electrodes[END_REF][START_REF] Kawada | Determination of Oxygen Vacancy Concentration in a Thin Film of La0.6Sr0.4CoO3-δ by an Electrochemical Method[END_REF][START_REF] Jamnik | A powerful electrical network model for the impedance of mixed conductors[END_REF]. It can be noticed that under thermodynamic control (fast diffusion kinetics) [START_REF] Van Herle | Electrochemical characterisation of oxygen nonstoichiometry and transport in mixed conducting oxidesApplication to La0.4Ba0.6Fe0.8Co0.2O3-δ[END_REF][START_REF] Vassiliev | Kinetic analysis of lithium intercalating systems: Cyclic voltammetry[END_REF], the peak current Ip corresponds to the inflection point on the δ vs ln pO2 curve (i.e. maximum of dδ d lnpO A B

). From a more general point of view, the theoretical response by linear sweep voltammetry of electrochemical insertion reaction is determined from mass-transfer equations, depending on the mass-transfer boundary conditions, using the transfer functions as described in [START_REF] Berthier | Numerical solution of coupled systems of ordinary and partial differential equations. Application to the study of electrochemical insertion reactions by linear sweep voltammetry[END_REF].

In LSCF, the insertion reaction ( 4) is coupled to chemical oxygen exchange reaction at the gas/LSCF interface according to:

V 3 •• LSCF + 1 2 O A + 2e E ↔ O 3 ! LSCF (6)
Reaction ( 6) involves a change of the oxidation state but corresponds to a simple chemical reaction as discussed in [START_REF] Adler | Electrode Kinetics of Porous Mixed-Conducting Oxygen Electrodes[END_REF][START_REF] Laurencin | Reactive Mechanisms of LSCF Single-Phase and LSCF-CGO Composite Electrodes Operated in Anodic and Cathodic Polarisations[END_REF]. This chemical reaction may modify the shape of the voltammograms in the same way as for an EC reaction [START_REF] Bard | Electrochemical Methods: Fundamentals and Applications[END_REF][START_REF] Girault | Electrochimie physique et Analytique[END_REF]. According to this interpretation, the main parameter determining the shape of the voltammograms is likely to be the chemical reaction rate, which is directly related to (i) a global surface exchange rate constant, k, depending on the chemistry of the material as defined in [START_REF] Maier | On the correlation of macroscopic and microscopic rate constants in solid state chemistry[END_REF], (ii) the oxygen partial pressure, pO2 [START_REF] Li | Surface Exchange and Bulk Diffusivity of LSCF as SOFC Cathode: Electrical Conductivity Relaxation and Isotope Exchange Characterizations[END_REF] and (iii) the LSCF specific surface area, SMIEC/gas, which is fixed by the electrode microstructure [START_REF] Hubert | Role of microstructure on electrode operating mechanisms for mixed ionic electronic conductors: From synchrotron-based 3D reconstruction to electrochemical modeling[END_REF].

Dependence on the microstructure

We have demonstrated that the shape of the voltammetry response was highly dependent on the LSCF microstructure. From our experimental results, we can suggest that the microstructural parameter, which is likely playing a key role, is the LSCF specific surface area, SMIEC/gas.

According to Eq. ( 1) combined with the f0 values reported in Table 1, SMIEC/gas can be suggested to be greatly higher for the porous film.

High SMIEC/gas

Thanks to the high specific surface area, the oxygen exchange at the LSCF/gas interface (chemical reaction ( 6)) is very fast. Under this condition, the extent or penetration depth of the reaction in the electrode must be limited. Both phenomena lead to mitigate the transient accumulation/depletion of oxygen in material. As a consequence, the "hysteresis" or intensity of anodic and cathodic peaks in the voltammogram is very limited for high specific surface area as observed for the SP electrode. Consequently, the voltammetry curve tends towards the polarization curve and the series resistance, Rs, does not vary as a function of the applied potential, as observed experimentally for the LSCF porous film with a fine microstructure under high pO2.

Low SMIEC/gas

At the opposite, the rate of oxygen exchange at the LSCF/gas interface is strongly lowered when the specific surface area is decreased. For a given current density, the reaction has to extend in the depth of the electrode. In these conditions the material is able to store or release oxygen under transient conditions. The "hysteresis" or intensity of peaks is then enhanced for a low specific surface area. Under those conditions, redox peaks attributed to oxygen mass transport within LSCF can be evidenced. Concomitantly, Rs increases under cathodic polarization due to V 3 •• concentration profile extending within LSCF. Synchrotron X-Ray studies of model LSCF electrode have shown that chemical expansion due to the creation of V * •• inside LSCF was higher for LSCF electrode with low specific surface area [START_REF] Chang | Synchrotron X-ray studies of model SOFC cathodes, part I: Thin film cathodes[END_REF].

It can be noticed that a limiting case, corresponding to no chemical reaction, is the one of an intercalation compound which has been described theoretically [START_REF] Diard | Cinetique électrochimique[END_REF][START_REF] Vassiliev | Kinetic analysis of lithium intercalating systems: Cyclic voltammetry[END_REF]. Under those conditions, the shape of the voltammograms is highly dependent on the electrode thickness and scan rate. For a thin film or a low scan rate, the cathodic and anodic peaks are rather symmetrical and Ip varies with a law of the type Ip ∝ v. It can be related to homogeneous diffusion (or finite length diffusion) and thermodynamic reaction rate control, similar to adsorption reaction [START_REF] Diard | Cinetique électrochimique[END_REF]. For a thick film or high scan rate, the situation is equivalent to the classical response of a fast redox system with a kinetics governed by semi-infinite diffusion, like in solution electrochemistry [START_REF] Bard | Electrochemical Methods: Fundamentals and Applications[END_REF][START_REF] Diard | Cinetique électrochimique[END_REF]. It is characterized by a variation of Ip according to Ip ∝ v 1/2 . In both cases, Epc and Epa are independent of the scan rate.

This behavior could correspond to that observed experimentally for the dense thin film under air. In conclusion, although LSCF cannot be strictly considered as an insertion compound due to the fact that the oxygen intercalation process is coupled with chemical oxygen exchange with the gas phase, it can be tentatively proposed that a transition from homogeneous diffusion of oxygen ions to semiinfinite diffusion is evidenced in the dense LSCF thin film under air. This transition shifts to higher scan rate as the temperature increases due to increasing the oxygen diffusion coefficient with the temperature.

Medium SMIEC/gas

For intermediate specific surface areas, the shape of the voltammograms is expected to be a combination of both limiting situations depicted previously, i.e. steady-state current and redox peak superimposed as shown in EC mechanism [START_REF] Bard | Electrochemical Methods: Fundamentals and Applications[END_REF]. For example, the voltammetry response could not correspond to the polarization curve without clearly evidencing the redox peaks. This situation could be the one encountered in the work of Kournoutis et al. [START_REF] Kournoutis | Cyclic voltammetry characterization of a La0.8Sr 0.2Co0.2Fe0.8O3 -δ electrode interfaced to CGO/YSZ[END_REF] for the response of porous La0.8Sr0.2Co0..2Fe0.8O3-δ under air. Indeed, in this work, the oxygen exchange rate at the gas/MIEC interface is expected to be in between both limiting cases described above, due to the likely less important specific surface area (higher sintering temperature) in addition to lowest Sr content. This intermediate oxygen exchange rate could lead to small variation of Rs with the dc cathodic potential and negligible peak currents. The small variation of Rs could be at the origin of the inverse hysteresis phenomenon observed in their work [START_REF] Kournoutis | Cyclic voltammetry characterization of a La0.8Sr 0.2Co0.2Fe0.8O3 -δ electrode interfaced to CGO/YSZ[END_REF] and in an old work of one of the authors on LSM [START_REF] Hammouche | Electrocatalytique properties and nonstoichiometry of the high temperature air electrode[END_REF].

In order to confirm this assumption, we have tested a porous thick sample with a columnar microstructure. The film was 34 μm thick, consisting of columns with a large amount of nanostructured porosity, with approximately 1 μm gaps visible throughout the surface as shown in Fig. 3 (e) and (f). In this sample, the LSCF specific surface area corresponded mainly to the surface area of the column walls as well as some open nanoporosity inside the columns. Therefore, it was expected to be lower than that of the porous SP LSCF film. The specific surface area variation was roughly estimated from the f0 frequency shift given in Table 1. We found that the specific surface area for the columnar film was almost 13 times lower than that of the porous film. The voltammogram and Rs vs E curve measured at 300 °C under pO2 = 0.21 atm for the columnar film are represented in Fig. 11a and 11b, respectively. Rs was found to slightly increase with the dc cathodic bias, probably because of a poor vacancies extension in the MIEC. It is worth noting that Rs was more important than that corresponding to the GDC electrolyte resistance. This could be attributed to in-plane resistance of the columnar microstructure, leading to constriction within LSCF. The reverse hysteresis was evidenced on the voltammograms. This phenomenon could be tentatively related to small Rs variation. Indeed, during the forward scan Rs increases with the cathodic polarization. Then, the E(j) curve shifted to the left although the opposite might occur during the reverse scan, with an E(j) curve shift to the right. For instance, the variation of Rs, ΔRs, estimated from the shift on the right at j = -2.0×10 -3 A.cm -2 was equal to 10.7 Ω.cm -2 , which is compatible with the variation of Rs in Fig. 11b. This phenomenon could be tentatively proposed as being at the origin of the reverse hysteresis.

Dependence on pO2

The experimental results obtained on the 10 µm porous LSCF layer have demonstrated that by decreasing pO2 from 0.21 to 1.8×10 -4 , the shape of the voltammograms changes from the polarization curve to an E(j) transient response, corresponding to a fast redox system with a kinetics limited by semi-infinite linear diffusion (Ep = constant and Ip ∝ v 1/2 ) coupled with a chemical reaction leading to the steady-rate current [START_REF] Bard | Electrochemical Methods: Fundamentals and Applications[END_REF][START_REF] Girault | Electrochimie physique et Analytique[END_REF]. Here again, it can be explained in terms of slow kinetics of reaction [START_REF] Baqué | High performance nanostructured IT-SOFC cathodes prepared by novel chemical method[END_REF]. Indeed, decreasing pO2 leads to decrease the rate of oxygen adsorption and incorporation in LSCF. This allows highest penetration of V 3 •• inside LSCF. Consequently, redox peaks related to V 3 •• diffusion are observed and concomitantly Rs increases as the applied potential becomes more negative. This result is in agreement with in-situ high-temperature XRD experiment performed by Kivi et al. [START_REF] Kivi | Oxygen Stoichiometry in La0.6Sr0.4CoO3-δ and La0.6Sr0.4Co0.2Fe0.8O3-δ Cathodes under Applied Potential as a Function of Temperature and Oxygen Partial Pressure, Measured by Electrochemical in Situ High-Temperature XRD Method[END_REF], which shows that pO2 has a noticeable and reversible influence on the crystallographic cell volume increase under polarization. The return peak is expected to highly depend on the value of k. The higher the value of the surface exchange rate k, the lower the surface area of the return peak. This is in agreement with our experimental results (see Fig. 9), which show that Ipa was always lower than Ipc.

Limitation of voltammetry

One of the interests of voltammetry is that it allows studying a material in a large potential and time-scale domain. However, a major problem with this technique is the ohmic drop. Indeed, uncompensated ohmic resistance introduces an additional term in the expression for the applied potential (see Eq. ( 2)), which results in a distortion of the voltammograms [50]. Most of the electrochemical apparatus enable iR compensation. However, this correction is possible only if Rs is a constant.

In the present work, we have evidenced that Rs may vary with the applied cathodic potential for the LSCF/GDC electrode. It results that iR drop compensation may be almost impossible to be achieved properly. So, the conditions assumed in the theoretical analysis would be difficult to be met in practice thus complicating quantitative analysis. With a small amplitude signal, the electrode behavior is nearly linear, so electrode impedance measurements should provide correct value of Rs for every electrode potential.

Conclusion

The electrode microstructure plays a key role on the shape of the voltammograms of the LSCF/GDC electrode under air at a high temperature as well as on the high-frequency series resistance, Rs, variation with the dc potential.

For a porous film with a fine microstructure, the voltammograms were identical to the polarization curve and Rs did not vary with the applied potential. Those results were interpreted in terms of high LSCF specific surface area, leading to fast kinetics of the oxygen exchange chemical reaction at the LSCF/gas interface. This situation was proposed to correspond to that of an EC mechanism with a fast chemical reaction rate.

For a LSCF film with a low specific surface area (dense LSCF), the voltammograms were found to be almost similar to those of an intercalation compound with symmetrical cathodic and anodic peaks. Concomitantly, Rs was found to increase under cathodic dc bias. Those results were attributed to oxygen stoichiometry change within LSCF, due to oxygen vacancy transfer at the LSCF/GDC interface and transport by diffusion within LSCF, followed by a slow oxygen chemical exchange rate at the LSCF/gas interface.

The oxygen partial pressure greatly affects the voltammetry response. Here again, the results were interpreted in terms of the oxygen chemical exchange rate at the LSCF/gas interface, which decreases as pO2 decreases.

The limitation of the voltammetry for the study of the LSCF/GDC electrode due to possible Rs variation was highlighted. This phenomenon could be tentatively proposed as being at the origin of the reverse hysteresis observed sometimes on the voltammetry response. (a) Cyclic voltammetry (pre-treatment 0.1 V for 600 s, T = 407 °C). (b) Rs dependence on applied dc potential (E) for different temperatures. For comparison Rs GDC calculated from Steele's data [START_REF] Steele | Appraisal of Ce 1-y Gd y O 2-y / 2 electrolytes for IT-SOFC operation at 500C[END_REF] at the same temperatures is represented by the dashed lines. .

Fig. 3c and

  Fig.3c and 3dgive the surface and cross-sectional SEM images of the dense LSCF layer prepared

Figure 1 Fig. 1 .

 11 Figure 1 Fig.1. Description of the three-electrode set-up. Cell dimensions and nature of the electrodes for

Figure 2 Fig. 2 .

 22 Figure 2

Figure 3 Fig. 3 .Figure 4 Fig. 4 .

 3344 Figure 3

Figure 5 Fig. 5 .

 55 Figure 5

Figure 6 Fig. 6 .

 66 Figure 6Fig. 6. (a) Peak current and peak potential determination mode. (b) Peak potential, ηp, determined

Figure 7 Fig. 7 .

 77 Figure 7

Figure 8 Fig. 8 .

 88 Figure 8Fig.8. Typical electrochemical measurements for the porous LSCF electrode under pO2 = 1.8×10-4

Figure 9 Fig. 9 .

 99 Figure 9 Fig. 9. Variation of the voltammetry parameters as a function of the scan rate for the porous film under pO2 = 1.8×10 -4 atm. (a) jpc (filled symbol) and jpa (empty symbol) at 300 °C (green) and jpc at

Figure 10 Fig. 10 .

 1010 Figure 10Fig. 10. Comparison of the polarization curves of the porous thick film (blue) under pO2 = 0.21 atm (empty symbol) and pO2 = 1.8×10 -4 atm (filled symbol) at 500 °C. A few points corresponding to

Figure 11 Fig. 11 .

 1111 Figure 11

Table 1 f0

 1

		f0, Hz	Diagram Shape Porosity, %	Particle size, μm	Pore size, μm
	Porous	26 ± 3	Ge	43±2	0.09	0.09
	Dense	<10 -1	FLGe	N/A	N/A	N/A
	Columnar	2	Ge	-	-	-

and diagram shape (Ge = Gerischer-type, FLGe = finite-length-Gerischer-type) measured at T = 500°C and PO2 = 0.21 atm for the different films tested in the present work. Microstructure parameters determined from image analysis on the porous sample.

Acknowledgements

This work was financially supported by the Institute of Engineering Univ. Grenoble Alpes (AGIR-POLE 2016). The authors would like to thank Dr C. Montella (LEPMI, Univ. Grenoble Alpes) for fruitful discussions on electrochemical kinetics and Dr F. Charlot (CMTC, Univ.

Grenoble Alpes) for making the SEM observations.


A Ribet

J-G Mattei

I Monnet

C Grygiel
email: grygiel@ganil.fr

Damage depth profile in α-Al2O3 induced by swift heavy ions

Keywords: Al2O3, ion irradiation, XRD, damage profile

diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The aluminium oxide α-Al2O3 has been studied a lot since some years as well in polycrystals as in single crystals and under different ion energy conditions (inelastic or elastic ranges) [1][2][3]. Under swift heavy ion (SHI) irradiation, Al2O3 behavior is a bit different compared to other insulators as it is intermediary between an amorphizable and a non-amorphizable material. Above a threshold in terms of electronic stopping power (Seth ~ 10 keV/nm), Al2O3 exhibits discontinuous tracks and amorphization after track overlap by the surface and at high fluence [4][5][6]. In polycrystals it was indeed previously reported that along the ion path, first an amorphous layer is observed beneath the surface, then an intermediary damaged layer, and finally very deep a free-defect region [6,7]. Grazing incidence X-Ray diffraction (GI-XRD) has shown on these pellets that the crystalline phase exhibits sensitivity to SHI by the formation of long range and short range strains and domain size decrease for example. However GI-XRD provides only average information on the diffracting grains, and in order to get a precise view of damage depth profile, high resolution XRD (HR-XRD) has been performed on Al2O3 single crystals irradiated by SHI. In contrast to previous studies using the XRD on single crystals by measuring only the out-of-plane reflection [8,9], the idea of the current paper is to show how the structural properties of sapphire are affected by measuring six different crystallographic directions. In this way, we aim to suggest how the damaging occurs along the ion path in the case of SHI by establishing a strain profile. A particular care is also to look at if strain relaxation will take place along the ten of micrometers of the ion path.

Experimental

Sapphire single crystal samples ((0001)-orientation, 500 µm thick) are irradiated with 92 MeV Xe 23+ ions at normal incidence and room temperature. Irradiation experiments are performed at IRRSUD beam line of the GANIL accelerator facility (Caen, France). Samples of dimensions 5 mm x 5 mm are irradiated homogeneously by a scanned ion beam. The samples are fixed on the irradiation holder by a conductive carbon tape which is an electrical conductor. The ion flux is kept to a low value (2-5x10 9 ion.cm -2 .s -1 corresponding to less than 2 W) to avoid macroscopic sample heating and the resulting effects. Using the Kinchin and Pease option of SRIM code [START_REF] Ziegler | The Stopping and Range of Ions in Solids[END_REF], the ion energy losses are calculated for 92 MeV 129 Xe in sapphire with theoretical density (4 g/cm 3 ) and displacement energies of 20 eV for Al and 50 eV for O. At this energy, the electronic regime is predominant on most of the ion beam path. At the surface the value of the electronic stopping power Se is 21 keV/nm well above the Se threshold for track formation. The Se value decreases along the ion path until an inversion of energy deposition processes, where nuclear stopping power Sn rises slightly at 7-8 µm near the end of the projected range (Rp=8.4±0.1 µm).

XRD measurements are carried out with a Bruker D8 Discover equipment using a parallel beam geometry with a Göbel mirror for Kα copper radiation source. The diffractometer has an Euler cradle allowing four-circle movements where sample and detector are rotated. 2θ is the diffraction angle between the incident beam and the detector, ω the incident angle between xray source and sample surface, chi the inclination angle (0-90°) between the crystallographic plane and the sample surface, and phi the azimuthal angle (0-360°) or the sample rotation on itself. Moreover, symmetric geometry uses 2θ = 2ω condition while asymmetric uses 2θ ≠ 2ω. Several reflections are recorded with different optics and geometries to study material behavior in many reciprocal space directions. First, triple-axis geometry using a 2-bounce Ge-220 monochromator, an analyser crystal and a scintillation detector enables high resolution symmetric patterns (0006 reflection), symmetric skew patterns (1014, 1123, 2134 reflections, chi≠0 and chi<90°), asymmetric patterns (0118(-)) reflections with (-) meaning "grazing" incident beam, chi=0°) and 2D maps. 2D maps are obtained by taking a series of 2θ_ω patterns (± 0.5° around the reference position) at successive ω values (± 0.5° around the reference position). Sketches of the geometries are seen ref. [START_REF] Moram | [END_REF]. These five reflections allow probing the irradiated material very deep even after the projected range. Table 1 displays the different characteristics of each reflection observed where depth values are measured taking 90% of I/I0 intensity ratio, the material density and a mass attenuation coefficient of 31.5 cm 2 /g. Also using in-plane geometry (chi=90°) with primary slits, equatorial slits (0.1°) and a LYNXEYE detector in 0D, (1120) reflection is recorded with an incident grazing angle of around 0.3° probing sample to 240±40 nm where the Se is the highest. Indeed the analysis of all these reflections allow to observe all damaged area, from the surface up to the projected range, and even deeper where the material remains virgin and non-irradiated. For the 2D map representations, the viewers are DxTools [12] for the reciprocal space or Bruker Diffrac Leptos software for the direct space. Leptos is also used to simulate the XRD patterns including contributions of irradiated material showing a damage profile.

Results and discussion

To get a general view of structural modifications induced in sapphire under 92 MeV Xe, 2D maps are recorded for four reflections at different ion fluences up to high value (1.2x10 15 ions/cm²), Fig. 1 shows these maps in the direct space. The dotted lines on the maps help to observe the contribution of the non-irradiated layer or virgin layer of Al2O3 samples, called the reference peaks. On the virgin sample and for all the reflections, fine and intense reflections are observed with streaks formation due to optics (monochromator and analyzer). It shows the high crystalline quality of the initial virgin sample. When the fluence increases up to 1.2x10 15 ion/cm 2 , a broadening of the reflections is noticed. On ω axis, the broadening means a slight tilt of diffracting domains and a slight increase of mosaicity along the cdirection of ± 0.02° at maximum. Additionally, a large broadening is observed on 2Ө axis with the formation of new contributions at relatively high intensities which are inevitably created by the ion irradiation. These 2Ө reflections are always extended towards low diffraction angles, meaning that tensile strain is induced by irradiation. Such broadening was already mentioned for the (0006) reflection measured with low resolution setups [8,9]. Otherwise the 2D maps show a lower variation of the lattice strains for the (1014), (1123) and (21 3 4) reflections. Moreover next to these large intensities, diffuse signal or scattering appears at higher angles for high fluences, which means compressive disorder and amorphous area formation. Thus high resolution symmetric measurements are performed in the center of each reflection (ie large intensities) to analyze the behaviour under irradiation with more accuracy.

Fig. 2 shows HR patterns for the (0006) reflection for several fluences. At higher angles (around 41.66°), fine reference peaks are clearly observed whatever the level of damage which is consistent with the X-ray absorption in Al2O3 and the depth probed by X-rays (32.5±0.5 µm) well above the Rp (8.4±0.1 µm) implying a huge ratio of non-irradiated matter. In addition, Fig. 2 reveals with a good resolution the aforementioned contributions close to reference peaks shifting towards low 2θ angles as function of the fluence. Furthermore, the HR patterns highlight that the peak corresponding to the maximum tensile strain (at the lowest angle on each pattern) shifts to lower angle or higher strain at each step of the fluence increase. This gap between the reference peak and the peak of maximum strain increases up to a full strain value (0.86±0.10% at 2x10 14 ion/cm 2 ) and thereafter decreases or seems to relax at the highest fluence (1.2x10 15 ion/cm 2 ). Thus, strain according to the c-parameter and parallel to the ion beam increases with fluence and corresponds to lattice expansion in this direction. The evolution of the maximum strain as function of fluence has been fitted by a Poisson law using a sigmoidal function to extract the cross section of the damaged cylinder and the kinetics of the damaging. A single impact kinetics better fits the strain evolution (R²=0.98) for an ion track radius of around 2.4±0.8 nm, whose track radius is consistent with those of amorphization requiring the overlap of at least two tracks [6]. As the amorphization process requires inelastic energy losses above a threshold, the strain formation is also at least partially linked to the electronic process. In addition, as several contributions are observed between the reference and maximum peaks, we consider that a gradient of strain is formed during irradiation and the number of contributions increases as function of the fluence. Oscillations are also noticed at 1.2x10 15 ions/cm 2 meaning interferences due to different diffracting layers certainly in terms of disorder or density, which are not further detailed.

In order to observe if the crystallographic direction perpendicular to ion beam is affected, two others reflections are measured: one in asymmetric configuration the (0118(-)) reflection and one in in-plane configuration the (1120) reflection. Both are benefiting of grazing incidence of the X-Ray beam allowing sensitivity to the full irradiated layer with 24±1 µm probed for (0118(-)) and sensitivity to irradiated surface layer 240±40 nm for the in-plane (1120). Fig. 3 shows 2D maps of the (0118(-)) reflection for the virgin and the 1.2x10 15 ions/cm 2 samples, where Qz value is directly linked for this reflection to c-parameter through the formula Qz=8*2π/c whereas Qx axis is linked to a-parameter with the formula Qx=4π/(a√3). Fine and intense reflection can be observed on the virgin sample with streaks coming from optics. When the fluence increases, several phenomena are noticed: formation of diffuse scattering and on the intense peaks broadening along Qz axis and almost no change on Qx axis (neither width nor position). Moreover, the 2D map at 1.2x10 15 ions/cm 2 shows the same evolution than previously observed: an intense reference peak (with same value of Qx and Qz than the virgin sample), and a strain gradient which extends to a much lower value of Qz (ie around Qz=3.84 or c=13.089 Å) corresponding to the maximum of strain. Even at this high fluence, the 2D map does not evidence besides the diffuse signal any variations of the intense peaks on Qx axis apart from a very small broadening. This highlights that there is almost no parameter variation along the a-axis whereas ion beam effect is well observed along c-axis, at least in the material depth probed during the (0118(-)) measurement. In order to be sensitive to the irradiated layer in surface where mainly inelastic energy is deposited, the (1120) in-plane reflection is measured as function of the irradiation fluence. The evolution of patterns on 2Ө axis is not represented as very few modifications of the peak are observed. However, the Fig. 4 illustrates the strain εa=ai-a0/a0 of the a-parameter extracted from the (1120) position. The uncertainty bars reveal the low resolution of this geometry on the contrary to all previous measurements. Very slight fluctuation around the virgin value is observed even up to high fluence. The highest fluences of 2x10 14 and 1.2x10 15 ions/cm 2 are not represented because the reflections were not measurable, which is consistent with the amorphization from the surface (amorphous depths measured by TEM about 500 nm and 3200 nm respectively). Regarding the intense peaks corresponding to the crystalline α-Al2O3 phase, we then conclude that no evolution of the in-plane lattice parameter is observed in the perpendicular direction to the ion beam. Thus (0001)-Al2O3 single crystals irradiated with SHI (92 MeV Xe) exhibit whatever the location along the 8.4±0.1 µm of ion path only tensile strain parallel to ion beam. Due to the effect of substrate inducing biaxial stress [13], where the substrate in our case is the nonirradiated material present beyond the Rp, no variation of the lattice parameter is observed in the orthogonal direction. Even if substrate effect was already reported for irradiated crystals at low ion energy [14,15], this result at high ion energy was not obvious as a relaxation of biaxial stress could have taken place along the ten micrometers of Rp, which is not the case.

From now, the purpose is to establish a depth profile of disorder induced in sapphire as function of the fluence. Simulations of diffraction patterns are done for irradiated sapphire containing signals from the non-irradiated layer, the maximum strain layer and all contributions of layers with intermediate strains, whose value and thickness vary with ion fluence. Hypotheses on layer location are done to simulate the depth profile as for a layer of given strain and thickness the position of the layer in depth could be slightly exchanged with another layer without significant change of X-Ray pattern. The location of the non-irradiated layer is obviously beyond the projected range. Considering the location of the maximum strain, at the surface or buried deep, we have previously concluded that the strain formation is partially linked to inelastic energy losses which are maximum at the entrance in the material and decrease continuously along the ion path. Indeed, the literature about Al2O3 singlecrystals reports studies done with RBS-C experiments on sapphire irradiated in similar conditions and for which the level of damage increases with fluence and from the surface [8,16]. It is also reported through TEM observations that the amorphous layer, induced by Se deposition, grows by the surface at high fluence with a maximum of damage at its border amorphous/crystalline [6,7,9]. We thus consider that the strain gradient exhibits a maximum level in the layer near the surface, the strain level decreases gradually through a certain number of layer contributions along the ion path down to a level strain free, ie the nonirradiated layer. Using such a stacking of layers with various levels of strain, for the sample irradiated at 2x10 13 ions/cm 2 the (0006) pattern is simulated (insert of Fig. 5) using Leptos and compared to the experimental curve. A good agreement is observed between the two curves. In the simulation several layers are used by adjusting for each of them thickness and c-parameter as detailed Fig. 5 as function of depth. Such simulation is performed for the different fluences. The layer number required for the better adjustment of the simulation increases as function of fluence. The simulations evidence that the c-parameter of the maximum strain layer, located at the surface or at the border amorphous/crystalline, increases as function of the fluence up to a full value about 13.107±0.005 Å at 2x10 14 ions/cm 2 . The maximum c-parameter for 1.2x10 15 ions/cm 2 is lower than for 2x10 13 and 2x10 14 ions/cm 2 due to the amorphization at the surface (where we supposed to be located the full strain), saturation of defects and material relaxation. The shift from the surface (depth=0) corresponds to the amorphous layer whose thickness grows with fluence, where no lattice parameter can be extracted. The Fig. 5 also evidences the progressive decrease of the tensile strain level as function of the depth along the ion path. By summing all the layer thicknesses (amorphous and strained), the damaged depth increases with fluence from around 1600 nm for 5x10 12 ions/cm 2 up to 8450 nm for 1.2x10 15 ions/cm 2 which is in the order of the projected range. This means that the tensile strain or unit-cell swelling induced along the ion path is not only due to electronic stopping power but also nuclear process as modification of lattice parameter is noticed all along the projected range, even if the maximum strain is located where the Se is dominant and Sn low. Swelling in alumina is already reported to be induced by Sn or Se or Sn and Se as in polycrystals where both energy losses contribute to unit-cell swelling [6,[17][18][19]. These results highlight that the evolution of Al2O3 behaviour as function of ion fluence is complex. This is not just a damage accumulation induced by latent tracks as soon as we are above a threshold, but the maximum strain grows with fluence increase, the damaged depth increases as well, and amorphization takes place by the surface. Such depth profiles of structural properties bring in this way new inputs to the understanding of Al2O3 under SHI.

Conclusions

In this work, sapphire single crystals have been irradiated with 92 MeV Xe 23+ ions at different fluences at the GANIL facility. HR and in-plane X-Ray diffraction experiments were performed to analyze the behaviour of α-Al2O3 under ion irradiation. Two signals have been measured: one diffuse observed at high fluence attributed to the radiation induced amorphous phase and one intense for the crystalline phase showing with ion fluence a progressive damaging described in the current study. A tensile strain is measured in the out-of-plane direction, parallel to the ion beam, whereas almost no variations are measured in the orthogonal direction to the ion beam. This highlights the significant effect of the nonirradiated layer, present deeper than the projected range, and still inducing a compressive biaxial stress along the ten of micrometers of ion path. To suggest a damage depth profile, hypotheses using data of RBS-C and TEM have been done to help simulation of X-Ray patterns considering that the layer of maximum strain is located at the amorphous/crystalline border. The profile emphasizes that the maximum strain grows with fluence increase, the damaged depth increases as well, while amorphization takes place by the surface and grows with fluence. It has been discussed that both electronic and nuclear contributions are required for such strain evolution. The characterization method carried out in the current study can be applied in the future to others crystalline systems to get comprehensive overview on structural properties evolution under swift heavy ion irradiation.

Figure captions

Fig. 1 :

 1 Fig.1: 2D maps for four reflections of sapphire irradiated with 92 MeV Xe. 2θ axis is from left to right, ω axis from bottom to top, the same scale is used on all the maps.

Fig. 2 :

 2 Fig. 2: HR-XRD patterns for the (0006) reflection as function of the ion fluences (in Xe/cm²). Patterns are shifted manually and arbitrarily for a better visibility.

Fig. 3 :

 3 Fig. 3: Reciprocal space maps of the reflection (0118(-)) as function of 92 MeV Xe fluence.

Fig. 4 :

 4 Fig. 4: Strain of a-parameter as function of 92 MeV Xe fluence.

Fig. 5 :

 5 Fig.5: c-parameter evolution as function of the depth and ion fluence (Xe/cm²). The shift from the surface (depth=0) corresponds to the amorphous layer whose thickness grows with fluence, where no lattice parameter can be extracted. Insert: HR-XRD and simulated patterns for the (0006) reflection at 2x10 13 ion/cm². The black line is the experimental HR pattern and the red line is the simulation.

TableTable 1 :

 1 Characteristics of measured reflections: Bragg angle (2θ), chi inclination angle and the corresponding probed depth.

Acknowledgements

The experiments were performed at the IRRSUD beamline of the Grand Accélérateur National d'Ions Lourds (GANIL), Caen, France. The authors thank the CIMAP staff, especially T. Madi, the CIRIL platform staff, the GANIL technical staff and the overall administrative staff. The authors would like to thank H. Lebius, E. Balanzat (CIMAP), A. Debelle (CSNSM, France) and A. Boulle (SPCTS, France) for fruitful discussions. This work was partially supported by the ANR funding "Investissements d'avenir" ANR-11-EQPX-0020 and ANR10-LABX-09-01 LabEx EMC3, the FEDER and by the Region Basse-Normandie.