PCCP PAPER. 1 Introduction. A. Nenning,* A. K. Opitz, T. M. Huber and J. Fleig. View Article Online View Journal View Issue

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1 PAPER View Article Online View Journal View Issue Cite this: Phys. Chem. Chem. Phys., 2014, 16, Receive 4th June 2014, Accepte 3r September 2014 DOI: /c4cp02467b 1 Introuction A novel approach for analyzing electrochemical properties of mixe conucting soli oxie fuel cell anoe materials by impeance spectroscopy A. Nenning,* A. K. Opitz, T. M. Huber an J. Fleig Mixe ionic an electronic conucting (MIEC) perovskite-type oxies may be applie in cathoes of intermeiate temperature soli oxie fuel cells (SOFCs) an are wiely investigate as porous or thin film electroes. 1 3 Some of these materials have high chemical stability also uner reucing conitions, which makes them potential caniates for SOFC anoes. Mixe conucting anoes may help solving some problems of the generally employe Ni YSZ composite anoes, such as carbon eposition, sulfur-poisoning an reox cycling stability. 2,4 Several stuies on porous perovskite anoes (e.g. (La 0.75 Sr 0.25 )(Cr 0.5 Mn 0.5 )O 3 (LSCM) 5 7 ), or cermet anoes involving perovskite-type an ceria-base mixe conuctors 6,8,9 were carrie out an partly reveale low area specific resistances. However, the perovskite-type materials were mostly stuie as porous anoes an mechanistic interpretation of the impeance spectra is therefore complicate ue to the complex an illefine geometry (e.g. effective surface area) an current paths. Thin film moel electroes offer well-efine geometry an Institute of Chemical Technologies an Analytics, Vienna University of Technology, Getreiemarkt 9, 1060 Vienna, Austria. anreas.nenning@tuwien.ac.at For application of acceptor-ope mixe conucting oxies as soli oxie fuel cell (SOFC) anoes, high electrochemical surface activity as well as acceptable electronic an ionic conuctivity are crucial. In a reucing atmosphere, particularly the electronic conuctivity of acceptor-ope oxies can become rather low an the resulting complex interplay of electrochemical reactions an charge transport processes makes a mechanistic interpretation of impeance measurements very complicate. In orer to etermine all relevant resistive an capacitive contributions of mixe conucting electroes in a reucing atmosphere, a novel electroe esign an impeance-base analysis technique is therefore introuce. Two interigitating metallic current collectors are place in a microelectroe, which allows in-plane measurements within the electroe as well as electrochemical measurements versus a counter electroe. Equivalent circuit moels for quantifying the spectra of both measurement moes are evelope an applie to simultaneously fit both spectra, using the same parameter set. In this manner, the electronic an ionic conuctivity of the material as well as the area-specific resistance of the surface reaction an the chemical capacitance can be etermine on a single microelectroe in a H 2 H 2 O atmosphere. The applicability of this new tool was emonstrate in SrTi 0.7 Fe 0.3 O 3 (STFO) thin film microelectroes, eposite on single-crystalline yttria-stabilize zirconia (YSZ) substrates. All materials parameters that contribute to the polarization resistance of STFO electroes in a reucing atmosphere coul thus be quantifie. surface area, simple charge transport paths an goo reproucibility, making them a very useful tool for the investigation of funamental reaction mechanisms. This was extensively shown for cathoe materials, but mechanistic electrochemical stuies on mixe conucting thin film anoes are only available for ceria-base materials. 9 Recently, also mechanistic stuies of the anoic surface reaction of ope an unope ceria were performe using ambient pressure XPS When acceptor-ope mixe conuctors are use as SOFC anoes rather than cathoes, not only the surface reaction changes, but also some crucial bulk parameters such as electronic an ionic conuctivity may change by orers of magnitue. Owing to the low chemical potential of oxygen in H 2 H 2 Oatmospheres, especially the electronic p-type conuctivity significantly ecreases. Accoringly, not only the surface reaction an ionic charge transport, but also electronic conuction may be rate limiting in the reucing atmosphere. This further complicates the interpretation of conventional impeance stuies on such anoes, even for thin film electroes. For example, moerate electronic conuctivity (in the orer of 1 S cm 1 ) may lea to meium-frequency features in the impeance spectra for electroes without aitional current collectors, 18 whereas in the case of much lower electronic conuctivity a current collector This journal is the Owner Societies 2014 Phys. Chem. Chem. Phys., 2014, 16,

2 is manatory. In ref. 9, the electronic an ionic conuctivity of ceria films were measure by a metho which however requires the film to be an excellent ionic conuctor an to exhibit an electrolytic conuctivity omain. The relevance of electronic an ionic charge transport in MIEC electroes was also confirme by numerical simulations. 19,20 In this contribution, we introuce a novel approach for an impeance spectroscopic analysis of thin film electroes with significant resistive contributions not only from the surface reaction but also from charge transport processes in the electroe bulk an thus for typical mixe conucting anoe materials. Two interigitating metallic current collectors are place in one thin film microelectroe. This allows an in-plane impeance measurement between these two current collectors as well as a classical measurement versus an extene counter-electroe. In this manner we obtain two complementary impeance spectra on one an the same electroe. For both measurement moes, equivalent circuit moels are evelope. Those can be use for simultaneous fitting of both acquire spectra with the same parameter set. Using this technique, electronic an ionic conuctivity as well as the area specific resistance of the surface reaction an the chemical capacitance can be quantifie on a single microelectroe. This novel metho is emonstrate to be applicable to SrTi 0.7 Fe 0.3 O 3 electroes in a H 2 H 2 O atmosphere. This oxie was alreay investigate as a cathoe material, revealing a highly catalytic surface in an oxygen atmosphere. 21,22 Also mechanistic stuies have been carrie out for the cathoic oxygen reuction, 22,23 but etaile stuies on the performance as a fuel cell anoe an investigation of the electrochemical reactions an efect chemistry in a H 2 H 2 O atmosphere have not been carrie out so far. 2 Experimental etails an measurement moes 2.1 Sample preparation an electroe esign Pulse laser eposition (PLD) was use to prouce ense thin films of SrTi 0.7 Fe 0.3 O 3 (STFO) with a thickness ranging from 103 to 310 nm on single-crystalline yttria-stabilize zirconia (YSZ) with 9.5 mol% Y 2 O 3. The YSZ substrates ha a size of mm 3 an [100] surface orientation. Thin films were eposite at a substrate temperature of C in 0.02 mbar oxygen. The eposition time was varie between 16.6 minutes (3000 pulses) an 50 minutes (9000 pulses) with the laser operating at a pulse energy of 400 mj (at the laser) an a repetition rate of 3 Hz. Prior to the STFO eposition, a microstructure platinum thin film was employe as an electronic current collector (Fig. 1a). For comparison, Pt current collectors were also eposite on top of the STFO layer (Fig. 2b). The platinum layer (100 nm thickness) was sputter eposite an micro-structure by photolithography an ion beam etching. To increase the stability of the Pt films, 5 nm of titanium were employe as an ahesion layer. SEM imaging inicate ense an flat films of STFO grown on YSZ an on platinum (see Fig. 2b). y 2y iffraction patterns measure on a Bruker D8 GADDS inicate single phase, [110] oriente thin films grown on YSZ (see Fig. 2b). Fig. 1 Schematic cross-section of an electroe with a current collector beneath (a) an on top (b) of the MIEC film. Optical microscope picture of an electroe use in this stuy (c). Fig. 2 SEM image of the STFO surface (a); top: film grown on YSZ, bottom: film grown on Pt. Diffraction pattern of the film (b). Other orientations were not observe. Breaking ege images of the film inicate a thickness of nm for the film eposite with 9000 pulses (0.034 nmperpulse).aftereposition of the STFO films an current collectors, rectangular microelectroes with a size of mm 2 were prouce by means of photolithography an ion beam etching. The geometry of the electroe an current collectors is isplaye in Fig. 3, an a microscopic picture is given in Fig. 1c. Three ifferent geometries for the current collectors with varying finger istance were use on the same substrate an the exact measures are given in Table Contacting moes an impeance measurements The two current collectors in each microelectroe reuce the impact of the electronic sheet resistance. Nevertheless, the resistances cause by charge transport processes may still be Phys. Chem. Chem. Phys., 2014, 16, This journal is the Owner Societies 2014

3 Fig. 3 Top view (a, c) an cross-section (b, ) of the two measurement moes. In the in-plane moe (a, b) the voltage is applie between the two metal finger structures. In the electrochemical moe (c, ), both current collectors are treate as one electrical terminal an measure against a macroscopic counter-electroe. Table 1 Dimensions of the electroes an current collectors. The meaner length an effective circumference are as shown in Fig. 3a No. of metal fingers Finger istance (2l) (mm) Finger with (2b) (mm) Meaner length (mm) Effective circumference (mm) MIEC imensions (mm 2 ) relevant compare to the resistance of the surface reaction (epening on the exact geometry, temperature an atmospheric conitions). In orer to separate resistive contributions of transport processes from those of the surface reaction, each microelectroe contains two interigitating Pt current collectors. By two ifferent contact configurations two measurement moes can be realize. This is isplaye in Fig. 3 in top view an cross section. In the in-plane measurement (Fig. 3a an b), the impeance is measure between the two metal finger structures. In the electrochemical moe (Fig. 3c an ) both current collectors are electrically treate as one terminal. The impeance is then measure against the macroscopic counter electroe of the same material, also containing a Pt current collector. This is the measurement moe which is usually applie for electrochemical characterization of microelectroes. Owing to the much larger counter electroe, the impeance in the electrochemical moe is almost entirely etermine by the microelectroe an the electrolyte. 10 These two measurement moes on one an the same electroe are the basis of the present stuy. In the following we erive equivalent circuits escribing the corresponing impeance measurements an explain why fitting of both moes enables the simultaneous etermination of all relevant resistive an capacitive materials parameters of the system, i.e. ionic conuctivity, electronic conuctivity, area-specific resistance of the surface reaction an interfacial resistance as well as the chemical capacitance. The STFO electroes were investigate using this novel technique in a H 2 H 2 O atmosphere an consistency of the analysis was confirme by geometry variations (see Section 4). Piezoelectric high-precision actuators (Newport Agilis) were employe to contact the current collectors in the electroes via gol-plate steel tips with a tip raius of 1 3 mm. Details of the measurement stage are given in ref. 24. The impeance spectra were acquire using a Novocontrol Alpha-A High Performance Frequency Analyser, equippe with a Novocontrol POT/GAL 30 V/2 A interface, in the frequency range of 0.01 Hz to 1 MHz at an AC amplitue of 10 mv RMS. The measurements were carrie out at temperatures between 490 an 800 1C in an atmosphere of 2.5% H 2 an about 2.5% H 2 O vapor in argon as a carrier gas. 3 Equivalent circuit moels for thin film electroes with current collectors 3.1 Transmission line circuit moel for transport losses in thin film electroes For a meaningful interpretation of the impeance measurements in both measurement moes, a thorough iscussion of the polarization an charge transport processes within mixe conucting thin film electroes with current collectors is require. In Fig. 4, the possible reaction paths for anoic current flow are shown. In a H 2 H 2 O atmosphere, the main resistive contributions aretypicallythehyrogenoxiationonthesurfaceofthemiec layer as well as electronic an ionic in-plane charge transport within the thin film. Aitionally, also a spreaing resistance in the electrolyte an an ionic interface resistance at the electrolyte MIECinterfacehavetobeconsiere;theseturneouttobe comparatively small in the case of STFO. This journal is the Owner Societies 2014 Phys. Chem. Chem. Phys., 2014, 16,

4 Fig. 4 Processes relevant for the impeance of a MIEC anoe with metal fingers below the anoe (left) an on top (right). Arrows inicate anoic current, although impeance spectroscopy probes both irections. Fig. 5 Equivalent circuit for MIEC electroes with high electronic an ionic conuctivity, accoring to ref. 12 an 25. As a starting point, the impeance response of MIEC electroes with very high electronic an ionic conuctivity an rate limiting surface kinetics will be iscusse. For such electroes, all ionic an electronic in-plane an across-plane charge transport processes are without resistance. Accoring to ref. 12 an 25 the equivalent circuit consists of a resistive offset cause by the electrolyte (R YSZ )anan electroe part containing the resistance relate to the surface reaction (R surface ) in parallel with the chemical capacitance of the MIEC bulk (C chem ). If the ionic transport across the electroe YSZ interface causes an aitional resistive contribution, an interfacial resistance an capacitance (R int an C int ) have to be ae, as epicte in Fig. 5. Also in cases where in-plane charge transport losses become relevant, this circuit will play a central role. As a next step we consier a thin film electroe with moerate or low electronic an ionic conuctivity. It was shown by Jamnik an Maier that for one-imensional systems the impeance of the MIEC bulk is escribe by a transmission line circuit. 25 In our case, one-imensionality is not given since in-plane as well as across-plane currents are important. However, still the concept of a transmission line, reflecting the electrochemical potentials an the transport of electrons an oxygen ions, is applicable. This is shown in the following. The geometry of our thin film electroes (Fig. 3) is characterize by a very large ratio between film thickness ( nm) an lateral finger istance or with (5 25 mm), i.e. an aspect ratio in the orer of 1 : 100. Moreover, the MIEC film is either in electric contact with an excellent electron conuctor (current collector) or a fast ion conuctor (YSZ). The combination of these two facts allows us to efine a fast an a slow carrier. Those are not istinguishe by their specific conuctivities in the MIEC. Rather, the fast carrier can easily move either in the current collector (electrons) or in the electrolyte (ions) an therefore its electrochemical potential is laterally homogeneous in the fast phase. Hence, only across-plane transport of this fast carrier has to be consiere in the MIEC. On the other han, for the slow carrier in-plane istances are much larger than across-plane istances an therefore only in-plane variations of its electrochemical potential in the MIEC are relevant. Owing to this lateral variation, the riving force for oxygen exchange (an stoichiometric polarization) becomes inhomogeneous along the electroe. This can be quantifie by a local polarization potential (Z*), which reflects the riving force of across-plane currents of fast carriers an the surface reaction. The imension of Z* is Volt, although it cannot be relate to an electrostatic potential step. In the simplest case of lossless lateral current within the electroe it is position inepenent an equals the applie voltage, see Appenix A.1. For in-plane transport losses (of the slow carrier), but lossless across-plane charge transport of the fast carrier (in the MIEC an across interfaces), the polarization potential is simply the local riving force of the surface reaction. It correlates with the change of the local chemical potential of oxygen in the electroe Dm oe O ue to an applie bias via Z ¼ Dmoe O 2F ¼ D~moe ion 2D~moe eon : (1) 2F The symbols ~m oe ion an ~m oe eon enote electrochemical potentials of oxygen ions an electrons in the MIEC, respectively; D inicates the ifference in the equilibrium value without applie bias. Therefore Dm oe O is also the ifference in the chemical potential of oxygen between the atmosphere an the polarize electroe. It varies in-plane in a polarize MIEC electroe. When across-plane charge transport losses of the fast carrier within the MIEC or across an interface are relevant, the polarization potential has to be efine in a more general manner. For the MIEC layer on top of the electrolyte an thus ions being fast carriers it is given by Z yte ¼ D~myte ion 2D~moe eon : (2) 2F In contrast to eqn (1), the electrochemical potential of oxygen ions is now locate in the electrolyte an Z* yte formally reflects the overall riving force of the reaction H 2 O+2e oe - H 2 +O 2 yte Phys. Chem. Chem. Phys., 2014, 16, This journal is the Owner Societies 2014

5 It correspons to the sum of kinetic losses of the surface reaction, the accoring across-plane ionic current within the MIEC an the ion transfer at the MIEC electrolyte interface. For a MIEC on top of the current collector, electrons are the fast an ions the slow carrier. The polarization potential can then be efine as Z metal ¼ D~moe ion 2D~mmetal eon 2F : (3) Here, the electrochemical potential of electrons is locate in the metal. Therefore, Z* metal correspons to the overall riving force of both, surface reaction an electronic across-plane current within the MIEC (an if relevant across a Schottky barrier at the MIEC current collector interface). Therefore it is the riving force of the reaction H 2 O+2e metal - H 2 +O 2 oe. For an electroe geometry consisting of long an thin metal fingers, the local polarization potential only epens on the istance from the metal fingers. In the following, it is explaine on an argumentative level that the one-imensional generalize transmission line circuits given in Fig.6canescribesuchasystem.InAppenixesA.2anA.3the impeance functions of these circuits are erive from the rate laws of charge transport an reactions for mixe conucting thin films. However, the following equivalent circuits are graphical an more intuitive representations of these equations. In-plane transport of the slow charge carrier can be quantifie by the sheet resistance elements (R eon or R ion ). The fast charge carrier moves either in a goo electronic or a goo ionic conuctor an therefore has laterally homogeneous electrochemical potential in the fast phase, irrespective of its conuctivity in the MIEC. This is treate by a short circuit in its transport rail of the equivalent circuit. The element Y ap escribes the (area-specific) across-plane amittance an is relate to surface reaction an transport of the fast carrier. Y ap also inclues charging an ischarging of the chemical capacitance as well as possible interfacial resistances. More specific circuits for this element will be introuce later. Defining this element as an amittance allows a mathematically consistent iscretization into small (or infinitesimal) elements. In Fig. 6 the resulting circuits for a MIEC on the electrolyte (Fig. 6a) an on the current collector (Fig. 6b) are shown. Also a symbolic representation of the transmission lines (r.h.s.) is given, which will be use in the following. The l.h.s. terms in Fig. 6 emphasize that the riving forces for the in-plane an across-plane currents are etermine by the electrochemical potentials of ions an electrons as given in eqn (2) an (3). The impeance of such a transmission line epens on the left-an right-han sie termination. When a thin film MIEC electroe with current collectors is escribe by such a circuit, the eges of the metal fingers are appropriate locations of the terminals. For negligible losses in the electrolyte an counter Fig. 6 Generalize transmission line circuit escribing a MIEC thin film on an electrolyte (a). Generalize transmission line circuit escribing a MIEC film on an electronic conuctor (e.g. current collector) (b). This journal is the Owner Societies 2014 Phys. Chem. Chem. Phys., 2014, 16,

6 electroe, the polarization potential at these points equals the applie voltage, which is either +U 0 or U 0, epening on the finger an measurement moe. 3.2 Application of the generalize transmission line circuit to MIEC electroes with interigitating current collectors In this section, we specify the equivalent circuits for the MIEC electroes use in this stuy. Those electroes consist of two regions with ifferent electrochemical properties: the region of the current collectors an the free MIEC area (electroe grown on YSZ without current collectors). The circuit of the free MIEC area oes not epen on the location of the current collectors (above or beneath the MIEC layer), whereas this location oes play an important role in the region of the current collectors. The circuits are very similar for electrochemical an in-plane measurement an iffer only at the terminal parts. Still, the impeance spectra for both moes are very ifferent. Across-plane charge transport of electrons is assume to be lossless in all cases Free MIEC area. A mixe conucting thin film on an ionic conuctor can be moele by the transmission line circuit isplaye in Fig. 6a. The element R eon represents the electronic sheet resistance (R eon = r eon /) with r eon an being the electronic resistivity an film thickness, respectively. The across-plane amittance (element Y ap of the circuit) reflects ionic across-plane charge transport resistances an oxygen exchange via the surface reaction an the chemical capacitance. In our STFO electroes, ionic across-plane charge transport within the MIEC is almost lossless, while a small resistance at the STFO YSZ interface coul be observe. Consequently, the element Y ap can be specifie by the simplifie equivalent circuit shown in Fig. 5 (without YSZ resistance). The terminals of the transmission line are at the eges of the metal fingers, see Fig. 7a. At the eges of the metal fingers the electrochemical potential of electrons is efine by the current collector, an the electrochemical potential of oxygen ions remains at its equilibrium value when neglecting the electrolyte resistance. Consequently, in the electrochemical measurement moe (Fig. 3c an ), the polarization potential oftheleftanrighthansieterminalistheapplievoltage+u 0, see Appenix A1. The electrolyte resistance will be introuce Fig. 8 Calculate normalize polarization potential (Z*/U 0 ) in the DC case for in-plane an electrochemical measurement moes. The circuit parameters are equal to the simulate spectra in Section 3.4. later as a terminal part. In the in-plane moe (Fig. 3a an b), the left an right-han sie terminals are oppositely polarize with +U 0 an U 0, respectively. This situation is shown in Fig. 7a. These conitions can also be escribe by simpler circuits that use only one voltage source: The electrochemical moe is equal to an open en terminal in the center of the transmission line (Fig. 7b), an the in-plane moe correspons to a short circuit in the center of the transmission line (Fig. 7c). This equivalence becomes clear when calculating the in-plane istribution of the polarization potential for both measurement moes, which is plotte in Fig. 8. The calculation also inclues the transmission line above the current collectors. In the electrochemical moe, the graient of Z* is zero in the center between the metal fingers (equal to an open en bounary). In the in-plane moe, Z* is zero in the center (equal to a short circuit). The corresponing equations are erive in the Appenixes A.3.2 an A.3.3. In the following circuits, the representation involving only one voltage source will be use, meaning that only half of the metal finger istance (l) is consiere in the circuit. The resulting transmission line for the free surface area is part of the final circuits in Fig. 9 an Region beneath the current collector. One possible realization of the electroe has metallic current collectors on top of the MIEC film (shown in Fig. 4, r.h.s.). Beneath the metal, the MIEC is conuctively connecte with the electrolyte Fig. 7 Terminals of the transmission line circuit which are set to the metal finger eges (a). For the electrochemical measurement moe (b), two circuits with ifferent given bounary conitions result in the same impeance function. The same is true for the in-plane measurement moe (c) Phys. Chem. Chem. Phys., 2014, 16, This journal is the Owner Societies 2014

7 Fig. 9 Equivalent circuit for an electroe with a current collector on top: (a) electrochemical moe, (b) in-plane moe. The elements R int, C int, C chem an R surface reflect area-specific resistances an capacitances, R eon is the electronic sheet resistance. an with an electronic conuctor, therefore both charge carriers can be treate as fast carriers. Accoringly, relevant ionic as well as electronic charge transport within the MIEC layer only occurs across-plane, so only the ionic STFO YSZ interface resistance has to be consiere for charge transport. The surface reaction, on the other han, is blocke by the ense platinum layer. Consequently, a well suite moel for this region is the simplifie equivalent circuit in Fig. 5 (without YSZ resistance) with R surface - N. The resulting circuit is the l.h.s. part of the circuits in Fig Region above the current collector. The MIEC region above the current collector exhibits a homogeneous electrochemical potential of electrons an can be moele by the transmission line circuit in Fig. 6b. R ion stans for the ionic sheet resistance (R ion = r ion /), with r ion being the ionic resistivity of the film on top of the current collector. The across-plane amittance Y ap can be escribe by a parallel connection of the chemical capacitance C chem an surface resistance R surface, provie an electronic interface resistance between MIEC an current collector is negligible. Due to the ifferent microstructure of the MIEC on YSZ an metal, also R surface an C chem might be ifferent on these two substrates. In the case of our STFO electroes, strong ifferences coul be exclue by geometry variations, see Section 4.2. Therefore, these parameters are set to be equal for the MIEC on YSZ an on the current collector. Fig. 10 Equivalent circuit for an electroe eposite on top of the current collectors: (a) electrochemical moe, (b) in-plane moe. The elements R int, C int, C chem an R surface reflect area-specific resistances an capacitances, R eon an R ion are electronic an ionic sheet resistance, respectively. Also for this transmission-line circuit, potentials at the terminals have to be efine. At the eges of the metal fingers oxygen ions are exchange between MIEC an electrolyte. Here, the ionic MIEC electrolyte interface resistance has to be consiere as a terminal part of the transmission line. If this interface resistance is small compare to the total resistance, p the terminal can be approximate by R int2 ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R int R ion (see Appenix A.3.4). Also a capacitance at the current-collector YSZ interface is likely to be relevant, 26 this is represente by the C Pt element which is place in parallel to the transmission line. The resulting circuit is the left-han sie transmission line in Fig. 10. Owing to symmetry reasons, the polarization potential at the two eges of a metal finger is equal. Equivalent to this symmetrical terminal polarization, the transmission line can also be terminate with an open en in the center of the metal finger. This termination is appropriate for both moes. Accoringly, only half of the metal finger with (b) isconsiere in the equivalent circuit Electrolyte resistance. Owing to the ifferent current paths, the magnitue of the electrolyte resistance is very ifferent in the electrochemical an in-plane moe an is treate ifferently in in-plane an electrochemical measurement moes. In the electrochemical moe, the entire measure current has to pass the electrolyte. Therefore, the electrolyte causes a simple resistive offset in this case (the element R ec YSZ in the final circuit Fig. 9a an 10a). This journal is the Owner Societies 2014 Phys. Chem. Chem. Phys., 2014, 16,

8 In the DC-case of the in-plane moe, a pure electronic current path is possible with the electrolyte not playing any role. In the high frequency regime, however, ionic current in the electrolyte between two ajacent metal fingers may become relevant for the impeance. This ionic current is capacitively couple to the current collecting fingers. An exact escription woul require numerical methos. For the absolute resistive contribution of the electrolyte being small compare to the in-plane DC resistance, which is the case for anoes with moerate or low electronic conuctivity, an approximation can be mae. The electrolyte resistance is place in series to the capacitively couple current path between the metal fingers (the element R ip YSZ in the final circuit Fig. 9b an 10b) so it causes a resistive offset in the high-frequency regime an plays no role in the DC-case. If the electronic sheet resistance is very high (exceeing the conition in eqn (5)), there will also be a DC ionic in-plane current in the electrolyte. However, in this case, the DC resistance of the in-plane moe will be orers of magnitue larger than the electrolyte resistance. The final equivalent circuits for in-plane an electrochemical moes iffer in only two points: The right-han sie bounary of the free electroe transmission line is either an open en or a short circuit an the electrolyte resistance is treate ifferently. The accoring analytic impeance functions are given in the Appenix A Fitting routine Given the rather complex circuits, concerns regaring overparametrisation may arise. This may inee be a problem when only one measurement moe is use for fitting of experimental results. However, the erive equivalent circuits are vali for in-plane an electrochemical measurement on one an the same electroe an therefore inclue ientical materials parameters. Both acquire impeance spectra can thus be simultaneously fitte with a single parameter set by minimizing the sum of square relative errors for both spectra. Such a simultaneous fit of two ifferent measurements strongly increases the significance of the fitting parameters in terms of accuracy an mechanistic interpretation, compare to the fitting of only one spectrum. This ual fit is key for being able to accurately euce all relevant resistive an capacitive parameters which contribute to the electroe impeance. In-plane electronic an ionic charge transport affects the spectra of the electrochemical moe in a very similar manner, but has very ifferent consequences in the in-plane moe. Before running the fitting routine, the measure impeance spectra have to be correcte for the electroe geometry. For the electrochemical moe, the spectra are normalize to the total circumference of both metal fingers. In the in-plane moe, the impeance is normalize to the meaner length between the fingers (see Fig. 3b). At the borers of the mixe conucting electroe, the in-plane current ensity is zero, irrespective of the use measurement moe. This conition is equivalent to the electrochemical measurement moe. Accoringly, also the in-plane measurement inclues a (small) contribution which correspons to the circuit of the electrochemical measurement moe, cause by the open en bounary conition at the MIEC borer. Since this contribution is proportional to the effective circumference of the MIEC layer (Fig. 3a), an accoring proportion of the current measure in the electrochemical moe has to be subtracte from the in-plane measurement. This is one even though the effect is rather small. After normalization to the metal finger circumference, the impeance has the unit of O cm, such as the circuit moel. The fitting parameters reflect area-specific capacitances an resistances for across-plane current (R surface, R int, C chem, C Pt, C int ) an the electronic an ionic sheet resistance for the in-plane current (R eon an R ion ). Only the electrolyte resistances of both moes are not correcte for geometry. However, after a calibration (comparison with circular electroes), they canbeusetoeterminetheionicconuctivityofthesubstrate. From a known conuctivity temperature relationship the electroe temperature can then be calculate Simulate spectra for current collectors above an beneath the electroe Theshapean sizeofimpeance spectra is typically very ifferent for in-plane an electrochemical moes an also strongly epens on the placement of the current collector an of course on the corresponing materials parameters. Examples of simulate spectra are shown in Fig. 11. Typical values obtaine in Section 4 have been chosen for the main resistive, capacitive an geometric parameters (surface area-specific resistance (ASR): 100 O cm 2, electronic resistivity: 200 O cm, ionic resistivity: 2000 O cm, chemical capacitance: 5 mf cm 2, film thickness: 100 nm, metal finger with an istance: 20 mm). Electrolyte as well as interfacial resistances an capacitances were set to 0 since they eliver only minor contributions to the impeance spectra consiere in this stuy. The most obvious ifference cause by the placement of the metal layer is a smaller DC resistance when the current collectors are beneath the electroe, which is cause by a larger area expose to the atmosphere. Fig. 11 Simulate spectra for current collectors on top (ashe lines) an beneath the electroe (soli lines). The inset shows a magnification of the in-plane spectra Phys. Chem. Chem. Phys., 2014, 16, This journal is the Owner Societies 2014

9 Also these spectra exhibit more features. This was also experimentally confirme (not shown) an inicates that this configuration is avantageous when aiming at the etermination of all relevant electrochemical properties. For electroes with metal fingers on top, the large chemical capacitance of the part covere by the current collectors is measure in parallel to the transmission line circuit of the free surface region. This parallel circuit isguises the Warburg-like impeance that is typically observe for transmission lines in the high-frequency range. Furthermore, the ionic conuctivity is not relevant in the corresponing circuit moel an thus not available. Also, the platinum current collectors may be catalytically active when place on top of the MIEC, which might further complicate the analysis. In the experiments shown in the following, only electroes eposite above the metal fingers have therefore been use. Accoring to the circuit moel, the electronic conuctivity is measure in-plane above the YSZ substrate, while the ionic conuctivity is measure in-plane above the current collector. 4 Experimental results an iscussion The suggeste metho for investigating mixe conucting electroes in a reucing atmosphere was applie to SrTi 0.7 Fe 0.3 O 3 electroes eposite on top of platinum current collectors (cf. Section 2). In the following, we first show measure impeance spectra an iscuss the origin of the ifferent features. Then, the consistency of the new metho is emonstrate by variations of the electroe geometry. Finally, information on the temperature epenence of the materials parameters is given. 4.1 Frequency epenence of the electroe polarization Fig. 12a isplays the in-plane an electrochemical impeance spectra after normalization, measure at 660 1C with a finger istance of 11.7 mm an a STFO film thickness of 103 nm. Both spectra reveal several impeance features, partly semicircle-like an partly with 451 slopes in the Nyquist plot. The circuits erive in Section 3 were use to simultaneously fit both spectra. Nine parameters are consiere in the equivalent circuits (R surface, R int, C chem, C Pt, C int, R eon, R ion, R ec YSZ an R ip YSZ). In orer to increase the numerical stability of the fitting routine, the electrolyte resistances (R ec YSZ, R ip YSZ) were etermine from the resistive offset in the high-frequency region of the two measurement moes an set as fixe values uring the fitting routine. Also the capacitance of the Pt Ti YSZ (C Pt ) interface was foun to be too large for a reliable etermination of the STFO YSZ interface capacitance, cf. C int coul therefore not be fitte an was fixe to 0 in the fitting routine. Hence, only six inepenent parameters were use to fit both spectra. (R surface, R int, C chem, C Pt, R eon, R ion ). The Nyquist plots in Fig. 12a also show fit lines that emonstrate the fit accuracy. In orer to unerstan the mechanisms causing the shape of both spectra, the fit parameters an the circuit moels were use to calculate the amplitue of the local polarization potential as a function of position an frequency. Fig. 12 (a) Measure (symbols) an fitte (lines) impeance spectra of an electroe with 103 nm thickness an 11.6 mm finger istance at 660 1C. (b ) The calculate lateral istribution of the polarization potential is plotte for three ifferent frequencies. From this, an important conclusion can be rawn: The fraction of the electroe area which is polarize strongly epens on the frequency, as shown in Fig. 12b. This is unerstanable on a qualitative level: At high frequencies (e.g. measurement at 3200 Hz, Fig. 12b), oxygen exchange in the film is possible via charging an ischarging of the chemical capacitance. Compare to this process, electronic an ionic in-plane charge transport exhibits comparatively high resistance. This results in a short attenuation length of the polarization potential. The impeance response of electrochemical an in-plane measurement in this frequency range is very similar (except for the electrolyte offset) an is mainly etermine by the chemical capacitance an the electronic conuctivity. At lower frequencies, the impeance of the chemical capacitance increases an the attenuation length becomes larger. For attenuation lengths comparable to or larger than the finger istance, the spectra of the two measurement moes become very ifferent (below 42 Hz in Fig. 12). The slightly asymmetric shape of the lowfrequency semicircle in the electrochemical moe as well as the small low-frequency semicircle in the in-plane measurement This journal is the Owner Societies 2014 Phys. Chem. Chem. Phys., 2014, 16,

10 (between 42 an 0.36 Hz) are relate to the resistance of the in-plane current of oxygen ions on top of the current collectors. For near-dc conitions oxygen exchange in the MIEC occurs primarily via the surface reaction, which is rate-limiting for the STFO electroes use in this stuy. Therefore the polarization is nearly homogeneous along the electroe in the electrochemical moe. Accoringly, the main contribution to the DC-resistance of the electrochemical measurement is the surface reaction. For in-plane measurements, the polarization potential varies linearly an the DC-resistance is mainly given by the electronic sheet resistance. However, for a large istance between the current collector fingers or very low electronic conuctivity, the attenuation length of the electroe polarization may be similar to or smaller than the finger istance in near-dc conitions. In this case, both spectra become very similar in shape an size (after normalization) an electron transport as well as oxygen exchange contribute to both spectra in the same way. This was also confirme experimentally at lower temperature (not shown). 4.2 Geometry variations The erive equivalent circuits are applicable to electroes of ifferent thickness an metal finger istance. The size an shape of the spectra changes with geometry, but the euce materials parameters shoul stay the same. In orer to prove this, a sample with a 103 nm thick STFO film was prepare. Three ifferent electroe geometries were realize on this sample. The with of the metal fingers was kept constant at 15 mm an the metal finger istance was varie between 5, 11.6 an 25 mm. Fig. 13 epicts typical impeance spectra incluing the fit for these three metal finger istances. The quality of the fits is very goo, given that there are only six inepenent parameters for the fit of two impeance spectra. The parameters etermine for ifferent geometries at a constant temperature of 660 1C are summarize in Fig. 14. Three ifferent electroes were measure an average for each finger istance. Although some parameters (surface ASR an ionic resistivity) exhibit substantial scatter even for nominally ientical electroes an thus partly large error bars, the fitte materials parameters are inepenent of the exact electroe geometry. The accurate fit of the measurements, combine with the inepenence of the fitting parameters on the metal finger istance, strongly suggests the valiity of the moel an the appropriateness of the metho. Also the error of the fitting routine for one electroe is smaller than the corresponing stanar eviation foun for geometrically ientical microelectroes, on one sample. The measurements were repeate for a three times thicker film (310 nm) an they confirme the consistency in terms of finger istance variation. The results of both film thicknesses are summarize in Table 2, average over all finger istances. Many parameters (chemical capacitance, electronic resistivity an area-specific resistance (ASR) of the ionic interface) only slightly epen on the film thickness, however, some parameters show significant trens. The capacitance of the Pt Ti YSZ interface is consierably smaller for the 310 nm film. Moreover, the Fig. 13 Impeance spectra (symbols) incluing fit (lines) for a 103 nm thick STFO microelectroe with ifferent finger istances at 660 1C. The insets show magnifications emphasising the in-plane measurements. surface ASR is larger for the 103 nm film, but even nominally ientical thin films exhibite similar scatter for this parameter. The (in-plane) ionic resistivity of the 310 nm film is significantly smaller. The electronic an ionic conuctivity of the thicker film are in reasonable agreement with values measure on sintere pellets of similarly ope (Sr 1 x Fe x )TiO 3. 28,29 Further investigations are require to unerstan the reasons behin the ifferent ionic resistivity of the two films. For example, a thickness epenent microstructure might be the origin of the higher lateral ionic Phys. Chem. Chem. Phys., 2014, 16, This journal is the Owner Societies 2014

11 4.3 Temperature epenence All relevant resistive materials parameters of STFO anoes are thermally activate. The etermination of these activation energies provies valuable information for both application an mechanistic interpretation. Even though it is not the scope of this paper to perform a etaile stuy of these temperature epenences an their efect chemical interpretation, first results can be given an some activation energies can be estimate. The activation energies of the ifferent resistive parameters are liste in Table 3. A constant activation energy in the investigate temperature range can be observe for electronic an ionic resistivity. Interestingly, the electronic an ionic resistivity iffers by less than one orer of magnitue. The chemical capacitance an interfacial capacitance (not shown) are also temperatureepenent, but not Arrhenius-type thermally activate. The increase of the chemical capacitance with increasing temperature probably reflects the increasing concentration of electronic an/or ionic efects. The surface reaction exhibits a rather low activation energy at low temperatures (o610 1C), which increases strongly at elevate temperature. Such a result might be explaine by two parallel reaction paths. However, also timeepenent changes of R surface were observe (activation with increasing temperature an egraation when again ecreasing the temperature). The Arrhenius plot in Fig. 15 therefore reflects both, temperature an time-epenent changes of the surface kinetics. Further investigations on this phenomenon are necessary for a etaile unerstaning. 4.4 Possibilities an restrictions The novel metho introuce in this paper is expecte to be applicable to a wie variety of mixe conuctors, especially for materials with high electronic sheet resistance. However, if certain parameters are either very large or very small, the impeance response of the electroes becomes insensitive to them. The most important value in this respect is the characteristic attenuation length of the polarization potential (l a ) in the DC-case, which is relate to the resistances of in-plane current an the surface reaction. It is given by rffiffiffiffiffiffiffiffiffiffiffiffiffiffi R surface l a ¼ ; (4) R sheet Fig. 14 Materials parameters of ifferent electroes at C with a film thickness of 103 nm, euce by fitting of the impeance spectra. The parameters are inepenent of the metal finger istance (ASR = area specific resistance). resistivity of the thinner film. In-plane tracer iffusion experiments coul reveal further information on ionic transport properties but those are far from trivial to perform on thin films Moreover, four-point conuctivity measurements 33 woul be helpful as crosscheck experiments but those require eposition of the films on an insulating substrate, which might affect the results. However, variation of the current collector geometry on the same thin film reveale consistent results in all fitting parameters. with R sheet being the ionic (R ion ) or electronic (R eon ) sheet resistance. If this length is much smaller than half of the metal finger istance, the center between the metal fingers is unpolarize in both measurement moes. Then the (geometry-correcte) impeance spectra for electrochemical an in-plane measurement become very similar an the fitting error strongly increases. For a reliable quantification of the ionic resistivity, the attenuation length above the metal fingers has to be larger than half of the metal finger with. For a typical thin film electroe with fine structure current collectors (thickness: 200 nm, finger with an istance: 5 mm), this leas to an upper limit of both electronic an ionic resistivity: r[o cm] o 320 cm 1 R surface [O cm 2 ] (5) This journal is the Owner Societies 2014 Phys. Chem. Chem. Phys., 2014, 16,

12 Table 2 Mean values of the fitting parameters an their stanar eviation for two ifferent thin film samples at 660 1C Electroe property 103 nm film 310 nm film Chemical capacitance (F cm 3 ) Surface ASR (O cm 2 ) STFO YSZ interface ASR (O cm 2 ) Pt Ti YSZ interface capacitance (mf cm 2 ) Ionic resistivity (O cm) Electronic resistivity Table 3 Activation energies of the resistive parameters, 310 nm film Resistive property Activation energy (ev) Electronic conuctivity Ionic conuctivity Surface ASR, T o 610 1C Surface ASR, T C Ionic interface ASR For the electronic resistivity, there are also lower bounaries: if the DC resistance of the in-plane measurement is comparable to or smaller than the corresponing electrolyte resistance, there exists no analytical moel for the impeance response of the in-plane measurement. In this case, only its DC-value can be use to etermine the electronic resistivity, but a simultaneous fit of two spectra is no longer possible. If the electronic conuctivity is very high, which is the case for many mixe conucting cathoes in air (c1 Scm 1 ), the resistance of the current collectors or a possible Schottky barrier between MIEC an metal (which was neglecte so far) may become similar or even larger than the sheet resistance. In such a case, a large separation of the current collectors or a 4-point measurement that eliminates possible contact resistances (e.g. Van er Pauw metho 33 ) is require for the etermination of the electronic sheet resistance. Accoringly our novel approach is not consiere to be a replacement of establishe methos, but rather a helpful complementary tool to investigate mixe conuctors with properties typically occurring in a reucing atmosphere. 5 Conclusions Many mixe conucting oxie materials exhibit low electronic conuctivity when place in a reucing atmosphere. Therefore, electronic an ionic charge transport as well as the electrochemical surface reaction can cause significant resistive contributions that lea to complex impeance spectra even for geometrically simple thin film electroes. We evelope a novel esign of thin film microelectroes with two interigitating current collectors per electroe. This configuration enables two ifferent measurement moes on one an the same microelectroe: an in-plane moe where the voltage is applie between both current collectors on one electroe an a conventional electrochemical measurement versus a macroscopic counter-electroe. An appropriate impeance moel was evelope for both measurement moes, base on two transmission lines representing a mixe conucting thin film either in contact with the current collector or the electrolyte. Both acquire impeance spectra can be simultaneously fitte to these equivalent circuits using a single parameter set. Hence, all relevant resistive an capacitive contributions can be quantifie an a possible overparametrization of the moel is avoie. A more etaile analysis showe that the polarization potential, which is relate to the local chemical potential of oxygen, varies laterally in the mixe conuctor. This variation strongly epens on the measurement moe as well as the frequency. This metho was successfully employe to SrTi 0.7 Fe 0.3 O 3 anoes, where electronic an ionic conuctivity, ASR of the surface reaction, chemical capacitance an the resistance of the electroe electrolyte Fig. 15 Arrhenius plot of the relevant resistive parameters an plot of the chemical capacitance between 490 an 760 1C Phys. Chem. Chem. Phys., 2014, 16, This journal is the Owner Societies 2014

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