The oxygen reduction reaction in solid oxide fuel cells: from kinetic parameters measurements to electrode design

The research and development of new Solid Oxide Fuel Cell cathode materials is an area of intense activity. The kinetic coefficients describing the O2-reduction mechanism are the O-ion diffusion ( D chem ) and the O-surface exchange coefficients ( k chem ). These parameters are strongly dependent on the nature of the material, both on its bulk and surface atomic and electronic structures. This review discusses the method for obtaining the kinetic coefficients through the combination of electrochemical impedance spectroscopy with focused ion-beam 3D tomography measurements on porous electrodes (3DT-EIS). The data, together with oxygen non-stoichiometry thermodynamic data, is analysed using the Adler-Lane-Steele model for macro-homogeneous porous electrodes. The results for different families of oxides are compared: single- and double-layered perovskites with O-vacancies defects, based on La-Sr cobalt ferrites (La0.6Sr0.4Co1-xFexO3-δ , x = 0.2 and 0.8) and La/Pr-Ba cobaltites (La0.5-xPrxBa0.5CoO3-δ , x = 0.0, 0.2 and 0.5), as well as Ruddlesden-Popper nickelates (Nd2NiO4 +δ ) with O-interstitial defects. The analysis of the evolution of molar surface exchange rates with oxygen partial pressure provides information about the mechanisms limiting the O2-surface reaction, which generally is dissociative adsorption or dissociation-limited. At 700 °C in air, the La-Ba cobaltite structures, La0.5-xPrxBa0.5CoO3-δ , feature the most active surfaces ( k chem ≃0.5–1 10−2 cm.s−1), followed by the nickelate Nd2NiO4 +δ and the La-Sr cobalt ferrites, with k chem ≃1–5 10−5 cm.s−1. The diffusion coefficients D chem are higher for cubic perovskites than for the layered ones. For La0.6Sr0.4Co0.8Fe0.2O3-δ and La0.6Sr0.4Co0.2Fe0.8O3-δ , D chem is 2.6 10−6 cm2.s−1 and 5.4 10−7 cm2.s−1, respectively. These values are comparable to D chem = 1.2 10−6 cm2.s−1, observed for La0.5Ba0.5CoO3-δ . The layered structure drastically reduces the O-ion bulk diffusion, e.g. D chem = 1.3 10−8 cm2.s−1 for the Pr0.5Ba0.5CoO3-δ double perovskite and D chem ≃2 10−7cm2.s−1 for Nd2NiO4 +δ . Finally, the analysis of the time evolution of the electrodes shows that the surface cation segregation affects both the O-ion bulk diffusion and the surface exchange rates.


Introduction
The O 2 reduction reaction (ORR) taking place on the surface of a solid material is a relevant reaction for energy conversion and storage systems such as solid oxide fuel cells (SOFC), gas separation membranes, and metal-air batteries. Considerable research activities are aiming to increase the comprehension of ORR mechanisms, because the efficiency of these devices is limited by the cathodic polarization resistance-and the associated overpotentials-especially when the operation temperature is reduced. Decreasing the operation temperature below 700 • C is important to improve the stability of the materials and reduce balance of plant costs, as is needed reaching a more widespread application of this technology. In order to achieve the reduction of the ORR overpotential of the cathode it is of crucial importance to understand the associated electrochemical processes. There are different electrochemical paths proposed depending on the capability of the solid to adsorb, incorporate, transfer charge or transport O-species, shown in a simplified scheme in figure 1. Generally speaking, the ORR mechanism involves O 2 gas transport, different alternatives of physisorption or chemisorption of either diatomic or atomic surface species ( The process that is the ORR rate limiting step depends on the characteristics of the specific cathode material. All steps involving surface process as physisorption, chemisorption, molecular dissociation, O-ion incorporation, including or not charge transfer, are well described by specific surface exchange coefficients (k chem ). Whereas the O-species diffusion in the solid, either on the surface or bulk are described by an oxygen diffusion coefficient (D chem ). Then, the so called 'kinetic parameters' , D chem and k chem coefficients, are accepted parameters for describing the ability of a material to transport oxygen and thereby facilitate the ORR.
In this work we analysed the applicability of the 3DT-EIS method and we compared the results for different families of oxides: single-and double-layered perovskites with O-vacancies defects, based on La-Sr cobalt ferrites (La 0.6 Sr 0.4 Co 1-x Fe x O 3-δ , x = 0.2 and 0.8) and La/Pr-Ba cobaltites (La 0.5-x Pr x Ba 0.5 CoO 3-δ , x = 0.0, 0.2 and 0.5), as well as Ruddlesden-Popper nickelates (Nd 2 NiO 4 +δ ) with O-interstitial defects. These materials have received a lot of attention as cathodes due to their properties. La 0.6 Sr 0.4 Co 1-x Fe x O 3-δ (LSCF) is a state-of-the-art mixed ionic and electronic conductor (MIEC) perovskite cathode [1], which shows ionic conductivity through an O-vacancy mechanism, high structural stability and presents low ASR values [2][3][4][5]. Also, it has a high degradation rate [6,7], as a consequence of Sr segregation. Although this is a very much studied material, there is still considerable research being conducted on it, with the aim of decreasing degradation rates and improving the electrochemical activity. Recent experimental and theoretical studies have highlighted the potential of perovskite oxides LnBaCo 2 O 6-δ (Ln = lanthanide), as candidate materials for intermediate temperature (600 • C-800 • C) solid oxide fuel cells (IT-SOFC) cathodes and oxygen separation membranes [8][9][10][11]. These materials show high rates of oxygen surface exchange [12] and diffusivity [13], and high electrical conductivity [14,15]. However, there is not enough information about Ba-segregation in Ba-cobaltite porous electrodes. In these perovskites, the Ba plays a key role since its large cation radii mismatch also distorts the cubic crystal structure promoting the oxygen vacancy formation and migration [16], thus reducing the R tot due to the improvement of the O-surface exchange and the O-ion diffusion. La 0.5-x Pr x Ba 0.5 CoO 3-δ , LPBC, cobaltites present a phase transition when substituting La for Pr, producing a change from isotropic to anisotopic ionic conductivity through an O-vacancy mechanism. This materials family presents low ASR, but a high rate of degradation, due to Ba segregation. Conversely, the Nd 2 NiO 4+δ is Ba and Sr-free material, which helps disabling the degradation by cation segregation, and is also a Co-free material, an advantage in economic and other terms. This material belongs to the Ruddlesden-Popper phase with K 2 NiF 4 -type structure, which conducts oxygen through interstitials, has similar values of thermal expansion coefficients to those of electrolyte materials [17,18] and presents thermal stability and chemical compatibility with La 0.9 Sr 0.1 Ga 0.8 Mg 0.2 O 2.85 (LSGM) electrolytes [19].
Although in this work the 3DT-EIS method is applied to these three types of materials, they represent a wide range of structures, chemical compositions and electrochemical behaviours and it should be noted that this method is applicable to any kind of MIEC materials.  surface analysis and IEDP measurements, obtaining different values of oxygen incorporation rate depending on the crystalline orientation of the surface exposed to O 2 .
Since both techniques need dense samples to carry out the experiments, unfortunately, it is not always an easy task to obtain single crystals with the adequate dimensions for IEDP and ECR experiments. For both, IEDP and ECR, the sample dimensions must be large enough to prevent the crossing of the concentration profiles in the center of the sample during the tracer annealing time, otherwise, the boundary conditions used in modelling the results might not be fulfilled [20]. Besides, the smallest dimension of IEDP or conductivity relaxation samples should be close to the characteristic distance, defined as: l = D k . If the ratio D/k is much lower than the sample dimensions, the results for D are accurate, but k will have considerable error. Conversely, if D/k is larger than the sample dimension, then k can be obtained accurately but D will have considerable inaccuracy [23]. ECR measurements can be performed on porous samples, but the accuracy in the determination of D and k depends heavily on the sample thickness [26]. Furthermore, the particle size for this method is typically much larger than D/k, so it can be difficult to measure k accurately. Thus, in IEDP and conductivity relaxation methods it may be necessary to employ multiple samples with different dimensions to obtain the kinetic parameters over the range of temperatures T and oxygen partial pressure pO 2 of interest.
Another drawback is that the fabrication of dense pellets requires much higher firing temperatures than those used for preparing real porous electrodes, producing uncontrolled changes in the nature of the material, such as surface segregation. These uncontrolled alterations can modify the measured exchange rate coefficients as much as an order of magnitude [28]. These kinds of experiments have very precise interpretations for the processes involved and allow computational modelling of the surface reactivity at the first-principles level. Nevertheless, they fail to represent a real porous electrode material, given that this approach does not take into account effects generated by surface curvature, surface composition, the sometimes nano-sized nature of the grains, surface segregation of species, etc.
An alternative solution for obtaining results that are more indicative of real electrodes was proposed by S B Adler's group [29]. They analysed the electrochemical response of one electrode, measured by Electrochemical Impedance Spectroscopy (EIS), in the frame of a semi-infinite macro-homogeneous porous electrode by applying the so called Adler-Lane-Steele (ALS) model [30,31]. The ALS model includes microstructural information that can be obtained by 3D tomography methods such as FIB-SEM [32][33][34][35], and thermodynamic information about O-defect concentration. The kinetic coefficients can be obtained by using this data in conjunction with fits to EIS spectra. In this work we will refer to the combination of 3D tomography with EIS data to obtain kinetic information as 3DT-EIS.
The main drawback of this approach is that it requires the use of advanced 3D tomographic characterization of the electrode microstructure. However, 3D tomography has been successfully applied to the study of a wide range of porous SOFC electrodes, from anode composites, e.g. Ni-YSZ (YSZ is Y stabilized ZrO 2 ) [32,36], Ni-GDC (GDC is Gd-doped CeO 2 ) [37], Ni-ScSZ (ScSZ is Sc-stabilized ZrO 2 ) [38]; infiltrated nanoscaled anodes, e.g. LSM infiltrated on YSZ scaffold [39], or single phase cathodes such as La-Sr-Ba cobaltites or cobalt-ferrites [29,[40][41][42][43][44][45][46] or La-Sr-Ca manganites [47]. In the present context where the focus is on single-phase MIEC oxides, the relevant microstructural parameters are the solid and pore volume fractions, surface areas, and tortuosities. An important advantage of the 3DT-EIS method is that it takes into account time evolution effects, such as species segregation [1,6,42,48,49], surface reconstructions [50], studying the effect of volatile species, etc. Also, the data collection is relatively fast compared with the time needed for carrying out IEDP experiments and is comparable with the length of ECR experiments. Also, the 3DT-EIS method allows testing several temperatures and pO 2 conditions in a single experiment, simplifying the samples preparation and reducing experimental time. Finally, this method allows to obtain both k and D simultaneously, in contrast to IEDP and ECR, which allow to obtain only one parameter with good accuracy at a time. In short, the 3DT-EIS method opens up new possibilities to study a wide variety of samples, taking into account the real conditions in which these are characterized electrochemically. These possibilities allow for a direct correlation of the kinetic parameters to the electrode electrochemical properties and for an advanced design of electrode materials. Table 1 shows a simplified comparison of the three methods presented in this work. The Sample Processing category represents the difficulty for preparing the samples, firing temperatures, quantity of samples needed. The Data Collection category mainly represents the time needed for carrying out the experiments and the difficulty of the experiments. The Data Processing category refers to the time needed and the difficulty of processing the acquired data and extracting the desired information. Finally, the Accuracy category refers to the accuracy of the method, in the statistical sense of distance of the extracted values to the 'true' values, related to the real conditions and characteristics of the electrode, and the independency on the determination of k and D. The closer the measured values to the 'true' values are, the better the accuracy of the method.
In this work, we discuss recent results obtained using 3DT-EIS to analyse the properties and performance of different SOFC porous electrodes, such as double perovskites based on La-Sr cobalt ferrites (La 0.6 Sr 0.4 Co 1-x Fe x O 3-δ , x = 0.2 and 0.8) and La/Pr-Ba cobaltites (La 0.5-x Pr x Ba 0.5 CoO 3-δ , x = 0.0, 0.2 and 0.5), as well as Ruddlesden-Popper nickelates (Nd 2 NiO 4 +δ ) with O-interstitial defects.
Also, modifications to adapt the electrochemical model from semi-infinite to finite-length electrodes are discussed. The mechanisms of surface reaction and O-ion diffusion are proposed from analysing the behaviour of the kinetic parameters with the O 2 partial pressure. In order to facilitate the comparison, the following relationships between the kinetic coefficients obtained by different techniques are used: and where A = (+/−) 1 2RT ∂µO 2 ∂lnx δ is the thermodynamic factor describing how oxygen non-stoichiometry varies with oxygen chemical potential (µ O2 ), with the (−) sign corresponding to O-vacancies and (+) sign to O-interstitials, R is the universal gas constant, T is the absolute temperature and the factor 1/2 is included to Table 1. Schematics of the strengths and weaknesses of the three methods commonly used for obtaining the kinetic coefficients. For the sample processing category, the difficulty for preparing the samples, firing temperatures, quantity of samples needed, were taken into account. The data collection category represents the time needed for carrying out the experiments and the difficulty of these experiments. The data processing category refers to the time needed and the difficulty of processing the acquired data. The accuracy category represents the overall accuracy of the methods, based mainly on how representative are the samples of real SOFC electrodes and of the conditions of real operating devices. The yellower the disk is, the better the performance of the method. take into consideration the relationship between molecular µ O2 and the atomic O-chemical potential in the solid (µ O = µ O2 /2) and x 0 δ is the molar fraction of O-defects at equilibrium, e.g.: for an electrode with perovskite structure (ABO 3-δ ), x 0 δ = δ eqb /3 that means that in the equilibrium, it distributes the O-vacancies (δ eqb ) in the 3 sites of O available per mol of perovskite.

The ALS model for semi-infinite porous electrodes
The ALS model is used to describe the response of a porous single phase MIEC electrode, whose EIS spectra can be fitted by a Gerischer type impedance [29]: where R G is the resistance and τ G the time constant. Although the model specifies a case where the ionic conductivity is dominated by O-vacancy species in the bulk of the MIEC, the same basic framework can be extended to O-interstitial or surface diffusion conduction mechanisms. The basic idea of this model is to solve the differential equation for 1D diffusion for an O-active species in a porous macro-homogeneous medium, which means that its microstructure can be described by average parameters, such as the electrode specific surface area a, porosity ε and the solid-phase tortuosity factor τ, the latter defined as the ratio between the effective path length traveled by the diffusive species to the straight distance τ = L ef L . Under these conditions, the following diffusion equation is valid: where c δ is the concentration of O-diffusive species, and D δ its diffusion coefficient. In this equation the diffusion is coupled or co-limited with a surface reaction (r), given that it also changes c δ (x, t). The net O 2 reduction rate at the surface (r) can be analysed in the frame of transition state theory, with a nonequilibrium thermodynamic rate expression: where λ is an integer parameter related to the rate-limiting step, ℜ o is the oxygen molar equilibrium surface rate and Λ is the free-energy driving force for the limiting mechanism controlling the surface process. As discussed above, the oxygen surface exchange involves a series of steps such as adsorption of O 2 molecules from the gas phase, dissociation of these molecules, incorporation of the O-atoms into the MIEC bulk, etc.
Then, the driving force for each individual step (Λ j ) is the difference in chemical potential of the reaction in the framework of nonequilibrium thermodynamics: Λ j = ∆µ j = ∆µ 0 j + RTlnQ j + ∆E j (6) and the net rate of any elementary reaction step j is where ∆G 0 f,j is the equilibrium free-energy barrier for step j, ∆E j is a shift in free-energy of reaction associated to the driving force, Q j is the law of mass action corresponding to step j, β j is a reaction symmetry parameter (analogous to the one used in electrochemical kinetics) and c i are the concentration of reacting species in the forward direction of the j-step. In the equilibrium limit (Λ j → 0) and small perturbations, the linearization of equation (7) is possible and ℜ o becomes the exchange rate, which can be estimated as: where A is the thermodynamic factor defined above. Thus, in general: where the dependence of ℜ o with pO 2 gives an indication of the limiting mechanism of the surface reaction. A more detailed discussion about the surface oxygen-exchange reaction can be found in [51]. and in section 1.2.
Besides solving the solid phase diffusion equation (equation (4)), the ALS model solves the O 2 -gas diffusion in gas phase (both inside the porous material and in the boundary layer) and the equation considering the interfacial charge-transfer reactions occurring at the mixed conductor/electrolyte interface (O-ion transfer, i O −2 ) and the mixed conductor/current-collector interface (e − transfer, i e− [30,31]). The solution of the diffusion problem with adequate boundary conditions, e.g.: c δ (x = L, t > 0) = c 0 δ and c δ (x = 0, t) = c 0 δ + ∆c δ cos (ωt), predicts that the zero-bias impedance of a symmetrical cell (electrode/electrolyte/electrode) is the sum of the electrolyte resistance, a charge-transfer impedance (across electrolyte-electrode interfaces) and a 'chemical' impedance associated with non-charge transfer or chemical reaction processes: The Z chem expression for a semi-infinite electrode, with non-charge-transfer processes, includes convoluted contributions of oxygen surface exchange and solid-state diffusion, and obeys a Gerischer-type impedance (equation (3)). Then, R G and τ G can be directly related to microstructural, thermodynamic and kinetic parameters by: where c O is the concentration of oxygen lattice sites involved in the diffusion mechanism, and the other parameters were already defined. This model has a characteristic utilization length l δ , defined as: The distance l δ refers to the depth into the electrode (from the electrolyte) over which the reaction takes place (≃ 3l δ ). Inside this zone, the gradient of O 2− concentration (i O 2− ) is maximum, whereas outside it the concentration is constant.

The ALS model and mechanisms of surface reaction
The ALS model was developed for electrodes with O-vacancy defects. This means that the overall ORR (in the Kröger-Vink notation) is, for a p-type conductor, expressed as follows: or for an n-type conductor: and h · or e ′ to an electron-hole or electron charge carrier, respectively. Given that perovskites used as O 2 -electrodes typically exhibit p-type conductivity, the following is based on equation (12). In the equilibrium of the global reaction, the difference between the chemical potentials is zero: where pO 2 is the gas oxygen partial pressure and fO 2 the oxygen fugacity in the solid. Equation (14) gives a relationship between defect concentrations (c δ ) and pO 2 near to equilibrium conditions. A specific mechanism can be proposed for the surface reaction with different steps, for example: is the fraction of charge involved in the individual step j (j = ads, dis, inc. for adsorption, dissociation and incorporation, respectively; and q ads + q dis + q inc = 2), s δ,surf refers to a surface site for adsorption (e.g.: a surface O-vacancy), O q− ads ,s 2 and O q− dis ,s refer to molecular and atomic O-adsorbed species, respectively. Then, in the framework of non-equilibrium thermodynamics of equation (6), each individual step can be expressed considering the individual mass action law for Q j = ∏ reactives i c i,j ∏ products n c n,j and the Rigid Band Model (RBM) formalism [52][53][54] for the relation ∆E j = q j ∆E. The RBM formalism considers itinerant charge carriers in a partially filled, wide, M3d-O2p band to estimate the contribution of charge carriers to the energy: where g (E F ) indicates the density of states at the Fermi level and, in the case of O-vacancy defects Depending on which is the ORR limiting step, different expressions can be observed for ℜ o (see equation (7)), which can be linearized in near equilibrium conditions (equation (8)) to obtain analytical expressions Note that c δ and k chem could also vary with pO 2 (see equations (7) and (14)), then the total pO 2 dependency is estimated as n = ∂lnℜo ∂lnpO2 . Tables 2 and 3 from [51] summarize this information. Below, we discuss possible surface rate mechanisms, co-limiting with O-ion diffusion: (a) Chemisorption-limited reaction (step I), the surface reaction is mediated by a highly unstable physisorbed diatomic intermediate, which is transformed to a more stable diatomic superoxide intermediate This reaction is limited by an energy barrier and n = 1 2 + q dis −(1−2β ads )q adss , where q ads = 1, q dis = 3, q inc = 0, β ads = 0.5 or 1 for metals or p-type semiconductors, respectively. The molar surface exchange rate is expressed as Table 3.
Measured diffusion coefficients (D chem ), molar exchange rates (ℜo), surface exchange coefficients (k chem ) and activation energies (Ea) for the electrodes studied by our group: La0.6Sr0.4Co1-xFexO LSCF6428 (2) [41] La0.8Sr0. (b) Dissociation-limited (step II), this step acquires importance when the chemisorption reaction is fast. This mechanism is mediated by an unstable diatomic superoxide intermediate that is transformed to a more stable single-atomic adsorbed intermediate, once an energetic activation barrier is overcome. Then n = , q ads = 1, q dis = 3, q inc = 0 and β dis = 0.5, The molar surface exchange rate is also expressed as (c) Dissociative adsorption-limited reaction. In this case the reaction is mediated by a highly unstable physisorbed diatomic intermediate, which is transformed to a more stable single-atomic adsorbed intermediate (step I and II collapse to a single step) and it is limited by the probability of finding a second vacancy near the diatomic intermediate. This reaction is limited by an entropy barrier and n = β dis q dis The molar surface exchange rate is expressed as (d) Incorporation-limited (step III), this step occurs if the surface is equilibrated with the gas, steps I and II are fast and the reaction is limited by exchange of oxygen vacancies with the bulk. In that case n = The molar surface exchange rate in this case is According to the reactions expressed in equations (12) and (13), the diffusive species in equation (4) is an O-ion with a mechanism of O-vacancies (V ·· O ); and the surface reaction mechanism involves steps I to III, then the O-ion diffusion happens once the O-ion is incorporated into the bulk of the non-stoichiometric oxide. Therefore, in this O-ion bulk diffusion mechanism it is expected that as pO 2 decreases, the concentration of V ·· O should increase, and hence a slight decrease of the contribution of bulk diffusion polarization resistance is also expected in EIS experiments. However, if the surface reaction is strongly s species can be accumulated on the surface, making a diffusion path through the surface possible. In these cases, as pO 2 decreases, the concentration of diffusive species decreases and, as a consequence, the contribution of surface diffusion polarization resistance increases. The strong increment of D chem with increasing pO 2 is an evidence of the superficial character of O-diffusion, as it was suggested by Lu et al [29] for La-rich cobaltite porous electrodes .

The ALS model for different kinds of O-lattice defects
All of the above discussion was proposed for electrodes with O-vacancy defects. However, there are also MIEC electrodes where the O-defects consist of extra O-atoms located in interstitials sites. In those cases, equation (12) must be re-written as: where s i is an empty interstitial site and O ′ ′ i is an oxygen ion located in the interstitial site. In this case, c δ refers to the molar concentration of O-interstitials.
Following the same concepts as for O-vacancies, a possible mechanism for the surface reaction could be: O-interstitial defects, the adsorption and dissociation steps are similar to those for O-vacancy defects. Then, an analogous analysis with similar results can be observed for chemisorption, dissociative adsorption or dissociation-limited reactions, with the consideration that c δ must be replaced by c s i , the concentration of empty O-interstitial sites. Note that c δ + c s i = N Vu.c. , where N is the number of O-interstitial sites by unit cell.
Also, the electroneutrality balance requires that c h · = 2c δ , which modifies the RBM energy expression and equilibrium condition (equation (14)) to: Then, the relation ℜ o ≃ k chem cs i A pO n ′ 2 is also valid. However, a few corrections must be included by considering the different sign of the thermodynamic factor depending on whether the defects are vacancies, Then, for Chemisorption and Dissociation-limited , respectively. For the case where the reaction is incorporation-limited, a similar analysis to that performed in [51] indicates that . In this case, the diffusive species is an O-ion by a mechanism of O-interstitials (O ′ ′ i ), which decreases its concentration as pO 2 decreases, and as a consequence the diffusion polarization resistance is expected to increase.
In summary, from the analysis of n = ∂lnℜo ∂lnpO2 , a surface exchange limiting reaction can be suggested; e.g.: considering an ORR involving O-vacancies formation with a mechanism following steps I-II-III, and q ads = 1, q dis = 3, q inc = 0, β ads = 1, β inc = 0.5n chemisorption > n dissociative−adsorption > n dissociation > n incorporation . This analysis would be reinforced by considering the diffusion coefficient and its dependence with pO 2 (m = ∂lnD chem ∂lnpO2 ) together with complementary thermodynamic data indicating the relation between defects concentration and pO 2 . Once the limiting-step is determined, k chem can be estimated from the relation Thus, k chem and D chem obtained for real porous electrodes in this way provides helpful information to improve electrode materials design by comparing materials with different crystallographic structures, compositions, microstructures, also for understanding degradation mechanisms, obtaining information about the effect of functionalized surfaces, etc.
The ALS model described by equations (10.1) and (10.2) is valid as long as two hypotheses hold true: (1) the electrode length can be approximated as semi-infinite, meaning that the electrode thickness (L) is much larger than the characteristic utilization length (L ≫ 3l δ ) and (2) the electrode is macro-homogeneous, meaning that 3l δ must be higher than the size of some characteristic morphological features, e.g.: the average particle diameter.
For the cases where the semi-infinite electrode condition fails, a simple modification can be done to the ALS model to describe the finite nature of the electrode.

The ALS model for a finite length porous electrode
Finite-length electrodes, where the electrode reaction takes place along the total electrode thickness (L ≃ l δ ), are usually well modeled by a transmission line model (TLM) [6,55]. The TLM was developed for electrodes characterized by two percolated networks of ionic and electronic conducting materials and it was applied to describe either composites, infiltrated and MIEC electrodes. In the particular case where the electronic conduction is much larger than the ionic conduction, the TLM is described by a distributed diffusion resistance (R d ) a distributed surface resistance (R s ), a surface capacitance (Q s ) and a time distribution exponent (α) as: Figure 2 shows the Nyquist representation of the TLM element in different regimes. The limits where the diffusion resistance is much higher than the surface resistance (R d ≫ R s or L ≫ l δ ) the TLM transforms to a Gersicher-like spectrum ( figure 2(a)). As surface resistance increases, or L ∼ l δ , a two arc spectrum typical of TLM appears ( figure 2(b)). In this condition, the high frequency part of the spectrum is dominated by the diffusion process, while the low frequency part of the spectrum is dominated by the surface process (this can be changed depending on the value of Q s ). Finally, it can be noted that in the limit of large surface reaction resistance, or large utilization length L ≪ l δ , equation (18) transforms to an R//CPE like element (figure 2(c)) [31,56].
Taking this into account it can be shown that Z TLM → Z G in the limit of L ≫ l δ , and the following identifications with the Gerischer impedance parameters can be established [57]: Furthermore, these relations can also be linked with the phenomenological ALS model to obtain information of the kinetic coefficients in the so-called ALS-TLM model, which models the response of finite-length porous macro-homogeneous electrodes.
Similarly, for the extreme situation when R d ≪ R s , or equivalently L ≪ l δ , the limit Z TLM → Z R//Cpe is valid, expressed as: where R s = RT 4F 2 1 4aℜo which can also provide information about k chem , in this condition.

Methods
In this work we compare the results obtained from the study of three families of porous electrodes deposited as symmetrical cells on La 0.9 Sr 0.1 Ga 0. 8  LSCF and LPBC are non-stoichiometric oxides with O-vacancy defects, whereas NNO can accommodate extra oxygen as O-interstitial defects. All porous electrodes were fabricated following a similar procedure: Powders of electrode materials were synthesized by sol-gel routes, followed by thermal treatments that yielded the desired phases. LSCF (both LSCF6482 and LSCF6428) [57] and one of the NNO electrodes (NNO-SG) [58] were obtained by a chemical method involving a sol-gel formation by polymerization of Acetyl-Acetone (AcAc) and Hexamethylenetetramine (HMTA) [59]. All LPBC electrodes (x = 0.0, 0.2 and 0.5) [60] and the second NNO (NNO-P) [61] electrodes were synthesized via a combined EDTA-citrate complexing sol-gel process derived from the Pechini method. In all cases the crystal structures were analysed by x-ray diffraction (XRD), using a Panalytical-Empyrean diffractometer, with Cu K α radiation.
LSGM and GDC commercial powders (Fuel Cell Materials) were uniaxially pressed and sintered for 6 h at 1450 • C and 1350 • C, respectively, yielding dense electrolytes. LSCF, LPBC and NNO inks were prepared using isopropyl alcohol, alpha-terpineol, polyvinyl butyral, polyvinyl pyrrolidone and LSCF in a weight ratio of 39:24:2:1:34, deposited on the electrolytes using the spin coating technique and calcined at 1000 • C for 1 h. LSCF and NNO electrodes were deposited on LSGM and LPBC on GDC electrolytes.
The microstructural analysis was carried out using 3D FIB-SEM tomography, performed on epoxy infiltrated cells in a FEI Helios Focused Ion Beam-Scanning Electron Microscope (FIB-SEM) using the backscattered electron detector. The images were aligned, filtered and segmented by using a semi-automated algorithm using IMOD [62] and in-house-made Matlab scripts. The image treatment and 3D reconstructions are more thoroughly described in the literature [43,63]. The porosity ε was calculated by counting the proportion of pore pixels and dividing by the total volume. The surface area a and tortuosity τ values were calculated by using codes written in IDL programming language [64]. Also, the microstructural, structural and compositional characterization was completed, in some cases, by electron microscopy (SEM and TEM), Synchrotron XRD, or inductively coupled plasma-optical emission spectrometry (ICP-OES) studies.
EIS measurements of porous electrodes were carried out using a symmetrical cell configuration. The EIS measurements were performed using a frequency response analyzer coupled to an AUTOLAB potentiostat. EIS spectra were recorded in the temperature range from 500 • C up to 700 • C in dry air. In addition, other EIS measurements were performed at 700 • C as a function of oxygen partial pressure (pO 2 ) within the range between 10 −4 to 1 atm., using Ar as the carrier gas. The pO 2 was measured and controlled by using a ZrO 2 -based, electrochemical oxygen pump and sensor [65]. For some specific electrodes, these measurements were complemented with similar studies as a function of pO 2 , but replacing Ar for He as gas carrier. Finally, for the LPBC electrodes, the study was complemented with the evaluation of the time evolution of the EIS spectra at 700 • C in atmospheric air over 400 h. The EIS spectra were fitted with electrical equivalent circuits using an open source MatLab code [66].

Electrode characterization
XRD provides information about crystal structure (e.g. symmetry, lattice parameters, unit cell volume) and thermogravimetry about defect concentration and how it changes with pO 2 , both pieces of information are required for the application of the 3DT-EIS method. Figure 3 shows schematically the crystal structures adopted by LSCF, LPBC and NNO electrodes. In each structure the MO6 (M = Fe, Co, Ni) octahedral unit is indicated. The LSCF compounds present cubic symmetries (S.G. Pm-3 m, figure 3(a).) in the whole range of temperatures and pO 2 of this study, with lattice parameters at 700 • C of a = b = c = 3.8877  The O-vacancies are mainly located between PrO and CoO2 layers. Note at the inset that La-rich LPBC is a mixture of cubic single and tetragonal double perovskites, (e)-(f) orthorhombic Fmmm symmetry adopted by the NNO compound with Ruddlesden-Popper structure, consisting of-NdO-NdNiO3-NdO-layers. Extra O-ions can be incorporated in the empty tetrahedral sites generated in the NdO layers. As temperature increases, O-interstitials concentration decreases and NNO adopts a tetragonal I4/mmm structure. This figure remarks one of the eight tetrahedral sites available in this structure. Figure 3(d) [60], figure 3(f) [58]. [69]. As La is replaced by Pr, the difference in the ionic radii of Pr +3 and Ba +2 promotes the cation ordering in a double perovskite layered structure (figure 3(c)) with tetragonal symmetry and lattice parameters a = b = 3.9055 compounds are also higher than those of LSCF, presenting values around A~10. Because, as a consequence of the synthesis conditions, La 3+ /Pr 3+ and Ba 2+ cations give place to cationic ordered and disordered structures, the La rich LPBC electrodes presented in this work show a unique microstructure where both, cubic and tetragonal structures, coexist [60].
Other perovskite-related layered structures are the Ruddlesden-Popper phases A n +1 B n O 3n +1 . In these compounds, within every n perovskite ABO 3 layers, a rock salt AO intercalated layer can be found. This structure, with n = 1, is adopted by NNO ( figure 3(e)). The rock-salt layers generate tetrahedral sites, where the structure can introduce extra O-interstitial sites. Figure 3(e) shows eight tetrahedral sites by unit cell, which include four Nd 2 NiO 4 +δ , thus x δ = δ/2 and x o = (2 − δ) /2. According to the amount of extra O-ions, the structure can adopt a tetrahedral or an orthorhombic symmetry. As an example, in air at room temperature the Nd 2 NiO 4 +δ can accommodate enough ions to make 4 + δ = 4.240, in an orthorhombic structure (S.G. Fmmm), with a = 5.3769, b = 5.4509 and c = 12.3647 Å. At 700 • C in air it can accommodate 4 + δ = 4.167 (x δ = 0.083) [58,70] in a tetragonal structure (S.G. I4mmm) with a = 3.8630, b = 3.8630 and c = 12.5089 (Å) [19,71]. The thermodynamic factor in these conditions is A~7. It can be noted that, as temperature increases and pO 2 decreases the materials with O-vacancies increase its number of defects, whereas those with O-interstitials decrease it.
The characterization of the microstructure of the electrode is a key piece of information for the application of the 3DT-EIS method. The left panels of figure 4 show typical 2D sections from FIB-SEM data sets of the porous electrodes, whereas the right panels illustrate the corresponding 3D image representations for (a)-(b) LSCF, (c)-(d) LPBC, (e)-(f) NNO-SG and (g)-(h) NNO-P electrodes. Analysis of the 3D data yields the parameters needed for the application of the ALS model analysis: porosity -ε-, solid phase tortuosity -τ-and specific surface area -a-, the latter defined as the cathode area per unit volume. Table 2 lists some characteristic microstructural parameters, obtained from the 3D FIB-SEM reconstructions. In this table, the effect of the synthesis route on the microstructural parameters can be noted by comparing the NNO electrodes. Despite both synthesis methods produce submicronic particles (<500 nm), the formation of denser agglomerates for NNO-P yields a lower specific surface area. In general, those electrodes synthesized by the HMTA-AcAc sol-gel method (LSCF and NNO-SG) exhibit the larger specific surface areas and lower tortuosity values. Also, from comparing LPBC electrodes before and after aging for 400 h in air at 700 • C (see table 2), a reduction of around 15% of the specific surface area is observed. To complement the time-evolution study, the cation surface concentration was measured using ICP-OES [60]. This study indicated that LPBC electrodes present larger amounts of segregated Ba, in the form of ≈ 20 nm sized Ba-rich particles on the perovskite surface. This is especially the case for Pr 0.5 Ba 0.5 CoO 3-δ , with double perovskite structure, which even just after the preparation of the electrode (before aging) showed a Ba rich surface, that increased about 50% after aging. The other LPBC electrodes increased the estimated amount of segregated BaO monolayers even more after the aging treatment (≈ 100%) [60]. Summarizing, there are two detected changes in the samples before and after aging, one originated in the particle coarsening and the other one associated with the surface cation segregation. However, it is worth noting that the percentage of reduction of specific surface area is significantly lower than the increment in the amount of Ba 2+ cations on the surface of the electrodes.

The impedance response
The EIS spectra, collected at 0 V using symmetrical cells with porous electrodes, present different contributions to the total impedances. The analysis of the spectra as a function of pO 2 allows to identify the nature of each contribution according to how the associated polarization resistances vary with pO 2 . For example, figure 5 shows selected EIS spectra collected at 700 • C and pO 2 = 10 −3 atm. for (a) La 0.6 Sr 0.4 Co 0.8 Fe 0.2 O 3-δ (LSCF6482), (b) La 0.3 Pr 0.2 Ba 0.5 CoO 3-δ (x = 0.2) and (c) Nd 2 NiO 4 +δ (NNO-SG and NNO-P). One advantage of following the evolution with pO 2 is that at low pO 2 it is easier to see separate arcs. This helps to interpret the arcs at high pO 2 values, where these might be overlapped. This is the case for LPBC electrodes (figure 5(c)), which exhibit two clear arcs at pO 2 = 10 −3 atm, one at high frequency (≃500 Hz) and the other at low frequency (≃1 Hz). The low frequency impedance was fitted with an R//Cpe circuit, which corresponds to O 2 gas diffusion according to its dependence with pO 2 (R LF ∝ pO −1 2 ) capacitance values (C ≃ 10 F cm −2 ) and its very low activation energy (E a ≃ 0 eV). Note that at normal ambient pO 2 the gas diffusion resistance contribution is extremely small; the focus here is on the other response that dominates under normal cell operating conditions. This high frequency arc is a Gerischer-type impedance, which is modelled with the ALS approach [60]. The resulting total fits are indicated with solid lines in the figure. For LPBC electrodes, both contributions are clearly distinguishable due to the differences in the characteristic frequencies and the low polarization resistance of the Gerischer-impedance. However, in some cases, the variation of pO 2 is not enough to properly separate overlapped contributions. This is the case of LSCF and NNO electrodes where, despite the Bode plots suggesting the presence of two arcs (see LSCF and NNO-P), the shape and size of the arcs is unclear (figures 5(a) and (e)). By changing the gas carrier from Ar to He, the identification of a high frequency TLM element (LSCF electrodes) or Gerischer-type impedance (NNO electrodes), and also a low frequency R//Cpe impedance, was possible. However, when changing from Ar to He, the R//Cpe impedances of the LSCF6428 and NNO-P electrodes do not show the expected reduction, associated with a ≃5 times higher diffusion coefficient of O 2 in He than O 2 in Ar. Then, only for the LSCF6482 electrodes the pure O 2 -gas diffusion was identified as a significant contributing process at very low pO 2 . On the contrary, in contrast to what was observed for LPBC electrodes, LSCF6428 and NNO-P show a response of the R//Cpe with the typical behaviour of a pure surface process, or a mixed contribution of both surface and O 2 gas diffusion processes [57,58,72]. These processes are evidenced by dependencies with pO 2 like R LF ∝ pO −1/2 2 or ∝ pO −3/4 2 and lower capacitance values (C ≃ 0.1-0.01 F cm −2 ) than the expected for gas diffusion. Finally, the NNO-SG electrode is fitted in the whole range of pO 2 by using a single Gerischer-type impedance. Figure 5 includes the result of fitting the EIS spectra with these electrical equivalent circuits. The Gerischer-type impedance increases following the trend LPBC < NNO ≈ LSCF, for resistances (e.g.: R G ) and time constants as well (e.g.: τ G ). Even though in all cases the dependency with pO 2 is R G ∝ pO −1/4 2 , a close examination of the slopes of diffusion and surface resistances with pO 2 shows that, in some cases, the R G ∝ pO −1/4 2 dependency is only due to the surface process (e.g.: LSCF6482). On the other hand, in other cases it is due to the combination of surface and diffusion resistances (e.g.: LSCF6428) [57]. However, analysing only EIS data, it is unclear if this fact is a consequence of the microstructures or an intrinsic characteristic of the MIEC electrodes, such as its  [57], (c)-(d) LPBC [60], (e)-(f) NNO [58,72]. Symbols correspond to experimental data and lines to the results of fitting. electrical conductivities, types of O-ion or electronic defects, crystal structures, surface characteristics, etc. In order to help shed light on this key question, in the next section the ALS approach is used to obtain and analyse the kinetic coefficients.
Finally, the evolution with time of the EIS spectra for LPBC electrodes was evaluated with the aim to identify the origin of the electrode degradation. Figures 6(b), (c), (e) and (f) show the EIS spectra, collected at different times, for LPBC (x = 0.0 and x = 0.5) electrodes. The polarization resistances associated with the contribution of each element are also plotted in figure 6(a) and (d). It is clear that for both electrodes, most of the degradation is in the Gerischer-type impedance (R G ), and that this effect is larger for the double perovskite Pr 0.5 Ba 0.5 CoO 3-δ than for the La 0.5 Ba 0.5 CoO 3-δ electrode.

The kinetic coefficients and the ORR limiting mechanisms
The molar surface exchange rate ℜ o and the O-diffusion coefficient D chem were obtained by combining R G and τ G , obtained from fitting the EIS spectra, with the microstructural parameters (ε, a and τ ) through equations (10.1) and (10.2). The microstructural parameters were extracted from 3D FIB-SEM reconstructions and thermodynamic information of oxygen non-stoichiometry (c O , x 0 δ and A). Table 3 [60] and (c) NNO [58] electrodes. Grey regions indicate ranges where surface reaction is chemisorption, dissociative adsorption, dissociation or incorporation-limited, according to the O-defects involved, thermodynamic factors, metallic or p-type semiconductor or alternative charge transfer amounts obtained by using methodology explained at [51]. [ * ] correspond to data from Adler's group [29].
For the LSCF6428 and NNO-P electrodes, for which the low frequency impedances -Z LF -were assigned to a surface process (according to its dependencies with pO 2 , capacitance values, activation energies, and effect of different gas carriers), its corresponding molar surface exchange rates ℜ o were calculated using equation (20). The normalized molar surface exchange rate values of La 0.6 Sr 0.4 Co 0.8 Fe 0.2 O 3-δ (LSCF6482) and La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ (LSCF6428) are also compared with La 0.8 Sr 0.2 CoO 3-δ (LSCF8210) and La 0.6 Sr 0.4 CoO 3-δ (LSCF6410) values, extracted from [29]. Figure 8 shows the chemical diffusion coefficients -D chem -versus pO 2 for (a) LSCF, (b) LPBC and (c) NNO electrodes. The pO 2 dependencies -m = ∂lnD chem ∂lnpO2 -are included in each plot. The D chem values of LSCF6482 and LSCF6428 electrodes are also compared with literature of La-Sr cobaltites data [29]. Figure 9 shows the estimated utilization lengths normalized to the electrode thickness, l δ /L, as a function of pO 2 . The dashed lines correspond to L = 3l δ , then if l δ /L ≫ 1 / 3 , the finite length electrode approximation is required. That is the case for LSCF electrodes, where the ALS-TLM approach is used to model the electrode response. For the other electrodes, l δ /L < 1 / 3 such that the conventional ALD model can be used. The behaviour of l δ is different for each sample, this is determined by the overall limiting mechanisms of the ORR. For example, at low pO 2 values, the lack of O 2 slows the surface reaction, giving time for O-ions to diffuse from longer distances, hence producing an increase in l δ /L in all samples as pO 2 decreases. For LPBC (x = 0.5) l δ /L ≪ 1, which is consistent with a low diffusion coefficient and high surface exchange rate, as shown in figure 8(b) and table 3. On the contrary, NNO shows similar values of diffusion coefficient to that of LPBC (x = 0.5), but the slow surface exchange rate makes the ratio l δ /L increase, making the reaction to happen all along the electrode. In the case of LSCF, the speed of the surface reaction is slow (see table 3), making all the electrode active.
Finally, the time evolution of the kinetic coefficients for LPBC electrodes is shown in figure 10. The percentage changes are included in the plot. On the one hand, it is notable how the surface exchange coefficient for the double perovskite decreases with time, whereas for the mixed cubic/tetragonal phase k chem did not show significant degradation or even improvement with time. On the other hand, the coefficients associated with O-ion bulk diffusion decrease drastically for all compositions. Figure 10 also includes results from a degradation study performed on a La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ (LSCF6428) commercial electrode [42]. Besides being performed twice as much time as that of the LPBC experiments, the LSCF6428 electrode was also aged at a higher temperature (800 • C) than the LPBC electrodes. Even so, the kinetic parameters of LSCF6428, obtained at 700 • C using the same methodology, show a lower degradation rate.

Discussion
In the Results section we showed how the combination of 3D FIB-SEM tomography with EIS and the ALS model can be used to obtain the kinetic parameters of a wide variety of porous MIEC electrodes. The change of ℜ o /ℜ o (1 atm) with pO 2 in figure 7 and the values reported in table 3 are in most cases compatible with a surface rate limiting mechanism controlled by dissociation or dissociative adsorption surface reactions. These surface processes contribute to the Gerischer-type impedance and are co-limiting with the O-diffusion. Figure 8 suggests that, whereas the behaviour of the diffusion coefficients of LPBC and NNO electrodes are consistent with an O-ion bulk path (D chem ∝ pO 0 2 ), the dependence of D chem with pO 2 indicates a certain surface character for O-ion diffusion in LSCF electrodes (D chem ∝ pO m 2 , m ≥ 0.2). All this information provides the basis for discussing the effect of different structural and chemical properties on the ORR mechanism. Based on these arguments, the rational design of SOFC electrodes becomes a more realistic endeavour. In what follows, we present a brief discussion about the effects of chemical composition, microstructure, and crystallographic structure on the kinetic coefficients and ORR limiting steps.

Effect of the microstructure on the ORR
The comparison between the Nd 2 NiO 4 +δ electrodes provides useful information regarding the effect of the microstructure on the kinetic coefficients. These samples were synthesized with different chemical methods, giving as main consequence a three times lower specific surface area for the NNO-P electrodes than for NNO-SG. The diffusion coefficient is not modified in its value or its nature by the change in microstructure. This is expected, considering that the diffusion of the O-ion in NNO is through the bulk of the material, and the change in surface areas, porosity, or tortuosity values should not change the bulk properties of the material. The contribution of surface processes to the impedance is greater for the lower specific surface area NNO-P sample compared to the NNO-SG sample. The main difference observed in the figure 7(c) is the appearance of a new contribution (evidenced by the low frequency impedance arc) for NNO-P. Considering the availability of interstitial sites and the poor electronic conductivity of these nickelates, the O-diffusion is expected to be co-limiting with a surface process involving charge transfer, e.g. O 2 -chemisorption. These charge transfer processes have large energy barriers [51,73], in agreement with those reported in table 3 for NNO electrode (>1.3 eV).
Note that R SG G ≃ √ aP √ aSG R P G , in agreement with equation (10.1) and the fact that both electrodes have similar values of molar surface exchange rates (see figure 7 and table 3). This confirms the assumption that the same diffusion and surface processes are associated with the Gerischer response. However, for NNO-P, with a specific surface area three times lower than NNO-SG, a second surface process becomes also rate limiting. Note that in this case R RCpe ∝ 1 a (see equation (20)) and the impact of changes in specific surface area is higher than in the Gerischer response. This second arc, associated with a surface process, also depends on the This secondary process in the impedance spectra is relevant only when a low specific surface area limits the availability of active surface sites. However, the possibility of these differences being also due to variations in cation and defect surface concentrations, associated with different processing methods, cannot be discarded. For example, complementary XPS studies indicate that the NNO-P surface is Nd-enriched (Nd +3 /Ni +2 ratio 70/30) in comparison with the NNO-SG surface (Nd/Ni ratio 55/45). This could be either from Nd-segregation or Ni evaporation during the electrodes processing.
Nevertheless, considering that the surface reaction impacts the resistances as R RCpe ∝ 1 a or R G ∝ 1 √ a , developing nano-scaled electrodes is one of the main issues in recent SOFC R&D [74,75]. Particularly, the infiltration of porous ion conductors scaffolds with MIEC oxides gives very low polarization resistances [76,77], however it also can activate degradation problems associated with particle coarsening processes [7].

Effect of A-site and B-site substitutions on the reaction mechanism
In this section, the effect of electrode composition is discussed, using the porous electrodes belonging to the single cubic perovskite family of La-Sr cobalt-ferrites as an example. Also for comparison, the La-rich LPBC electrodes are included which, despite having a mixture of cubic and tetragonal phases, present similar characteristics to the cubic perovskites.
The main difference found between these perovskites is in the surface exchange limiting step. The Co-rich compositions, characterized by a metallic band structure (LSCF6482 and LPBC-have electronic conductivities greater than 10 3 S.cm −1 [69,78,79] [51,73]. LSF is chemisorption-limited with a high activation energy, whereas LSC is dissociative adsorption-limited, authors also considered that the metallic band structure of LSC helps stabilizing physisorbed O 2 relative to p-type semiconducting LSF. Differences in the mechanism of O-diffusion are also observed. The O-ion bulk diffusion mechanism acquires a more superficial character for those compositions with lower O-vacancies, e.g.: La-Sr cobalt ferrites seem to have O-diffusion closer to the surface than La-Ba cobaltites. This is evidenced by the increment of the diffusion coefficient dependence with pO 2 . These results are similar to those reported by Lu et al [29] when comparing La 0. 6  Taking these results into account, it is possible to propose strategies to improve electrode materials according to the origin of the mechanisms controlling both the surface reaction and the O-ion diffusion, without modifying the electrode bulk composition or microstructure. An example following this logic is the surface modification of charge transfer limited materials with high electronic conducting materials, with the aim of assisting the charge transfer reactions. These kind of strategies have already been put into practice in recent years, with promising results, by infiltrating, for example: LSCF6428 cathodes with PrO x [80,81], La 0.8 Sr 0.2 MnO 3-δ (LSM) [82], Ag nanoparticles and coatings [83]; or Co 3 O 4 and Ag particles and coatings into LSF electrodes [84,85] or amorphous FeO x coatings on SrSc 0.2 Co 0.8 O 3-δ (SSC) [86], among many others. Also, the materials with low oxygen vacancy availability on its surfaces have been modified with ion-conducting materials. An example is the infiltration of LSCF with GDC coatings or nanoparticles [87,88], where the polarization resistance of a La 0.8 Sr 0.2 Co 0.5 Fe 0.5 O 3-δ cathode was reduced from 0.65 to 0.2 Ωcm 2 , at 700 • C, when it is infiltrated with large amounts of GDC [89]. Similar results were found for a LSCF6428-GDC composite cathode coated with GDC nanoparticles, where the polarization resistance decreases from 0.4 to 0.05 Ωcm 2 at 700 • C with the consequent 20% increment of the SOFC power density [87].

Effect of A-site substitution on electrode degradation
One of the main issues causing instability of Sr-rich electrodes is Sr-surface segregation [90,91]. In this section, the effect of composition on the segregation process is considered by comparing the time-dependent response of La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ [42] and La 0.5 Ba 0.5 CoO 3-δ [60] porous electrodes.
One of the main differences observed between these two electrodes is the larger Ba-cation surface segregation in comparison with the Sr-segregation: Ba surface concentration increases at approximately twice the rate of the Sr concentration (see [42] and [60]). This is in agreement with the idea proposed in [92] that segregation is linked to the elastic energy generated by the size mismatch at the A site between the host (La) and dopant (Sr 2+ /Ba 2+ ). Thus, a larger dopant (Ba) tends to segregate faster towards the surface due to the greater amount of elastic energy generated in the system.
The effect of segregation on the kinetic coefficient also varies considerably in the different materials. While Sr-segregation in La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ causes both kinetic parameters to decrease~50% after aging, for La 0.5 Ba 0.5 CoO 3-δ the diffusion coefficient decreases by nearly 100%, but the surface exchange rate actually increases by 66%. In both kinds of electrodes, the surface exchange rates were associated with dissociative adsorption. The extensive literature related to the Sr-segregation problem associates the degradation of the polarization resistance to the fact that the segregation of SrO species blocks the surface exchange process [93]. However, the effect of Ba-segregation is not entirely clear. A few works studying the effect of BaCO 3 nanoparticles decorating the surface of LSCF [94] and LSF [95] cathodes demonstrated that Ba ions improve the chemical oxygen surface exchange coefficients, and that the barium ions on the surface might play a key role in the adsorption of oxygen molecules and the formation/decomposition of intermediates [96]. This could be the case of La 0.5 Ba 0.5 CoO 3-δ , where the formation of Ba-rich nanoparticles on the surface of the aged electrode was observed.
The degradation of D chem deserves a separate consideration because the pO 2 dependence suggested an O-ion bulk diffusion mechanism. Then, it is reasonable to assume that this decrease would be associated with a negative impact of the Ba/Sr depletion in the sub-surface region, which naturally accompanies the cation-surface enrichment during segregation. It is plausible that the loss of Ba/Sr could produce a local lattice distortion affecting the O-ion transport, affecting the surface diffusion processes.
The Ba/Sr segregation may be controlled or reduced, for example, the Sr segregation on LSCF decreases substantially by reducing the operation temperature [42,97]. Also, taking into account that the cation segregation is promoted by the increase in elastic energy due to the size mismatch at the A-site, a simpler alternative would be to reduce the elastic energy by specifically doping with smaller cations -e.g.: partial substitution of Sr 2+ by Ca 2+ , or Ba 2+ by Sr 2+ in La-Sr and La-Ba cobaltites, respectively-or by generating free space in A-site deficient materials. However, both cation substitution and A site-deficiency also modify the kinetic parameters. Another alternative could be to prevent the Ba/Sr segregation by decorating the surface. This decoration could either modify the local elastic energy or the electroneutrality of the surface to prevent cation segregation. For example, the stable operation of La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ electrodes after aging was assigned to the suppression of SrO segregation by a surface decoration with GDC nano-particles [98]. Cation surface segregation is also promoted by the increase of surface oxygen vacancy concentration and, for this reason, an alternative to suppress this effect is covering the surface with less reducible cations such as Hf or Zr [99]. More details about this kind of strategies to mitigate Sr and Ba segregation can be found in [91].

Effect of crystal structure on the reaction mechanism
To analyze the effect of crystal structure on the mechanism of reaction, the results of the layered electrodes (Pr-rich LPBC and NNO) are compared with those of single cubic perovskite electrodes (La-rich LPBC and LSCF). In general, the main effect of the structuring of perovskites in layered structures is to reduce the diffusion coefficients. Thus, cubic perovskites present higher diffusion coefficients than layered nickelates-with interstitial O-ion conduction -, which in turn present larger diffusion coefficients than layered perovskites with O-vacancy conduction mechanisms.
Unlike LSCF and LPBC electrodes, NNO electrodes have O-interstitials instead of O-vacancies. These kind of defects are highly mobile [100], but it has been theoretically [101] and experimentally [102] demonstrated that in these nickelates the O-ion diffusion is highly anisotropic through the a-b plane in NdO layers (see figure 3(e)). Thus, although the mobility of O-interstitials is high, it is reasonable to assume that the lower O-diffusion coefficient for NNO than for isotropic cubic perovskite structures must be a consequence of a 2D diffusion path for O-migration.
On the other hand, theoretical [101,103,104] and experimental [79] studies also confirm the anisotropic oxygen diffusion in layered Ln-Ba-Co-O structures, characterized by migration from the Ln-O layer to the Co-O layer or vice versa. This anisotropic migration reduces the ionic conductivity for tetragonal PrBaCo 2 O 6-δ [69] and the polarization resistance of LaBaCo 2 O 6-δ cathodes [10] respect to those of cubic La 0.5 Ba 0.5 CoO 3-δ perovskites. However, the difference between the tetragonal perovskites studied in [10,69] and the La-rich LPBC presented in this work, is that the latter are a mixture of cubic and tetragonal phases. This phase mixture could be the cause of the improvement in the ORR polarization resistance, as it was proposed for two-phases composites prepared by mixing different order Ruddlesden-Popper nickelates [105]. However, neither the simple mixture of two phases or the isotropic diffusion for cubic perovskites can explain the two orders of magnitude difference in D chem between the pure tetragonal Pr-rich LPBC (D chem ≃ 10 −8 cm 2 .s −1 ) and the cubic-mixed-with-tetragonal La-rich electrodes (D chem ≃ 10 −6 cm 2 .s −1 ) discussed here. The reason for this difference seems to be related to the fact that La-rich LPBC electrodes are not a regular composite resulting from a simple phase mixture. These electrodes show a unique microstructure, where the cubic and tetragonal phases coexist intimately mixed (see figure 3(d)), forming heterostructured interphases. This microstructure is highly distorted, with highly defective interfaces that can promote fast O-grain boundary diffusion as it was proposed to happen for a La 0.3 Pr 0.2 Ba 0.5 CoO 3-δ dense membrane with highly distorted structure, which showed an ionic conductivity one order of magnitude higher than pure cubic and tetragonal phases [69].
This kind of anomalous behaviour in the ORR has already been reported in the case of a specially designed heterostructure, with LSC-113/214 interfaces, formed by La 1-x Sr x CoO 3-δ (LSC-113) and the Ruddlesden-Popper (La 0.5 Sr 0.5 ) 2 CoO 4-(LSC-214) phases [106][107][108][109]. These studies consistently show that, when compared to bulk or thin LSC-113 or LSC-214 films, the LSC-113/214 heterointerfaces dramatically enhance the oxygen exchange rate and ORR kinetics. The authors explained this improvement through an A-site cation interdiffusion across the LSC-113/214 interface, which leads to the increase in the O-vacancy concentration enhancing the interfacial conductivity, surface oxygen exchange and therefore the ORR kinetics [110]. Thus, a similar situation could be expected for La-rich LPBC electrodes, where the presence of highly active interfaces could explain the two orders of magnitude higher diffusion coefficient. This opens a door for new design ideas for SOFC electrodes including complex heterointerfaces. Figure 10 shows that time evolution affects both, the diffusion coefficient and the surface exchange rate for LPBC electrodes. In all cases, the O-ion bulk diffusion decreases around 100% independently of the structural effect discussed in the previous section. On the other hand, although the mechanism of surface reaction is the same for all LPBC electrodes, the value of k chem is noticeably higher for the layered structures than for other electrodes (See table 3). Also a different evolution with time behavior is observed for tetragonal perovskite e.g.: k chem decreases with time for Pr-rich LPBC electrodes while it increases or stays almost constant for La-rich LPBC electrodes ( figure 10). From the analysis of the time evolution of the polarization resistance (figure 6), microstructure and surface cation concentration, it was concluded that degradation is mainly due to the Ba-surface segregation (increases about 50%-100% during aging) rather than particle coarsening (reduce specific surface about 15%) [60].

Effect of crystal structure on electrode degradation
Note that Ba-segregation is so fast that it also takes place during the sample processing. However, the Ba segregation is especially high for the tetragonal phase (Pr 0.5 Ba 0.5 CoO 3-δ ), where the estimated number of monolayers in the as-prepared electrodes is more than twice as much as the observed for the other LPBC electrodes and, as with other electrodes, also increases with time [60]. It has also been argued that Ba-segregation probably has an active role in two competing processes; on the one hand it seems to play a positive role in the formation/decomposition of intermediates for O 2 adsorption [96], whereas on the other hand it can block the surface exchange process [93], in a similar fashion to what is observed with Sr segregation.
Considering that the tetragonal phase (LPBC x = 0.5) has the higher Ba-surface concentration and the higher initial k chem , the highly negative impact in the surface exchange rate observed is expected to be due to the -almost complete-blocking of surface sites for reaction. But for the La-rich LPBC electrodes with lower surface exchange rate, the low Ba-surface concentration can either have a neutral effect or even improve the surface reaction, by assisting in the dissociative adsorption through the promotion of the O-vacancies formation. However, in all cases, the global impact of Ba-segregation is detrimental to the response of the electrode and, as discussed above, the implementation of strategies to avoid cation surface segregation are strongly recommended.

Conclusions
In this review, the 3DT-EIS method for obtaining the ORR kinetic parameters (k chem and D chem ) for porous MIEC materials, with applications to SOFC electrodes and other energy devices is discussed. This method combines EIS and 3D FIB-SEM tomography measurements with analysis done using the ALS model. Besides the understanding of the basic mechanisms controlling the responses of the electrodes, the 3DT-EIS method allows the identification of specific effects produced by differences in nano/microstructure, surface compositions, crystal structure and A or B specific doping effects on the kinetic parameters of real porous electrodes. This method has advantages compared with other experimental techniques, including the ability to measure both k and D over a wide range of conditions, and obtaining quantities that are relevant to actual electrodes prepared under normal processing conditions. Also note that the increasing availability of 3D FIB-SEM tomography, in combination with the widely-used EIS measurements, makes this experimental approach more readily accessible, such that a more widespread use is expected to be seen in the near future.
For the discussion, results of La-Sr cobalt ferrites (La 0.6 Sr 0.4 Co 1-x Fe x O 3-δ , x = 0.2 and 0.8), La/Pr-Ba cobaltites (La 0.5-x Pr x Ba 0.5 CoO 3-δ , x = 0.0, 0.2 and 0.5) and Ruddlesden-Popper nickelates (Nd 2 NiO 4+δ ) were shown as specific examples about the effect of the chemical composition, crystal structure, and microstructure on the ORR and electrode degradation mechanisms.
The analysis of the dependence of molar surface exchange rates with oxygen partial pressure provides information about the mechanisms limiting the O 2 -surface reaction. According to the interplay between electronic conductivity and availability of surface empty sites, two alternative surface reaction paths were observed: dissociative-adsorption, limited by the availability of near empty surface sites On the contrary, the diffusion coefficients D chem are higher for cubic perovskites than for the layered ones. For La 0.6 Sr 0.4 Co 0.8 Fe 0.2 O 3-δ and La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ , D chem is 2.6 10 −6 and 5.4 10 −7 cm 2 .s −1 , respectively. These values are comparable to the D chem value of 1.2 10 −6 cm 2 .s −1 observed for La 0.5 Ba 0.5 CoO 3-δ . However, whereas the large O-vacancy content allows for an O-ion bulk diffusion mechanism for La/Pr-Ba cobaltites, as Fe content increases in La-Sr cobalt ferrites, the surface character of O-ion diffusion also increases. The layered structure drastically reduces the O-ion bulk diffusion due to anisotropy effects, e.g.: D chem = 1.3 10 −8 cm 2 .s −1 for the Pr 0.5 Ba 0.5 CoO 3-δ double perovskite. However, in the case of Nd 2 NiO 4+δ , this effect is compensated by a high mobility of O-interstitials (D chem ≃ 10 −7 cm 2 .s −1 ).
Analysis of the time evolution of the electrodes shows that surface cation segregation affects both the O-ion bulk diffusion and the surface exchange rates. Although the impact of the cation surface segregation on the diffusion coefficient is negative in all cases-e.g.: diffusion coefficients are reduced 100% for both La-Sr and La-Ba single and double layer perovskites-the surface exchange rate can be impacted either negatively or positively. This depends on the competition between two possible effects, the ORR surface sites blocking by Sr/Ba-segregation or the dissociative adsorption assistance by BaO nanoparticles.
Finally, some strategies to reduce the cathode polarization losses are discussed, with specific examples and proposals for materials design strategies.