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Fundamentals of SOFC

Fuels cells are electrochemical devices that can directly convert the energy stored within the chemical bonds of a fuel into electrical energy and heat. The main difference between a fuel cell and heat engine is that in heat engines chemical energy is first converted into mechanical energy and then into electrical energy which in turn result in loss of energy. On the contrary, the working principle to generate electricity through electrochemical reactions is similar to batteries; however, a fuel cell produces electricity as long as it has a fuel supply, while the battery must be recharged after being used up. The operation of a fuel cell or any other combustion cell is simply the combustion of a mole of hydrogen gas (fuel) and half a mole of oxygen gas (oxidant) producing a mole of water.
This is a reaction involving bond splitting of one mole of H-H bonds and half a mole of O-O bonds to form two O-H bonds. Energy is provided by the combination of atoms and decrease of the entropy. The excess energy is released as heat. In a combustion engine, this heat is converted into mechanical energy and then into electrical energy, which brings about loss of energy in each stage. On the other hand, an electrochemical fuel cell benefits from spatial separation of hydrogen in the anode and oxygen in the cathode compartments (Figure 1-1). The two half reactions are combined by the electron transfer. Therefore, since the electrons move from the fuel species to the oxidant species, they represent an electrical current. The two electrochemical half reactions are: the oxidation reaction at the anode: + 2− →+2 − 1-2
the reduction reaction at the cathode: 1 + 2 − → 2− 1-3
As shown in Eq. 1-4 and Eq. 1-5, chemical energy is formed from chemical reaction between the oxidizing gas (oxygen, O2) on the cathode side and the fuel gas (in this case hydrogen, H2) on the anode side. The resulting reaction products (in this case water vapor, H2O) are carried out from the anode side. The dense electrolyte separates the two compartments. This results in an oxygen partial pressure gradient between the cathode side and the anode side, which is maintained by the continuous feeding and removal of the gases. Because of the gradients, oxygen ions are transported from the cathode side to the anode side. On the cathode side, the oxygen ions are provided from the oxygen molecules in the gas phase, while the electrons are received from the anode side by the external circuit. On the anode side, the oxygen ions react with hydrogen to give water vapor and return in the gas phase.
The transport of oxygen ions is accompanied by a depletion of electrons on the cathode side and an accumulation on the anode side, where an ideal electrolyte has only the conductivity for oxygen ions. Accordingly, a potential difference is created between the electrodes. The potential differences can be balanced through the external circuit, thereby providing the electrical energy for the consumer.
In the case of an open circuit, an equilibrium situation will be reached after a relaxation period. The potential gradient, which at first causes oxygen ions to move from cathode to anode side, is balanced by an electrical gradient opposite to the direction of the diffusion force. In this situation the Nernst-voltage ENernst arises between cathode and anode as shown in the following equation: = − ( 2 ) 1-6 0 1/2 2 where E0 the standard cell potential, R the gas constant, F the Faraday constant, n the number of electrons involved, T the temperature, p the partial pressure of reactants and products. In typical operation temperatures (800 °C) of a SOFC operated on hydrogen and air values around 1.1 V is obtained as Nernst voltage.

Electrochemical Processes at MIEC Cathodes

The proposed reactive pathway is decomposed into a succession of steps that combines a “bulk” and a “surface” path (Figure 1-2). Both pathways are joined in a common reaction corresponding to the oxygen desorption/adsorption that produces/consumes gaseous oxygen molecules in the electrode porosities. They are in competition and occur parallel to each other. The slowest process in such a situation is referred to as rate determining step. However, the knowledge about this reaction is still limited, even though considerable research have been made over the years.
The oxygen surface exchange reactions involving are suggested to comprise adsorption of O2 on the cathode surface and its dissociation into two oxygen atoms. Oxygen is then incorporated as an oxygen ion (O2−) into a vacancy (VO••) in the vicinity of the surface ( ) with a number of steps. These steps are summarized in 4 steps from Eq. 1.7 to Eq. 1.10. The charge transfer steps includes adsorption of gaseous O2 onto an open surface vacancy, dissociation of O2 by the occupation of a neighboring surface vacancy, and incorporation of the surface oxygen into the bulk .

Power Losses in SOFCs

The performance of a fuel cell can be depicted from an I-V curve as shown in Figure 1-3. The current is normalized to the area of the fuel cell (A cm-2) in order to be comparable with other systems. The voltage output of a real fuel cell is less than the thermodynamically predicted voltage output due to irreversible kinetic losses. The more current drawn from the system, the greater is the voltage drop from the ideal voltage. Three major losses account for the difference between the two curves, namely; ohmic, activation and concentration polarizations.
The overall cell voltage can be calculated using the following equation: UC : Real output voltage of the fuel cell : Thermodynamically predicted voltage output of the fuel cell from Eq. 1.4 ηohm : Ohmic losses based on total fuel cell current including fuel crossover loss : Activation losses based on total fuel cell current. Superscript a and c refer to anode and cathode, respectively. : Concentration losses based on total fuel cell current. Superscript a and c refer to anode and cathode, respectively.
Ohmic losses, ηohm, occur during the electronic or ionic transport through the electrodes and the electrolyte, since every component has a finite conductivity. The overall ohmic resistance is the sum of each individual ohmic contribution Rs. According to Ohm’s law, the ohmic overpotential linearly increases with the current density j. ℎ = ∙ ∑ = ∙ ℎ 1-12
Concentration polarization, , is another significant loss, which originates from the transport of gaseous species through the porous electrodes by bulk diffusion and Knudsen diffusion. From the Nernst equation (Eq. 1.6), it is clear that decreasing the partial pressure of reactants causes a voltage drop. Electrode microstructures, pore sizes and pore morphology (tortuosity) are shown to influence the transport of gaseous species. Smaller electrode thicknesses are suggested to avoid concentration polarization losses [3].
Activation polarization, , describes the electrochemical loss mechanisms taking place mainly at the three-phase boundary (TPB) where ionic-conducting, electronic-conducting and gas phases meet. An activation energy is necessary in order to overcome the energy barrier that prevents a spontaneous reaction. The higher the temperature, the higher the probability for reactants to gain the necessary activation energy, therefore the overpotential is reduced. A commonly used equation for describing the influence of activation overpotential on current density is the well-known Butler-Volmer equation: a nF c nF 1-13 jjo exp( ) exp( ) where is the exchange current density, n is the number of electrons involved in each electrode reaction, a and c are the anodic and cathodic charge transfer coefficients, and η is the activation overpotential of the electrode.

Triple Phase Boundary

In a system where the cathode is purely electronic while the electrolyte is ionic conductor (e.g. LSM), the electrode reactions are bound to happen on the triple phase boundary points (TPB) as illustrated in Figure 1-4a. In this case, the presence of all three phases is essential to support the oxygen reduction reactions. In composite electrodes comprising electronic and ionic conductivity such as LSM/YSZ or a mixed ionic-electronic conductor (MIEC) such as LSCF, the process of charge transfer extended at the electrode/electrolyte interface, beyond the triple phase boundary (TPB) points as depicted in Figure 1-4b. This means that the microstructural requirements can be less stringent; however in the case of LSM/YSZ, percolation of each phase between the electrolyte and current collector remains a pre-requisite for electrochemical activity. In this case an ‘active two phase boundary’ defines the solid/pore interface.
Figure 1-4 a) Electrode reaction sites restricted in TPB regions in electronic conducting cathode. b) Electrode reactions sites are extended to the whole volume of the electrode in a MIEC cathode. Reprinted from ref. [4].
In view of the connectivity of the phases by the percolation theory, some active and inert TPBs must be considered. A connected pathway of ionic conductor is required to deliver oxide ions from electrode to the electrolyte. Similarly, a continuous pore network is essential to deliver gas species to the surface of the electrode. Therefore, an isolated pore will not contribute to the gas transport, thus reducing the overall porosity and active surface area.
In the case of composite electrodes comprising a MIEC and an ionic conductor (e.g. LSCF/CGO) the percolation of the CGO phase will be crucial when the ionic conductivity of the MIEC falls down in a great extent at low temperatures and when it behaves as a pure electronic conductor. In such a case, active and inert TPBs determine the overall performance. As an example, TPB1 can be considered theoretically active as there is a contiguous ionic, electronic and pore network. However, TPB2 and TPB3 are inactive because of a lack of connectivity in the electronic and ionic phases, respectively (Figure 1-5).
Figure 1-5 Representative composite cathode, blue is ionic conducting phase, red is electronic conducting phase. Reprinted from ref. [5].
In summary, most of the power losses in a SOFC cell originate from the electrode and the electrolyte. The rate of electrode kinetics and charge transfer properties in the solid state depend on the physical and chemical properties of the SOFC elements. Furthermore, since the individual losses scale with the relevant geometrical parameters, the geometry of electrode (microstructure) and the electrolyte (thickness) are decisive in SOFC performance. Accordingly, the main focus of the development of SOFCs is directed on the reduction of polarization and ohmic losses through the material choice and the microstructural design. A fine microstructure would increase the active sites for oxygen reduction reactions (ORR) and facilitates the electrode kinetics. Particularly, the amount and the scale of the porosity have great significance in rate determining steps. An open porosity helps bringing the oxygen to the active sites. At the same time, porosity in the nano-scale increases the surface area, thus enabling more oxygen exchange at the surface. The electrochemically active zone in a cathode material is restricted from some hundreds of nanometers to a few micrometers. This could be further exploited by engineering the structure of the pores; nano-scale porosity near the electrode/electrolyte interface and micro-scale porosity above the active length to convey the bulk diffusion of oxygen. Hierarchically structured porous materials are increasingly being recognized by their high performance in many applications for energy conversion and storage devices [6,7]. It has been shown that while macro-pores facilitates mass transport, nano porous network enhances electrochemical reactions in the SOFC electrodes [8]. Nevertheless, hierarchical porosity should be well tailored according to the percolation of electronic and ionic phases. All these factors play a key role on the polarization resistance of SOFC electrodes [9–11]. In the following, after a quick review on the state-of-the-art electrolyte and anode materials, more detailed information on the cathode materials are given.

State-of-the-art SOFC components

Numerous materials and material combinations have been considered since the SOFC research has emerged. Nevertheless, only a few candidates take the lead for SOFC components. Common materials for electrolytes and anodes are presented in the following sections. According to the focus of this work, detailed information will be given on the cathode materials, in particular La0.6Sr0.4Co0.2Fe0.8O3-δ will be discussed.

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Electrolyte materials

The main task of the solid electrolyte is to separate the cathode and the anode gas space and connect them by only ion conduction. The membrane must therefore be gas-tight and have high ionic conductivity ( ic) and low electronic conductivity ( ec). Doped zirconium oxide (ZrO2) has established itself as one of the most preferred electrolyte material as it best meets the requirements. The high ionic conductivity of the material results from the substitution of Zr+4 cation by a trivalent cation from transition group metals. Typically, yttrium or scandium are used, although other cations such as the alkaline earth metals, calcium or magnesium (low ionic conductivity) or the rare earth samarium, neodymium, dysprosium or gadolinium, would also be possible [12]. The oxygen vacancies are formed by this substitution in the crystal lattice, thus leading to an improvement in the ionic conductivity, which is based on a hopping mechanism [13]. This process is thermally activated, so that high temperatures up to 1000 °C are required for high ionic conductivity. Most commonly yttrium is used as a doping element with 8 mol. % Y2O3 in ZrO2 (8YSZ). With this doping amount the fluorite phase is stabilized in the cubic phase up to the melting point above 2500 °C [12]. The linear thermal expansion coefficient of 8YSZ in the temperature range of 30 to 800 °C is 8YSZ = 10.5•10-6 K-1 [14]. Besides 8YSZ, 3YSZ (3 mol. % Y2O3 in ZrO2) has also been extensively studied in the past. It is mechanically much more stable (higher tensile strength, elastic) than 8YSZ, but has a significantly lower ionic conductivity [12,15]. The highest ionic conductivity of doped zirconia is achieved with a doping of 10 mol. % Sc2O3. This is attributed to the lower distortion of crystal lattice (ionic radii of Sc+3 is close to Zr+4), leading to a smaller energy for defect association, which increases mobility and thus conductivity [16,17] (Figure 1-6).
In addition to the zirconium oxide-based electrolyte materials, there are other interesting alternatives to YSZ, especially for lower operating temperatures, such as ceria-based or lanthanum gallate-based materials [4,16]. The most common doping of ceria-based electrolyte materials are gadolinium (CGO), samarium (SDC) and yttrium (YDC), wherein cerium oxide doped with gadolinium and samarium ions have the highest ionic conductivity due to similar ionic radii of Gd3+ and Sm3+ to that of Ce4+. For CGO, there are often inconsistent experimental reports for the optimal doping concentration of gadolinium that exhibits the maximum conductivity. For instance, 10 mol. % [18], 15 mol. % [19] or 20 mol. % [20] have been reported as optimum. Some authors suggested that the peak concentrations were temperature dependent. For example, shifts from 15 to 21 % mole fraction of the dopant with a temperature increase from 500 to 800 °C [21], from 20 to 24 % mole fraction with a temperature increase from 700 to 800 °C [22], and from 15 % mole fraction of the dopant below 400 °C to 20 % above 400 °C [20] have been reported. The scatter in the data can be mainly attributed to the sample preparation, e.g. fabrication technique, sintering temperature, the amount of impurities in the starting powders. Steele reported a considerable grain boundary resistivity in the presence of SiO2 in ceria-based materials [23]. He described SiO2 as an omnipresent impurity in minerals, which can also easily be introduced from the furnace refractories during sintering procedure. Kharton et al. reported the best stability for 10 mol.% Gd doped ceria (Ce0.9Gd0.1O2-δ) in reducing atmospheres and at temperatures below 1000 K, which makes Ce0.9Gd0.1O2-δ the most appropriate electrolyte material for IT-SOFCs [24]. The linear thermal expansion coefficient of Ce0.9Gd0.1O2-δ in the temperature range of 30 to 800 °C is CGO = 13.4•10-6 K-1 [24]. In comparison to zirconium oxide-based electrolytes, doped ceria electrolytes have the advantage of being chemically stable with highly active cathode materials such as (La,Sr)CoO3- (LSC), (La,Sr)(Co,Fe)O3- (LSCF), and La(Ni,Fe)O3- (LNF). Therefore, they are used as barrier layer between otherwise incompatible combinations of 8YSZ and the aforementioned electrodes [25,26].
Figure 1-6 Temperature-dependent ionic conductivity of solid electrolyte materials. The two lateral lines represent the theoretical ionic conductivity for 1 and 10 μm thick electrolytes. Reprinted from [27].
Unfortunately, ceria undergoes partial reduction to Ce3+ in a reducing atmosphere, such as the one existing at the anode [28,29]. The electrolyte becomes mixed conductor, resulting in an internal short circuit of the cell. Studies on Ce0.9Gd0.1O1.95 have shown that this is particularly pronounced at temperatures greater than 600 °C [30]. However, this may be acceptable for applications at lower temperatures [30]. Nevertheless, the electronic conductivity cannot be completely eliminated even by a thin, electron-blocking intermediate layer of doped zirconia [31,32].
The lanthanum gallate perovskites, especially doped with strontium and magnesium, La1−xSrxGa1−yMgyO3- with x, y = 0.1-0.2 (LSGM), possess the highest ionic conductivity at temperatures greater than 650 °C compared to the previously mentioned materials (see the trend in Figure 1-6). Furthermore, the linear thermal expansion coefficient of LSGM in the temperature range of 30-800 °C is in the range of LSGM = 10.4 -10.9•10-6 K-1 [14]. However, this material show several chemical instabilities, e.g. Ga evaporation during sintering [33], formation of a poorly conducting second phase in combination with nickel-containing anodes, degradation during long-term exposure in reducing environments (gallium oxide depletion) [34], which make them dubious candidates for further application in SOFCs.
For an electrolyte resistance less than 0.1 Ω cm2 (consistent with a desired power density greater than 1 W cm-2) and a typical electrolyte thickness of ~ 10 μm, the conductivity of the electrolyte should be greater than 0.01 S cm-1. Following Figure 1-6, the operating conditions of YSZ should be higher than 700 °C. Otherwise, reducing the thickness of the YSZ to 1 μm, allows the operating temperature to be lowered to 600 °C. Apart from that, higher conductivity electrolyte materials such as ScSZ, CGO or LSGM or the combination of two ionically conducting bi-layered electrolytes can be used for intermediate to low temperature SOFCs.

Anode materials

At the anode, the fuel gas reacts with oxygen ions coming from the electrolyte at the TPB, giving two electrons per oxygen ion. In the case of hydrogen (H2) as fuel gas, water vapor is produced (Eq. 1-1).
In principle, the following requirements should be fulfilled: The anode must have high electrical conductivity, high catalytic activity and high number of reaction sites (TPB). It should also be sufficiently porous in order to ensure the supply and removal of the fuel gas and the reaction products. Furthermore, it must be chemically stable and chemically compatible with the electrolyte material. These requirement profiles are best met in a combination of nickel and YSZ [35]. This composite anode shows a percolation threshold in the conductivity vs. the amount of Ni curve. The percolation of the two conducting phases, Ni the electronic conductor and YSZ the ionic conductor, is required to ensure a well-functioning anode [36]. Pure metallic nickel has a very high thermal expansion coefficient (TEC) (16.9•10-6 K-1), compared to 8YSZ (10.5•10-6 K-1). When both are mixed, they form a Ni-YSZ cermet which has a reduced TEC (12.7•10-6 K-1, for 40 vol. % of Ni + 60 vol. % YSZ).
Although, the potential of Ni-YSZ cermet as anode material is beyond doubt, there are still some problems such as agglomeration of nickel, sulphur poisoning and carbon deposition when natural gas is used as the fuel. Issues similar to electrolyte materials may come up, regarding the expansion of its volume upon redox cycling which may even cause cracking of the anode (cermet) and/or thin electrolyte coating. This may lead to gradual degradation in output power.

Cathode Materials

Cathode polarization resistance is a dominant cell loss mechanism with relatively high activation energy associated with oxygen reduction especially at low temperatures. A good candidate should possess sufficient electronic conductivity to minimize ohmic losses. A thermal expansion coefficient matching reasonably well with the electrolyte material is also desirable to avoid thermo-mechanical stresses. Phase stability with the electrolyte is another issue to be concerned about for long-term usage.
Three main families of perovskite based MIEC cathodes have been extensively studied for IT-SOFCs: the cubic type perovskites (ABO3), the layered perovskites (AA’B2O6) and the Ruddlesden-Popper (An+1BnO3n+1) phases. Since a cubic type perovskite is used in this thesis, only the crystal structure of ABO3 type perovskite is shown in Figure 1-7. These materials possess an oxygen 6-fold coordinated transition metal scaffold (BO6) where alkaline earth or lanthanides ions (A) are located on the vertices of the cube containing the octahedral. The alkaline earth (Ca, Sr, Ba) and/or lanthanide (Ln = La, Pr, Nd, etc.) cations are randomly distributed on A-sites and O-vacancy defects are also randomly distributed on the O-sub-lattice [37].
Among the many possible combinations, the La1-xSrxCo1-yFeyO3-δ family of compounds have been widely studied and applied to SOFCs as electrode components. The cubic perovskite structure is stable over the full composition space because of the similar ionic radii (Sr2+ (XII) = 1.44 and La3+ (XII) =1.36, Co3+/4+ (VI) = 0.53-0.61 and Fe3+/4+ (VI) = 0.55–0.645 Å). In general, these compounds have high electrical (100–1000 S cm-1) and ionic conductivity (0.001–0.1 S cm-1) at 600 °C. The compositions in both A-site and B-site were explored to find an optima in MIEC properties. The x > 0.2 of Sr in the A-site results in increased TEC [38]. The electrical conductivity increases for x < 0.4 and decreases for x > 0.4 for Co-rich compounds [38,39], while compounds with rich Fe content in the B-site decrease the TEC [39]. La0.6Sr0.4Co0.2Fe0.8O3-δ is therefore the best compromise between high TEC values and low conductivity. It has a rhombohedral structure at room temperature [38].

Table of contents :

Objective of the thesis
1.1 Fundamentals of SOFC
1.2 Electrochemical Processes at MIEC Cathodes
1.3 Power Losses in SOFCs
1.4 Triple Phase Boundary
1.5 State-of-the-art SOFC components
1.6 Cathode Materials
1.7 Microstructural factors affecting the cathode performance
1.8 Modelling of SOFC cathodes
1.9 Degradation problems and long term stability
2.1 Fabrication of the cell constituents
2.2 Film Characterization Techniques
2.3 Electrochemical Impedance Spectroscopy (EIS)
2.4 Materials and cell preparation for symmetrical cells
2.5 Materials and cell preparation for anode supported cell
2.6 Summary
3.1 Introduction
3.2 The effect of microstructure on the pure LSCF electrode performance
3.3 The effect of CGO addition in LSCF electrode in columnar-type microstructure
3.4 The effect of sintering temperature on 60:40 LSCF/CGO film performance
3.5 Conclusion
4.1 Introduction
4.2 The architecture of cathode films
4.3 The influence of CCL thickness on the performance of double layer electrode
4.4 The influence of CFL thickness on the performance of double layer electrode
4.5 Aging of the selected double layer LSCF cathode in symmetrical cell
4.6 Integration of state-of-the-art double layer LSCF cathode on anode-supported SOFC
4.7 Conclusion
5.1 Introduction
5.2 Which Geometry?
5.3 Simulations and assumptions
5.4 3D FEM: Model 1
5.5 3D FEM: Model 2
5.6 Conclusion
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E


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