Simulation of sintering kinetics and microstructure evolution of composite solid oxide fuel cells electrodes
Highlights
► The sintering kinetics of SOFC electrodes is studied by a 3D Monte Carlo model. ► LSM–YSZ composites are selected as the example electrodes. ► The three-phase boundary length, porosity, and tortuosity factor are calculated. ► The effects of particle size distribution and sintering temperature are studied.
Introduction
Solid-state sintering is an indispensable process in fabricating composite electrodes of solid oxide fuel cell (SOFC) by thermally treating the ionic and electronic conducting particles to strengthen the bonding between them. A typical sintered composite electrode is shown in Fig. 1a. Prior to sintering, the powder compact is usually formed by mixing the electrode materials thoroughly with an organic slurry former, then coating onto a dense electrolyte with a thin-film technique such as screen printing [1]. Subsequently, the slurry former is burnt out in the heating stage of the sintering, leaving a porous packing of the electronic and ionic phase particles that are held together by weak surface bonds. During sintering, the bonding between particles is augmented, leading to enhancement in mechanical strength and ionic/electronic conductivities. More importantly, the sintering process creates three-phase boundaries (TPBs), where the ionic particles, electronic particles, and pores meet with each other. Since TPBs provide the sites for charge-transfer reaction, the activation polarization loss of the electrode is directly linked with the length of the TPB [2]. Apart from the TPB length, the porous structures (i.e. the porosity and the tortuosity factor) influence the gas transport processes and thus contribute to the concentration polarization loss [3], [4]. These basic parameters, such as TPB length, porosity and tortuosity of pores are needed input parameters in the computational fluid dynamics modeling for single cell [5], [6] or cell stack optimization [7]. A high performance SOFC electrode requires efficient transport of reactant/product gases in pores, efficient transport of electrons and ions through solid structures, and large TPB length for efficient electrochemical reactions. All these are governed by the microstructures of SOFC electrodes through sintering processes.
Both experimental and mathematical modeling approaches can be employed to capture the important microstructure information of SOFC electrodes. Recently, the TPB length, the porosity, and tortuosity factor of pores are successfully extracted from the three-dimensional (3D) structures by Focused Ion Bean-Scanning Electron Microscopy (FIB-SEM) reconstruction [8], [9], [10], [11], [12], enabling investigation of microstructure evolution during sintering. For instance, Scott Cronin et al. [11] reconstructed the 3D microstructure of a composite Ni–Yttria-stabilized Zirconia (YSZ) anode by FIB-SEM technique. The microstructure change after 100 h sintering at 1100 °C was observed. However, the FIB-SEM technique is disadvantageous in systematically investigating the sintering kinetics, as it is complicated and time consuming. Besides, materials can be broken away during milling and phase identification procedures in SEM image processing. For comparison, mathematical modeling offers an efficient and economic way of investigating the sintering kinetics of composite electrodes of SOFC. Both analytical models and numerical approaches have been applied to simulate the sintering of SOFC electrodes, treating the electrode powders as spherical particles. In the analytical models [13], [14], [15], [16], sintering stages are characterized by the contact angle between particles. The contact angle can vary from 15° to 90° depending on the sintering conditions, and is usually estimated from the SEM image of electrode microstructure. In the numerical models, particles are dropped within a domain to form loose particle compact with point-to-point contacts, followed by sintering simulation. For examples, Abbaspour et al. [17] modeled the sintering by enlarging particle size to obtain a certain degree of overlap between particles. In another study, Kenney et al. [18] captured the degree of sintering by varying the minimum allowable distance between contacting particles. In Metcalfe et al.’s work [19], a sintering neck is added to particle intersection region to represent the material diffusion in sintering process. These models simulate sintering from geometry perspective without the physics of sintering kinetics, i.e. without considering mass conservation.
Fully understanding the sintering kinetics of microstructure evolution is of great significance to optimize the electrode microstructure, and accordingly to improve the electrochemical performance of the cell. The kinetic Monte Carlo (kMC) models are powerful tools to simulate the 3D microstructure evolution during all sintering stages, from loose compacts to dense bulks [20], [21], [22]. However, the-state-of-the-art kMC models can only be applied for two-phase systems, such as porous single-phase compacts. In this work, we develop a kMC model to simulate the sintering of three-phase systems used for the composite SOFC electrodes. Porous Lanthanum Strontium Manganite (LSM)–YSZ composite electrodes are studied as the typical SOFC cathodes. A novel method is proposed to generate the initial LSM–YSZ particle compacts as the inputs of kMC sintering simulation. The evolution of TPB length, porosity, and tortuosity factor of pores with sintering time are calculated at different sintering temperatures, particle size, and particle size distribution of the starting materials.
Section snippets
The model
The starting powders are usually fabricated with solid-state reaction [23], co-precipitations [24], sol–gel method [25] or combustion [26]. The particles are thus micron sized or even nano-sized. So it is rational to consider each particle as a grain of the green compact. As the random-orientation of grains, the facets where they meet form grain boundaries and sintering necks. For a composite electrode shown in Fig. 1a, there are three kinds of grain boundaries/sintering necks formed by
Structure generation and parameter calculation
The powder compacts before sintering are input structures of the kMC model. In this work, spherical particles are randomly packed in a 3D domain of specified dimensions to simulate the initial compacts. In the present kMC model, the particles and domain are divided into pixels with a resolution of 50 nm. Before dropping particles, pixel values of the 3D domain are initialized to be zero, indicating an empty container. The pixels belonging to the top, bottom, and lateral domain faces serve as
Model validation
Two sets of literature data reported by Mitterdorfer and Gauckler [34] and Chen et al. [35] are used to scale kMCS and kT/J with the realistic sintering time and temperature, as well as to validate the kMC model. These two studies both experimentally investigated the sintering kinetics and the variation of TPB length for porous LSM electrodes on YSZ electrolytes under different conditions. In the report by Mitterdorfer and Gauckler [34], the LSM particles with a radius of about 0.1 μm were
Conclusion
A kMC model is combined with a morphological dilation method to study the sintering kinetics and microstructure evolution of composite LSM–YSZ electrodes. The model is validated by comparing the simulation results with the experimental data from the literature. Microstructure parameters, such as TPB length, porosity, and tortuosity factor of pores are calculated during kMC sintering. The following conclusions can be obtained:
- (1)
The evolution of TPB length can be divided into three sintering stages
Acknowledgments
This research was supported by a grant from The Hong Kong Polytechnic University (Project No. A-PK48), Hong Kong and the Ministry of Science and Technology of China (2012CB215403).
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