Simulation of sintering kinetics and microstructure evolution of composite solid oxide fuel cells electrodes

Abstract

A three-dimension (3D) kinetic Monte Carlo (kMC) model is developed to study the sintering kinetics and microstructure evolution of solid oxide fuel cell (SOFC) composite electrodes during the co-sintering processes. The model employs Lanthanum Strontium Manganite (LSM) – Yttria-stabilized Zirconia (YSZ) composites as the example electrodes but can be applied to other materials. The sintering mechanisms include surface diffusion, grain boundary migration, vacancy creation, and annihilation. A morphological dilation method is used to generate the initial LSM–YSZ compacts as the input structures for the kMC simulation. The three-phase boundary (TPB) length, porosity, and tortuosity factor of the composite cathodes are calculated during kMC sintering. Simulation results are compared with literature data and good agreement is found. Parametric study is conducted to investigate the effects of particle size, size distribution, and sintering temperature on sintering kinetics as well as the evolution of electrode microstructures. The kMC model is capable of simulating the initial and a part of intermediate sintering stages of SOFC electrodes by considering various sintering mechanisms simultaneously. It can serve as a useful tool to design and optimize the sintering processes for composite SOFC electrodes.

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.