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Electro-Chemical Potential Analysis of Zirconium Based on the Reaction-Diffusion Equations of Oxygen Ion and Electron Considering Phase Transformation

In order to simulate oxygen potential in 8YSZ including the phase transformation, we employ the electro-chemo analyses developed in our previous report [1]. In the simulation, we use diffusion-reaction equations representing the evolutions of potentials of oxygen ion and electron. These evolution equations are coupled in the terms of the time based on the theory of local equilibrium law for the potential of oxygen. The equations have reaction terms to present the reaction currents generating due to the electrode reaction in electrodes. The non-stationary terms are modelled with the capacitance of oxygen and electron. The relation between electro-chemical potentials and currents of oxygen ion and electron are described by the Ohm’s law in this model. The material properties such as electric conductivities, capacitances and reaction currents of oxygen ion and electron depend on both the temperature and partial pressure of oxygen. These governing equations are solved after the discretization into finite elemental equations.

In the previous report [1], the experimental data are used for the material properties in the calculation. However, the degradation due to phase transformation is not be considered. In this study, evolution equations for the electric conductivities of oxygen ion and electron are proposed. The equations represent the temporary deterioration in 8YSZ in terms of the electric conduction. The effects of the control period can be taken into account in the evolution equations. The phase transformation occurs depending on the equilibrium partial pressure of oxygen between Ni and NiO. The time constants, which are related to the duration of degradation of materials, are different in Ni and NiO, i.e., cubic structure or tetragonal structure material. The hole conductivity is also considered in the electric conductivity of electron. The time constants are associated with the temperature both in the materials before and after transformation. The tendencies of oxygen potentials calculated for 8YSZ are discussed with the experimental data.

Based on the present model, the calculations are conducted for the 8YSZ electrolyte with Ni-YSZ for anode and LSCF for cathode in the both sides end. The boundary conditions of oxygen ion and electron are given as Neumann conditions with zero flux at both the end of anode and cathode, which is considered as the open circuit voltage (OCV) condition. The temperature is set as 1173K during the calculation, and partial pressure of oxygen is changed to 1.0×10^{-19} atm from 0.21 atm while partial pressure of hydrogen is changed to 0.97 atm to 1.0×10^{-19} atm during the initial 200s. Then, the 0.21 atm of partial pressure of oxygen and 1.0×10^{-19} atm of partial pressure of hydrogen are kept. As the result, the phase transformation due to the equilibrium pressure between Ni-NiO and degradation during long period control are reproduced. The phase transformation occurs in the area between the center of electrolyte and anode. After the completion of phase transformation, the gap of the oxygen potential migrates to anode due to the degradation of 8YSZ.

[1] K. Terada, T. Kawada, K. Sato, F. Iguchi, K. Yashiro, K. Amezawa, M. Kubo, H. Yugami, T. Hashida, J. Mizusaki, H. Watanabe, T. Sasagawa and H. Aoyagi, “Multiscale Simulation of Electro-Chemo-Mechanical Coupling Behavior of PEN Structure under SOFC Operation”, *ECS Trans.*, **35**, 923-933 (2011).