Dependence of Proton Diffusivity on Dopant Concentration in Yttrium-Doped Barium Zirconate; First-Principles Study
Authors: Shitara Kazuki , Kuwabara Akihide , Okuyama Yuji , Yamazaki Yoshihiro 
Published: February 2024

Yttrium-doped barium zirconate (BaZrO3) has high proton conductivity and thermal stability, attracting attention to apply solid electrolytes to medium-temperature fuel cells. It has been reported that the proton conductivity decreases as the concentration of Y in BaZrO3increases, and it is desired to elucidate its origin. In order to perform a theoretical analysis associated with such a high-concentration solid solution state, it is necessary to consider a solid solution model that simultaneously includes two or more point defect complexes. Though the number of atomic arrangements is huge, only the structures along the path with the lowest activation energy contribute to proton conduction. In this study, we found the structures that contribute to proton conduction by pathfinding based on the combination of first-principles calculations and graph theory. From the structures on the conduction path with the lowest activation energy, we extracted the parameters that contribute to the improvement of proton conduction by performing the feature analysis.
The solution models of the 2×2×2 supercell of BaZrO3 with 12.5 and 25 mol% Y were constructed in which one and two atoms of dopant element Y were substituted to Zr sites, respectively, and the same number of protons were introduced. The total energy calculation was performed for all the symmetrically independent structures. The conduction path search based on the graph theory was performed using the obtained energies of structures, and the association and activation energies of conduction in long-range diffusion were evaluated. A feature regression analysis of total energies was conducted to extract the dominant factors of energies of the structures along the conduction path.
The association and activation energies were evaluated from the structural energies of the structures along the obtained conduction path. The difference between the highest and lowest energies with protons at the stationary positions along the searched path is considered the association energy and the energy difference between the highest energy on the path and the highest energy with the proton at the stationary positions is considered to correspond to the mobile activation energy of the proton. The mobile activation and association energies were increased with the increase of Y concentration, which is in good agreement with the experiments.
To clarify the parameters which affect the mobile activation and association energies, we performed regression analysis for the energy of the Y 25 mol% using the random forest to extract the dominant factor of the structural energy along the diffusion path in the heavily doped system. The regression parameters of rotation and distortion of octahedra were considered as well as direct descriptors of H-Y configurations. Though the parameters such as a distance of H-Y directly related to the configuration of H and Y appeared to be less important, the parameters related to the rotation of Zr(Y)O6 octahedra, are the first and second highest important parameters. They have an almost linear relationship with high negative correlation coefficients around -0.7 for the structures along the searched diffusion path including H at the transition positions. It is suggested that the rotation of octahedra declines the energy and contributes to the stabilization of the structures along the searched diffusion path. To confirm the rotation effect on the structural energy of Y contents, we calculated the energies as a function of octahedron rotation for the Y 12.5 and 25 mol% models. The larger the Y concentration, the larger the energy change concerning octahedron rotation, suggesting that the Y 25 mol% model is stiffer in terms of octahedron rotation than Y 12.5 mol%. This stiffening of octahedron rotation with Y addition is a key factor of mobile activation and association energies, which are dominant in proton conduction.
This work was supported by the Japan Science and Technology Agency CREST (JPMJCR18J3) and JSPS KAKENHI (JP22H05146 and JP22K14465). This work was also supported by MEXT Program: Data Creation and Utilization Type Material Research and Development Project Grant Number JPMXP1122683430.