Research on mathematical algorithm to determine the chemical diffusion coefficient of hydrogen in CaZrO3 based proton conductor at high temperature

Abstract

To study hydrogen diffusion properties is of importance in design of new proton conductors. In the past, the chemical diffusion coefficient of hydrogen in proton conductor was usually obtained by the manual calculation method that largely depends on judgment ability of researchers, so calculation accuracy is difficult to control. To solve this problem, a mathematical algorithm and C language computer program were designed to calculate the chemical diffusion coefficient based on Fick's second law and Romberg numerical integral, in which the chemical diffusion coefficient is obtained by fitting measured electrical resistance relaxation curve based on. In addition, the algorithm can be extended to calculate the chemical diffusion coefficient in some special cases with incomplete measured electrical resistance relaxation curve or inaccurate measured values of R0 and R∞ based on modified algorithm of R0 and R∞, what cannot be handled by the manual calculation method. The chemical diffusion coefficient of self-synthesized Yb doped CaZrO3 proton conductor were calculated by using the algorithm and compared with the manual calculation method. The results show that the algorithm has the advantages of high precision and powerful computing function. The new algorithm is potential to be widely applied to the calculation of the chemical diffusion coefficient for hydrogen in proton conductors to replace the manual calculation method.