Comprehensive theoretical study on ionic transport numbers of triple ionic-electronic conducting oxides determined by the electromotive force method

Abstract

Triple ionic-electronic conducting (TIEC) oxides, as an emerging class of materials with complex conduction properties, are used in diverse electrochemical energy devices. Accurately determining the transport numbers ($t_x$) of TIEC oxides is significant. In this study, we theoretically evaluate the reliability of the electromotive force (EMF) method in determining $t_x$ of TIEC oxides and address the issue that $t_x$ obtained by the EMF method is an apparent value ($t_x^{app}$). Initially, based on a precise defect distribution model, it reveals the non-uniform distributions of transport numbers within the TIEC membrane. Subsequently, through a comprehensive multiple-factor analysis, it discloses that compared with temperature and thermodynamic parameters of defect reactions, the gradient of gas partial pressure in concentration cells is the primary influencing factor affecting $t_x^{app}$. Notably, under conditions of relatively small gradients of gas partial pressure, $t_x^{app}$ can be approximated as the average value of $t_x$ at both sides of the membrane. Motivated by these findings, we propose a new EMF method, which can determine the accurate $t_x$ of materials at a specific gas composition, rather than an apparent one. Overall, the finding of this study furnishes valuable insights into determining transport numbers of TIEC oxides.