Derivation of the equation of state for a superionic conductor

Abstract

The purpose of this article is an analytical consideration of the features of the physical characteristics of the quantities of a hightemperature ceramic solid oxide superionic conductor, using the example of an oxygen pump made of stabilized zirconia. Based on the consideration of an elementary axial section of a superionic tube with geometric data on the length, thickness, and diameter of the tube, an equation was obtained that relates all adjustable quantities of an oxygen pump in the entire range of oxygen dosing, in particular, to select the geometric dimensions of the device and the optimal ratios of controlled quantities. The derivation of such an equation for the pumping section of an oxygen pump is based on a number of assumptions as for an idealized oxygen pump. The currentvoltage characteristic of an oxygen pump in the region of deep pumping, associated with the appearance of electronic conductivity of the ceramics of the pumping section of the oxygen pump, leading to its destruction, electrochemical aging or degradation, has been studied. It is substantiated that the volt-ampere characteristic of the oxygen pump is the only informative curve, which is used to judge the correct mode of operation of the superionic pump and prevent the onset of electrochemical degradation. When developing a research method and setting problems for a ceramic oxide superionic conductor, a number of assumptions were taken into account, as for an idealized electrolyte. The considered solid oxide superionic conductor or solid electrolyte is a ceramic material in the form of tubes, test tubes, tablets, initially containing impurity cations of lower valence, such as calcium, yttrium, scandium, than zirconium. It is these impurity cations that create the presence of vacancies or holes in the solid cubic structure of zirconium dioxide. Through these vacancies, under the influence of external factors, high temperature and direct current electric field, only oxygen anions will be transported. The research method is based on the measurement of the electromotive force, which is recorded at the boundary section: air/electrode/superionic, unambiguously related mathematically to the oxygen concentration in the air flow. Mathematical formulas are given for calculating the desired oxygen concentration depending on various external conditions. Theoretical conclusions and substantiations on the possibility of using the phenomenological transport properties of a superionic conductor under production conditions are presented.