Empirical decay relationship between ionic conductivity and porosity of garnet type inorganic solid-state electrolytes

Abstract

Ionic conductivity is one of the crucial parameters for inorganic solid-state electrolytes. To explore the relationship between porosity and ionic conductivity, a series of Li6.4Ga0.2La3Zr2O12 garnet type solid-state electrolytes with different porosities were prepared via solid-state reaction. Based on the quantified data, an empirical decay relationship was summarized and discussed by means of mathematical model and dimensional analysis method. It suggests that open porosity causes ionic conductivity to decrease exponentially. The pre-exponential factor obeys the Arrhenius Law quite well with the activation energy of 0.23 eV, and the decay constant is averaged to be 2.62%. While the closed porosity causes ionic conductivity to decrease linearly. The slope and intercept of this linear pattern also obey the Arrhenius Law and the activation energies are 0.24 and 0.27 eV, respectively. Moreover, the total porosity is linearly dependent on the open porosity, and different sintering conditions will lead to different linear patterns with different slopes and intercepts.