On Space Charge and Spatial Distribution of Defects in Yttria-Stabilized Zirconia

Abstract

Space charge in 8YSZ is examined theoretically. The Poisson-Boltzmann equation is solved by free energy minimization. The Helmholtz free energy of a crystal containing various defects is minimized subject to two constraints: The total dopant concentration is fixed and the maximum amount of surface charge is limited by site density. Large dopant concentration leads to defect concentrations which deviate from Boltzmann distribution. When free energy isminimized assuming all defects attain their equilibrium distributions, the corresponding electrochemical potentials are equilibrated through the crystal. These calculations correspond to long annealing times. Calculations are also conducted for a case in which only oxygen vacancies are allowed to equilibrate at lower temperature after a high temperature anneal. At lower temperatures, cations are frozen corresponding to high temperature anneal. In this case, only the electrochemical potential of oxygen vacancies equilibrates. In all cases Y segregates to grain boundaries/free surfaces lowering the corresponding oxygen vacancy concentration, consistent with reported effect of space charge on grain boundary conductivity. The results show a significant concentration of oxygen vacancies form defect complexes with Y dopant. Thus, free oxygen vacancy concentration is considerably lower than the usually assumed electroneutrality condition based on total dopant concentration.