The influence of cation and vacancy distributions on the ionic conductivity of acceptor doped oxygen ion conductors

We present a simple model for the ionic conductivity of an acceptor doped oxygen ion conductor. (A(1-xB)B(xB))O2-xB/2, which can be applied to yuria doped zirconia (YSZ). The model considers repulsive interaction between the dopant cations and interactions between oxygen vacancies and dopant cations, which may be zero, attractive or repulsive. For simplicity, we consider a two-dimensional triangular lattice, where the oxygen ions occupy triangles formed by the cations. At first we calculate the fractions of B-clusters consisting of B-pairs, B-triplets and B-quartets and then the fractions of AAA-, AAB-, ABB- and BBB-triangles. The vacancies are distributed to the triangles using quasichemical reactions for the exchange between the different sites. The resulting vacancy distribution is used in a simplified model for the oxygen ion conductivity which considers jump rates between different oxygen sites that depend on their local neighbourhood and the nature of the cation-cation edge which has to be crossed during a jump. Strongly reduced jump rates through A-B and B-B edges are necessary to obtain a maximum of the conductivity as a function of the dopant fraction. The most beneficial effect of the acceptor dopant is obtained for repulsive interaction between vacancies and dopant ions, such as Y, Gd or Sm, which are known to cause high oxygen ion conductivities. For dopants with attractive V-B interaction our model predicts only small oxygen ion conductivities.