Grain size effects on activation energy and conductivity: Na- β ″-alumina ceramics and ion conductors with highly resistive grain boundary phases

As for many ion conductors, the electrical conductivity of polycrystalline Na-β″-alumina reported in literature varies by over two decades at a given temperature. This is often ascribed to a combination of variable effects related to grain size, composition, phase content, porosity and impurities, but the dominating factors are rarely identified. Based on an extensive set of Li2O-stabilized Na-β”-alumina ceramics sintered at different conditions, we evaluate a sample series with constant composition and phase content but variable conductivity. The total conductivity of the polycrystalline samples features pronounced non-Arrhenius temperature dependence. To explain this effect, we present a simple microstructural model describing the influence of grain size effects in Arrhenius-type ion conductors with highly resistive grain boundaries as a second phase. We show that this model further predicts a linear relationship between conductivity and effective activation energy at a given temperature, which we also observe experimentally. Based on this, we are able to identify to which extent conductivity variations in a given data set may be explained by grain size effects only. As the same microstructural model relates fundamental transport properties of the corresponding grain and grain boundary phases with the experimentally observed linear relationship, we further discuss how these parameters can be extracted, e.g. by taking into account experimentally determined grain size data. Comparison with literature data indicates for which Na-β″-alumina samples additional effects such as changes in composition and percolation of coarse grains are relevant for the transport properties. Our findings on the relation between effective conductivity and corresponding activation energy are applicable to Arrhenius-type ion conductors with highly resistive grain boundary phases in general.