Conduction model of oxide ions at grain boundary of solid electrolyte

Abstract A flux of oxide ions of solid electrolyte at a grain boundary was correlated to the difference of activity ( a r ) of oxide ions within two adjacent grains with different curvature at a given electric field. The flux leads to two types of conductivity: increased conductivity ( σ i (+)) and decreased conductivity ( σ i (−)) with decreasing grain size. Both the conductivities reach a maximum or minimum value at r = r c where a r = 1 (for r > 0) or a r = a 0 2 (for r a 0 is the activity for r = ∞). In the grain size range of r c > r , σ i (+) or σ i (−) is independent of grain size. As a result, total conductivity σ ( t ) (=( σ i (+) + σ i (−))/2) is expressed as a curve of second degree of reciprocal grain size (1/ r ) and reaches a maximum value at r = r c . The dependence of activation energy of conductivity on the grain size is theoretically small in the wide grain size range of ∞ > r > r c . The derived theory was compared with the experimental data of the grain boundary conductivity of sintered Gd-doped ceria. A good agreement was recognized between the theory and experiments for the dependence of conductivity and activation energy on grain size.