Conduction model of oxide ions at grain boundary of solid electrolyte

A flux of oxide ions of solid electrolyte at a grain boundary was correlated to the difference of activity (ar) 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 (σi(+)) and decreased conductivity (σi(−)) with decreasing grain size. Both the conductivities reach a maximum or minimum value at r = rc where ar = 1 (for r > 0) or ar=a02 (for r < 0, a0 is the activity for r = ∞). In the grain size range of rc > r, σi(+) or σi(−) is independent of grain size. As a result, total conductivity σ(t) (=(σi(+) + σi(−))/2) is expressed as a curve of second degree of reciprocal grain size (1/r) and reaches a maximum value at r = rc. The dependence of activation energy of conductivity on the grain size is theoretically small in the wide grain size range of ∞ > r > rc. 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.