“…The activation energy, E a for oxygen ionic conduction is the sum of E o and the migration energy E M [19]. The Nernst-Einstein formula for the ionic conductivity due to oxygen ion migration is represented by = 4e 2 ND/k B T, where 4e 2 is the square of the valence of an oxygen ion, and D ∝ exp(−E M /k B T) is the diffusion co-efficient of O 2− ions, N ∝ exp(−E O /k B T) is the density of the mobile free oxygen vacancies in thermal equilibrium because the assistance of vacancies is necessary in the O 2− diffusion, k B is the Boltzmann constant [8,27]. In the present oxide system, where the dielectric relaxation process do not show up in the loss factor ε , the activation energy is usually estimated by employing the approximation that the loss tangent is proportional to the loss factor, i.e., tan ı ∝ ε , then the maximum loss tangent has a form [8,9,11,[22][23][24][25][26][27][28][29].…”