Activation entropy and Gibbs free energy for conduction in yttria–stabilized-zirconia single crystals

Abstract

The temperature dependence of the activation Gibbs free energy [ΔG(T)] and entropy [ΔS(T)] associated with electric conduction in 12 mol % yttria–stabilized-zirconia single crystals was analyzed. In order to determine the ΔG(T) and ΔS(T) functions exactly, it was necessary to impose temperature-behavior conditions on the activation Gibbs free energy to give ΔS(T→∞)=0. The temperature dependence of the entropy was similar to that of the activation enthalpy. Both reach stable values at low temperatures (extrinsic associated range). In this temperature range, ΔG(T) shows a linear behavior. At higher temperatures, ΔG(T) decreases asymptotically to a value approximately equal to the migration enthalpy of the oxygen vacancies. A value of 5.6×10−7 eV/K was calculated for the variation of entropy associated with the migration of the vacancies. Assuming the cation-vacancy-cation association to be a first-neighbor structure, a value of 4.85×10−4 eV/K was found for the association entropy of the vacancies. These results are in very good agreement with those obtained by applying the method used in alkaline halide studies.