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

Abstract

The temperature dependence of the activation Gibbs free energy [\ensuremath{\Delta}G(T)] and entropy [\ensuremath{\Delta}S(T)] associated with electric conduction in 12 mol % yttria--stabilized-zirconia single crystals was analyzed. In order to determine the \ensuremath{\Delta}G(T) and \ensuremath{\Delta}S(T) functions exactly, it was necessary to impose temperature-behavior conditions on the activation Gibbs free energy to give \ensuremath{\Delta}S(T\ensuremath{\rightarrow}\ensuremath{\infty})=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, \ensuremath{\Delta}G(T) shows a linear behavior. At higher temperatures, \ensuremath{\Delta}G(T) decreases asymptotically to a value approximately equal to the migration enthalpy of the oxygen vacancies. A value of 5.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ 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\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ 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.