Defect formation inLaGa(Mg,Ni)O3−δ: A statistical thermodynamic analysis validated by mixed conductivity and magnetic susceptibility measurements

Abstract

A statistical thermodynamic approach to analyze defect thermodynamics in strongly nonideal solid solutions was proposed and validated by a case study focused on the oxygen intercalation processes in mixed-conducting $\mathrm{La}{\mathrm{Ga}}_{0.65}{\mathrm{Mg}}_{0.15}{\mathrm{Ni}}_{0.20}{\mathrm{O}}_{3\ensuremath{-}\ensuremath{\delta}}$ perovskite. The oxygen nonstoichiometry of Ni-doped lanthanum gallate, measured by coulometric titration and thermogravimetric analysis at $923\char21{}1223\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in the oxygen partial pressure range $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}0.9\phantom{\rule{0.3em}{0ex}}\mathrm{atm}$, indicates the coexistence of ${\mathrm{Ni}}^{2+}$, ${\mathrm{Ni}}^{3+}$, and ${\mathrm{Ni}}^{4+}$ oxidation states. The formation of tetravalent nickel was also confirmed by the magnetic susceptibility data at $77\char21{}600\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and by the analysis of $p$-type electronic conductivity and Seebeck coefficient as function of the oxygen pressure at $1023\char21{}1223\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The oxygen thermodynamics and the partial ionic and hole conductivities are strongly affected by the point-defect interactions, primarily the Coulombic repulsion between oxygen vacancies and/or electron holes and the vacancy association with ${\mathrm{Mg}}^{2+}$ cations. These factors can be analyzed by introducing the defect interaction energy in the concentration-dependent part of defect chemical potentials expressed by the discrete Fermi-Dirac distribution, and taking into account the probabilities of local configurations calculated via binomial distributions.