Disorder in La1−x Ba1+x GaO4−x/2 ionic conductor: resolving the pair distribution function through insight from first-principles modeling

Ionic conduction in dry LaBaGaO4 occurs through the vacant oxygen sites formed by the substitution of Ba for La. The resulting La1−x Ba1+x GaO4−x/2 solid solution shows significant disorder characteristics. The local structure of compositions x = 0, 0.20 and 0.30 was studied using the pair distribution function (PDF). Unfortunately, increasing peak overlap and the number of independent structural parameters make PDF modeling challenging when dealing with low-symmetry phases. To overcome this problem, density functional theory (DFT) was employed to create different structural models, each one with a different relative position for the substitutional Ba ion with respect to the oxygen vacancy. The atomic distributions generated by DFT were used as a starting point to refine experimental PDF data. All models result in the formation of Ga2O7 dimers, with their major axis oriented along the c axis. At the local scale, the most stable DFT model also provides the best fit of the PDF. This accounts for the dopant as first and second neighbors of the vacancy and of the O bridge in the dimer, suggesting that substitutional barium ions act as pinning centers for oxygen vacancies. Above 6 Å the average orthorhombic structure fits the PDF better than the DFT models, thus indicating that Ga2O7 dimers are not correlated with each other to form extended ordered structures. The combination of DFT simulations and X-ray diffraction/PDF refinements was used successfully to model the local atomic structure in La1−x Ba1+x GaO4−x/2, thus suggesting that this approach could be positively applied in general to disordered systems.