Understanding the anomalous behavior of Vegard's law in Ce1−xMxO2 (M = Sn and Ti; 0 < x ≤ 0.5) solid solutions

Abstract

The dependence of the lattice parameter on dopant concentration in Ce_1−xM_xO₂ (M = Sn and Ti) solid solutions is not linear. A change towards a steeper slope is observed around x ∼ 0.35, though the fluorite structure (space group Fm3m) is preserved up to x = 0.5. This phenomenon has not been observed for Ce_1−xZr_xO₂ solid solutions showing a perfectly linear decrease of the lattice parameter up to x = 0.5. In order to understand this behavior, the oxidation state of the metal ions, the disorder in the oxygen substructure and the nature of metal–oxygen bonds have been analyzed by XPS, ¹¹⁹Sn Mössbauer spectroscopy and X-ray absorption spectroscopy. It is observed that the first Sn–O coordination shell in Ce_1−xSn_xO₂ is more compact and less flexible than that of Ce–O. The Sn coordination remains symmetric with eight equivalent, shorter Sn–O bonds, while Ce–O coordination gradually splits into a range of eight non-equivalent bonds compensating for the difference in the ionic radii of Ce⁴⁺ and Sn⁴⁺. Thus, a long-range effect of Sn doping is hardly extended throughout the lattice in Ce_1−xSn_xO₂. In contrast, for Ce_1−xZr_xO₂ solid solutions, both Ce and Zr have similar local coordination creating similar rearrangement of the oxygen substructure and showing a linear lattice parameter decrease up to 50% Zr substitution. We suggest that the localized effect of Sn substitution due to its higher electronegativity may be responsible for the deviation from Vegard's law in Ce_1−xSn_xO₂ solid solutions.