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

The dependence of the lattice parameter on dopant concentration in Ce1-xMxO2 (M = Sn and Ti) solid solutions is not linear. A change towards a steeper slope is observed around x similar to 0.35, though the fluorite structure (space group Fm3m) is preserved up to x = 0.5. This phenomenon has not been observed for Ce1-xZrxO2 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, Sn-119 Mossbauer spectroscopy and X-ray absorption spectroscopy. It is observed that the first Sn-O coordination shell in Ce1-xSnxO2 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 Ce1-xSnxO2. In contrast, for Ce1-xZrxO2 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 Ce1-xSnxO2 solid solutions.