Interplay of composition and crystal size in controlling lattice parameters of nanocrystalline cerium–dysprosium oxide solid solutions

This study investigates the influence of crystal size variations on the lattice parameters and crystal structure of cerium-dysprosium (Ce_1-xDy_xO_2-x/2) solid solutions for X values of 0.2, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9 (specifically Ce₄DyO_9.5, Ce₃Dy₂O₉, CeDyO_3.5, Ce₂Dy₃O_8.5, Ce₃Dy₇O_16.5, CeDy₄O₈, and CeDy₉O_15.5 respectively). The powder samples were synthesized using the sol-gel method and subsequently calcined at temperatures ranging from 300 to 1200 °C for a duration of 3 h to facilitate crystal growth. This temperature variation enabled the exploration of a broad spectrum of crystal sizes. Characterization of the powders was conducted through X-ray diffraction (XRD) and high-resolution scanning electron microscopy (HR-SEM). The findings indicate that the Ce-Dy-O system behaves as a continuous ternary solid solution comprising nano meter-sized to micron-sized crystals. Notably, the crystal structure transitions smoothly from fluorite (similar to pure ceria, space group Fm-3m) to C-type, accompanied by the presence of oxygen vacancies. A non-linear relationship between lattice parameter and concentration was observed, demonstrating that the relationship between lattice parameter and crystal size is non-monotonic. In the lower range of the nanoscale, lattice parameters increased due to the reduced ionic attraction among smaller particles. Conversely, a slight decrease in lattice parameter was noted in the middle range, attributed to the surface stress effects of small crystals. Finally, in the upper nanoscale to microscale range, the lattice parameters converged to values comparable to those observed in bulk materials.