Structure and microstructure characterization of the mixed sesquioxides (Gd_1−xYb_x)₂O₃ and (Gd_1−xHo_x)₂O₃ prepared by sol–gel process

Polycrystalline samples of (Gd_1−xYb_x)₂O₃ and (Gd_1−xHo_x)₂O₃ (0.0 ≤ x ≤ 1.0) were synthesized by a sol–gel process. X-ray diffraction data were collected and crystal structure and microstructure analyses were performed using the Rietveld refinement method. All samples were found to have the same crystal system and formed solid solutions over the whole range of x. For the system (Gd_1−xHo_x)₂O₃, the cationic distribution over the two non-equivalent sites 8b and 24d of the space group Ia were found to be random for all values of x. For (Gd_1−xYb_x)₂O₃, the distribution is random in the range 0.0 < x ≤ 0.5 and preferential in the range 0.5 < x ≤ 1.0. The lattice parameters are found to vary linearly with the composition x. Replacing Gd³⁺ and Yb³⁺, or Gd³⁺ and Ho³⁺, by each other introduces slight changes in relative atomic coordinates. Crystallite size and microstrain analyses were performed along different crystallographic directions and both are found to vary anisotropically with the composition parameter (x). The obtained values of microstrain are correlated with the distribution of the rare earth ions over the two cationic sites of the structure. The average crystallite size ranges from 45 to 144 nm and the root mean square (r.m.s.) strain from 0.018 to 0.409 × 10⁻².