Locally Modulated Structures of Fluorite-Related Y₂O₃-Nb₂O₅ Solid Solutions

Modulated structures formed in defect fluorite-type (Y₂O₃)_1-x(Nb₂O₅) _x (0.21 ≤ x ≤ 0.27) solid solutions have been investigated by electron diffraction. [110] diffraction patterns showed a pair of diffuse spots in the [112] direction at both sides of the 1/21/21/2 reciprocal-lattice point. The distance between the diffuse spots decreased from 0.064 to 0.045 Å^-1 with increasing x from 0.21 to 0.27. High-resolution electron microscopy images revealed the existence of small domains with an antiphase structure. The two-dimensional antiphase structure projected on the (110) plane is described by compositional waves of Y³⁺/Nb⁵⁺ and O^2-/vacancy and displacive waves of Y³⁺ + Nb⁵⁺ and O^2- along the [112] direction. The composition at cation sites is expressed by a sinusoidal wave with occupation changes between Y and 0.58Y + 0.42Nb. The occupation probability of O at anion sites is also expressed by a sinusoidal wave with occupation changes between 0.806 and 0.904. Amplitudes of the displacive waves for anions and cations were determined to be about 0.3 and 0.02 Å, respectively.