Defect Crystal Structure of α-Na_0.5–xR_0.5+xF_2+2x (R = Dy–Lu, Y) According to X-ray and Electron Diffraction Data: 1. The Method of Defect Structure Modeling on the Example of α-Na_0.35Dy_0.65F_2.30

The α-Na_0.35Dy_0.65F_2.30 crystal has been investigated for the first time by X-ray diffraction at 293 and 85 K and by electron diffraction at 293 K. The unified cluster model of the defect structure of fluorite-type nanostructured crystals, based on the polymorphism of ordered KR₃F₁₀ phases (R = Er, Yb), is extended by the matrix part model based on the KYF₄ structure. The unified cluster model is applied to construct the defect structure of α-Na_0.35Dy_0.65F_2.30. The matrix part of the crystal is found to contain Na⁺ and Dy³⁺ cations in a ratio of 1 : 1. Some of matrix anions are displaced to 32f sites (sp. gr. Fm \(\bar {3}\) m). Excess Dy³⁺ cations and Na⁺ cations form octa-cubic clusters [ \({\text{N}}{{{\text{a}}}_{{14-n}}}{\text{D}}{{{\text{y}}}_{n}}{{{\text{F}}}_{{64 + n}}}\) ] with cores in the form of distorted and regular {F₁₂} cuboctahedra. They are composed by interstitial anions at two 32f sites and one 48i site. The cluster component of the α-Na_0.35Dy_0.65F_2.30 crystal contains octa-cubic clusters of the f, f–i, and i types. The electron diffraction study revealed that α-Na_0.35Dy_0.65F_2.30 is a nanostructured crystal. Its cluster component includes platelike precipitates ~5 nm thick with superstructural ordering and unit octa-cubic clusters. A model is proposed for their structure. A decrease in the temperature to 85 K increases the number of interstitial F_(32f)1 anions in the matrix component of the crystal.