Defect Crystal Structure of α-Na0.5–xR0.5+xF2+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-Na0.35Dy0.65F2.30

The α-Na0.35Dy0.65F2.30 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-Na0.35Dy0.65F2.30. 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-Na0.35Dy0.65F2.30 crystal contains octa-cubic clusters of the f, f–i, and i types. The electron diffraction study revealed that α-Na0.35Dy0.65F2.30 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.