Evolution of the Cluster Structure of Fluorite Nonstoichiometric Crystals of the Homologous Series $${\text{C}}{{{\text{a}}}_{{1-x}}}{{R}_{x}}{{{\text{F}}}_{{2 + x}}}$$ (R = Sc, Y, La–Lu) in the Composition–Temperature System

The unified model of the cluster structure of nanostructured fluorite crystals in the temperature–composition (T–x) system, proposed by the authors, was used to clarify the evolution of the cluster structure of crystals of the homologous series $${\text{C}}{{{\text{a}}}_{{1-x}}}{{R}_{x}}{{{\text{F}}}_{{2 + x}}}$$ (R = La–Lu, Y). The defect structures of Ca0.75Nd0.25F2.25, Ca0.80Tb0.20F2.20, and Ca0.75Y0.25F2.25 were studied by X-ray diffraction analysis at 293 and 85 K. They are based on octa-cubic clusters with cuboctahedron cores {F12}. The cores are formed by interstitial anions at the positions 32f (f-type clusters in Ca0.75Nd0.25F2.25 and Ca0.80Tb0.20F2.20) and 48i (i-type clusters in Ca0.75Y0.25F2.25). Obtaining diffraction data with a resolution of 0.29 Å made it possible to identify cation displacements at the positions 24e and 32f in Ca0.75Y0.25F2.25 and clarify the occupancies of these positions. Lowering the temperature from 293 to 85 K does not change the cluster structure of Ca0.75Nd0.25F2.25, Ca0.80Tb0.20F2.20, and Ca0.75Y0.25F2.25. An electron diffraction study of the Ca0.75Nd0.25F2.25 crystal revealed (for the first time) diffuse scattering from structural defects with sizes on the order of one unit cell in crystals of the homologous series $${\text{C}}{{{\text{a}}}_{{1-x}}}{{R}_{x}}{{{\text{F}}}_{{2 + x}}}$$ .