Homologous Series of 15 RF3 (ZR = 57La–71Lu) in the Categorical Crystallochemical Tetrahedron: “Polymorphism–Isomorphism–True Morphotropy–Structural Homology”

The homologous series of 15 RF3 (R = 57La–71Lu) is based on the atomic number (Z) of the chemical elements ZR. It is a T–x quasi-system (QS) “LaF3–LuF3” of 14 partial QS-N systems (N ranges from 1 to 14): 57LaF3–58CeF3, 58CeF3–59PrF3, and further to 70YbF3–71LuF3 (ΔZ = 1). The members of the crystallochemical categorical triad—isomorphism, polymorphism, and morphotropy—are the “homologous parameters” of the RF3 series. The series was first proposed as the vertex “structural homology” (SH) of the crystal-chemical tetrahedron. The SH vertex is linked with the vertices isomorphism and polymorphism by five and nine QS-N, respectively. On the edge “SH–true morphotropy,” there are QS-8 (GdF3–TbF3) with peritectic and QS-11 (HoF3–ErF3) with eutectic phase reactions of absolute true morphotropic transformation.