Fundamentals of Cubic Phase Synthesis in PbF₂-EuF₃ System

Fluoride solid solutions exhibit exceptional optical and thermodynamic properties that make them valuable for advanced technological applications, and the PbF₂-EuF₃ system represents a particularly promising quasi-binary system for developing high-performance materials. However, the comprehensive understanding of the thermodynamic conditions governing phase equilibria and the precise boundaries of homogeneity regions in this system remains incomplete, limiting the rational design of single-phase materials with desired properties. Therefore, we conducted a comprehensive investigation of the thermodynamic conditions (temperature and composition) controlling the existence of cubic and rhombohedral phases within the homogeneity regions of the PbF₂-EuF₃ system. Solid solution samples were synthesized using both solid-phase synthesis and co-precipitation techniques from aqueous nitrate solutions. Phase equilibria were systematically investigated in two critical regions: the solvus line spanning 0-10 mol% EuF₃ and the ordered rhombohedral R-phase region spanning 35-45 mol% EuF₃. Structural characterization was performed at temperatures below the phase transition temperature in lead fluoride (365 °C) using X-ray phase analysis, optical probing, and Raman scattering. Our investigation successfully demonstrated the possibility of obtaining cubic preparations of high purity across the 0-37 mol% EuF₃ composition range. Additionally, we precisely defined the region of existence of the ordered rhombohedral R-phase within the concentration range of 37-39 to 43-44 mol% EuF₃. These findings provide essential thermodynamic data for the rational design of PbF₂-EuF₃ solid solutions and establish clear compositional boundaries for obtaining desired phase structures in this technologically important fluoride system.