# Fundamentals of Cubic Phase Synthesis in PbF2–EuF3 System

## TL;DR

The study identifies specific composition ranges for synthesizing pure cubic and rhombohedral phases in the PbF2-EuF3 system, aiding in the design of high-performance fluoride materials.

## Contribution

The paper provides precise thermodynamic boundaries for phase stability in the PbF2-EuF3 system, enabling controlled synthesis of desired solid solutions.

## Key findings

- High-purity cubic phases can be synthesized in the 0–37 mol% EuF3 range.
- The ordered rhombohedral R-phase exists between 37–39 to 43–44 mol% EuF3.

## Abstract

A high-purity cubic phase could be synthesized in the 0–37 mol% EuF3 composition range in a quasi-binary PbF2-EuF3 system.

The ordered rhombohedral R-phase exists in the concentration range from 37–39 to 43–44 mol% EuF3 in the quasi-binary PbF2-EuF3 system.

Isothermal cross-sections of T-X-Y projection of ternary Pb-Eu-F diagram in the 50–550 °C temperature range are reconstructed.

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.