Heat capacity and thermodynamic functions of sodium rare earth ternary fluorides

Sodium rare earth ternary fluorides, NaREF₄ (RE = rare earth), are intermediate phases for rare earth element extraction and have important technological applications. To better understand their physical properties, energetics, and stability, we measured the heat capacity of three β-structured NaREF₄ compounds, NaNdF₄, NaYbF₄, and NaYF₄, from 1.8 to 300 K. Our measurements show an upturn in the low-temperature heat capacity of each sample which we attribute to the splitting of degenerate nuclear magnetic states. We provide calculations of the effective field causing the splitting for each sample. We also report standard entropy, enthalpy, and Gibbs energy increments at selected temperatures from 0 to 300 K. The enthalpy of formation of the three NaREF₄ from the elements (ΔΗ°_f,el) and the fluorides (ΔΗ°_f,fl) were measured previously, enabling us to calculate the Gibbs energies of formation from the elements and fluorides. The Gibbs energy of NaREF₄ relative to the elements at 298.15 K was calculated to be −1483.5 kJ∙mol⁻¹, −1502.2 kJ∙mol⁻¹, and −1497.8 kJ∙mol⁻¹ with an estimated standard uncertainty of 1% for NaNdF₄, NaYF₄, and NaYbF₄ respectively. The Gibbs energy of NaREF₄ relative to the fluorides at 298.15 K was calculated to be –5.39 kJ∙mol⁻¹, −18.12 kJ∙mol⁻¹, and −19.1 kJ∙mol⁻¹ with an estimated standard uncertainty of 1% for NaNdF₄, NaYF₄, and NaYbF₄ respectively. Each sample's negative Gibbs energy relative to both the elements and the fluorides indicates stability relative to these compounds. The results confirm that these three NaREF₄ compounds are thermodynamically stable relative to the elements and binary fluorides.