CALPHAD-Based Thermodynamic Assessment of the Neodymium–Thallium System with DFT Support

Abstract

The thermodynamic assessment of the Nd-Tl binary system was performed using the CALPHAD approach, supported by ab initio calculations based on density functional theory (WIEN2k). The enthalpies of formation of six stable intermetallic compounds (Nd₃Tl, Nd₂Tl, Nd₅Tl₃, NdTl, Nd₃Tl₅, and NdTl₃) were evaluated and used to constrain the Gibbs energy models. The optimized description reproduces the available experimental phase boundaries, invariant reactions, and the measured calorimetric data for NdTl₃ within experimental uncertainty. Calculated lattice parameters are consistent with literature values, with deviations below 0.1 Å. The phase diagram is well reproduced, including the congruent melting of NdTl and NdTl₃ and the peritectic equilibria of Nd₃Tl, Nd₂Tl, and Nd₅Tl₃. Minor discrepancies remain in the Tl-rich region, attributed to the narrow stability range of NdTl₃. The present work provides the first consistent thermodynamic description of the Nd-Tl system, suitable for database development and future applications in rare-earth alloys.