Thermodynamic properties of the Nd-Bi system via emf measurements, DFT calculations, machine learning, and CALPHAD modeling

Thermodynamic properties of the Nd-Bi system were investigated using a combination of experimental measurements, first-principles calculations based on density functional theory (DFT), data mining and machine learning (DM + ML) predictions, and calculation of phase diagrams (CALPHAD) modeling. The electromotive force (emf) of Nd-Bi alloys in molten LiCl-KCl-NdCl₃ at 773–973 K was measured via coulometric titration of Nd into Bi for the determination of thermochemical properties such as activity coefficients and solubilities of Nd in Bi. A new peritectic reaction of [liquid + NdBi₂ = Nd₃Bi₇] at 774 K was confirmed using differential scanning calorimetry, structural (X-ray diffraction), and microstructural (scanning electron microscopy) analyses. The unknown crystal structure of NdBi₂ was suggested to be a mixture of the anti-La₂Sb configuration and the La₂Te-type configuration based on ML predictions for over 26,000 data-mined AB₂-type configurations together with DFT-based verifications. Using the newly acquired experimental data and DFT-based calculations, the thermodynamic description of the Nd-Bi system was remodeled, and a more complete Nd-Bi phase diagram was calculated, including the Nd₃Bi₇ compound, invariant transition reactions, and liquidus temperatures.