Phase equilibria and thermodynamic description of the Tb-Fe-B system

A thermodynamic assessment of the Tb-Fe-B ternary system was conducted using the CALPHAD approach, which integrates experimental measurements with ab initio calculations. Phase equilibria of the Tb-Fe-B system at 600 °C were investigated through X-ray diffraction (XRD) and electron probe microanalysis (EPMA) on annealed alloys. Based on microstructure analysis performed on as-cast and annealed Tb-Fe-B ternary alloys using XRD and EPMA, along with thermal analysis via differential scanning calorimetry (DSC), nine primary phases in the as-cast alloys and four invariant reactions were identified. The enthalpies of formation for Tb-B, Tb-Fe and Tb-Fe-B compounds at ground states were computed by ab initio calculations and incorporated into thermodynamic modeling. Reliability of the obtained thermodynamic parameters for the Tb-B, Tb-Fe and Tb-Fe-B systems were validated by comparing the calculated phase equilibria and thermodynamic data with the available experimental data, including isothermal sections, vertical sections, liquidus projection, invariant reactions and enthalpies of formation. Additionally, a comprehensive reaction scheme of the Tb-Fe-B system across the whole composition range was presented. The Scheil solidification paths and phase fractions of representative Tb-Fe-B alloys were calculated and analyzed, which can provide crucial theoretical guidance for design and optimization of the Tb-Fe-B alloys.