Thermodynamic assessment of the Gd–Bi and the Ho–Bi systems

The Gd–Bi and the Ho–Bi systems were thermodynamically assessed by CALPHAD (CALculaton of PHAse Diagram) approach based on the available experimental data including thermochemical properties and phase equilibria. The formation enthalpies (at 0 K) of the compounds of the Gd–Bi and the Ho–Bi systems were calculated by the first-principles method and used in the present thermodynamic optimization. The excess Gibbs energies were formulated with the Redlich–Kister polynomial. The intermetallics, Gd5Bi3, Gd4Bi3, GdBi, GdBi2, Ho5Bi3 and HoBi, were treated as stoichiometric compounds. A good agreement between the calculated results and the experimental data was obtained.

► The Gd–Bi and Ho–Bi binary systems were optimized.
► The first-principles method was used to calculate formation enthalpies of compounds.
► A self-consistent set of thermodynamic parameters was obtained.
► The experimental and calculated data were well reproduced by the optimized results.