Thermodynamic assessment of the Bi–Er and the Bi–Dy systems

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

Based on the available experimental data, the Bi–Er and the Bi–Dy binary systems have been assessed thermodynamically using the CALPHAD (CALculaton of PHAse Diagram) technique. The formation enthalpies at 0 K of the compounds, Bi3Er5, BiEr, Bi3Dy5 and BiDy, were calculated by the first-principles method and Birch–Murnaghan equation of state, and the calculated results were used in the present thermodynamic optimization. All these compounds in the Bi–Er and the Bi–Dy systems were treated as stoichiometric compounds. The liquid phase was modeled as a substitutional solution phase based on random mixing of the constituent atoms and the excess Gibbs energy was formulated with the Redlich–Kister polynomial. Good agreements were obtained between the calculated results and the experimental data for both the thermochemical properties and the phase equilibrium relations.