First-principles calculations and thermodynamic re-modeling of the Hf-W system

An integrative approach coupling first-principles calculations and the CALculation of PHAse Diagram (CALPHAD) method provides a more thermodynamically accurate model of the Hf-W system when compared to previous models. A two-sublattice model is used for describing the solid solubility of the HfW ₂ Laves phase. The modeling of the Laves phase includes input from first-principles total energy calculations and predictions of finite temperature properties from the Debye-Grüneisen model. In addition, first-principles calculations performed on hcp and bcc special quasirandom structures (SQS) predicted a positive enthalpy of mixing in both solid solution phases. Predicting the finite temperature properties of bcc SQS with the Debye-Grüneisen model was necessary to balance the positive, asymmetric enthalpy of mixing found in the bcc solid solution. The model produced by the coupling of CALPHAD modeling with first-principles calculations agrees well with experimental data. It also reproduces the Hf-W phase diagram with fewer parameters than previous models, which were created without the aid of first-principles calculations.