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 HfW2 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.