Phase stability of the Hf-Nb system: From first-principles to CALPHAD

Hf-Nb is representative of a large number of alloy systems where the phase diagram is known but experimentally measured thermodynamic data is unavailable. This motivated us to investigate solid-state phase stability of this system employing ab-initio techniques based on electronic density functional theory (DFT). The total energy calculations are performed at the generalized gradient approximation level to account for non-locality of the exchange-correlation functional within DFT. The zero-temperature heat of formation of bcc-, hcp-and fcc-based ordered phases (virtual) and the finite temperature heat of mixing of bcc, hcp and fcc solid solutions are calculated. The latter properties are obtained by the cluster expansion technique coupled with Monte-Carlo simulations. In an effort to build multicomponent thermodynamic and kinetic databases containing Hf and Nb, we demonstrate a hybrid approach to integrate the ab-initio results with CALPHAD formalism to obtain thermodynamic data for the Hf-Nb system. The similarities and differences between previous CALPHAD assessment and our results are discussed.