Thermodynamic modelling of the partially ordered solid solution Hf5−Nb Ge4 supported by ab initio calculations

The site preferences in the solid solution phase Hf5−x Nb x Ge4 (0< x <3.8) were modelled with the “Compound Energy Formalism” model. The ground state energies of the end members calculated from ab initio density functional theory were taken as input parameters for the model. These ground state energies were computed for models with either fixed atomic positions or fully relaxed structures. The results of the former computation were used for the construction of a simplified model. Site fractions modelled with both, original and simplified models fit well to the experimental values, confirming the almost stepwise substitution mechanism in this compound. Non-linear trends of the lattice parameters found experimentally could be reproduced very well.