Thermodynamic modeling of Laves phases in the Cr–Hf and Cr–Ti systems: Reassessment using first-principles results

The Cr–Hf and Cr–Ti belong to interesting systems exhibiting the existence of all polytypes of Laves phases, i.e. lower-temperature cubic C15 and higher-temperature hexagonal C14 and C36, although in the Cr–Hf phase diagram only C14 and C15 phases occur. Comparison of total energies of these structures calculated from first principles with the total energy of the ideal mixture of elemental constituents reveals the relative stability of Laves phases in these systems. The effect of magnetic order in the Laves phases is also briefly discussed. lculated total energies of formation of all the three polytypes are employed in two- and three-sublattice models to revise the thermodynamic description of both the systems published recently. New remodeled Gibbs energies of Laves phases require less fitting parameters than those obtained in previous treatments and corresponding phase diagrams provide an excellent agreement with the experimental phase data found in the literature. The proposed procedure allows us to compare the optimised heat capacity differences with those determined experimentally or theoretically and to use them in phase diagram calculations.