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.