Assessment of the Hf–N, Zr–N and Ti–N phase diagrams athigh pressures and temperatures: balancing between MN andM3N4 (M = Hf, Zr, Ti)

Abstract

We study the nitrogen-rich part of the phase diagram Hf–N, Zr–N andTi–N, employing first-principle calculations for an assessment of energyand enthalpy as a function of pressure. At zero pressure the novel cubicTh3P4-type structures are metastable modifications ofM3N4 (M = Hf,Zr). The lowest energy configuration of both compounds is an orthorhombicZr3N4-type. This orthorhombic structure will transform into theTh3P4-type at 9 and6 GPa, for Hf3N4 and Zr3N4, respectively. The lowest energy configuration ofTi3N4 isa CaTi2O4-type structure. It will first transform into the orthorhombicZr3N4-type at 3.8 GPa, then further transform into the cubicTh3P4-type at 15 GPa. The spinel type is metastable throughout the phase diagram for all threesystems.The phase boundary between mononitrides MN and theM3N4-phases is accessed as a function of pressure. We include the entropyof gaseous nitrogen from tabulated data to estimate the free enthalpyΔG of the nitride phases. The orthorhombic modification ofHf3N4 turns out to be thermodynamically stable with respect to a decompositioninto the mononitrides and nitrogen for temperatures up to about1000 °C. Thestability of Zr3N4 is in question; within the estimated error no final conclusion can be drawn.Ti3N4, on the other hand, will only be metastable. At higher pressures, however, the free energyof nitrogen is substantially reduced and the 3:4 compositions become more stable. Wereproduce the experimental requirements (18 GPa and 2800 K) for the synthesis of the novelHf3N4. At 2800 K the pressures needed to synthesize cubic phases ofZr3N4 and Ti3N4 are estimated to be 40 and 100 GPa, respectively.