Assessment of the Hf-N, Zr-N and Ti-N phase diagrams at high pressures and temperatures:: balancing between MN and M3N4 (M = Hf, Zr, Ti)

We study the nitrogen-rich part of the phase diagram Hf-N, Zr-N and TiN, employing first-principle calculations for an assessment of energy and enthalpy as a function of pressure. At zero pressure the novel cubic Th3P4-type structures are metastable modifications Of M3N4 (M = Hf, Zr). The lowest energy configuration of both compounds is an orthorhombic Zr3N4-type. This orthorhombic structure will transform into the Th3P4-type at 9 and 6 GPa, for Hf3N4 and Zr3N4, respectively. The lowest energy configuration of Ti3N4 is a CaTi2O4-type structure. It will first transform into the orthorhombic Zr3N4-type at 3.8 GPa, then further transform into the cubic Th3P4-type at 15 GPa. The spinel type is metastable throughout the phase diagram for all three systems. The phase boundary between mononitrides MN and the M3N4-phases is accessed as a function of pressure. We include the entropy of gaseous nitrogen from tabulated data to estimate the free enthalpy A G of the nitride phases. The orthorhombic modification of Hf3N4 turns out to be thermodynamically stable with respect to a decomposition into the mononitrides and nitrogen for temperatures up to about 1000 degreesC. The stability 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 energy of nitrogen is substantially reduced and the 3:4 compositions become more stable. We reproduce the experimental requirements (18 GPa and 2800 K) for the synthesis of the novel Hf3N4. At 2800 K the pressures needed to synthesize cubic phases of Zr3N4 and Ti3N4 are estimated to be 40 and 100 GPa, respectively.