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 Ti–N, employing first-principle calculations for an assessment of energy and enthalpy as a function of pressure. At zero pressure the novel cubic Th 3 P 4 -type structures are metastable modifications of M 3 N 4 (M = Hf,Zr). The lowest energy configuration of both compounds is an orthorhombic Zr 3 N 4 -type. This orthorhombic structure will transform into the Th 3 P 4 -type at 9 and 6 GPa, for Hf 3 N 4 and Zr 3 N 4 , respectively. The lowest energy configuration of Ti 3 N 4 is a CaTi 2 O 4 -type structure. It will first transform into the orthorhombic Zr 3 N 4 -type at 3.8 GPa, then further transform into the cubic Th 3 P 4 -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 M 3 N 4 -phases is accessed as a function of pressure. We include the entropy of gaseous nitrogen from tabulated data to estimate the free enthalpy Δ G of the nitride phases. The orthorhombic modification of Hf 3 N 4 turns out to be thermodynamically stable with respect to a decomposition into the mononitrides and nitrogen for temperatures up to about 1000 °C. The stability of Zr 3 N 4 is in question; within the estimated error no final conclusion can be drawn. Ti 3 N 4 , 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 Hf 3 N 4 . At 2800 K the pressures needed to synthesize cubic phases of Zr 3 N 4 and Ti 3 N 4 are estimated to be 40 and 100 GPa, respectively.