Thermodynamic Ground States of Platinum Metal Nitrides

The thermodynamic stabilities of various phases of the nitrides of the platinum-metal elements are systematically studied using density functional theory. It is shown that for the nitrides of Rh, Pd, Ir, and Pt two new crystal structures, in which the metal ions occupy simple tetragonal lattice sites, have lower formation enthalpies at ambient conditions than any previously proposed structures. The region of stability with respect to those structures extends to 17 GPa for ${\mathrm{PtN}}_2$. Calculations show that the ${\mathrm{PtN}}_2$ simple tetragonal structures at this pressure are thermodynamically stable also with respect to phase separation. The fact that the local density and generalized gradient approximations predict different values of the absolute formation enthalpies as well different relative stabilities between simple tetragonal and the pyrite or marcasite structures are further discussed.

Figure 1

Top: projections of all possible distinct nitrogen dimer orientations derived from the 12-atom conventional unit cell, along with the space group number and Hermann-Maugin symbol of the corresponding structure. Bottom: energy/f.u. vs volume curves from LDA for the above relaxed structures (solid lines) in the case of ${\mathrm{PdN}}_2$. Each structure can be identified by matching the line color to the corresponding triangle color. Note that structure 7 corresponds to the black line. The green and red dashed lines correspond to the ${\mathrm{ST}}_{AA}$ and ${\mathrm{ST}}_{AB}$ structures, respectively.

Figure 2

Conventional unit cells of ${\mathrm{ST}}_{AA}$ (left) and ${\mathrm{ST}}_{AB}$ (right) viewed along the $c$ axis. Red, blue, and yellow spheres represent metal ions, nitrogens in layer $A$ and nitrogens in layer $B$, respectively.

Figure 3

LDA formation enthalpies per formula unit of (a) ${\mathrm{RuN}}_2$, (b) ${\mathrm{RhN}}_2$, (c) ${\mathrm{PdN}}_2$, (d) ${\mathrm{OsN}}_2$, (e) ${\mathrm{IrN}}_2$, and (f) ${\mathrm{PtN}}_2$ as a function of pressure for marcasite or baddeleyite (MB), pyrite, and the two simple tetragonal structures.

Figure 4

GGA formation enthalpies per formula unit of (a) ${\mathrm{RuN}}_2$, (b) ${\mathrm{RhN}}_2$, (c) ${\mathrm{PdN}}_2$, (d) ${\mathrm{OsN}}_2$, (e) ${\mathrm{IrN}}_2$, and (f) ${\mathrm{PtN}}_2$ as a function of pressure for marcasite or baddeleyite (MB), pyrite, and the two simple tetragonal structures.