Theoretical study of the crystal structure, stability, and properties of phases in the V-N system

Stable compounds in the V-N binary system are systematically investigated and four new phases are found: $Pbam\text{\ensuremath{-}}{\mathrm{V}}_{5}{\mathrm{N}}_{2}, Pnma\text{\ensuremath{-}}{\mathrm{V}}_{2}\mathrm{N}, P\overline{3}m1\text{\ensuremath{-}}{\mathrm{V}}_{2}{\mathrm{N}}_{3}$, and $I4/mcm\text{\ensuremath{-}}{\mathrm{VN}}_{2}$. All the predicted high-pressure vanadium nitrides are dynamically stable at ambient pressure. Moreover, the thermodynamic stability of vanadium nitrides in the temperature range of 0--1500 K at different pressures (0, 20, 40, 60, and 120 GPa) was also evaluated within the harmonic approximation. The sequence of phases of ${\mathrm{V}}_{2}\mathrm{N}$ under pressure is $\ensuremath{\varepsilon}{\text{-Fe}}_{2}\text{N}\phantom{\rule{0.16em}{0ex}}\text{type}\ensuremath{\rightarrow}\ensuremath{\zeta}{\text{-Fe}}_{2}\text{N}\phantom{\rule{0.16em}{0ex}}\text{type}\ensuremath{\rightarrow}{\text{Fe}}_{2}\text{C}\phantom{\rule{0.16em}{0ex}}\text{type}\ensuremath{\rightarrow}Pnma{\text{-V}}_{2}\text{N}$. In addition, relative stability and lattice dynamics properties of several vanadium mononitrides are systematically calculated and discussed. Structural features, mechanical properties, electronic structures, and chemical bonding of all the V-N compounds are analyzed at 0 GPa. Among these vanadium nitrides, WC-type VN has the highest Vickers hardness ($\ensuremath{\sim}37\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$) and superior fracture toughness (4.3--6.1 MPa ${\mathrm{m}}^{1/2}$), which mainly originate from its strong V-N bonding as well as its strong three-dimensional V-N covalent bond network. The configuration of the strong and short N-N covalent bonds enables the new phase $I4/mcm\text{\ensuremath{-}}{\mathrm{VN}}_{2}$ to exhibit good mechanical properties. Our results also reveal that the formation of a strong covalent-bond network topology in a crystal is a fundamental principle for designing a hard or superhard structure.