Theoretical study of the structural phase transformation and elastic properties of the zirconium nitride under high pressure

Pressure Induced Phase Transition of ZrN and HfN: A First Principles Study

“…The calculated total energies are fitted to the Birch Murnaghan equation of state (EOS) [22] to determine the ground state properties such as equilibrium lattice constant and cell volume. The calculated volume V 0 ( Å3 ), lattice parameters a and c ( Å), TM-N bond length ( Å), c/a ratio, valence electron density ρ (electrons/ Å) obtained using VASP code are given in Table 2, along with experimental [3][4]10] and theoretical [5][6][7][8][9]11] results. From the Table 2, it is observed that the calculated lattice constants are in good agreement with the experimental and previous theoretical results.…”

“…(3) must always be positive for all possible values of the set {e i }; otherwise the crystal would be mechanically unstable. The calculated elastic constants C ij (GPa), bulk modulus B 0 (GPa) and its derivative B ′ 0 , Young's modulus E(GPa), Shear modulus G(GPa), Poisson's ratio (v)), B/G ratio, elastic anisotropy A and micro hardness H(GPa) for ZrN and HfN are given in Table 4, along with the experimental [3] and theoretical data [8,11,[29][30]. Obviously, the calculated results are in accordance with the experimental data [3] and previous theoretical results [8,11,[29][30].…”

“…The measured bulk modulus was 215 GPa (ZrN) and 306 GPa (HfN) by neutron scattering experiments. There are many theoretical as well as experimental investigations on the structural stability ZrN and HfN [4][5][6][7][8][9][10][11]. But there are many disagreements between the theory and experiments in the prediction of stable structure, equilibrium lattice constant and bulk modulus of these transition metal nitrides TMNs (TM-Zr, Hf).…”

First principle study on the predicted phase transition of MN (M = Zr, La and Th)

“…For cubic crystal, the elastic constants C 11 , C 12 and C 44 exhibit mutually independent characteristics. The mechanical stability can be checked by following [2,26,[31][32][33]…”

Theoretical Analysis of the Structural Phase Transformation and Elastic Properties in the ZrN under High Pressure

“…These results are amazing because earlytransition metal nitrides almost have NaCl structure (B1), while in the case of some late-transition metal nitrides, their structures are zinc-blende structure [7]. Some studies about 4d-and 5dtransition metal mononitrides have also been carried out [8][9][10][11][12][13][14][15][16][17]. In particular, zirconium nitride (ZrN) is of great technological and fundamental importance because of excellent wear resistance, high hardness, good lubricity and ductility and better chemical stability, which makes it an attractive coating material for machine tools.…”