First-principles calculations of the structural, elastic and electronic properties of MN_xC_1-x (M = Ti, Zr, Hf; 0 ≤ x ≤ 1) carbonitrides at ambient and elevated hydrostatic pressure

The structural, electronic, and elastic properties of three mixed transition metal carbonitrides TiN_xC_1-x, ZrN _xC_1-x, and HfN_xC_1-x (0 ≤ x ≤ 1) with the rock-salt structure were calculated at ambient and elevated up to 50 GPa hydrostatic pressures in the framework of the density functional theory methods. The lattice constants, densities, and bulk moduli of the considered compounds were shown to behave as linear functions of the nitrogen concentration x. The obtained linear dependencies of all these parameters allow for getting their estimates at any value of x in the range from 0 to 1. Gradual enhancement of the ionicity of the chemical bonds with gradual replacement of carbon by nitrogen was demonstrated by calculating the bond orders and electron density difference distributions.