  The structural, electronic, and elastic properties of three mixed transition
metal carbonitrides TiNxC1-x, ZrNxC1-x, and HfNxC1-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.
