First-principles study of elastic and stability properties of ZrC–ZrN and ZrC–TiC alloys

Ab initio calculations of the elastic constants for several cubic ordered structures of zirconium carbonitride (ZrC(x)N(1-x)) and zirconium-titanium carbide (Zr(x)Ti(1-x)C) alloys were carried out. The calculations of total and formation energies, bulk modulus and elastic constants as functions of composition were performed with an ab initio pseudo-potential method. The predicted equilibrium lattice parameters are slightly higher than those found experimentally (on average by 0.2-0.4%). The predicted formation energies indicate that the ZrC(x)N(1-x) alloys are stable even at 0 K in the whole concentration range, while the homogeneous Zr(x)Ti(1-x)C alloys can be stabilized only at high temperatures. Spinodal decomposition of the latter alloys into cubic domains takes place over a wide range of compositions and temperatures. For the carbonitrides, the shear modulus G, the Young's modulus E and the Poisson ratio σ reach an extremum for carbon-rich alloys, and this is attributed to a maximum value of the shear modulus C(44) that corresponds to a valence-electron concentration in the range of 8.2-8.3. This extremal behavior finds its origin in the response of the band structure of ZrC(x)N(1-x) alloys for 0≤x≤1, caused by the monoclinic strain that determines this shear modulus. In contrast, the other shear modulus [Formula: see text] does not exhibit any extremum over the whole composition range. These results are in contrast with those for Zr-Ti carbides for which the elastic properties gradually increase from ZrC to TiC.