First-principles calculation of the structural and elastic properties of ternary metal nitrides TaxMo1-xN and TaxW1-xN

First-principles pseudo-potentials calculations of the mixing enthalpy, of the lattice constants a(0) and of the single-crystal elastic constants c(ij) for ternary metal nitrides TaxMe1-xN (Me=Mo or W) alloys considering the cubic B1-rocksalt structure is carried out. For disordered ternary alloys, we employ the virtual crystal approximation VCA in which the alloy pseudo-potentials are constructed within a first-principles VCA scheme. The supercell method SC is also used for ordered structures in order to evaluate clustering effects. We find that the mixing enthalpy still remains negative for TaxMe1-xN alloys in the whole composition range which implies these cubic TaxMo1-xN and TaxW1-xN ordered solid solutions are stable. We investigate the effect of Mo and W alloying on the trend of the mechanical properties of TaN. The effective shear elastic constant c(44), the Cauchy pressure (c(12)-c(44)), and the shear to bulk modulus G/B ratio are used to discuss, respectively, the mechanical stability of the ternary structure and the brittle/ductile behavior in reference to TaN, MeN alloys. We determine the onset transition from the unstable structure to the stable one B1-rocksalt from the elastic stability criteria when alloying MeN with Ta. In a second stage, in the frame of anisotropic elasticity, we estimate by one homogenization method the averaged constants <C-ij> of the polycrystalline TaxMe1-xN alloys considering the special case of an isotropic medium with no crystallographic texture.