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First-principles pseudopotential calculations of the lattice constants and of the single-crystal elastic constants for Ti_xTa_1−xN (0≤x≤1) alloys with B1-rocksalt structure were first carried out. These calculations were performed using density functional perturbation theory (DFPT) within the virtual crystal approximation (VCA) for the disordered alloys and the supercell method (SC) for the ordered alloys, with the ABINIT program. For disordered structures, partial comparisons of the lattice constants and of the bulk modulus are provided with calculations that used the coherent potential approximation (CPA) with the exact muffin-tin orbitals (EMTO). For the exchange-correlation potential we used the generalized gradient methods (GGA). The calculated equilibrium lattice parameters by VCA are in good agreement with the stress-free lattice parameters a₀ and exhibit a positive deviation from Vegard's rule corresponding to a …