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Multicomponent nitrides are a hot research topic in the search of hardcoatings. The effect of substitutions on the phase stabilities, magnetic, andelastic properties of $Al_{1-x-y}Cr_{x}Ti_{y}N$ $(0\leq x,y\leq1)$ was studiedusing first principles calculations based on the density functional theory.These calculations provide the lattice parameter, formation energy, mixingenthalpy and elastic constants. The calculated values are in good agreementwith experiments and compare well with other theoretical results. A magnetictransition from antiferromagnetic to ferromagnetic state occurs atconcentrations of B1-TiN higher than 60$\%$. The quaternary zone has a loweraluminum solubility than the constituent ternary systems. The Poisson's ratio,Shear and Young modulus were used as predictors of the hardness, indicatingthat the higher hardness values are found on the transition line from B1 to B4.The obtained results enable the design of new $Al_{1-x-y}Cr_{x}Ti_{y}N$-basedmaterials for coating applications.

Phase stability and elastic properties in the $Al_{1-x-y}Cr_{x}Ti_{y}N$ system from first principles