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Alloying-related trends from first principles: An application to the Ti--Al--X--N system

Tailoring and improving material properties by alloying is a long-known and used concept. Recent research has demonstrated the potential of ab initio calculations in understanding the material properties at the nanoscale. Here we present a systematic overview of alloying trends when early-transition metals (Y, Zr, Nb, Hf, Ta) are added in the Ti$_{1-x}$Al$_x$N system, routinely used as a protective hard coating. The alloy lattice parameters tend to be larger than the corresponding linearised Vegard's estimation, with the largest deviation more than 2.5% obtained for Y$_{0.5}$Al$_{0.5}$N. The chemical strengthening is most pronounced for Ta and Nb, although also causing smallest elastic distortions of the lattice due to their atomic radii being comparable with Ti and Al. This is further supported by the analysis of the electronic density of states. Finally, mixing enthalpy as a measure of the driving force for decomposition into the stable constituents, is enhanced by adding Y, Zr and Nb, suggesting that the onset of spinodal decomposition will appear in these cases for lower thermal loads than for Hf and Ta alloyed Ti$_{1-x}$Al$_x$N.