Phase stability, elastic properties, and hardness of Ti_1-xAl_xN from first-principles calculations

The curve of the hardness of ternary nitride Ti1-xAlxN against the Al content x is convex shaped with a maximum at x similar to 0.6, of which the mechanism remains to be further explored. The present work scrutinizes the phase stability and elastic modulus of Ti1-xAlxN against the Al content x by using a first principles method as they are highly pertinent to the hardness of the system. It is shown that the cubic B1 structure is more stable than the hexagonal structure (Bk) for x < similar to 0.75 whereas the hexagonal structure (B4) is more stable than the cubic B1 structure for x > similar to 0.75. The hardness of both B1- and B4-Ti1-xAlxN evaluated with the calculated elastic modulus become higher with increasing x. B1-Ti1-xAlxN is harder than B4-Ti1-xAlxN. Besides the composition dependent hardness of the individual B1- and B4-Ti1-xAlxN, the phase decomposition contributes to the convex shaped hardness of Ti1-xAlxN against x. The work presents a clear picture on how the chemical composition and phase transition influence jointly on the hardness of Ti1-xAlxN.