Ab initiocalculations of elastic properties of isotropic and oriented Ti1−xAlxN hard coatings

In the present study, the elastic properties of Ti 1− x Al x N (0 ≤ x ≤ 0.75) hard coatings were studied by ab initio calculations. The bulk ( B ), shear ( G ) and Young's ( E ) moduli and Poisson's ratio (υ) were calculated for isotropic materials. In addition, the anisotropy of the elastic moduli ( G 12 , G 23 , E 11 , E 22 ) and the Poisson's ratios (ν 12 , ν 21 , ν 23 ) are described with respect to particular crystallographic planes. The results of the calculations enable us to relate the experimentally observed increase in hardness to an increasing Al content, at least within the range 0 ≤ x ≤ 0.5, to an increase in G and E and to a decrease in B . The calculated longitudinal Young's modulus E 11 (1 1 1) of Ti 1− x Al x N (0 ≤ x ≤ 0.4) is in good agreement with experimental data taken from the coatings with the (1 0 0) preferred orientation.