Surface energetics of AlxTi1-xN alloys

The (100), (110) and (111) surface energies of random AlxTi1-xN alloys with homogeneous concentration profile are determined in first-principles calculations. The (100) surface has the lowest energy of 1.25 J/m(2) in the case of TiN and 1.32 J/m(2) for cubic AlN and exhibit very little concentration dependence. The (110) and (111) surfaces have much higher energy for all the compositions. The segregation energies of Ti and Al were obtained for the (100) surface of pure TiN and cubic AlN as well as Al0.5Ti0.5N and Al0.9Ti0.1 N random alloys. In the latter case, we have used two different methods: direct averaging of the substitution energies with respect to the local environment of the substitution site and the cluster expansion technique (CLE). We find that the segregation of Ti is favorable in the whole concentration range of random AlxTi1-xN alloys. However, it is weak in almost the whole concentration range except in the Al-rich alloys: Al0.9Ti0.1N -/+ and cubic AlN. The strengthening of the surface segregation of Ti in the latter case is related to the sharp increase in phase separation tendency in AlxTi1-xN alloys at compositions close to pure AlN. The increased tendency for Ti segregation close to pure AlN helps explain the formation of a lamella structure in industrially important AlxTi1-xN coatings. As for nitrogen vacancies, their segregation energies are relatively small in the whole concentration range, but for pure AlN where they exhibit strong preference for the surface. The latter is obviously connected with the fact that cubic AlN has a high degree of ionic bonding and a vacancy creation on the nitrogen sublattice is highly energetically unfavorable, especially in the bulk due to a larger number of Al-N ionic bonds.