First, the effect of aluminum alloying on the electronic structure and Ti-N bonding energy was considered. Random supercells in which aluminum atoms replace 25 and 50% of titanium atoms were constructed. The equilibrium lattice parameters obtained (normalized to the 1×1×1 cubic cell) are 4.218 and 4.177 Å for Ti 1-x Al x N solutions with x=0.25 and 0.5, respectively, i.e. it is observed an almost linear decrease in the lattice parameter with increasing aluminum concentration. The atoms in the lattice are shifted from the ideal positions due to atomic relaxation.