On the spinodal nature of the phase segregation and formation of stable nanostructure in the Ti-Si-N system

The free energy of the mixed Ti-Si-N system is calculated according to a semi-empirical thermodynamic formula based on the sub-lattice model for different activities of nitrogen. The results show that the phase segregation in the ternary Ti-Si-N systems is of chemically spinodal nature at a nitrogen pressure and deposition temperature typically used for the deposition of the superhard nc-TiN/a-Si₃N₄ nanocomposites, i.e. p_N2 ≥ 10^{- 3} mbar and T_dep 550-600 °C, respectively. Only at much lower nitrogen pressure and much higher temperature, can the chemically spinodal decomposition be restrained. A simple estimate of the interfacial strain energy for a semi-coherent interface, as expected for this system, shows that this contribution is unlikely to hinder the system being also coherently spinodal. It is further shown that kinetic constraints, such as T_dep ≤ 300 °C and low p_N2, although within the range where the stoichiometric nitrides should be fully spinodally segregated, will kinetically hinder the system to reach the thermodynamically driven equilibrium.