1. The phase diagram of TiAlN (a) The stable TiN-AlN pseudo binary phase diagram^[61], among which the Al solubilities of fcc phase is negligible; (b) The critical Al solubilities (x_max) in Ti_1-xAl_xN by different calculation methods compared with the experimental data^{[35-37, 40-41, 49-52, 61-66]}

2. Schematic diagram of the atomic models in the thin films prepared by magnetron sputtering

3. Structure of the coatings deposited at room temperature compared with the phase diagrams of (a) Al-Cu^[59,71], (b) Al-Ni^[59,72] and (c) Al-Fe^[59,70]

4. (a) Diffusion distance versus temperature of Cu-11.5at% Sn obtained by Saunders and Miodownik^[60] based on diffusion equation; (b) Diffusion distance versus temperature of Cu-19.5at% Sn^[60] obtained by Saunders and Miodownik based on diffusion equation; (c) Phase diagram of the Cu-Sn system^[73]

5. Flow chart of simulating metastable phase formation diagram of PVD coatings^[58]

6. (a) Calculated and predicted metastable Cu-W phase formation diagram compared with the experimental data^[58]; (b) Calculated and predicted metastable Cu-V phase formation diagram compared with the experimental data^[58]; (c) Phase diagram of the Cu-W system^[74]; (d) Phase diagram of the Cu-V system^[75]

7. (a) Phase diagram of the Pt-Ir^[86] system; (b) Phase diagram of the Pt-Au system^[87]; (c) Phase formation of the Pt-Ir^[85] sputtered thin films; (d) Phase formation of the Pt-Au^[85] sputtered thin films

8. Metastable Ti_1-xAl_xN phase formation diagrams (a) The predicted diagrams at different power densities; (b) The predicted diagram compared with the experimental data with power density of 2.3 W·cm^-2 at 100-550 ℃; (c) The predicted diagram compared with the experimental data with power density of 4.6 W·cm^-2 at 100-550 ℃; (d) The predicted diagram compared with the experimental data with power density of 6.8 W·cm^-2 at 100-550 ℃