Effects of pressure and vibration on the thermal decomposition of cubic Ti_1-x Al _x N, Ti_1-x Zr _x N, and Zr_1-x Al _x N coatings: A first-principles study

Thermodynamic properties as well as the miscibility gap (binodal) and spinodal decompositions of the cubic Ti_1-x Al _x N, Ti _1-x Zr _x N, and Zr_1-x Al _x N coating alloys have been computed using first-principles calculations. Herein, the cluster expansion method and especially the special quasirandom structure are employed to describe the disordered alloys. The effects of pressure and lattice vibration on the miscibility gaps and spinodal decompositions of the above alloys have been investigated by means of Helmholtz free energy with the vibrational contribution depicted with the Debye-Grüneisen model. It is found that the application of hydrostatic pressure promotes the isostructural decomposition of Ti_1-x Al _x N, Ti_1-x Zr _x N, and Zr_1-x Al _x N alloys, whereas the vibrational contribution decreases the consolute temperature of the phase separation. Our results indicate that the improved age-hardening behavior of cubic Ti_1-x Al _x N coatings with the addition of Zr arises from the enlarged composition range of binodal and spinodal curves at specified temperatures. Our results are in good agreement with the available experimental data and provide a useful insight into the investigation of age-hardening and characterization of Ti-Al-Zr-N-based coatings for high-temperature applications.