## 4 Discussion  
In this study, we examined the tensile strength and failure properties of the three terminated ZrO\({}_{2}\)/Al\({}_{2}\)O\({}_{3}\) interfaces using first-principle calculations. Among the three interface terminations, the calculated results indicate that the O-terminated interface has  
Figure 4: Pictorial representation showing the evolution of the interfacial atomic bonds for the c-ZrO\({}_{2}\)/\(\alpha\)-Al\({}_{2}\)O\({}_{3}\) interfaces under the tension loading. (**a**) O-terminated, (**b**) 2O-terminated, and (**c**) Zr-terminated. the strongest resistance to tensile failure, while the Zr-terminated interface is the most prone to failure. Due to the bond energy of the anion-cation, the bonds across the interfaces in the O-model are stronger than those of the other two models. Moreover, the stabilizing cation-cation interactions across the interface also increase the adhesive energy of the O-model. In addition, the failure position of the three interface terminations occurs at the interface, indicating the weak adhesion of the interface. In addition, the fracture modes of the O-terminated and Zr-terminated interfaces tend to be ductile fractures, while the fracture mode of the 2O-terminated interface tends to be a brittle fracture. In our shear simulations [39], the O- \(<\)1120\(>\) model had a maximum shear strength of 5.69 GPa and unstable stacking energy of 612 mJ/m\({}^{2}\). The Zr- \(<\)1101\(>\) model had a minimum shear strength of 2.94 GPa and work of adhesion of 245 mJ/m\({}^{2}\). It was found that the shear strength of the \(<\)-ZrO\({}_{2}\)(001)/\(\alpha\)-Al\({}_{2}\)O\({}_{3}\)(1102) interfaces had the same trend; that is, the O-terminated interface had the greatest shear resistance, while the Zr-terminated interface had the weakest shear resistance. However, compared with the shear strength, the tensile strength was much higher than the shear strength in the same termination. This implies that the \(<\)-ZrO\({}_{2}\)(001)/\(\alpha\)-Al\({}_{2}\)O\({}_{3}\)(1102) interfaces have a stronger tensile resistance and are more prone to shear failure. According to our investigations through these first-principle calculations, shear failure requires only the breaking of some bonds at the interface, whereas tensile failure requires the breakage of all the bonds near the interface. [PERSON] et al. investigated the ZrO\({}_{2}\)(001)/\(\alpha\)-Al\({}_{2}\)O\({}_{3}\)(1102) interfaces by first-principles calculations to understand the electronic, structural, and energy properties [30] Their calculated adiabatic work of adhesion was about 1200 mJ/m\({}^{2}\). Our calculated work of adhesion for the O-terminated interface was consistent with this value. In order to fully investigate the mechanical properties of the c-ZrO\({}_{2}\)(001)/\(\alpha\)-Al\({}_{2}\)O\({}_{3}\)(1102) interfaces, we also examined the Zr-terminated and 2O-terminated interfaces. The calculated results imply that the adhesive strength of the interface is strongly influenced by the termination of c-ZrO\({}_{2}\)(001), while the interfaces of all the models adhered weakly. In fact, when looking closely at the atomic snapshots of these interfaces, it is seen that the length increments of the two Al-O bonds are quite different at each displacement loading step. The three terminations are completely separated along the intermediate layer between the initial ZrO\({}_{2}\) and Al\({}_{2}\)O\({}_{3}\) slabs. This also suggests that the interaction between ZrO\({}_{2}\) and Al\({}_{2}\)O\({}_{3}\) is weak. Moreover, as the interface in the TBC system, this weak interaction absolutely affects the lifetime of the TBC system. Another interface in the TBC system, i.e., the Ni(111)/\(\alpha\)-Al\({}_{2}\)O\({}_{3}\)(0001) interface, has been investigated by [PERSON] et al. [25] through a comparative study between the uniaxial extension and uniaxial tension simulations.