First-principles calculations have been widely used to describe the ground state properties of materials over almost 20 years. Recently, a great progress was made in the first-principle calculations. Thermodynamic properties can also be gotten by calculations of the phonon densities of states (phonon DOS) and phonon dispersions of materials, which show widely potential applications in material researches. In the present work, the energetics and bonding properties of interfaces between ZrO2 and Ni metal were given by first-principles calculations. The results show that alloy element impurities (Al, Cr and Y) influence remarkably the adhesion of the ceramic and metal. On the other hand, the phonon densities of states and phonon dispersions of ZrO2 were calculated with density functional perturbation theory. From the phonon DOS, the thermodynamic properties were derived and the phase transformation of ZrO2 was discussed. By this method, the thermodynamic properties of material can be gotten from atom and electron levels without any experiment data. It is a new approach to design and study the thermodynamic properties in new material system.