In this study, we considered the structural stability, electronic properties, and phonon dispersion of the cubic (c-ZrO₂), tetragonal (t-ZrO₂), and monoclinic (m-ZrO₂) phases of ZrO₂. We found that the monoclinic phase of zirconium dioxide is the most stable among the three phases in terms of total energy, lowest enthalpy, highest entropy, and other thermodynamic properties. The smallest negative modes were found for m-ZrO₂. Our analysis of the electronic properties showed that during the m–t phase transformation of ZrO₂, the Fermi level first shifts by 0.125 eV toward higher energies and then decreases by 0.08 eV in the t–c cross-section. The band gaps for c-ZrO₂, t-ZrO₂, and m-ZrO₂ are 5.140 eV, 5.898 eV, and 5.288 eV, respectively. Calculations based on the analysis of the influence of doping 3.23, 6.67, 10.35, and 16.15 mol. %Y₂O₃ onto the m-ZrO₂ structure showed that the enthalpy of m-YSZ decreases linearly, which accompanies further stabilization of monoclinic ZrO₂ and an increase in its defectiveness. In this case, the position of the Fermi level changes abruptly, and the energy gap decreases. It has been established that, not only for pure systems but including those doped with Y₂O₃, the main contribution to the formation of the conduction band is made by the p-states of electrons. The t-ZrO₂ (101) and t-YSZ (101) surface models were selected as optimal surfaces for water adsorption based on a comparison of their surface energies. An analysis of the mechanism of water adsorption on the surface of t-ZrO₂ (101) and t-YSZ (101) showed that H₂O on unstabilized t-ZrO₂ (101) is adsorbed dissociatively with an energy of -1.22 eV, as well as by the method of molecular chemisorption with an energy of - 0.69 eV and the formation of a hydrogen bond with a bond length of 1.01 Å. In the case of t-YSZ (101), water is molecularly adsorbed onto the surface with an energy of -1.84 eV. Dissociative adsorption of water occurs at an energy of -1.23 eV, near the yttrium atom. The obtained results complement the database of research works carried out in the field of the application of biocompatible zirconium dioxide crystals and ceramics in green energy generation and can be used in designing humidity-to-electricity converters and creating solid oxide fuel cells based on ZrO₂.

The paper considers the issues of structural stability, electronic properties, and phonon dispersion of the cubic, tetragonal, and monoclinic phases of ZrO₂. It was found that the monoclinic phase of zirconium dioxide is the most stable among the other two phases in terms of total energy, lowest enthalpy, highest entropy, and other thermodynamic values. The smallest negative modes were found for m-ZrO₂. An analysis of the electronic properties showed that during the m–t phase transformation of ZrO₂, the Fermi level first shifts by 0.125 eV towards higher energies, and then decreases by 0.08 eV in the t–c cross section. The band gap for c-ZrO₂, t-ZrO₂, and m-ZrO₂ is 5.140 eV, 5.898 eV, and 5.288 eV, respectively. Calculations based on the analysis of the influence of doping 3.23, 6.67, 10.35 and 16.15 mol. %Y₂O₃ on the m-ZrO₂ structure showed that the enthalpy of m-YSZ decreases linearly, which accompanies further stabilization of monoclinic ZrO₂ and an increase in their defectiveness. In this case, the position of the Fermi level changes abruptly, and the energy gap decreases. It has been established that not only for pure systems, including those doped with Y₂O₃, the main contribution to the formation of the conduction band is made by the p-states of electrons. An analysis of the mechanism of water adsorption on the surface of t-ZrO₂ (101) and t-YSZ (101) showed that H₂O on unstabilized t-ZrO₂ (101) is adsorbed dissociatively with an energy of -1.22 eV, as well as by the method of molecular chemadsorption with an energy of -0 .69 eV and the formation of a hydrogen bond with a bond length of 1.01 Å. In the case of t-YSZ (101), water is molecularly adsorbed onto the surface with an energy of -1.84 eV. Dissociative adsorption of water occurs at an energy of -1.23 eV, near the yttrium atom.

In this study, we considered the structural stability, electronic properties, and phonon dispersion of the cubic (c-ZrO₂), tetragonal (t-ZrO₂), and monoclinic (m-ZrO₂) phases of ZrO₂. We found that the monoclinic phase of zirconium dioxide is the most stable among the three phases in terms of total energy, lowest enthalpy, highest entropy, and other thermodynamic properties. The smallest negative modes were found for m-ZrO₂. Our analysis of the electronic properties showed that during the m–t phase transformation of ZrO₂, the Fermi level first shifts by 0.125 eV toward higher energies and then decreases by 0.08 eV in the t–c cross-section. The band gaps for c-ZrO₂, t-ZrO₂, and m-ZrO₂ are 5.140 eV, 5.898 eV, and 5.288 eV, respectively. Calculations based on the analysis of the influence of doping 3.23, 6.67, 10.35, and 16.15 mol. %Y₂O₃ onto the m-ZrO₂ structure showed that the enthalpy of m-YSZ decreases linearly, which accompanies further stabilization of monoclinic ZrO₂ and an increase in its defectiveness. A doping-induced and concentration-dependent phase transition in ZrO₂ under the influence of Y₂O₃ was discovered, due to which the position of the Fermi level changes and the energy gap decreases. It has been established that, not only for pure systems but including those doped with Y₂O₃, the main contribution to the formation of the conduction band is made by the p-states of electrons. The t-ZrO₂ (101) and t-YSZ (101) surface models were selected as optimal surfaces for water adsorption based on a comparison of their surface energies. An analysis of the mechanism of water adsorption on the surface of t-ZrO₂ (101) and t-YSZ (101) showed that H₂O on unstabilized t-ZrO₂ (101) is adsorbed dissociatively with an energy of -1.22 eV, as well as by the method of molecular chemisorption with an energy of - 0.69 eV and the formation of a hydrogen bond with a bond length of 1.01 Å. In the case of t-YSZ (101), water is molecularly adsorbed onto the surface with an energy of -1.84 eV. Dissociative adsorption of water occurs at an energy of -1.23 eV, near the yttrium atom. The results show that ab initio approaches are able to describe the mechanism of doping-induced phase transitions in (ZrO₂+Y₂O₃)-like systems, based on which it can be assumed that DFT calculations can also flawlessly evaluate other physical and chemical properties of YSZ, which have not yet been studied quantum chemical research. The obtained results complement the database of research works carried out in the field of the application of biocompatible zirconium dioxide crystals and ceramics in green energy generation and can be used in designing humidity-to-electricity converters and creating solid oxide fuel cells based on ZrO₂.