A Detailed Comparative Analysis of the Structural Stability and Electron-Phonon Properties of ZrO2: Mechanisms of Water Adsorption on t-ZrO2 (101) and t-YSZ (101) Surfaces

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 the 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 the main contribution to the formation of the conduction band is made by the p-states of electrons, not only for pure systems, but also those doped with Y2O3. 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 in creating solid oxide fuel cells based on ZrO2.


Introduction
With the ongoing threat of the energy crisis and global warming caused by the increase in the use of fossil fuels, the search for sustainable and environmentally friendly sources of energy is one of the most pressing challenges facing human civilization today [1,2].Fossil fuels' continued use worldwide threatens our energy supply and significantly burdens the environment.Research on the use of sustainable green energy represents one of the ways to mitigate the growing threat of global environmental problems and the energy crisis, which is very intense and active worldwide.Solar panels and wind turbines have become familiar to us.However, new advances in nanotechnology and materials science make it possible to collect energy from other sources, and will help to implement Nikola Tesla's idea of "Getting an electric current from the air".Recently, scientists and engineers have been developing innovative devices for converting humidity into electricity, which will expand the range of known renewable energy sources.These use galvanic converters that convert air humidity into electricity.Such devices can collect electricity from atmospheric humidity and supply an electrical current, similar to how solar panels capture sunlight and generate electricity.
Moisture, which is ubiquitous on Earth (approximately 71% of the Earth's surface is covered by water), contains a large reservoir of low-potential energy in the form of gaseous water molecules and water droplets.It has been found that a number of functional nanomaterials, such as TiO 2 , CaSiO 3 , ZrO 2 , SnO 2 , and Al 2 O 3 , as well as biofibers and carbon materials, can generate electricity directly when interacting with moisture [2].This presents the possibility of generating electrical energy from atmospheric moisture, allowing the creation of self-powered devices.While this technology is still evolving, there are already some strategies for improving the energy conversion efficiency and power output of these devices.
Zirconium ceramics have been extensively studied in recent years because of their excellent electrical, optical, and mechanical properties.They are also biocompatible and have a wide range of biomedical applications.Tetragonal phase yttria-stabilized zirconia (Y-TZP) has been used in various medical applications since the 1980s, particularly for dental crowns [2].In addition, bulk materials and nanocomposites based on ZrO 2 are used in electrochemical cells because of their high oxide ion conductivity and catalytic activity, low thermal conductivity, mechanical/chemical stability, and compatibility with electrolytes, which make them structurally advantageous [3,4].
Pure zirconium dioxide undergoes a phase transformation from monoclinic to tetragonal (at about 1173 • C) and then to cubic (at about 2370 • C), accompanied by a change in volume, and accordingly, strength [12][13][14].For the application of zirconia in advanced zirconia ion-conducting ceramic devices, it is important that the stabilized material has an adequate level of conductivity and that it has the desired mechanical-chemical stability in both oxidizing and reducing atmospheres.Obtaining a stable material from zirconia is difficult due to a noticeable change in volume during the phase transition.Stabilization of zirconium dioxide is achieved by replacing some Zr 4+ ions with larger ions in the crystal lattice [15][16][17].For example, numerous studies have shown that doping with polyvalent oxides, including certain concentrations of yttrium oxide, stabilizes the high-temperature cubic and tetragonal phases of ZrO 2 at room temperature.This also leads to an increase in the concentration of oxygen vacancies and in oxygen-ion conductivity, which makes it possible to use stabilized ZrO 2 as an electrolyte in fuel cells [17].The ionic conductivity of ZrO 2 strongly depends on the phase modification and the content of stabilizing additives in the system, as shown in the phase diagram given in [18].
Many technological applications of zirconia (pure ZrO 2 or its stabilized alloys) are directly related to its interaction with water.Examples are internal steam reforming in solid oxide fuel cells [19], catalysis [20], gas sensors [21], or its use as a biocompatible material [22].ZrO 2 surfaces have also been proposed as suitable materials for hydrogen storage [21][22][23].However, little is known about the interaction of water with ZrO 2 surfaces at a fundamental level, which is mainly due to the lack of suitable samples.This is quite different for other oxide substrates [23][24][25].Water is weakly adsorbed by many defect-free oxide surfaces in an ultra-high vacuum, then stripped at a temperature below room temperature.Usually, at 160-250 K [26], water can bind more strongly to surfaces with defects, as was shown for rutile (TiO 2 (110)) [27].In these cases, H 2 O dissociates into an OH group, which fills the oxygen vacancy, and into a hydrogen atom, which binds to surface oxygen and forms a second OH group.These OH groups are stable for up to 490 K on TiO 2 [28].On a defect-free surface oxides (e.g., a-Cr 2 O 3 (001) [29], a-Fe 2 O 3 (012) [30], and oxides of alkaline earth metals, including Ca 3 Ru 2 O 7 (001) [31]), water can be strongly bound if the end of the surface includes highly active cations.Then, it can easily dissociate.On the surfaces of RuO 2 (110), PdO (101), and Fe 3 O 4 (001), water binds coordinatively unsaturated cations and partially dissociated forms of the structure stabilized by hydrogen bonds [32][33][34].Highenthalpy adsorption of low-H 2 O powder materials (≥2 eV on monoclinic and ≈1.5 eV on tetragonal ZrO 2 ) has been reported to decrease liquid-water binding (0.45 eV) at coverages of approximately 2-4 H 2 O/nm 2 [35].In another study, Droshkevich et al. [36] reported on the chemo-electronic conversion of water adsorption energy into electricity on the surface of zirconium dioxide nanopowders that were synthesized at sizes of 7.5 nm, when doped with 3 mol.%Y 2 O 3 .
However, despite numerous studies in this area, water adsorption on ZrO 2 surfaces has not been studied in detail, and only a few reports on H 2 O adsorption can be found in the literature.In particular, H 2 O adsorption on well-defined monoclinic surfaces of zirconia (m-ZrO 2 (101) and m-ZrO 2 (101) and its doped structures) has not been studied.For example, it is especially difficult to experimentally study pure ZrO 2 single crystals grown from a melt; they exhibit phase transformations upon cooling; therefore, their doped structures (e.g., YSZ) are usually investigated.However, the surface chemistry of YSZ is more complex than pure ZrO 2 , as shown for CO and CO 2 adsorption [37].In another work, Kobayashi et al. [38] found that YSZ slowly decomposed at about 250 • C due to the t-m transformation.In a humid atmosphere, this t-m transformation is accompanied by microcracks and a loss in material strength.This discovery cooled the excitement caused by the discovery of PPT in zirconia-based ceramics.This t-m transformation due to the presence of water or a humid environment in zirconia-based ceramic materials has been termed low-temperature degradation, or aging of ZrO 2 crystals.This topic has been researched extensively over the past couple of decades, including many hypotheses and discussions.The most reliable hypothesis about YSZ is based on filling oxygen vacancies present in the matrix to maintain a stable t-YSZ phase.Thus, the filling of these O vacancies with water radicals, either O 2 or OH, destabilizes the t-YSZ phase.However, the YSZ stabilization mechanism has not been fully studied, and is still the subject of numerous discussions.Therefore, the theoretical study and modeling of water adsorption on these surfaces is necessary as a starting point for a good understanding of ongoing processes and phenomena from a fundamental point of view.On the other hand, aspects of the shift in the Fermi level after doping with yttrium oxide in ZrO 2 , as well as when it is under the influence of water adsorption, are still not clear due to the difficulty of their detection.
For these reasons, to obtain detailed information on the process of the adsorption of water molecules onto ZrO 2 and YSZ surfaces, as well as the effect of doping on their electronic and structural properties, we conducted quantum chemical calculations within the framework of density functional theory (DFT).
We conducted ab initio quantum chemical calculations on the basis of density functional theory [49].All three phases of ZrO 2 (Figure 1a-c) were first relaxed using generalized gradient approximation (GGA) functionals (PBE) [50] and strictly bounded normalized potentials (SCAN) [51].To obtain the most accurate value of the ground state energy, the total energy was calculated within the framework of the GGA exchange-correlation potential and SCAN were used to correctly estimate the lattice parameters.The calculations were carried out using the Vienna ab initio Simulation Package (VASP 6.3.2) [52].We found a stable ZrO 2 phase by comparing the total energy in the unit cell.For stabilization at room temperature, a 2 × 2 × 2 supercell was created to simulate the effect of 3.23, 6.67, 10.34, and 16.15 mol.%Y 2 O 3 on the stability of ZrO 2, as well as to evaluate the influence of Y 2 O 3 doping on the position of the Fermi level.We performed an orbital analysis by summing the contributions of the individual atomic species in the unit cell and showing the contributions of the main atoms at the meeting point of the valence and conduction bands.Vacancies were taken into account by removing one O atom with each subsequent substitution of 2 Y 3+ ions to the Zr 4+ position.The atomic orbitals of H (1 s ), O (2 s , 2 p ), Zr (4 d , 5 s ), and Y (4 s , 4 p , 4 d , 5 s ) were considered valence electrons, while the remaining electrons were considered nuclear electrons and remained frozen.The PAW method was used to describe the interactions between valence electrons and electrons in the nucleus.The kinetic energy cutoff was fixed at 600 eV, and all calculations were carried out while taking spin-polarized effects into account.First-principles (ab initio) methods within the framework of DFT are successfully used in modern materials science regarding condensed matter physics [39][40][41][42][43][44][45][46][47][48].
We conducted ab initio quantum chemical calculations on the basis of density functional theory [49].All three phases of ZrO2 (Figure 1a-c) were first relaxed using generalized gradient approximation (GGA) functionals (PBE) [50] and strictly bounded normalized potentials (SCAN) [51].To obtain the most accurate value of the ground state energy, the total energy was calculated within the framework of the GGA exchange-correlation potential and SCAN were used to correctly estimate the lattice parameters.The calculations were carried out using the Vienna ab initio Simulation Package (VASP 6.3.2) [52].We found a stable ZrO2 phase by comparing the total energy in the unit cell.For stabilization at room temperature, a 2 × 2 × 2 supercell was created to simulate the effect of 3.23, 6.67, 10.34, and 16.15 mol.%Y2O3 on the stability of ZrO2, as well as to evaluate the influence of Y2O3 doping on the position of the Fermi level.We performed an orbital analysis by summing the contributions of the individual atomic species in the unit cell and showing the contributions of the main atoms at the meeting point of the valence and conduction bands.Vacancies were taken into account by removing one O atom with each subsequent substitution of 2 Y 3+ ions to the Zr 4+ position.The atomic orbitals of H (1 s ), O (2 s , 2 p ), Zr (4 d , 5 s ), and Y (4 s , 4 p , 4 d , 5 s ) were considered valence electrons, while the remaining electrons were considered nuclear electrons and remained frozen.The PAW method was used to describe the interactions between valence electrons and electrons in the nucleus.The kinetic energy cutoff was fixed at 600 eV, and all calculations were carried out while taking spin-polarized effects into account.Next, ab initio calculations were carried out to study the mechanism of the adsorption of a water molecule on the surface of ZrO2 and ZrO2 by stabilized Y2O3, where we found the adsorption energies of a water molecule on ZrO2 and YSZ surfaces.We also conducted an orbital analysis and estimated the shift in the Fermi level.Next, ab initio calculations were carried out to study the mechanism of the adsorption of a water molecule on the surface of ZrO 2 and ZrO 2 by stabilized Y 2 O 3 , where we found the adsorption energies of a water molecule on ZrO 2 and YSZ surfaces.We also conducted an orbital analysis and estimated the shift in the Fermi level.
For such specific problems, the choice of the adsorbed surface is very important.To obtain results consistent with the experiment, we had to accurately select a suitable surface with the lowest density of broken surface bonds and electrostatic repulsion of neighboring layers, while considering the thermodynamic stability of the surface.The higher the surface energy, the more thermodynamically unstable it is [53] and the more difficult it is to create the corresponding surface, because surface energy is closely related to the number of atoms in the surface structure and the depth of the vacuum layer.
To select a suitable optimal surface for water adsorption and study the water's behavior on this surface, we calculated the surface energy (σ) using Equation (1) [54]: where S is the total surface area of the plate; E slab is the total plate energy; E bulk is the total energy of an optimized bulk structure; N and n represent the total numbers of atoms in the surface structure and unit cell, respectively; and 2 represents the two surfaces of the calculated structure in the direction of the z-axis.Models of the crystal wafer surface were constructed based on an extended 2 × 2 supercell with a vacuum space of 35 Å along the z-direction to minimize the interaction of neighboring layers.Taking into account the accuracy and calculation time, the lower layers of the surface plate were frozen, and the upper part was allowed to relax.Monkhorst-Pack grids with a 3 × 3 × 1 k-point grid were used to sample the reciprocal space for the 2 × 2 plate calculations.Each molecule in the gas phase was placed in a large box (11 × 13 × 10 Å 3 ) to avoid side interactions.
Single H 2 O molecules were initially located at a height of 2.5 Å above the chosen surface; different orientations, the relaxing of H 2 O molecules, and the upper layers of the plate for each initial adsorption site were compared.For each molecule, we tested four initial adsorption centers (above the Zr atom, above the terminal oxygen Ou (top) or Od (bottom), and in the center above the Zr position (see Figure 1d)).We also investigated various initial adsorption sites for the YSZ surface model-namely, above the Zr atom, the extreme oxygens, Ou (top) and Od (bottom), in the oxygen vacancy position, the yttrium atom, and the Ou-Od-Zr center (see Figure 1e)-to determine the most favorable adsorption sites leading to stable configurations.We did not study the nonequivalent initial adsorption sites in detail.
The adsorption energy (E ads ) was calculated as the difference between the energy of the plate with adsorbed water (E H2O/sur f ace ) and the sum of the energies of the surface (E sur f ace ) and H 2 O molecules (E H2O ), according to the following equation: To take into account long-range uncoupled interactions, we considered Van der Waals effects as the difference between the calculated Van der Waals energy of a plate with adsorbed H 2 O molecules (E vdW H2O /sur f ace ) and the sum of the calculated Van der Waals energies of the surface (E vdW sur f ace ) and H 2 О molecules (E vdW H2O ): where the interaction energy vdW is taken into account by the Leonard-Jones potential.

Structural Stability and Electron-Phonon Properties of ZrO 2
In the first stage of modeling, the structural energy relaxation of pure ZrO 2 phases was carried out using the VASP package.To find the optimal cutoff energy for the ENCUT plane-wave basis functions and the corresponding number of k-points in the Brillouin zone, we tested the convergence of the total unit cell energy as a function of ENCUT and KPOINTS.
Convergence tests to select an appropriate k-point grid were first performed for all three ZrO 2 phases with an initial value of ENCUT = 1.3 × ENMAX.The smallest grid of 4 × 4 × 4 k-points with the Monkhorst-Pack scheme was optimal for the geometric relaxation of all studied ZrO 2 phases.However, when calculating the electronic structures of these compounds, the number of k-points was at least doubled to obtain a better density of states (DOSs).
Similar tests were carried out to establish the cutoff energy.They showed that 600 eV was suitable for the calculations, and further increasing this energy increased the cost of calculations without improving their accuracy.Therefore, all further calculations were conducted at ENCUT = 600 eV.
According to the results given in Table 1, lattice distortion during the transition between the high-and low-temperature phases causes a displacement of O ions in the c-direction by the value of dz, expressed in relative units.As a result of distortion in the tetragonal phase, all Zr-O bonds will become nonequivalent.E − E m (eV/ZrO 2 ) 0.833 0.833 0.087 0.140 [61] Table 2 compares the total unit cell energies calculated using the GGA method for the monoclinic, tetragonal, and cubic phases of ZrO 2 .Among all systems, m-ZrO 2 is the most stable phase with the lowest energy.That is, in terms of field energy at low temperatures, the stable phase is monoclinic with the space group P21/c.As shown in Table 3, the SCAN functionality describes the geometry better than the standard GGA-PBE.However, the available data also show that GGA and SCAN describe the energy difference between the monoclinic and tetragonal phases of ZrO 2 almost identically.Since the SCAN exchange-correlation functional describes the structural properties well, we decided to use this functional in the future when describing the geometry of other systems.Furthermore, we calculated the thermodynamic properties and phonon spectra of the ZrO 2 phase using the Phonopy code in the VASP package for a more detailed discussion and substantiation of the ZrO 2 monoclinic phase's structural stability.Figure 2 shows the change in the entropy of unit cells of the ZrO 2 phase as a function of temperature.properties well, we decided to use this functional in the future when describing the ge ometry of other systems.Furthermore, we calculated the thermodynamic properties and phonon spectra o the ZrO2 phase using the Phonopy code in the VASP package for a more detailed discus sion and substantiation of the ZrO2 monoclinic phase's structural stability.Figure 2 show the change in the entropy of unit cells of the ZrO2 phase as a function of temperature.Figure 2 shows that with the transition from the monoclinic phase to the tetragona and cubic phases, the entropy of these compounds decreases, which corresponds to th criterion of the inverse dependence of enthalpy or direct dependence of entropy on th stability of solid systems [63].Thus, the monoclinic phase is the most stable, with the high est entropy among the three ZrO2 phases.This pattern can be clearly observed after ana lyzing the pattern of phonon frequencies of the three ZrO2 phases (Figure 3a-c), from which it is clearly seen that the monoclinic phase has smaller negative modes than th other two phases.Figure 2 shows that with the transition from the monoclinic phase to the tetragonal and cubic phases, the entropy of these compounds decreases, which corresponds to the criterion of the inverse dependence of enthalpy or direct dependence of entropy on the stability of solid systems [63].Thus, the monoclinic phase is the most stable, with the highest entropy among the three ZrO 2 phases.This pattern can be clearly observed after analyzing the pattern of phonon frequencies of the three ZrO 2 phases (Figure 3a-c), from which it is clearly seen that the monoclinic phase has smaller negative modes than the other two phases.Figure 5a-c presents the results of the calculations of the density of phonon states, which indicate that during the transition from the monoclinic phase to the tetragonal and cubic phases, the density of electronic states increases.These results also agree with those shown in Figure 3, confirming that the monoclinic phase is the most stable among the ZrO 2 phases.The energy/volume chart presented by Teter et al. also supports these results [64].Therefore, for further stabilization by doping with Y 2 O 3 , it is reasonable to choose a monoclinic phase.Figure 5a-c presents the results of the calculations of the density of phonon states, which indicate that during the transition from the monoclinic phase to the tetragonal and cubic phases, the density of electronic states increases.These results also agree with those shown in Figure 3, confirming that the monoclinic phase is the most stable among the ZrO2 phases.The energy/volume chart presented by Teter et al. also supports these results [64].Therefore, for further stabilization by doping with Y2O3, it is reasonable to choose a monoclinic phase.Next, using the well-optimized structures of the three phases of ZrO 2 , we performed calculations to study their electronic properties.We found the band gaps of these systems (Table 3) using the GGA and SCAN functionals, as well as the HSE06 hybrid functional, analyzed their orbital structure, and modeled the change in the position of the Fermi level.
As seen in Table 3, the GGA and SCAN functionals showed a rather small band gap compared to the HSE06 hybrid functional [65], the results of which were much closer to the experimentally determined band gap.On the other hand, the standard SCAN and GGA functionals greatly underestimate the band gap.Given the suitability of HSE06 for estimating the band gap energy, we further used this hybrid functional to describe all the problems associated with the electronic properties of the systems under study.Next, using the well-optimized structures of the three phases of ZrO2, we performed calculations to study their electronic properties.We found the band gaps of these systems (Table 3) using the GGA and SCAN functionals, as well as the HSE06 hybrid functional, analyzed their orbital structure, and modeled the change in the position of the Fermi level.
As seen in Table 3, the GGA and SCAN functionals showed a rather small band gap compared to the HSE06 hybrid functional [65], the results of which were much closer to the experimentally determined band gap.On the other hand, the standard SCAN and GGA functionals greatly underestimate the band gap.Given the suitability of HSE06 for estimating the band gap energy, we further used this hybrid functional to describe all the problems associated with the electronic properties of the systems under study.
In the next step, we calculated the density of available electronic states at the Fermi level for ZrO2 structures relaxed using the HSE06 functional (Figure 6), which is crucial for interpreting the electronic properties of ZrO2 and the transport characteristics of electronic devices.In the next step, we calculated the density of available electronic states at the Fermi level for ZrO 2 structures relaxed using the HSE06 functional (Figure 6), which is crucial for interpreting the electronic properties of ZrO 2 and the transport characteristics of electronic devices.
Figure 7 shows the partial density of states for the three ZrO 2 phases.The contribution of Zr atoms to the formation of the valence band is greater than that of oxygen O, and the contribution of O atoms to the formation of the conduction band is greater than that of Zr atoms.
According to Figure 6, the density of electronic states for c-ZrO 2 is somewhat overestimated compared to the other phases.In addition, secondary energy gaps are observed in the energy diagram of the tetragonal and cubic phases.Furthermore, this gap increases during the transition from the tetragonal phase to the cubic phase.
Figure 7 shows the partial density of states for the three ZrO2 phases.The contribution of Zr atoms to the formation of the valence band is greater than that of oxygen O, and the contribution of O atoms to the formation of the conduction band is greater than that of Zr atoms.Figure 7 shows the partial density of states for the three ZrO2 phases.The contribution of Zr atoms to the formation of the valence band is greater than that of oxygen O, and the contribution of O atoms to the formation of the conduction band is greater than that of Zr atoms.Next, we determined the position of the Fermi level in ZrO 2 crystals and its shift during their phase transformation.As seen in Figure 8, if we assign the position of the Fermi level (maximum of the valence band) for the monoclinic phase as a reference point, this level first shifts by 0.125 eV towards higher energies during the m-t phase transformation of ZrO 2 (towards the valence band).Then, in the t-c section, it decreases by 0.08 eV.This is also observed in the band stacking results of the orbital analysis, which are shown in Figure 9 for the three phases of ZrO 2 .
in the energy diagram of the tetragonal and cubic phases.Furthermore, this gap increases during the transition from the tetragonal phase to the cubic phase.
Next, we determined the position of the Fermi level in ZrO2 crystals and its shift during their phase transformation.As seen in Figure 8, if we assign the position of the Fermi level (maximum of the valence band) for the monoclinic phase as a reference point, this level first shifts by 0.125 eV towards higher energies during the m-t phase transformation of ZrO2 (towards the valence band).Then, in the t-c section, it decreases by 0.08 eV.This is also observed in the band stacking results of the orbital analysis, which are shown in Figure 9 for the three phases of ZrO2.During the transition from the monoclinic to the tetragonal and cubic phases, the contribution of the p-orbitals becomes more significant in the conduction band.The sorbitals make a small contribution, while the d state shows a different trend.This behavior may be associated with a change in the crystal field and covalence of ZrO2 during the phase transformation.in the energy diagram of the tetragonal and cubic phases.Furthermore, this gap increases during the transition from the tetragonal phase to the cubic phase.
Next, we determined the position of the Fermi level in ZrO2 crystals and its shift during their phase transformation.As seen in Figure 8, if we assign the position of the Fermi level (maximum of the valence band) for the monoclinic phase as a reference point, this level first shifts by 0.125 eV towards higher energies during the m-t phase transformation of ZrO2 (towards the valence band).Then, in the t-c section, it decreases by 0.08 eV.This is also observed in the band stacking results of the orbital analysis, which are shown in Figure 9 for the three phases of ZrO2.During the transition from the monoclinic to the tetragonal and cubic phases, the contribution of the p-orbitals becomes more significant in the conduction band.The sorbitals make a small contribution, while the d state shows a different trend.This behavior may be associated with a change in the crystal field and covalence of ZrO2 during the phase transformation.During the transition from the monoclinic to the tetragonal and cubic phases, the contribution of the p-orbitals becomes more significant in the conduction band.The sorbitals make a small contribution, while the d state shows a different trend.This behavior may be associated with a change in the crystal field and covalence of ZrO 2 during the phase transformation.

Structural and Energy Properties of m-ZrO 2 Doped with Y 2 O 3 : The Electronic Properties of YSZ
We created supercells of 96 atoms with a size of 2 × 2 × 2 to simulate the effect of Y 2 O 3 on the stability and electronic properties of the most stable (monoclinic) ZrO 2 phase.To dope ZrO 2 with yttrium, it was necessary to replace some formula units of ZrO 2 with Y 2 O 3 in a 2 × 2 × 2 supercell, with each replacement creating one oxygen vacancy.A schematic description of the generation of YSZ structures is provided below: which can be considered the union of x ZrO 2 with the kY 2 O 3 formula units located on the initial lattice of the x + kZrO 2 units, leading to the formation of m oxygen defects.Based on this, we determined that the percentage of vacancies is equal to the percentage of yttrium units in the final structure.Thus, starting with a pure 96-atom ZrO 2 supercell, we mainly focused on four different concentrations of Y 2 O 3 in our calculations (Table 4).After the final preparation of the YSZ structures, we performed geometric optimization and doping relaxation of the Y 2 O 3 supercell using the GGA and SCAN potentials.Figure 10 shows a diagram of the dependence of the change in the enthalpy of formation of YSZ on the concentration of Y 2 O 3 , calculated using Formula (4): from which it is clearly seen that doping with Y 2 O 3 reduces the enthalpy and leads to the stabilization of zirconium dioxide.The empirical formula obtained using the least squares method states that the enthalpy of formation energy decreases linearly according to the law ∆Н = −1.0407x+ 63.532, where x is the concentration of Y 2 O 3 in YSZ.
on the stability and electronic properties of the most stable (monoclinic) ZrO2 phase.T dope ZrO2 with yttrium, it was necessary to replace some formula units of ZrO2 with Y2O in a 2 × 2 × 2 supercell, with each replacement creating one oxygen vacancy.A schemati description of the generation of YSZ structures is provided below: which can be considered the union of x ZrO2 with the kY2O3 formula units located on th initial lattice of the x + kZrO2 units, leading to the formation of m oxygen defects.Base on this, we determined that the percentage of vacancies is equal to the percentage of yt trium units in the final structure.Thus, starting with a pure 96-atom ZrO2 supercell, w mainly focused on four different concentrations of Y2O3 in our calculations (Table 4).After the final preparation of the YSZ structures, we performed geometric optimiza tion and doping relaxation of the Y2O3 supercell using the GGA and SCAN potentials Figure 10 shows a diagram of the dependence of the change in the enthalpy of formatio of YSZ on the concentration of Y2O3, calculated using Formula (4): from which it is clearly seen that doping with Y2O3 reduces the enthalpy and leads to th stabilization of zirconium dioxide.The empirical formula obtained using the least square method states that the enthalpy of formation energy decreases linearly according to th law ΔН = −1.0407x+ 63.532, where x is the concentration of Y2O3 in YSZ.Thus, the number of oxygen vacancies in YSZ increases with the increase in the Y2O concentration, and the growth of these O vacancies is considered a stabilizing mechanism Thus, the number of oxygen vacancies in YSZ increases with the increase in the Y 2 O 3 concentration, and the growth of these O vacancies is considered a stabilizing mechanism of the monoclinic zirconium phase, as indicated by a decrease in the enthalpy of formation.
Table 5 shows the geometric parameters of the ZrO 2 and YSZ supercells at various Y 2 O 3 concentrations after thorough relaxation using the SCAN functional.Table 6 presents the numerical values of the enthalpy of formation energies.After obtaining the optimized structures, the energy of formation (E f ) for ZrO 2 and YSZ, as well as the energy of formation of vacancies (E df ) for YSZ were calculated as follows: where E tot is the total energy of the system, E tot (x) is the total energy of individual com- ponents, and δ is the number of vacancies (defects) in the crystal.Table 6 presents the calculated values of E f and E d f for each atom.
Figure 11 shows the nature of the changes in E f and E d f with the yttrium oxide concentration, from which the regularity of their linear decrease is clearly visible.
of the monoclinic zirconium phase, as indicated by a decrease in the enthalpy of formation.
Table 5 shows the geometric parameters of the ZrO2 and YSZ supercells at various Y2O3 concentrations after thorough relaxation using the SCAN functional.Table 6 presents the numerical values of the enthalpy of formation energies.After obtaining the optimized structures, the energy of formation (Ef) for ZrO2 and YSZ, as well as the energy of formation of vacancies (Edf) for YSZ were calculated as follows: where  is the total energy of the system,  () is the total energy of individual components, and δ is the number of vacancies (defects) in the crystal.Table 6 presents the calculated values of  and  for each atom.Figure 11 shows the nature of the changes in  and  with the yttrium oxide concentration, from which the regularity of their linear decrease is clearly visible.Next, calculations were performed to study the electronic structure of Y2O3-stabiliz ZrO2 supercells to reveal the effect of doping on the density of states, the behavior of t Fermi energy, and the orbital components.Figure 12 shows plots of changes in the dens of electronic states of YSZ for all doping concentrations of Y2O3.As seen in Figure 12, new energy states do not appear in the TDOS patterns af doping with Y2O3 due to the introduction of defects.In other words, there are no notic ble changes except for a decrease in the band gap, which can be explained by orbital an ysis (Figure 13) and Fermi level mixing estimates (Figure 14   As seen in Figure 12, new energy states do not appear in the TDOS patterns after doping with Y 2 O 3 due to the introduction of defects.In other words, there are no noticeable changes except for a decrease in the band gap, which can be explained by orbital analysis (Figure 13) and Fermi level mixing estimates (Figure 14 Next, calculations were performed to study the electronic structure of Y2O3-stabilized ZrO2 supercells to reveal the effect of doping on the density of states, the behavior of the Fermi energy, and the orbital components.Figure 12 shows plots of changes in the density of electronic states of YSZ for all doping concentrations of Y2O3.As seen in Figure 12, new energy states do not appear in the TDOS patterns afte doping with Y2O3 due to the introduction of defects.In other words, there are no noticea ble changes except for a decrease in the band gap, which can be explained by orbital anal ysis (Figure 13) and Fermi level mixing estimates (Figure 14).The band gaps are 4.71 eV 4.92 eV, 4.75 eV, and 4.72 eV, respectively, for ZrO2 doped with 3.23, 6.67, 10.34, and 16.15 mol.%Y2O3.In Figure 13, after doping 3.23 mol.%Y2O3 into pure m-ZrO2, the Fermi level drops by 0.067 eV, and then shifts by 0.007 eV toward the conduction band upon doping with 6.67 mol.%Y2O3.At a doping concentration of 10.34 mol.%Y2O3, it still increases by 0.01 eV, which is 0.017 eV more than in the case of 3.23 mol.%Y2O3.However, after doping with 16.15 mol.%Y2O3, it drops to 0.012 eV.The PDOS diagram also interprets the stepped conduction band pattern in terms of the s-, p-, and d-orbital contributions.Understanding these features makes it possible to tune the Fermi energies in the band structure to solve the most important problems of materials science and instrumentation.
The problems of studying the influence of yttrium oxide doping on the properties and stability of tetragonal and cubic zirconia remains the subject of future research.

Water Adsorption on ZrO2 and YSZ Surfaces
As previously mentioned, to model the water adsorption mechanism on the corresponding surface correctly, the most important point is the choice of the surface with the lowest surface energy.To select the optimal adsorbing surface, we calculated the surface energy (σ) for several different surface models according to Equation (1) after their geometric relaxation.Table 7 shows the calculated values of the surface energies of ZrO2.As shown in Table 7, the most stable surfaces can be obtained from the tetragonal and monoclinic phases, namely t-ZrO2 (101) and m-ZrO2 (111).The results obtained agree The problems of studying the influence of yttrium oxide doping on the properties and stability of tetragonal and cubic zirconia remains the subject of future research.

Water Adsorption on ZrO 2 and YSZ Surfaces
As previously mentioned, to model the water adsorption mechanism on the corresponding surface correctly, the most important point is the choice of the surface with the lowest surface energy.To select the optimal adsorbing surface, we calculated the surface energy (σ) for several different surface models according to Equation (1) after their geometric relaxation.Table 7 shows the calculated values of the surface energies of ZrO 2 .As shown in Table 7, the most stable surfaces can be obtained from the tetragonal and monoclinic phases, namely t-ZrO 2 (101) and m-ZrO 2 (111).The results obtained agree qualitatively with Maliki et al. [66], who reported that the most stable surface can be obtained from t-ZrO 2 (101).As for comparing the results to experimental data, there are no reported data in the literature because the surface energies of solid metal oxides are difficult to measure experimentally.In total, measurements of the surface energies of some types of zirconium dioxide surfaces using multiphase balancing at high temperatures has been reported [67].Based on the results obtained, we chose the t-ZrO 2 (101) surface for this study, as the most stable surface for water molecule adsorption.
After the final surface preparation, single H 2 O molecules were initially located at a height of 2.5 Å above the selected surface with different orientations, which is greater than the bond distance between Zr and O (2.12 Å) in the solid state.The structures were then optimized by freezing the bottom layers of the wafer (Figure 15a).
qualitatively with Maliki et al. [66], who reported that the most stable surface can be obtained from t-ZrO2 (101).As for comparing the results to experimental data, there are no reported data in the literature because the surface energies of solid metal oxides are difficult to measure experimentally.In total, measurements of the surface energies of some types of zirconium dioxide surfaces using multiphase balancing at high temperatures has been reported [67].Based on the results obtained, we chose the t-ZrO2 (101) surface for this study, as the most stable surface for water molecule adsorption.
After the final surface preparation, single H2O molecules were initially located at a height of 2.5 Å above the selected surface with different orientations, which is greater than the bond distance between Zr and O (2.12 Å) in the solid state.The structures were then optimized by freezing the bottom layers of the wafer (Figure 15a).The optimized structure of the H2O + t-ZrO2 (101) system is shown in Figure 15b, which shows that the H2O molecule is dissociatively adsorbed with an energy of −1.221 eV, even in the most favorable region (where the system has the minimum energy of the stable configuration).Korhonen et al. [68] also observed dissociative adsorption of water on ZrO2, where it was experimentally and theoretically proven that water dissociates on the surface of m-ZrO2 at a low coverage.The adsorption energy we calculated on t-ZrO2 (101) for [H+OH]-ZrO2 (101) is similar to their results for monoclinic (111) and (101) surfaces with an energy of −1.20 eV.We also found that water is adsorbed on this surface via molecular chemisorption, in which the water's oxygen coordinates the surface cation, and a slight elongation of one O-H water bond (1.13 Å) occurs in the form of hydrogen bonding of water with the surface oxygen ion (Figure 15c).In this case, the adsorption energy is 0.69 eV, and the distance between the oxygen of the water molecule and the surface The optimized structure of the H 2 O + t-ZrO 2 (101) system is shown in Figure 15b, which shows that the H 2 O molecule is dissociatively adsorbed with an energy of −1.221 eV, even in the most favorable region (where the system has the minimum energy of the stable configuration).Korhonen et al. [68] also observed dissociative adsorption of water on ZrO 2 , where it was experimentally and theoretically proven that water dissociates on the surface of m-ZrO 2 at a low coverage.The adsorption energy we calculated on t-ZrO 2 (101) for [H+OH]-ZrO 2 (101) is similar to their results for monoclinic (111) and (101) surfaces with an energy of −1.20 eV.We also found that water is adsorbed on this surface via molecular chemisorption, in which water's oxygen coordinates the surface cation, and a slight elongation of one O-H water bond (1.13 Å) occurs in the form of hydrogen bonding of water with the surface oxygen ion (Figure 15c).In this case, the adsorption energy is 0.69 eV, and the distance between the oxygen of the water molecule and the surface zirconium atom is 2.205 Å.In this case, the proton (H) in the water molecule and oxygen from the surface of the plane form a hydrogen bond with a bond length of 1.01 Å.
To study the mechanism of water adsorption on the surface of t-YSZ, we replaced two Zr (from the uppermost and subsurface O-Zr-O trilayers) by Y with the removal of one oxygen from the third nearest atomic layer to the Y atoms to obtain a surface similar to t-YSZ (101).Our results showed that the water molecule is molecularly adsorbed and also dissociated on the t-YSZ (101) surface.Molecular adsorption of water in the optimal configuration occurs at an energy of −1.84 eV, and the bond length of water with the t-YSZ (101) surface increases to 2.73 Å (Figure 16a).In this case, the O-H distance in the water molecules will remain unchanged.
Nanomaterials 2023, 13, x FOR PEER REVIEW 18 of 24 to t-YSZ (101).Our results showed that the water molecule is molecularly adsorbed and also dissociated on the t-YSZ (101) surface.Molecular adsorption of water in the optimal configuration occurs at an energy of −1.84 eV, and the bond length of water with the t-YSZ (101) surface increases to 2.73 Å (Figure 16a).In this case, the O-H distance in the water molecules will remain unchanged.The dissociative adsorption of water was accompanied by the movement of oxygen in the area of the plate vacancies, leading to strong adsorption of −1.23 eV, and blocking surface areas for oxygen activation.In both cases, H2O is adsorbed near the yttrium atom (Figure 16b).
Doping with Y2O3 stabilizes t-ZrO2 (101) and is accompanied by large relaxations of O atoms.Calculations based on the GGA functional greatly underestimate the band gap of the system (3.24eV for H2O-ZrO2 (101) and 3.21 eV for H2O-YSZ (101)).However, despite the presence of the Oth vacancy, the average gap energy states did not appear in the t-YSZ band diagram, as observed in the systems under study.A comparative analysis of the H2O-ZrO2 (101) and H2O-YSZ (101) systems' electronic structures indicate that the H2O interaction practically does not change the electronic configuration of the system (except for an increase in the density of state) during the transition of the system to being modified by Y impurities (Figure 17).However, water molecules are predominantly prone to molecular adsorption on the t-YSZ (101) surface, whereas they are more often dissociatively adsorbed on t-ZrO2 (101).Table 8 lists some key data obtained by modeling water adsorption on the t-ZrO2 (101) and t-YSZ surfaces.17).water molecules are predominantly prone to molecular adsorption on the t-YSZ (101) surface, whereas they are more often dissociatively adsorbed on t-ZrO 2 (101).Table 8 lists some key data obtained by modeling water adsorption on the t-ZrO 2 (101) and t-YSZ surfaces.In such studies, it is also important to take into account the hydrophilic nature of ZrO2.Studies show that in addition to physically adsorbed water, the substrate surface also contains terminal, bi-bridging, and triple bridging OH groups, which are actively involved in the surface reaction [69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85].Surface hydroxyl groups and H2O adsorbed on the surface can partially block active sites (lattice oxygen ions on the surface) of YSZ oxidation.Figure 18a shows the surface configuration model for fully hydroxylated t-YSZ (101).The results show that the OH groups form strong bonds on the surface.Figure 18b shows the adsorption structure of a single water molecule on a fully hydroxylated YSZ surface.In such studies, it is also important to take into account the hydrophilic nature of ZrO 2 .Studies show that in addition to physically adsorbed water, the substrate surface also contains terminal, bi-bridging, and triple bridging OH groups, which are actively involved in the surface reaction [69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85].Surface hydroxyl groups and H 2 O adsorbed on the surface can partially block active sites (lattice oxygen ions on the surface) of YSZ oxidation.Figure 18a shows the surface configuration model for fully hydroxylated t-YSZ (101).The results show that the OH groups form strong bonds on the surface.Figure 18b shows the adsorption structure of a single water molecule on a fully hydroxylated YSZ surface.
When water is adsorbed on a hydroxylated surface, two strong hydrogen bonds are formed at distances of 1.56 and 1.63 Å from each other.In this case, water is adsorbed with an adsorption energy of 0.34 eV.It can be seen that neither the repulsive forces of oxygen and hydrogen atoms in a water molecule or OH atoms on a completely hydroxylated surface prevent the adsorption of an H 2 O molecule on t-YSZ (101).The adsorption model of a single water molecule and other similar systems will help us study more complex models in detail in the future, including the multilayer hydration structure of the interface (Figure 18).Although this model requires large computational power for DFT calculations, it can be assumed that in the layer closest to the surface (hydroxyl hydration layer), most of the water molecules can be adsorbed dissociatively.Furthermore, due to hydrogen bonds, H 2 O molecules will continue to be adsorbed and be regularly located on the hydroxylated surface, forming primary and secondary hydrated layers.The regular arrangement of H 2 O molecules in the outer layer can be considered a transition layer, and the hydration structure of the first three H 2 O layers located near the surface can be considered a group of water molecules can both be stably adsorbed and exist on the m-NSC surface (101).However, a detailed study of the complete model of t-YSZ (101) surface hydration remains the subject of future research.
H-O-H bond angle, (°) 111.3 105.54 In such studies, it is also important to take into account the hydrophilic nature of ZrO2.Studies show that in addition to physically adsorbed water, the substrate surface also contains terminal, bi-bridging, and triple bridging OH groups, which are actively involved in the surface reaction [69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85].Surface hydroxyl groups and H2O adsorbed on the surface can partially block active sites (lattice oxygen ions on the surface) of YSZ oxidation.Figure 18a shows the surface configuration model for fully hydroxylated t-YSZ (101).The results show that the OH groups form strong bonds on the surface.Figure 18b shows the adsorption structure of a single water molecule on a fully hydroxylated YSZ surface.

Conclusions
We investigated the stability, electronic properties, and dispersion of phonons in the three phases of ZrO 2 using quantum chemical calculations.The stable phase is defined in terms of the total energy, enthalpy, entropy, and band structure of phonons.We established that during the m-t phase transformation of ZrO 2 , the Fermi level first shifts by 0.125 eV toward higher energies, then decreases by 0.08 eV in the t-c region.An analysis of the influence of doping 3.23, 6.67, 10.35, and 16.15 mol %Y 2 O 3 on the m-ZrO 2 structure showed that the m-YSZ enthalpy decreases linearly, which accompanies further stabilization of monoclinic ZrO 2 .An analysis of the mechanism of water adsorption on the surfaces of t-ZrO 2 (101) and t-YSZ (101) showed that H 2 O on unstabilized t-ZrO 2 (101) was adsorbed dissociatively with an energy of −1.22 eV, as well as by 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 was 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.Thus, with an increase in Y 2 O 3 concentration, the number of oxygen vacancies in YSZ increases.The growth of these O vacancies is considered a stabilizing mechanism of the monoclinic zirconium phase, as indicated by a decrease in the enthalpy.These oxygen vacancies also give YSZ a high ionic conductivity, making it suitable for use in full solid oxide cells.This study will help build more accurate calculation models for other types of surfaces like YSZ by characterizing their structural and electronic properties.

Figure 1 .
Figure 1.Optimized cells of the (a) cubic, (b) monoclinic, and (c) tetragonal phases of ZrO2; (d) model of 2 × 2 × 2 supercell of monoclinic ZrO2 doped with Y2O3; (e,f) yttrium substitution sites in the surface matrix, and (g) a box with a 35 Å vacuum containing water molecules from the surface of the ZrO2 substrate.

Figure 1 .
Figure 1.Optimized cells of the (a) cubic, (b) monoclinic, and (c) tetragonal phases of ZrO 2 ; (d) model of 2 × 2 × 2 supercell of monoclinic ZrO 2 doped with Y 2 O 3 ; (e,f) yttrium substitution sites in the surface matrix, and (g) a box with a 35 Å vacuum containing water molecules from the surface of the ZrO 2 substrate.

Figure 2 .
Figure 2. Entropy as a function of absolute temperature per unit cell.

Figure 2 .
Figure 2. Entropy as a function of absolute temperature per unit cell.

Figure
Figure 4a-c shows the temperature dependence of the free energy, entropy, and heat capacity of a 12-atom supercell for m-ZrO2, t-ZrO2, and с-ZrO2.

Figure
Figure 4a-c shows the temperature dependence of the free energy, entropy, and heat capacity of a 12-atom supercell for m-ZrO 2 , t-ZrO 2 , and с-ZrO 2 .Figure5a-c presents the results of the calculations of the density of phonon states, which indicate that during the transition from the monoclinic phase to the tetragonal and cubic phases, the density of electronic states increases.These results also agree with those shown in Figure3, confirming that the monoclinic phase is the most stable among the ZrO 2 phases.The energy/volume chart presented by Teter et al. also supports these results[64].Therefore, for further stabilization by doping with Y 2 O 3 , it is reasonable to choose a monoclinic phase.

Figure 8 .
Figure 8. Conduction (red) and valence (green) band changes for c-ZrO2, t-ZrO2, and m-ZrO2.The position of the Fermi level corresponds to the maximum of the valence band at each of the sites.

Figure 9 .
Figure 9. Composite PDOS diagram showing the main contributions of the s-, p-, and d-orbitals to the states that form the conduction band bottom for c-ZrO2, t-ZrO2, and m-ZrO2.Top valence band (green) scaled to zero.

Figure 8 .
Figure 8. Conduction (red) and valence (green) band changes for c-ZrO 2 , t-ZrO 2 , and m-ZrO 2. The position of the Fermi level corresponds to the maximum of the valence band at each of the sites.

Figure 8 .
Figure 8. Conduction (red) and valence (green) band changes for c-ZrO2, t-ZrO2, and m-ZrO2.The position of the Fermi level corresponds to the maximum of the valence band at each of the sites.

Figure 9 .
Figure 9. Composite PDOS diagram showing the main contributions of the s-, p-, and d-orbitals to the states that form the conduction band bottom for c-ZrO2, t-ZrO2, and m-ZrO2.Top valence band (green) scaled to zero.

Figure 9 .
Figure 9. Composite PDOS diagram showing the main contributions of the s-, p-, and d-orbitals to the states that form the conduction band bottom for c-ZrO 2 , t-ZrO 2 , and m-ZrO 2 .Top valence band (green) scaled to zero.

Figure 10 .
Figure 10.Enthalpy formation energy for YSZ as a function of Y2O3 concentration.

Figure 10 .
Figure 10.Enthalpy formation energy for YSZ as a function of Y 2 O 3 concentration.

Figure 11 .
Figure 11.Formation energy (a) and formation energy of an oxygen vacancy (b) for YSZ as a function of Y2O3 concentration.

Figure 11 .
Figure 11.Formation energy (a) and formation energy of an oxygen vacancy (b) for YSZ as a function of Y 2 O 3 concentration.Next, calculations were performed to study the electronic structure of Y 2 O 3 -stabilized ZrO 2 supercells to reveal the effect of doping on the density of states, the behavior of the

Figure 13 .
Figure 13.Composite PDOS diagram showing the main contributions of the s-, p-, and d-orbitals states forming the conduction band bottom for ZrO2 doped with 3.23, 6.67, 10.34, and 16.15 m %Y2O3.Top valence band (green), scaled to zero.

Figure 13 .
Figure 13.Composite PDOS diagram showing the main contributions of the s-, p-, and d-orbitals to states forming the conduction band bottom for ZrO2 doped with 3.23, 6.67, 10.34, and 16.15 mol %Y2O3.Top valence band (green), scaled to zero.

Figure 13 .
Figure 13.Composite PDOS diagram showing the main contributions of the s-, p-, and dorbitals to states forming the conduction band bottom for ZrO 2 doped with 3.23, 6.67, 10.34, and 16.15 mol.%Y 2 O 3 .Top valence band (green), scaled to zero.

Figure 14 .
Figure 14.Conduction (red) and valence (green) band changes for ZrO2 doped with 3.23, 6.67, 10.34, and 16.15 mol.%Y2O3.The position of the Fermi level corresponds to the maximum valence band in each section.

Figure 14 .
Figure 14.Conduction (red) and valence (green) band changes for ZrO 2 doped with 3.23, 6.67, 10.34, and 16.15 mol.%Y 2 O 3 .The position of the Fermi level corresponds to the maximum valence band in each section.In Figure 13, after doping 3.23 mol.%Y 2 O 3 into pure m-ZrO 2 , the Fermi level drops by 0.067 eV, and then shifts by 0.007 eV toward the conduction band upon doping with 6.67 mol.%Y 2 O 3 .At a doping concentration of 10.34 mol.%Y 2 O 3 , it still increases by 0.01 eV, which is 0.017 eV more than in the case of 3.23 mol.%Y 2 O 3 .However, after doping with 16.15 mol.%Y 2 O 3 , it drops to 0.012 eV.The PDOS diagram also interprets the stepped conduction band pattern in terms of the s-, p-, and d-orbital contributions.Understanding these features makes it possible to tune the Fermi energies in the band structure to solve the most important problems of materials science and instrumentation.The problems of studying the influence of yttrium oxide doping on the properties and stability of tetragonal and cubic zirconia remains the subject of future research.

Figure 15 .
Figure 15.Configuration of water molecule adsorption on the surface of t-ZrO2 (101): (a) model of a lamellar t-ZrO2 (101) cell with the initial configuration of water on its surface, (b) dissociative adsorption in a side view, (c) model of molecular physisorption of water on the surface of t-ZrO2 in a side view.

Figure 15 .
Figure 15.Configuration of water molecule adsorption on the surface of t-ZrO 2 (101): (a) model of a lamellar t-ZrO 2 (101) cell with the initial configuration of water on its surface, (b) dissociative adsorption in a side view, (c) model of molecular physisorption of water on the surface of t-ZrO 2 in a side view.

Figure 16 .
Figure 16.Molecular (a) and dissociated adsorption of water to form surface hydroxyls (b) in the H 2 O-YSZ (101) model.The dissociative adsorption of water was accompanied by the movement of oxygen in the area of the plate vacancies, leading to strong adsorption of −1.23 eV, and blocking surface areas for oxygen activation.In both cases, H 2 O is adsorbed near the yttrium atom (Figure 16b).Unlike water adsorption on t-ZrO 2 (101), H 2 O is more stably adsorbed on t-YSZ (101) since the adsorption energy of H 2 O-YSZ (101) is more favorable than (H+OH)-YSZ (101).Doping with Y 2 O 3 stabilizes t-ZrO 2 (101) and is accompanied by large relaxations of O atoms.Calculations based on the GGA functional greatly underestimate the band gap of the system (3.24eV for H 2 O-ZrO 2 (101) and 3.21 eV for H 2 O-YSZ (101)).However, despite the presence of the Oth vacancy, the average gap energy states did not appear in the t-YSZ band diagram, as observed in the systems under study.A comparative analysis of the H 2 O-ZrO 2 (101) and H 2 O-YSZ (101) systems' electronic structures indicate that the H 2 O interaction practically does not change the electronic configuration of the system (except for an increase in the density of state) during the transition of the system to being modified by

Table 1 .
Relaxation parameters of the ZrO 2 phase.The calculation results are compared to experimental and previous theoretical results.

Table 2 .
GGA-calculated total electron energies of ZrO 2 unit cells.

Table 3 .
Calculated and experimental band gap of ZrO 2 in eV.

Table 3 .
Calculated and experimental band gap of ZrO2 in eV.

Table 4 .
The number of Zr, Y, and O ions for various mol.%Y 2 O 3 , taking into account the oxygen vacancies.

Table 4 .
The number of Zr, Y, and O ions for various mol.%Y2O3, taking into account the oxyge vacancies.

Table 6 .
GGA-calculated values of enthalpy (∆Н) and energy of formation (E f ) for ZrO 2 and YSZ.Oxygen vacancy formation energy (E d f ) for YSZ.

Table 7 .
Calculated values of surface energies (σ) for the main types of ZrO2 plate.

Table 7 .
Calculated values of surface energies (σ) for the main types of ZrO 2 plate.