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Article

A First-Principles Study on Defects in Zirconium Monoxide

by
Hanyu Shi
1,
Zhixiao Liu
1,*,
Dong Wang
2,3,*,
Tianguo Wei
2,3 and
Yi Zhao
2,3
1
College of Materials Science and Engineering, Hunan University, Changsha 410082, China
2
National Key Laboratory of Nuclear Reactor Technology, Nuclear Power Institute of China, Chengdu 610212, China
3
State Key Laboratory of Advanced Nuclear Energy Technology, Nuclear Power Institute of China, Chengdu 610212, China
*
Authors to whom correspondence should be addressed.
Metals 2025, 15(4), 449; https://doi.org/10.3390/met15040449
Submission received: 4 March 2025 / Revised: 8 April 2025 / Accepted: 11 April 2025 / Published: 16 April 2025
(This article belongs to the Section Computation and Simulation on Metals)
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Abstract

:
Zirconium monoxide (ZrO) plays a key role in the water-side corrosion resistance of Zr alloys as cladding materials in nuclear reactors. This study investigates the behavior of intrinsic defects in ZrO through first-principles calculations, and the influence of main alloying elements (Cr, Fe, Nb and Sn) is also evaluated. We focus on the formation and migration properties of vacancies and interstitials. The results show that the formation energy of oxygen vacancy is 5.31 eV. The formation energy of interstitial Oi-tet in ZrO is −4.04 eV, indicating that Oi-tet can be formed spontaneously. Another interstitial oxygen Oi-mid with a formation energy of 0.03 eV can also be found in large quantities in ZrO. As for the migration properties, oxygen vacancy in ZrO without doping tends to diffuse along Path 2, and the diffusion barrier is 2.96 eV. Cr and Fe reduce the migration barriers of oxygen vacancies, while Nb and Sn increase them. In contrast, alloying elements generally hinder the formation of oxygen interstitials and increase their migration barriers, particularly in the case of Cr and Fe. The migration barrier of interstitial oxygen diffusion along Path a in pure ZrO is 2.91 eV. However, the migration barriers of interstitial oxygen in ZrO with Cr or Fe doping could increase to more than 4 eV. These findings provide critical insights into the role of alloying elements in modifying defect dynamics, offering a theoretical basis for improving the corrosion resistance and performance of zirconium alloys in practical applications.

1. Introduction

With the continuous development of the global economy, energy issues and global warming have become prominent concerns over the past few decades [1]. Traditional fossil fuels release significant amounts of Greenhouse Gases (GHGs). In contrast, nuclear energy, as a clean and reliable renewable energy source, plays a crucial role in meeting the energy needs and at the same time in mitigating GHG emissions. Consequently, it has garnered significant global attention [2].
Light water reactors, including pressurized water reactors (PWRs) and boiling water reactors (BWRs), constitute the majority of commercial nuclear reactors worldwide [3]. The widespread use of zirconium (Zr) alloys for nuclear fuel cladding in water-cooled reactors is attributed to their excellent corrosion resistance and mechanical properties, as well as their low capture cross section for thermal neutrons [4,5]. These Zr alloy claddings form the first containment barrier for fission products, and their mechanical integrity must be maintained throughout their operational lifetime in the reactor [6]. The service life of the fuel elements largely depends on the waterside corrosion resistance of the Zr alloy [7,8,9,10].
The aqueous corrosion process of zirconium alloys is complicated, involving various complex interfacial reactions and ion transport mechanisms. As a result, the investigation of the metal/oxide interface has consistently been a focal point of experimental observations. It has been found that the growth of the zirconium alloy oxide film is influenced by the diffusion of O2− ions through the oxide layer [11]. After an initial rapid oxidation stage, the forming oxide layer causes the oxidation rate to slow due to the restrained transition of charged species through the oxide layer. Once the thickness of the oxide layer reaches a critical value, the protection of the oxide layer breaks down, leading to an abrupt acceleration in the corrosion rate at a point termed the “breakdown” or “transition” [12,13]. Recently, researchers believe that the tetragonal ZrO2 in the oxide layer plays a key role in suppressing of diffusion of the O2− ions. An increase in the volume of the tetragonal phase correlates with a decrease in the oxidation rate of zirconium alloys. Studies have also shown that t-ZrO2 is the main component of corrosion resistance in oxides [14]. However, numerous studies have demonstrated the presence of a thin oxide layer at the oxidation interfaces of zirconium alloys [15,16]. Electron energy loss spectroscopy (EELS) [17] and atom probe tomography (APT) [18,19] have also identified a sub-oxide layer whose composition closely resembles that of ZrO. Interestingly, this sub-oxide layer is found before the fast oxidation stage and disappears while the oxidation rate increases [20]. Despite the lack of direct evidence indicating that ZrO positively influences the deceleration of the oxidation rate, an in-depth investigation of ZrO offers a critical theoretical foundation for comprehending the oxidation mechanism. While numerous studies have investigated the diffusion barrier of O2− ions in ZrO2, the ZrO intermediate layer is situated at the interface between the metal and oxide; consequently, O2− ions must traverse this intermediate layer before reaching the metal surface to form new oxides. However, the migration barrier of O2− in the ZrO phase has not been previously reported.
Additionally, the corrosion resistance of zirconium alloy is also influenced by alloying elements. For the distribution of metal alloys, most of the alloying elements exist in the form of precipitated phases, but some can be dissolved in the matrix, which is related to other alloying elements and microstructure characteristics [21]. It has been confirmed that Nb can improve the performance of zirconium alloys in nuclear reactors by refining grains and increasing hardness [22], and it has also been shown that Nb can affect the phase stability in zirconium alloys [23,24]. In addition to niobium (Nb), other commonly employed alloying additions in commercial zirconium alloys include chromium (Cr), iron (Fe), and tin (Sn). These elements are strategically incorporated to optimize specific performance metrics, such as corrosion resistance, mechanical strength, and radiation tolerance in nuclear reactor applications.
Based on the above analysis, the current understanding of ZrO remains ambiguous. As an intermediate layer critically influencing oxide–metal interfaces, the underlying mechanism by which ZrO exhibits corrosion-retarding effects has yet to be elucidated. To address this knowledge gap, the present study employs density functional theory (DFT) to investigate the intrinsic defect behavior in ZrO at the atomic scale. Special emphasis is placed on elucidating oxygen diffusion mechanisms within the ZrO layer and evaluating the effects of alloying elements. This work aims to provide theoretical insights into the corrosion inhibition mechanisms operative in ZrO-containing phases, thereby establishing a foundational framework for the rational design of corrosion-resistant interfacial systems.

2. Computational Methods

According to previous literature, the structure of ZrO was identified based on the experimentally observed Ti monoxide crystal. This structure belongs to the hexagonal close-packed (hcp) configuration (space group: P-62m), with measured lattice parameters for ZrO of a = 5.285 Å and c = 3.179 Å. In the ZrO oxide, the Zr atoms occupy two inequivalent Wyckoff sites, which are 1a (0, 0, 0) (labeled as Zr1 in Figure 1) and 2d (1/3, 2/3, 1/2) (labeled as Zr2 in Figure 1), while the O atoms occupy the Wyckoff 3f (0.407, 0, 0) site.
Before calculating the defect properties in ZrO, we refer to manuscripts on the defect properties in ZrO2. Youssef [25] constructed a 2 × 2 × 2 t-ZrO2 supercell to investigate the properties of defect, and the lattice parameter of the supercell was about a = b = 10.8 Å, c = 10.5 Å; Zheng [26] also constructed a 2 × 2 × 2 supercell when calculating the defect properties of m-ZrO2, and the lattice parameter of the supercell was a = 10.4 Å, b = 10.5 Å and c = 10.5 Å. Therefore, to investigate the behavior of intrinsic defects and the influence of alloying elements in ZrO, we constructed a 2 × 2 × 3 ZrO supercell model containing 72 atoms. Density functional theory (DFT) [27,28] calculations were performed using the Vienna Ab-initio Simulation Package (VASP) [29,30] with Version 6.3. The electron–ion interaction was described using the projector augmented wave (PAW) [31,32] method, while the exchange-correlation potential was modeled using the Perdew–Burke–Ernzerhof (PBE) [33] form of generalized gradient approximation (GGA). The sufficiency of PBE alone without an extra on site Coulomb interaction (DFT + U) to describe t-ZrO2 has been demonstrated recently in the course of studying electron transfer on the surfaces of metal oxides [34]. Furthermore, Youssef et al. [35] systematically validated the efficacy of the standard PBE functional, without incorporating on-site Coulomb corrections (DFT + U), in characterizing defect properties within t-ZrO2. Building upon this methodological benchmarking, the present study exclusively employs the PBE functional to compute defect-related energetics and electronic configurations. Additionally, the HSE06 [36] Hybrid Function (HF) was only performed in order to verify the density of states.
The first Brillouin zone was sampled using a k-point mesh generated by the Monkhorst-Pack (MP) [37] scheme, and the Brillouin-zone grids were set as 2 × 2 × 2 for ZrO supercell. The k-point mesh has tested for ZrO primitive cell before calculations. As shown in Table 1, the error in total energy with respect to calculations performed using a 12 × 12 × 12 was found to be less than 3 meV per ZrO. Based on equilibrium time and accuracy considerations, the energy cutoff of all calculations was set as 500 eV. Prior to property calculations, all structures were fully optimized, including the relaxation of atomic positions and supercell volumes, until the force between any two atoms was less than 0.01 eV/Å, to ensure the accuracy of the calculation. The migration barriers of ions were calculated by the climbing image nudged-elastic band (CI-NEB) [38,39] method. The spring constant was set to 5 eV/Å2. Linear interpolation is used between the initial state and the final state, and the interpolation point method is every 0.8 Å.
The formation energies of a defect D with is denoted by E D f and defined as [35]:
E D f = E d e f e c t e d − E p e r f e c t + ∑ k ∆ n k μ k
where E d e f e c t e d and E p e r f e c t are the DFT energies of the supercell that contains the defect and the perfect crystal supercell, respectively. Δ n k is the number of atoms of species k in the perfect crystal supercell less the number of the atoms of the same species in the defected cell. μ k is the chemical potential of the species k. The chemical potential of Zr and O are defined as follows:
μ Z r = E Z r D F T
μ O = 1 2 E O 2 D F T
where E Z r D F T is the DFT energy of the unit atom of Zr in the perfect metal crystal zirconium, and the E O 2 D F T is the DFT energy of the unit formula of O2 in the O2 molecule.

3. Results and Discussion

3.1. Basic Properties

To investigate the structural information and the defect properties of ZrO, it is essential to establish a reasonable structure prior to calculations. In general, the structural stability of a solid is determined by the formation enthalpy (ΔH) [40,41,42]. The formation enthalpy of ZrO is given by Refs. [43,44]:
Δ H = E t o t a l Z r O − E Z r − E O
where E t o t a l Z r O , E Z r , and E O are the calculated total energy of ZrO oxide, pure Zr, and pure O, respectively.
Table 2 lists the calculated lattice parameters, volume and formation enthalpy of the perfect ZrO. From Table 2, it is evident that the calculated formation enthalpy of perfect ZrO is −5.38 eV/atom which indicates that ZrO is a thermodynamically stable. In addition, the calculated lattice parameter of ZrO is in good agreement with the Puchala′s data.
The electronic properties of a solid are analyzed by the density of state (DOS) [47,48,49,50,51]. Figure 2 shows the calculated density of state (DOS) of the perfect ZrO. Since the PBE method may introduce errors in the density of states for metallic crystals, the HSE06 hybrid functional is employed for verification. From Figure 2, it is obvious that the total density of states at the Fermi level is nonzero and there are partial waves crossing the Fermi level, which indicates that ZrO behaves as a metal (conductor).

3.2. Intrinsic Defects in ZrO

First, we calculate the defect formation energies of intrinsic defects in ZrO, including vacancy defects and interstitial defects. For vacancies, there are three types of atomic positions (as shown in Figure 1), resulting in three kinds of vacancy defects labeled as VZr1, VZr2, and VO. As for interstitial defects, due to the lower symmetry of the hexagonal structure, we identify two types of interstitial defects, as shown in Figure 1, which are named Xi-tet and Xi-mid (X = O/Zr). The former is located in the tetrahedral interstitial position while the latter is situated between two Zr atoms.
Table 3 lists all the defect formation energies of intrinsic defects in ZrO. We observe that the formation energy of VO is 5.31 eV. The vacancy formation energy of VZr1 is 3.94 eV, while that for VZr2 is 1.99 eV, indicating that VZr2 is easier to form than VZr1. However, all vacancies exhibit positive formation energies, suggesting that vacancies are unfavorable to form in ZrO. The lowest formation energy corresponds to the oxygen interstitial defect Oi-tet, with a formation energy of −4.04 eV. This indicates that oxygen interstitials can form spontaneously in ZrO. The other interstitial defect of Oi-mid exhibits a slightly positive formation energy of 0.03 eV. This suggests that interstitial oxygen could exist in high concentrations in ZrO under equilibrium. The ZrO phase incorporates a significant amount of dissolved oxygen (O). Once oxygen is dissolved within the solid, it can no longer diffuse further into the underlying metal layer. When the concentration of dissolved oxygen reaches a critical threshold, ZrO undergoes oxidation, leading to the disappearance of the ZrO phase. Without this phase to accommodate additional oxygen, a large amount of oxygen accumulates at the metal/oxide interface, thereby triggering the corrosion transition stage. This phenomenon appears to explain why the ZrO phase emerges prior to the corrosion transition stage but disappears once the transition occurs. The formation energies of Zr interstitial defects are significantly higher than those of O interstitial defects, likely due to atomic size. The larger diameter of Zr atoms makes it challenging for Zr interstitials to stably occupy tetrahedral interstitial positions. In addition, interstitial sites only coordinate with Zr atoms at lattice sites. The coulombic repulsion between metallic atoms in the oxide also significantly increases the formation energies of interstitial Zr atoms in ZrO.
Similarly, the formation energies of interstitial Zr are excessively positive (both exceeding 5 eV), leading us to exclude the migration of Zr interstitial defects from further discussion. The elevated formation energies of Zri are consistent with the observation that ZrOx (0 < x < 1) is a metastable phase. Overall, the most stable defect in pure ZrO is Oi in the tetrahedral interstitial position.
Based on the density of states (DOS) diagram, we conclude that ZrO behaves as a metallic conductor; thus, the properties of charged defects are not considered in the subsequent studies. As shown in Table 4, previous calculations for t-ZrO2 by Youssef et al. [25] indicate that the formation energies of intrinsic defects are higher in t-ZrO2. Compared with the calculation results in this paper, it can be found that intrinsic defects form more readily in ZrO rather than in the tetragonal phase. Zheng et al. [26] provided a detailed analysis of intrinsic defects in m-ZrO2. According to their findings, the formation energy of oxygen vacancy exceeds 6 eV, while the formation energy of Zr vacancy also approaches nearly 6 eV. The formation energies of other interstitial defects were higher than those observed in our study, suggesting that point defects are more likely to form in ZrO.
In general, ZrO exhibits the lowest formation energies of defects, with minimal differences in the formation energies of oxygen vacancies across the three phases of zirconium oxide. Notably, there is a significant discrepancy in the formation energies of interstitial oxygen among the three zirconium oxides: the formation energy of Oi in ZrO is negative, indicating that it can form spontaneously under appropriate conditions, whereas the formation energy in the other two types of ZrO2 is positive, suggesting that it would not be formed spontaneously.
Furthermore, we investigated the migration behaviors of intrinsic defects in ZrO oxide using the climbing image nudged elastic band (CI-NEB) method [52]. As shown in Figure 3, we assumed that the oxygen vacancy could diffuse in two directions: intra-plane and inter-plane. For intra-plane diffusion, we selected two diffusion paths to analyze the migration of the oxygen atom. One path (Path 1) is between the nearest two neighboring vacancies, separated by 2.798 Å, while the other path (Path 2) is between the next-nearest two neighboring vacancies separated by 3.734 Å. For inter-plane diffusion, we considered two vertical oxygen vacancies (Path 3) in the c-direction.
Table 5 presents the migration energies of the oxygen vacancies. According to the results obtained from the climbing image nudged elastic band (CI-NEB) method, it is evident that the oxygen atom is more inclined to diffuse along Path 2, which has a migration barrier of 2.96 eV. The migration barrier for oxygen vacancy diffusion along Path 1 is 3.28 eV. Interestingly the longer diffusion path results in a lower migration energy. The migration barrier for oxygen vacancies diffusing between planes lies between the barriers of the other two paths, suggesting that the diffusion of oxygen vacancies is inherently difficult.
Additionally, Youssef et al. [53,54] calculated the migration barriers of O vacancies in t-ZrO2 and m-ZrO2, finding ranges of 1.35 eV~3.96 eV and 1.84 eV~2.48 eV, respectively. This indicates that the diffusion of oxygen vacancies in ZrO2 is more favorable.
Since Zr has two types of inequivalent positions, we consider migration between equivalent sites and non-equivalent sites. As shown in Figure 4, we selected four migration paths for Zr vacancies. The migration paths are named as follows: Since the formation energy of VZr2 is lower than that of VZr1, the system energy naturally tends to decrease, indicating that Zr vacancy migrates from VZr1 to VZr2. This migration is called Path I. The interplanar diffusion of VZr1 along the c direction is named Path II. The in-plane diffusion of VZr2 is called Path III, which is the shortest diffusion path for the Zr vacancy. The diffusion of VZr2 between planes along the c direction is set as Path IV. Table 6 displays the migration barriers for Zr vacancy defects. From our previous calculations of defect formation energies, it is evident that VZr2 is easier to form. However, in the calculation of CI-NEB calculations, we found that the diffusion of VZr between two VZr1 sites has the lowest diffusion barrier of 2.44 eV. This indicates that the Zr vacancies tend to migrate between vacancies at the VZr1 site, while the diffusion barrier is maximized when the Zr vacancy moves between the VZr1 site and VZr2 sites. Furthermore, it is apparent that Zr vacancies residing at equivalent positions exhibit relatively lower migration barriers when diffusing along shorter paths, which aligns with our previous speculations.
The two interstitial positions of the oxygen atom in ZrO exhibit distinct formation energies. The interstitial oxygen in the tetrahedral interstitial position has a significantly lower defect formation energy compared to that in the mid-position between Zr atoms; thus, we do not consider the case of Oi-mid in subsequent discussions. As shown in Figure 5, for the interstitial oxygen in the tetrahedral interstitial position, we investigated two diffusion mechanisms, selecting two paths for each mechanism. In the hop mechanism, the interstitial oxygen atom diffuses from one tetrahedral interstice to another. In contrast, the kick-off mechanism involves the diffusion of two oxygen atoms: the interstitial atom moves from the tetrahedral interstice to the nearest lattice site, while an atom from the original lattice site migrates to another tetrahedral interstice.
Table 7 presents the migration energies associated with all aforementioned paths. The results indicate that all migration paths of interstitial oxygen atoms in ZrO exhibit high migration barriers. The path with the lowest migration energy occurs in the intra-plane hop mechanism, corresponding to a migration energy of 2.91 eV. This suggests oxygen atoms in tetrahedral interstices encounter significant difficulty in diffusing, which aligns with the experimental observations. Moreover, the migration of interstitial atoms via the kick-off mechanism typically has a lower migration barrier. Notably, the intra-plane hop mechanism for oxygen interstitials is energetically favored in ZrO. Conversely, migration between planes adheres to general trends, as interstitial atoms typically do not traverse across a plane.

3.3. Effect of Alloying Elements in ZrO

Many researchers have demonstrated that the incorporation of alloying elements significantly affects the corrosion rate of zirconium alloys [55,56,57,58]. Appropriate additions of these elements can enhance the corrosion resistance of the matrix. In our investigation, we selected four common alloying elements used in zirconium alloys: Cr, Fe, Nb, and Sn. Given that zirconium possesses two inequivalent sites, we first evaluated the favorable substitution sites for each alloying element. Table 8 presents the substitution energies of all identified defects. Notably, the substitution energies are all positive, indicating that substitution does not occur spontaneously; however, sites with lower substitution energies are still considered stable. The substitution of Cr at the Zr2 site is more favorable, corresponding to a substitution energy of 3.27 eV. Similarly, Fe tends to substitute at the Zr2 site, with a corresponding substitution energy of 3.26 eV. Conversely, Nb and Sn exhibit lower substitution energies at the Zr1 site, corresponding to substitution energies of 2.04 eV and 3.17 eV, respectively. As indicated by the density of states (DOS) diagram, ZrO behaves as a metallic crystal; hence, we do not account for the charged state of the substituting elements.
Once the substitution sites of the alloying elements were determined, we investigated their influence on the behavior of oxygen defects. Regardless of where the substitution defects occur, we considered both the nearest and next-nearest oxygen vacancies. Table 9 summarizes the calculated formation energies of oxygen vacancies with and without substitution defects.
By comparing the formation energies of oxygen vacancies in pure ZrO and those in ZrO with substitution defects, we found that the presence of alloying elements reduces the formation energies of oxygen vacancies, indicating that it becomes easier to form oxygen vacancies in ZrO when substitution defects are present. The results in Table 9 further demonstrate that, regardless of the substitution site, the likelihood of losing an oxygen atom from the nearby lattice to form an oxygen vacancy increases. A positive formation energy for the oxygen vacancy indicates that oxygen vacancies do not form spontaneously in ZrO. The formation energy of an oxygen vacancy with SnZr in ZrO is reduced to 4.39 eV, the lowest among the four substitution defects. Additionally, as the distance between the oxygen vacancy and the substitution defect increases, the impact of the substitution defect on reducing vacancy formation energy diminishes. Notably, the formation energy of the oxygen vacancy near the substitution defect FeZr is the highest.
To elucidate the mechanism by which alloying elements enhance corrosion resistance, we investigated the diffusion barriers of oxygen vacancies in ZrO with substitutions using the climbing image nudged elastic band (CI-NEB) method. Similar to the migration paths in pure ZrO, we considered three types of paths: diffusion of the oxygen vacancy between the two nearest positions adjacent to the substitution defect (Path 1), diffusion between the nearest and next-nearest positions (Path 2), and vertical diffusion (Path 3). Table 9 displays the migration energies for these paths in ZrO with substitution defects.
It is evident that the oxygen vacancy has a lower migration energy with a CrZr substitution defect in ZrO, with calculated migration barriers decreasing by 1.34 eV, 0.16 eV, and 1.13 eV, for Path 1, Path 2, and Path 3, respectively. These results suggest that oxygen vacancies in ZrO with Cr dopants exhibit higher mobility compared to those in pure ZrO. For Path 2, the migration energy reaches 2.80 eV, which may indicate that Cr exerts a certain repulsive effect on the oxygen atom. In the case of the alloying element Fe, a strong chemical interaction appears to exist between Fe and the oxygen atom, resulting in non-convergence of the calculation for Path 3. However, for Paths 1 and 2, the migration barriers for oxygen vacancies both decreased. Interestingly, the Fe atom also migrated alongside the vacancy during the relaxation process. Conversely, in ZrO with Nb dopants, the results are quite different: the migration barriers for Paths 2 and 3 slightly increase, while the barrier for Path 1 decreases by 0.69 eV from 3.28 eV to 2.59 eV. The migration barriers of oxygen vacancies in ZrO with Sn dopants increase to 3.95 eV and 3.76 eV, respectively, for Path 2 and Path 3, while the calculation of the migration barrier for Path 1 does not converge, as the oxygen atom transitions to a tetrahedral interstice position during the calculation.
Overall, the migration barriers of oxygen vacancies provide insight into the motion of oxygen atoms. Based on the calculated formation energies of oxygen vacancies, it is evident that oxygen vacancies are more mobile in ZrO with substitution defects. Thus, migration barriers serve as a standard for evaluating the influence of alloying elements. Consequently, it is clear that Sn acts as a beneficial alloying element that decreases the mobility of oxygen atoms.
Additionally, to further understand the influence of alloying elements on the corrosion resistance of zirconium oxide, we investigated the behavior of interstitial oxygen atoms in ZrO doped with alloying elements. Similar to the interstitial oxygen located in pure ZrO, we chose the tetrahedral interstitial sites, composed of three zirconium atoms and one substitutional alloying atom, as the preferred interstitial positions. Based on previous calculations, we observed that the effect of substitutional atoms on oxygen vacancies depends on the distance between the oxygen atom and the alloying atom. Therefore, we sought to determine whether the same trend applies when interstitial oxygen atoms are introduced into the system.
To explore this, we selected three tetrahedral interstitial sites at varying distances from the substitutional alloying atom, denoted as Oia, Oib, and Oic, with increasing distance from the alloying defect as shown in Figure 6. Table 10 summarizes the calculated formation energies for interstitial oxygen atoms in both pure ZrO and ZrO doped with alloying elements.
Table 11 lists the formation energies of all interstitial oxygen atoms. Compared to pure ZrO, we found that the formation energies of interstitial oxygen atoms in ZrO doped with substitutional defects generally increase, although they remain negative. This implies that, while the interstitial oxygen atoms exhibit slightly higher formation energies in doped systems, they are still thermodynamically stable and would persist in ZrO regardless of doping.
Interestingly, the influence of alloying elements on the formation energy of interstitial oxygen varies depending on the specific dopant. For Cr and Fe substitutions, no consistent trend was observed with respect to the distance between the substitutional alloying atom and the interstitial oxygen atom. However, in the case of NbZr and SnZr defects, the formation energies of interstitial oxygen decreased as the distance between the substitutional defect and the interstitial oxygen increased. This suggests that alloying elements such as Nb and Sn have a stabilizing effect on interstitial oxygen at greater distances, while Cr and Fe exhibit more localized or complex interactions.
We schematically depict the migration pathways of interstitial oxygen atoms in Figure 7. Two migration mechanisms were considered, as in the case of pure ZrO: the hop and kick-off mechanisms. However, an additional factor must be accounted for in the doped system. While we already understand that the effect of alloying elements on the formation energy of interstitial oxygen is not dependent on distance, it remains necessary to confirm whether their influence on the migration behavior of interstitial oxygen is distance-dependent.
Table 12 presents the migration energies of interstitial oxygen in both pure ZrO and ZrO doped with alloying elements. Interestingly, although the formation of interstitial defects becomes more challenging in all doped systems, the migration of oxygen atoms exhibits varying behaviors based on the type of alloying element.
The results can be categorized based on the substitution sites of the alloying elements. When Nb and Sn occupy the Zr1 site, they reduce the migration barrier of oxygen atoms in nearby interstitial sites. As with Cr and Fe, the influence of Nb and Sn diminishes with increasing distance from the interstitial defect. Notably, Sn maximizes the formation probability of interstitial oxygen defects while minimizing the migration barrier of nearby interstitial oxygen atoms.
In contrast, when Cr and Fe occupy the Zr2 site, they increase the migration barrier of the interstitial oxygen atom in nearby sites. As the distance between the substitutional atom and the interstitial oxygen atom increases, the migration barrier decreases, suggesting that the effect of alloying elements on the migration barrier is distance-dependent. The kick-off mechanism consistently exhibits a lower barrier compared to the hop mechanism. Additionally, the impact of Cr and Fe on migration barriers follows a similar trend.

4. Conclusions

In this study, we investigated the behavior of intrinsic defects in ZrO, with a focus on the effects of alloying elements. Our key findings are as follows:
  • Intrinsic defects in pure ZrO: oxygen interstitial defects are preferentially formed in pure ZrO supercells, followed by oxygen vacancies, while the formation of interstitial Zr atoms is highly unfavorable due to the significantly higher formation energies.
  • The present manuscript focuses on investigating the diffusion properties of defects in the bulk phase rather than the oxide/water interface. According to our present results, it can be found that diffusion barriers of interstitial O and O vacancy are higher than those in the ZrO2 phase. Therefore, ZrO can act as a buffer layer for slowing oxygen transporting from the oxide/water interface to the Zr substrate, which subsequently suppresses the oxidization of Zr cladding.
  • Effects of Alloying Elements:
    • Alloying elements facilitate the formation of oxygen vacancies in ZrO. Specifically, Cr and Fe reduce the migration barriers of oxygen vacancies, while Nb and Sn increase these barriers in their vicinity.
    • The introduction of alloying elements makes the formation of interstitial oxygen defects more difficult. Furthermore, Cr and Fe cause a notable increase in the migration barriers of nearby interstitial oxygen atoms.
The results of this study provide a deeper understanding of how intrinsic defects behave in ZrO, particularly when alloying elements are introduced. These insights form a foundation for future microscopic studies on defect behavior in zirconium oxides, with implications for enhancing the corrosion resistance and performance of zirconium alloys in practical applications.

Author Contributions

Conceptualization, Z.L. and D.W.; Methodology, H.S., Z.L., D.W. and Y.Z.; Software, H.S.; Validation, H.S. and T.W.; Formal analysis, H.S., Z.L., D.W., T.W. and Y.Z.; Investigation, H.S.; Resources, Z.L.; Data curation, H.S.; Writing—original draft, H.S.; Writing—review & editing, H.S., Z.L., D.W., T.W. and Y.Z.; Visualization, H.S.; Supervision, Z.L.; Project administration, D.W.; Funding acquisition, D.W. All authors have read and agreed to the published version of the manuscript.

Funding

This work is financially supported by National Natural Science Foundation of China (grant numbers: 52471009 and 12405301). The authors also thank computational resources supplied by National Supercomputing Changsha Center.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Conflicts of Interest

There are no conflicts of interest to declare.

References

  1. International Energy Agency. Global Energy and CO2 Status Report 2019. Pairs. 2019. Available online: https://www.iea.org/reports/global-energy-co2-status-report-2019 (accessed on 10 April 2025).
  2. Karakosta, C.; Pappas, C.; Marinakis, V.; Psarras, J. Renewable energy and nuclear power towards sustainable development: Characteristics and prospects. Renew. Sustain. Energy Rev. 2013, 22, 187–197. [Google Scholar] [CrossRef]
  3. Motta, A.T.; Couet, A.; Comstock, R.J. Corrosion of zirconium alloys used for nuclear fuel cladding. Annu. Rev. Mater. Res. 2015, 45, 311–343. [Google Scholar] [CrossRef]
  4. Wang, H.; Wang, Y.; Wang, X.; Wang, R.; Weng, L.; Zhang, Y. Overview of influence factors about corrosion resistance of zirconium alloys. Mater. Rev. 2013, 1, 022. [Google Scholar]
  5. Guo, X. Property degradation of tetragonal zirconia induced by low-temperature defect reaction with water molecules. Chem. Mater. 2004, 16, 3988–3994. [Google Scholar] [CrossRef]
  6. Barbour, O.; Crocombette, J.P.; Schuler, T.; Tupin, M. Ab-initio calculations of hydrogen diffusion coefficient in monoclinic zirconia. J. Nucl. Mater. 2020, 539, 152333. [Google Scholar] [CrossRef]
  7. Zhang, H.-H.; Xie, Y.-P.; Yao, M.-Y.; Xu, J.-X.; Zhang, J.-L.; Hu, L.-J. Effects of oxygen chemical potential on the anisotropy of the adsorption properties of Zr surfaces. Phys. Chem. Chem. Phys. 2018, 20, 14410–14419. [Google Scholar] [CrossRef]
  8. Zhang, H.-H.; Li, X.-D.; Xie, Y.-P.; Hu, L.-J.; Yao, M.-Y. First-principle study of the oxygen adsorption on Zr surface with Nb or Ge. Acta Phys. Sin. 2016, 65, 096802. [Google Scholar] [CrossRef]
  9. Li, S.; Geng, J. Effect of adding Cu on the corrosion resistance of M5 alloy in superheated steam at 500 °C. Acta Met. Sin. 2011, 47, 163–168. [Google Scholar]
  10. Xu, C.-H.; Xie, Y.-P.; Yao, M.-Y.; Hu, L.-J.; Lin, X.-D. First-principles computational tensile tests of grain boundaries of zirconia with Cu segregation. J. Nucl. Mater. 2022, 560, 153498. [Google Scholar] [CrossRef]
  11. Lustman, B.; Kerze, F.; Straumanis, M. The metallurgy of zirconium. J. Electrochem. Soc. 1957, 104, 254Ca. [Google Scholar] [CrossRef]
  12. Natesan, K.; Soppet, W. Hydrogen Effects on Air Oxidation of Zirlo Alloy; Division of Systems Analysis and Regulatory Effectiveness, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission: Washington, DC, USA, 2004.
  13. Bell, B.; Murphy, S.; Burr, P.; Comstock, R.; Partezana, J.; Grimes, R.; Wenman, M. The influence of alloying elements on the corrosion of Zr alloys. Corros. Sci. 2016, 105, 36–43. [Google Scholar] [CrossRef]
  14. Daroonparvar, M.; Yajid, M.A.M.; Yusof, N.M.; Bakhsheshi-Rad, H.R.; Hamzah, E.; Nazoktabar, M. Investigation of three steps of hot corrosion process in Y2O3 stabilized ZrO2 coatings including nano zones. J. Rare Earths 2014, 32, 989–1002. [Google Scholar] [CrossRef]
  15. Sabol, G.P. Zirconium in the Nuclear Industry: Twelfth International Symposium; ASTM International: West Conshohocken, PA, USA, 2000; Volume 1354. [Google Scholar]
  16. Yilmazbayhan, A.; Breval, E.; Motta, A.T.; Comstock, R.J. Transmission electron microscopy examination of oxide layers formed on Zr alloys. J. Nucl. Mater. 2006, 349, 265–281. [Google Scholar] [CrossRef]
  17. Ni, N.; Lozano-Perez, S.; Sykes, J.; Grovenor, C. Quantitative EELS analysis of zirconium alloy metal/oxide interfaces. Ultramicroscopy 2010, 111, 123–130. [Google Scholar] [CrossRef] [PubMed]
  18. Ni, N.; Hudson, D.; Wei, J.; Wang, P.; Lozano-Perez, S.; Smith, G.; Sykes, J.; Yardley, S.; Moore, K.; Lyon, S. How the crystallography and nanoscale chemistry of the metal/oxide interface develops during the aqueous oxidation of zirconium cladding alloys. Acta Mater. 2012, 60, 7132–7149. [Google Scholar] [CrossRef]
  19. Dong, Y.; Motta, A.T.; Marquis, E.A. Atom probe tomography study of alloying element distributions in Zr alloys and their oxides. J. Nucl. Mater. 2013, 442, 270–281. [Google Scholar] [CrossRef]
  20. Nicholls, R.J.; Ni, N.; Lozano-Perez, S.; London, A.; McComb, D.W.; Nellist, P.D.; Grovenor, C.R.; Pickard, C.J.; Yates, J.R. Crystal Structure of the ZrO Phase at Zirconium/Zirconium Oxide Interfaces. Adv. Eng. Mater. 2015, 17, 211–215. [Google Scholar] [CrossRef]
  21. Yilmazbayhan, A.; Delaire, O.; Motta, A.; Birtcher, R.; Maser, J.; Lai, B. Determination of the alloying content in the matrix of Zr alloys using synchrotron radiation microprobe X-ray fluorescence. J. Nucl. Mater. 2003, 321, 221–232. [Google Scholar] [CrossRef]
  22. Syrtanov, M.S.; Korneev, S.P.; Kashkarov, E.B.; Sidelev, D.V.; Moskvichev, E.N.; Kudiiarov, V.N. Barrier Properties of Cr/Ta-Coated Zr-1Nb Alloy under High-Temperature Oxidation. Metals 2024, 14, 645. [Google Scholar] [CrossRef]
  23. Kong, X.; Kuang, H.; Li, A.; Yu, Y.; Kharchenko, D.O.; Mao, J.; Wu, L. The effect of niobium on the mechanical and thermodynamic properties of zirconium alloys. Metals 2024, 14, 646. [Google Scholar] [CrossRef]
  24. Feng, X.; Chen, X.; Yi, X.; Li, W.; Liu, C.; Meng, X.; Gao, Z.; Cao, X.; Wang, H. Influence of β-Stabilizing Nb on Phase Stability and Phase Transformation in Ti-Zr Shape Memory Alloys: From the Viewpoint of the First-Principles Calculation. Metals 2024, 14, 1192. [Google Scholar] [CrossRef]
  25. Youssef, M.; Yildiz, B. Intrinsic point-defect equilibria in tetragonal ZrO2: Density functional theory analysis with finite-temperature effects. Phys. Rev. B—Condens. Matter Mater. Phys. 2012, 86, 144109. [Google Scholar] [CrossRef]
  26. Zheng, J.; Ceder, G.; Maxisch, T.; Chim, W.; Choi, W. First-principles study of native point defects in hafnia and zirconia. Phys. Rev. B—Condens. Matter Mater. Phys. 2007, 75, 104112. [Google Scholar] [CrossRef]
  27. Hohenberg, P.; Kohn, W. Inhomogeneous electron gas. Phys. Rev. 1964, 136, B864. [Google Scholar] [CrossRef]
  28. Kohn, W.; Sham, L.J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965, 140, A1133. [Google Scholar] [CrossRef]
  29. Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169. [Google Scholar] [CrossRef]
  30. Kresse, G.; Hafner, J. Ab initio molecular dynamics for open-shell transition metals. Phys. Rev. B 1993, 48, 13115. [Google Scholar] [CrossRef]
  31. Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953. [Google Scholar] [CrossRef]
  32. Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758. [Google Scholar] [CrossRef]
  33. Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865. [Google Scholar] [CrossRef]
  34. Garcia, J.C.; Deskins, N.A. Detailing ionosorption over TiO2, ZrO2, and HfO2 from first principles. J. Phys. Chem. C 2012, 116, 16573–16581. [Google Scholar] [CrossRef]
  35. Youssef, M.; Yildiz, B. Hydrogen defects in tetragonal ZrO2 studied using density functional theory. Phys. Chem. Chem. Phys. 2014, 16, 1354–1365. [Google Scholar] [CrossRef] [PubMed]
  36. Heyd, J.; Scuseria, G.E.; Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 2003, 118, 8207–8215. [Google Scholar] [CrossRef]
  37. Monkhorst, H.J.; Pack, J.D. Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13, 5188. [Google Scholar] [CrossRef]
  38. Sheppard, D.; Xiao, P.; Chemelewski, W.; Johnson, D.D.; Henkelman, G. A generalized solid-state nudged elastic band method. J. Chem. Phys. 2012, 136, 074103. [Google Scholar] [CrossRef]
  39. Smidstrup, S.; Pedersen, A.; Stokbro, K.; Jónsson, H. Improved initial guess for minimum energy path calculations. J. Chem. Phys. 2014, 140, 214106. [Google Scholar] [CrossRef]
  40. Pan, Y.; Yu, E. First-principles investigation of structural stability, mechanical and thermodynamic properties of Pt3Zr5 compounds. Phys. B Condens. Matter 2021, 611, 412936. [Google Scholar] [CrossRef]
  41. Bao, L.; Kong, Z.; Qu, D.; Duan, Y. First-principles investigation on the structures, energies and electronic properties of low-index surfaces of Mg2Pb. Mater. Chem. Phys. 2021, 260, 124028. [Google Scholar] [CrossRef]
  42. Bao, L.; Kong, Z.; Qu, D.; Duan, Y. Insight of structural stability, elastic anisotropies and thermal conductivities of Y, Sc doped Mg2Pb from first-principles calculations. Chem. Phys. Lett. 2020, 756, 137833. [Google Scholar] [CrossRef]
  43. Pan, Y. Structural prediction and overall performances of CrSi2 disilicides: DFT investigations. ACS Sustain. Chem. Eng. 2020, 8, 11024–11030. [Google Scholar] [CrossRef]
  44. Zhang, K.; Zhan, Y. Adhesion strength and stability of Cu(111)/TiC(111) interface in composite coatings by first principles study. Vacuum 2019, 165, 215–222. [Google Scholar] [CrossRef]
  45. Zhang, J.; Oganov, A.R.; Li, X.; Mahdi Davari Esfahani, M.; Dong, H. First-principles investigation of Zr-O compounds, their crystal structures, and mechanical properties. J. Appl. Phys. 2017, 121, 155104. [Google Scholar] [CrossRef]
  46. Puchala, B.; Van der Ven, A. Thermodynamics of the Zr-O system from first-principles calculations. Phys. Rev. B 2013, 88, 094108. [Google Scholar] [CrossRef]
  47. Pan, Y.; Guan, W. Prediction of new phase and electrochemical properties of Li2S2 for the application of Li-S batteries. Inorg. Chem. 2018, 57, 6617–6623. [Google Scholar] [CrossRef] [PubMed]
  48. Zhang, X.; Dong, T.; Ma, H.; Yu, H.; Li, X.; Wang, F. Insight into the vacancy effects on mechanical and electronic properties of V5Si3 silicides from first-principles calculations. J. Mol. Graph. Model. 2020, 98, 107600. [Google Scholar] [CrossRef]
  49. Chen, S.; Pan, Y. Influence of group III and IV elements on the hydrogen evolution reaction of MoS2 disulfide. J. Phys. Chem. C 2021, 125, 11848–11856. [Google Scholar] [CrossRef]
  50. Chen, S.; Pan, Y. Noble metal interlayer-doping enhances the catalytic activity of 2H–MoS2 from first-principles investigations. Int. J. Hydrogen Energy 2021, 46, 21040–21049. [Google Scholar] [CrossRef]
  51. Pan, Y. The influence of N-vacancy on the electronic and optical properties of bulk InN nitrides. Mater. Sci. Eng. B 2021, 271, 115265. [Google Scholar] [CrossRef]
  52. Henkelman, G.; Uberuaga, B.P.; Jónsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 2000, 113, 9901–9904. [Google Scholar] [CrossRef]
  53. Yang, J.; Youssef, M.; Yildiz, B. Oxygen self-diffusion mechanisms in monoclinic ZrO2 revealed and quantified by density functional theory, random walk analysis, and kinetic Monte Carlo calculations. Phys. Rev. B 2018, 97, 024114. [Google Scholar] [CrossRef]
  54. Youssef, M.; Yildiz, B. Predicting self-diffusion in metal oxides from first principles: The case of oxygen in tetragonal ZrO2. Phys. Rev. B 2014, 89, 024105. [Google Scholar] [CrossRef]
  55. Jeong, Y.H.; Kim, H.G.; Kim, T.H. Effect of β phase, precipitate and Nb-concentration in matrix on corrosion and oxide characteristics of Zr–xNb alloys. J. Nucl. Mater. 2003, 317, 1–12. [Google Scholar] [CrossRef]
  56. Huang, J.; Yao, M.-Y.; Gao, C.-Y.; Liang, X.; Peng, J.-C.; Zhang, J.-L.; Zhou, B.-X. The influence of second phase particles on the crack formation in oxide films formed on zirconium alloys. Corros. Sci. 2015, 99, 172–177. [Google Scholar] [CrossRef]
  57. Harada, M.; Kimpara, M.; Abe, K. Effect of alloying elements on uniform corrosion resistance of zirconium-based alloys in 360 °C water and 400 °C steam. In Zirconium in the Nuclear Industry: Ninth International Symposium; ASTM International: West Conshohocken, PA, USA, 1991. [Google Scholar]
  58. Takeda, K.; Anada, H. Mechanism of corrosion rate degradation due to tin. In Zirconium in the Nuclear Industry: Twelfth International Symposium; ASTM International: West Conshohocken, PA, USA, 2000. [Google Scholar]
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Figure 1. The crystal structure of ZrO consists of two types of Zr atoms in different sites and one type of O atom, and there are also two different interstitial positions. Large green spheres represent Zr atoms. Small red spheres represent O atoms and grey spheres represent interstitial atoms.
Figure 1. The crystal structure of ZrO consists of two types of Zr atoms in different sites and one type of O atom, and there are also two different interstitial positions. Large green spheres represent Zr atoms. Small red spheres represent O atoms and grey spheres represent interstitial atoms.
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Figure 2. Density of states of ZrO, with Fermi level set to 0.
Figure 2. Density of states of ZrO, with Fermi level set to 0.
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Figure 3. The diffusion paths of oxygen vacancies in ZrO. The grey spheres represent vacancy atoms.
Figure 3. The diffusion paths of oxygen vacancies in ZrO. The grey spheres represent vacancy atoms.
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Figure 4. Diffusion paths of Zr vacancies in ZrO. Large green and grey spheres represent Zr atoms in lattice sites and vacancy sites.
Figure 4. Diffusion paths of Zr vacancies in ZrO. Large green and grey spheres represent Zr atoms in lattice sites and vacancy sites.
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Figure 5. The migration paths of Oi: (a) is a top view of the supercell, showing the path of diffusion in the plane; (b) is a side view of the supercell, showing the path of diffusion between planes. Path a and Path b are the hop mechanisms; Path c and Path d are the kick-off mechanisms. Small red and black spheres represent O atoms in lattice sites and interstitial sites.
Figure 5. The migration paths of Oi: (a) is a top view of the supercell, showing the path of diffusion in the plane; (b) is a side view of the supercell, showing the path of diffusion between planes. Path a and Path b are the hop mechanisms; Path c and Path d are the kick-off mechanisms. Small red and black spheres represent O atoms in lattice sites and interstitial sites.
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Figure 6. Interstitial oxygen atoms when substituting defects are included. (a) shows the position of interstitial oxygen atoms when the substitution defect occurs at the Zr1 position; (b) shows the position of interstitial oxygen atoms when the substitution defect occurs at the Zr2 position.
Figure 6. Interstitial oxygen atoms when substituting defects are included. (a) shows the position of interstitial oxygen atoms when the substitution defect occurs at the Zr1 position; (b) shows the position of interstitial oxygen atoms when the substitution defect occurs at the Zr2 position.
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Figure 7. Migration paths of Oi when substitution exists: (a) shows the migration paths of interstitial oxygen atoms when the substitution defect occurs at the Zr1 position; (b) shows the migration paths of interstitial oxygen atoms when the substitution defect occurs at the Zr2 position. Path A, Path B, and Path D represent the hop mechanism, while Path C represents the kick-off mechanism.
Figure 7. Migration paths of Oi when substitution exists: (a) shows the migration paths of interstitial oxygen atoms when the substitution defect occurs at the Zr1 position; (b) shows the migration paths of interstitial oxygen atoms when the substitution defect occurs at the Zr2 position. Path A, Path B, and Path D represent the hop mechanism, while Path C represents the kick-off mechanism.
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Table 1. The total energy of ZrO using different k-point mesh.
Table 1. The total energy of ZrO using different k-point mesh.
k-Point MeshEnergy (eV/per ZrO)
4 × 4 × 6−56.364
6 × 6 × 6−56.362
12 × 12 × 12−56.361
Table 2. Calculated lattice parameters (Å), volume V (Å3) and formation enthalpy (eV/atom) of ZrO.
Table 2. Calculated lattice parameters (Å), volume V (Å3) and formation enthalpy (eV/atom) of ZrO.
a (Å)c (Å)V (Å3)ΔH (eV/atom)
Present work5.3183.18077.878−5.384
Ref [45]5.3333.218----
Ref [46]5.2853.179----
Ref [20]5.313.20
Table 3. Defect formation energy of intrinsic defect in ZrO.
Table 3. Defect formation energy of intrinsic defect in ZrO.
Defect TypesFormation Energies/eV
VO5.31
VZr13.94
VZr21.99
Oi-tet−4.04
Oi-mid0.03
Zri-tet7.74
Zri-mid7.51
Table 4. Formation energies (eV) of different types of defects in ZrO, t-ZrO2, and m-ZrO2. Only the stable defect formation energy is presented in the table.
Table 4. Formation energies (eV) of different types of defects in ZrO, t-ZrO2, and m-ZrO2. Only the stable defect formation energy is presented in the table.
VOVZrOiZri
ZrO5.311.99−4.047.51
t-ZrO2 [25]5.595.651.7912.91
m-ZrO2 [26]6.155.781.3114.28
Table 5. Migration barriers (eV) of oxygen vacancies.
Table 5. Migration barriers (eV) of oxygen vacancies.
Migration PathPath 1Path 2Path 3
Migration barrier (eV)3.282.963.15
Table 6. Migration barriers of Zr vacancies.
Table 6. Migration barriers of Zr vacancies.
Migration PathPath IPath IIPath IIIPath IV
Migration barrier (eV)3.472.442.873.17
Table 7. The migration barriers (eV) of O interstitial atoms.
Table 7. The migration barriers (eV) of O interstitial atoms.
Migration PathPath aPath bPath cPath d
Migration barrier (eV)2.914.973.563.27
Table 8. Substitution energies (eV) of different alloying elements.
Table 8. Substitution energies (eV) of different alloying elements.
Cr-SubFe-SubNb-SubSn-Sub
Zr1-site4.084.742.043.17
Zr2-site3.273.262.554.04
Table 9. Formation energies (eV) of O vacancies in ZrO with substitution and in pure ZrO supercell.
Table 9. Formation energies (eV) of O vacancies in ZrO with substitution and in pure ZrO supercell.
Cr-SubFe-SubNb-SubSn-SubPure ZrO
Nearest VO14.975.124.934.395.31
Next nearest VO25.366.115.125.28/
Table 10. The migration barriers (eV) of VO. --- indicates that the calculation did not converge.
Table 10. The migration barriers (eV) of VO. --- indicates that the calculation did not converge.
Cr-SubFe-SubNb-SubSn-SubPure ZrO
Path 11.942.912.59---3.28
Path 22.802.513.153.952.96
Path 32.02---3.213.763.15
Table 11. Formation energies (eV) of interstitial oxygen atoms in ZrO. ---- indicates that Oib and Oic do not exist in pure ZrO.
Table 11. Formation energies (eV) of interstitial oxygen atoms in ZrO. ---- indicates that Oib and Oic do not exist in pure ZrO.
Cr-SubFe-SubNb-SubSn-SubPure ZrO
Oia−4.20−4.04−3.91−3.43−4.04
Oib−3.95−3.98−4.09−3.86----
Oic−4.01−3.99−4.06−3.95----
Table 12. Migration energies (eV) of interstitial oxygen atoms in ZrO.
Table 12. Migration energies (eV) of interstitial oxygen atoms in ZrO.
Cr-SubFe-SubNb-SubSn-SubPure ZrO
Path A4.174.12.722.012.79
Path B3.923.983.783.54
Path C2.152.083.002.013.15
Path D2.542.623.974.29
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Shi, H.; Liu, Z.; Wang, D.; Wei, T.; Zhao, Y. A First-Principles Study on Defects in Zirconium Monoxide. Metals 2025, 15, 449. https://doi.org/10.3390/met15040449

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Shi H, Liu Z, Wang D, Wei T, Zhao Y. A First-Principles Study on Defects in Zirconium Monoxide. Metals. 2025; 15(4):449. https://doi.org/10.3390/met15040449

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Shi, Hanyu, Zhixiao Liu, Dong Wang, Tianguo Wei, and Yi Zhao. 2025. "A First-Principles Study on Defects in Zirconium Monoxide" Metals 15, no. 4: 449. https://doi.org/10.3390/met15040449

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Shi, H., Liu, Z., Wang, D., Wei, T., & Zhao, Y. (2025). A First-Principles Study on Defects in Zirconium Monoxide. Metals, 15(4), 449. https://doi.org/10.3390/met15040449

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