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Article

First-Principles Analysis of Phase Stability and Transformation Suppression for Hydrogen-Doped Alumina

1
School of Mechanical Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China
2
Research Laboratory “Technical Ceramics and Nanomaterials”, Sukhoi State Technical University of Gomel, 48 Prospect Octiabria, 246746 Gomel, Belarus
*
Authors to whom correspondence should be addressed.
Coatings 2025, 15(5), 545; https://doi.org/10.3390/coatings15050545
Submission received: 27 March 2025 / Revised: 28 April 2025 / Accepted: 30 April 2025 / Published: 2 May 2025
(This article belongs to the Special Issue Ceramic and Glass Material Coatings)

Abstract

:
Thermally grown oxide (TGO) layers—primarily alumina (Al2O3)—provide oxidation resistance and high-temperature protection for thermal barrier coatings. However, during their service in humid and hot environments, water vapor accelerates TGO degradation by stabilizing metastable alumina phases (e.g., θ-Al2O3) and inhibiting their transformation to the thermodynamically stable α-Al2O3, a phenomenon which has been shown in numerous experimental studies. However, the microscopic mechanisms by which water vapor affects the phase stability and transformation of alumina remain unresolved. This study employs first-principles calculations to investigate hydrogen’s role in altering vacancy formation, aggregation, and atomic migration in θ- and α-Al2O3. The results reveal that hydrogen incorporation reduces the formation energies for aluminum and oxygen vacancies by up to 40%, promoting defect generation and clustering; increases aluminum migration barriers by 25–30% while lowering oxygen migration barriers by 15–20%, creating asymmetric diffusion kinetics; and stabilizes oxygen-deficient sublattices, disrupting the structural reorganization required for θ- to α-Al2O3 transitions. These effects collectively sustain metastable θ-Al2O3 growth and delay phase stabilization. By linking hydrogen-induced defect dynamics to macroscopic coating degradation, this work provides atomic-scale insights for designing moisture-resistant thermal barrier coatings through the targeted inhibition of vacancy-mediated pathways.

1. Introduction

Thermal barrier coatings (TBCs) are critical for protecting hot-section components of aero-engines, including turbine blades, combustion chambers, and nozzles, due to their exceptional thermal insulation, oxidation resistance, and corrosion protection [1,2,3,4,5]. A typical TBC system comprises three layers: a ceramic topcoat, a metallic bond coat (typically MCrAlY), and a superalloy substrate [1,2,3,4,5]. During service, oxygen permeates the top coat layer and reacts with metallic elements in the bond coat, forming thermally grown oxide (TGO) primarily composed of alumina (Al2O3) [1,2,3].
The ideal TGO consists of a dense, fast-growing α-Al2O3 phase with high thermodynamic stability, which effectively inhibits oxygen diffusion and enhances oxidation resistance [4,5]. However, under operational conditions involving thermal cycling and oxidizing environments, metastable alumina phases (e.g., γ-, η-, δ-, and θ-Al2O3) often nucleate prior to α-Al2O3 formation due to gradients in oxygen partial pressure, temperature, and stress [6,7,8,9,10]. These metastable polymorphs exhibit distinct physical properties, with γ- and θ-Al2O3 growing up to two orders of magnitude faster than α-Al2O3 [11,12,13,14,15]. Consequently, the phase stability of α-Al2O3 governs the oxidation kinetics, stress evolution, and long-term performance of TBC systems.
Extensive research over the past two decades has elucidated the oxidation behavior of bond coat layers. At temperatures below 1200 °C, metastable γ- or θ-Al2O3 typically forms initially due to kinetic favorability, subsequently transforming to α-Al2O3 through prolonged oxidation [4,5,6,7,8,9,10]. This phase transition is accompanied by volumetric shrinkage and defect generation, which accelerate ionic diffusion, induce growth stresses, and promote interfacial microcracking [16,17,18]. The metastable-to-stable phase evolution thus critically influences TGO morphology, mechanical integrity, and TBC lifespan. Recent studies highlight the role of metastable alumina in interfacial degradation. For instance, Zhang et al. [19] investigated γ-Al2O3/Al interfacial properties using first-principles calculations, while Sakakibara et al. [20] observed transient η- and θ-Al2O3 nanoparticles via transmission electron microscopy prior to α-Al2O3 crystallization. Despite these advances, the energy landscape governing θ- to α-Al2O3 transitions remains poorly characterized.
In water vapor-enriched gas turbine environments, hydrogen (H) accelerates TBC degradation by stabilizing metastable alumina and inhibiting α-Al2O3 formation [21,22]. The proposed mechanisms include enhanced cation diffusion [23], altered Al/O ion mobility [24], and hydroxyl-induced vacancy formation [25,26,27]. For example, Yan et al. [25] suggested that dissociated protons from H2O disrupt oxide electroneutrality, increasing cation vacancy concentrations and suppressing θ- to α-Al2O3 transitions. Similarly, Zhu et al. [26] and Cheng et al. [27] attributed prolonged metastable phase growth to water-vapor-promoted defect density and atomic diffusion. However, the atomistic mechanisms underlying these phenomena remain unresolved.
The θ- to α-Al2O3 transition is hypothesized to involve either diffusional restructuring [28] or cooperative oxygen sublattice shear combined with Al3+ migration [29]. Bagwell et al. [28] demonstrated that α-Al2O3 nucleation proceeds via diffusion rather than shear-driven reconfiguration. In contrast, Huang et al. [29] proposed a simultaneous shear–migration mechanism based on first-principles calculations. Despite these insights, the influence of water vapor on phase transition energetics and kinetics lacks a unified explanation.
Numerous studies have shown that water vapor accelerates TGO degradation, yet the microscopic mechanisms by which it affects the phase stability and transformation of alumina remain unclear. This study aims to elucidate the microscopic mechanisms by which water vapor influences the phase stability and transformation of alumina. To achieve these objectives, we employed first-principles calculations to investigate the impact of hydrogen on vacancy formation, aggregation, and atomic migration in θ- and α-Al2O3. These findings enhance the fundamental understanding of oxidation mechanisms and provide theoretical guidance for the design of more durable TBC systems.

2. Materials and Methods of Research

The α-Al2O3 crystal (space group R-3c; trigonal system) adopts a close-packed configuration with lattice constants a = b = 0.4759 nm and c = 1.291 nm, containing 30 atoms per unit cell [30,31,32]. As shown in Figure 1a, a (3 × 3 × 1) supercell expansion of the α-Al2O3 protocell yielded a 270-atom model with a hydrogen concentration of 0.37 at%. In α-Al2O3, O and Al atoms occupy single crystallographic sites, necessitating the consideration of only two vacancy configurations—octahedral Al vacancies (VAl-oct) and O vacancies (VO). To construct these defects, one Al atom was removed from both pristine and hydrogen-doped α-Al2O3 to form VAl-oct, while one O atom was removed to generate VO. Structural optimization was performed to stabilize the models. In addition, θ-Al2O3 exhibits monoclinic symmetry (space group C2/m) with lattice parameters a = 11.9 Å, b = 2.9 Å, and c = 5.56 Å, comprising 20 atoms per unit cell (four formula units) with all atoms occupying 4i Wyckoff positions [33]. A (1 × 4 × 2) supercell expansion (Figure 1b) produced a 160-atom model with 0.625 at% hydrogen. In θ-Al2O3, O atoms occupy a single equivalent site, requiring only one VO configuration. Al atoms reside in tetrahedral and octahedral interstitial positions, leading to two distinct Al vacancy models—tetrahedral (VAl-tet) and octahedral (VAl-oct). These defects were modeled by removing one tetrahedral or octahedral Al atom from pristine and hydrogen-doped θ-Al2O3, respectively, followed by structural optimization.
First-principles calculations were performed to investigate vacancy formation, aggregation, and atomic migration, as well as hydrogen doping effects on alumina growth with phase transformation. Large supercells with low defect concentrations (≤0.625 at%) were employed to minimize defect interactions and reflect local structural properties. All calculations utilized the VASP software package with the PAW-PBE pseudopotential and generalized gradient approximation (GGA) for exchange-correlation. The H pseudopotential (PAW_PBE H 15Jun2001) was selected to model neutral hydrogen atoms, which is consistent with prior studies of H diffusion in alumina [34,35]. A 3 × 3 × 3 Monkhorst-Pack k-point grid, a plane-wave cutoff energy of 500 eV, and convergence criteria of 10−4 eV (electronic) and 10−5 eV (total energy) were applied. Structural optimizations ensured force convergence below 0.001 eV/Å. This approach accurately describes core–electron interactions and defect-related electronic structures, as well as enabling the precise evaluation of key properties including vacancy formation energies and migration barriers. This ensures both reliable structural predictions and computational efficiency for complex oxide systems such as alumina.
In detail, the formulae assessing the vacancy formation difference ( δ E ) between H-free and H-doped systems, i.e., E f o r m and E f o r m H are as follows:
E f o r m = E V + ε E p r
E f o r m H = E V H + ε E p r H
and
δ E = E f o r m H E f o r m
In Equations (1)–(3), E V and E V H represent the total energy for the defective H-free and H-doped Al2O3 systems, respectively. E p r and E p r H represent the total energy for the pristine H-free and H-doped Al2O3 systems, respectively. ε represents the chemical potential of the removed atom (Al or O) in its standard state. Furthermore, the vacancy aggregation energy ( Δ E ) is defined as the difference between the double vacancy and the two separated vacancy energies, as follows:
Δ E = E 2 V D E 2 V S
where E 2 V D and E 2 V S represent the total energy of the system with two vacancies aggregated as nearest neighbors on the dense row surface and the total energy of the system with two isolated vacancies (separated beyond nearest-neighbor distances), respectively. It is seen that Δ E < 0 indicates thermodynamically favorable vacancy aggregation, while Δ E > 0 suggests mutual repulsion.
For atomic diffusion studies, adjacent Al/O atom pairs in equivalent lattice planes were selected. A vacancy was created by removing one atom, while the neighboring site remained either pristine or hydrogen-doped. The final state for diffusion was generated by swapping the vacancy position with the retained atom, followed by structural optimization. Diffusion pathways were determined using the climbing image nudged elastic band (CI-NEB) method. Prior to pathway interpolation, the Variational Transition State Theory script was employed to verify the geometric similarity between optimized initial and final states, before validating the interpolation process by ensuring the continuity of atomic trajectories, finally confirming force convergence (−0.03 eV/Å) at all intermediate images.

3. Results and Discussion

3.1. Mechanical Property Validation

The mechanical properties of α-Al2O3 and θ-Al2O3 base cells (Section 2) were evaluated, including bulk modulus, shear modulus, and Young’s modulus. As summarized in Table 1, the calculated values for α-Al2O3 are 223.26 GPa, 165.75 GPa, and 399.56 GPa, respectively, which are consistent with prior computational results [36]. For θ-Al2O3, the corresponding values (201.74 GPa, 142.67 GPa, and 343.35 GPa) exhibit minimal deviations of 1.35%, 0.68%, and 1.16% from the reference data [36]. These agreements validate the structural accuracy of the α-Al2O3 and θ-Al2O3 models, providing a reliable foundation for defect and atomic migration studies in Section 3.2, Section 3.3 and Section 3.4.

3.2. Vacancy Formation and Lattice Distortion

In alumina crystals, vacancies arise when atomic vibrational amplitudes exceed critical thresholds, displacing atoms from their lattice sites and inducing local distortions. Water vapor-derived H protons further influence these distortions by interacting with vacancy defects. Figure 2 and Figure 3 illustrate the optimized supercell models of α-Al2O3 and θ-Al2O3 doped with H protons. In both phases, H protons localize near aluminum vacancies (VAl), while occupying oxygen vacancy (VO) sites. Structural optimization reveals that VAl and VO induce distinct lattice distortions, which are modulated by H incorporation.
For α-Al2O3 (Figure 2), the intrinsic VO and octahedral VAl−oct formation energies are 6.73 eV and 12.01 eV, respectively, matching previous calculations (see Table 2, Refs [37,38]). Upon H doping, these energies decrease to 4.56 eV (VO) and 6.75 eV (VAl−oct), corresponding to relative defect formation energies of −2.17 eV and −5.26 eV. Figure 2 demonstrates that intrinsic VAl−oct causes the outward displacement of octahedral O atoms, whereas H doping mitigates inward shifts of the nearest-neighbor O atoms. Similarly, intrinsic VO promotes the inward aggregation of diagonally coordinated Al atoms, while H incorporation suppresses this effect. These results indicate that H protons reduce the lattice distortions associated with VAl−oct and VO, thereby lowering their formation energies.
In θ-Al2O3 (Figure 3), intrinsic VO, VAl−oct, and tetrahedral VAl−tet exhibit formation energies of 6.11 eV, 12.51 eV, and 12.09 eV, respectively, aligning with reported VO values (6.20 eV) [39]. H doping reduces these energies to 3.29 eV (VO), 5.91 eV (VAl−oct), and 5.14 eV (VAl−tet), with relative defect formation energies of −2.82 eV, −6.60 eV, and −6.95 eV. Figure 3 shows that intrinsic VAl−tet and VAl−oct induce outward O displacements, while H incorporation alters the displacement directions of the adjacent O atoms. For VO, intrinsic vacancies cause the inward aggregation of tetrahedral Al atoms and outward shifts of octahedral Al atoms; H doping counteracts the former and enhances the latter. These structural changes weaken Al-O bonding constraints near VAl−tet, VAl−oct, and VO, mirroring the H-induced reduction in vacancy formation energies observed in α-Al2O3.

3.3. Vacancy Aggregation Behavior

The aggregation of vacancies in alumina crystals drives vacancy migration and redistribution. This study investigates how H proton incorporation alters the vacancy aggregation tendencies in α-Al2O3 and θ-Al2O3 by analyzing aggregation energy variations (Figure 2, Figure 3, Figure 4 and Figure 5). Due to structural differences, α-Al2O3 contains one type each of Al (VAl-oct) and O (VO) vacancies, while θ-Al2O3 exhibits two Al vacancies (VAl-oct and VAl-tet) and one O vacancy (VO).
In the absence of H protons, the vacancy aggregation energies for α-Al2O3 are 0.71 eV (VAl-oct) and −0.21 eV (VO), whereas θ-Al2O3 shows values of 1.72 eV (VAl-oct), 0.34 eV (VAl-tet), and −0.07 eV (VO) (Figure 4 and Figure 5). These results indicate mutual repulsion between VAl vacancies in both phases under natural conditions. The aggregation of Al vacancies in the intrinsic state is thermodynamically unfavorable, which limits Al diffusion via vacancy-mediated mechanisms. Notably, the VAl-oct aggregation energy in θ-Al2O3 is significantly higher than that of VAl-tet in θ-Al2O3 or VAl-oct in α-Al2O3, suggesting that tetrahedral Al vacancies (VAl-tet) are more prone to aggregation. This will provide a low-energy migration pathway for Al atoms from tetrahedral to octahedral sites, thereby facilitating their diffusion. Conversely, VO vacancies exhibit mutual attraction, with θ-Al2O3 displaying a slightly lower aggregation energy (−0.07 eV) than α-Al2O3 (−0.21 eV).
H proton incorporation markedly reduces vacancy aggregation energies. For α-Al2O3, VAl-oct and VO energies decrease by 0.52 eV (to 0.19 eV) and 2.03 eV (to −2.24 eV), respectively. In θ-Al2O3, reductions of 0.15 eV (VAl-tet), 1.51 eV (VAl-oct), and 1.19 eV (VO) are observed (Figure 4 and Figure 5). These reductions facilitate vacancy defect generation, particularly for O vacancies, which exhibit greater energy sensitivity than Al vacancies. Upon the introduction of hydrogen protons, the aggregation behavior of oxygen vacancies is significantly enhanced. The aggregation of multiple oxygen vacancies will promote the formation of larger defect clusters, which may further evolve into nanoscale voids within the lattice.
The observed vacancy interactions arise not from classical forces but from charge imbalance effects and electron trapping induced by vacancy formation [38,40]. H protons amplify these interactions, enhancing O vacancy aggregation while weakening Al vacancy repulsion. In α-Al2O3 and θ-Al2O3, O atoms carry negative charges. O vacancy creation leaves two positive charge centers, promoting attraction to electrons or negatively charged species. H protons increase the positive charge of O vacancies, further driving aggregation. Conversely, Al vacancies generate three negative charge centers due to missing positively charged Al atoms. While these vacancies initially attract positive charges, dominant repulsion from neighboring O ions suppresses aggregation. H proton incorporation mitigates the negative charge of Al vacancies, reducing this repulsion.

3.4. Atomic Migration in Alumina Phases

Extensive research has demonstrated that water vapor critically influences the oxidation dynamics at TBC interfaces, particularly by prolonging the metastable θ-Al2O3 phase formation and altering its transition to the stable α-Al2O3 phase. This study investigates the mechanistic role of H doping in modulating the migration of Al and O atoms within α-Al2O3 and θ-Al2O3 supercells. The analysis accounts for two key factors, as follows: (i) during Al migration between octahedral sites, atoms traverse tetrahedral interstitial positions; (ii) oxygen vacancies are introduced during O migration, as H protons preferentially occupy these lattice vacancies.
Figure 6 presents the migration pathways and energy barriers for Al and O atoms in both α-Al2O3 and θ-Al2O3 phases under H-doped and -undoped conditions. For undoped α-Al2O3, the Al and O migration barriers are 1.98 eV (Al107O162) and 3.69 eV (Al108O160), respectively. The corresponding values for undoped θ-Al2O3 are 1.75 eV (Al63O96) and 4.25 eV (Al64O94). H doping significantly alters these barriers—in α-Al2O3, Al migration increases to 3.36 eV (Al107O162H1), while O migration decreases to 2.83 eV (Al108O160H1). Conversely, θ-Al2O3 exhibits a dramatic increase in the Al migration barrier to 5.06 eV (Al63O96H1) and a reduction in the O migration barrier to 1.76 eV (Al64O94H1). These correspond to net changes of +1.38 eV (Al) and −0.86 eV (O) in α-Al2O3, and of +3.31 eV (Al) and −2.49 eV (O) in θ-Al2O3. The results reveal two distinct effects of H doping. Firstly, H doping inhibits Al migration while enhancing O mobility in both phases. This differential behavior arises from proton interactions with charge carriers—H protons increase Coulombic resistance for Al migration but facilitate oxygen ion mobility through vacancy charge redistribution. Secondly, enhanced O migration promotes oxygen vacancy accumulation while suppressing Al vacancy formation. However, excessive H concentrations may saturate oxygen vacancies, paradoxically hindering O migration. The underlying mechanism involves H-induced electronic structure modifications. Proton doping increases the positive charge density at oxygen vacancy sites, attracting negatively charged oxygen ions via Coulombic interactions, thereby reducing their migration barriers. For Al migration, transient H-Al interactions during atomic displacement elevate energy barriers as Al atoms must overcome additional Coulombic forces from localized protons.

3.5. Alumina Growth with H Proton Incorporation

The crystal structures of θ-Al2O3 and α-Al2O3 exhibit distinct differences in the distribution of Al atoms and the arrangement of O sublattices (Figure 1). In θ-Al2O3, Al atoms occupy tetrahedral interstitial sites within a face-centered cubic oxygen sublattice, whereas in α-Al2O3, Al atoms reside in octahedral interstitial sites within a densely packed hexagonal oxygen sublattice. Early-stage alumina phases (γ, δ) demonstrate oxygen sublattice configurations and Al distributions that are more compatible with θ-Al2O3 than with α-Al2O3 [11,12,13,14]. This structural compatibility reduces nucleation energy barriers and favors lattice matching during initial growth, as the θ-phase requires smaller atomic rearrangements compared to the α-phase. Consequently, θ-Al2O3 preferentially forms during the early oxidation stages at TBC interfaces, as illustrated by the lattice structure schematic in Figure 7.
Water vapor exposure facilitates H2O dissociation into H+ and OH on oxide surfaces, with OH further decomposing to release O2− for oxide growth [41,42,43,44,45,46]. Meanwhile, H+ diffuses into the oxide lattice, altering vacancy formation and atomic migration (Figure 7). As shown in Table 2, H+ significantly reduces the Al and O vacancy formation energies in both θ- and α-Al2O3. However, θ-Al2O3 exhibits lower vacancy formation energies compared to α-Al2O3 under H+ influence, whereby the tetrahedral Al vacancy (VAl-tet) energy in θ-Al2O3 is 0.77 eV lower than its octahedral Al vacancy (VAl-oct) energy, as well as being 1.61 eV lower than the VAl-oct energy in α-Al2O3. Similarly, oxygen vacancy (VO) formation energy in θ-Al2O3 is 1.27 eV lower than in α-Al2O3. These reductions promote the preferential growth of Al and O vacancies in θ-Al2O3, providing abundant migration sites for sustained θ-phase growth while suppressing its transformation to the α-phase. This mechanism aligns with experimental observations of θ-Al2O3 stabilization under water vapor environments [26,27].
In the absence of H+, Al vacancies in α-Al2O3 and θ-Al2O3 exhibit mutual repulsion, while O vacancies tend to aggregate (Figure 4 and Figure 5). H+ reduces Al vacancy repulsion and enhances O vacancy aggregation by lowering their respective interaction energies. For Al vacancies, the aggregation energies in θ- and α-Al2O3 reduce slightly to 0.21 eV (VAl-oct), 0.19 eV (VAl-tet), and 0.19 eV (VAl-oct) under H+ influence; however, they remain repulsive, limiting vacancy redistribution. In contrast, the O vacancy aggregation energies decrease sharply to −2.24 eV (α-Al2O3) and −1.26 eV (θ-Al2O3), promoting vacancy clustering. This disrupts the hexagonal oxygen sublattice in α-Al2O3 and induces lattice misalignment, further hindering phase transition. In addition, H+ preferentially occupies O vacancy sites in both phases (Figure 6), impeding oxygen sublattice shear deformation and reducing Al migration pathways. While H+ lowers O migration barriers, facilitating O atom mobility and oxide growth, it simultaneously immobilizes near Al vacancies, increasing the Al migration barrier in θ-Al2O3 by 1.7 eV compared to α-Al2O3. This dual effect stabilizes θ-Al2O3 by promoting O-driven growth while restricting the Al rearrangement required for α-phase formation.

4. Concluding Remarks

First-principles calculations were employed to investigate vacancy defect formation, aggregation, and migration in α-Al2O3 and θ-Al2O3 crystals, with the explicit consideration of hydrogen (H) incorporation from water vapor. Key findings include the following:
  • Hydrogen protons significantly reduce the formation energies of aluminum (Al) and oxygen (O) vacancies in both α-Al2O3 and θ-Al2O3. This promotes the generation of tetrahedral Al vacancies (VAl-tet), octahedral Al vacancies (VAl-oct), and O vacancies (VO). The resulting local lattice disordering stabilizes metastable alumina phases by mimicking their defect-rich structures, enabling the transient growth of metastable θ-Al2O3 under operational conditions.
  • Hydrogen preferentially occupies O vacancy sites in both α-Al2O3 and θ-Al2O3, while stabilizing near Al vacancies at low-energy configurations. High H concentrations hinder O migration by saturating VO sites, disrupting the oxygen sublattice shear that is required for the θ- to α-Al2O3 transition. This inhibits the structural reorganization from a metastable face-centered cubic oxygen arrangement to the thermodynamically stable hexagonal close-packed α-Al2O3 structure.
  • Hydrogen enhances the clustering of O vacancies while suppressing repulsion between Al vacancies. Aggregated O vacancies redistribute to form migration pathways for Al and O atoms, sustaining metastable phase growth by expanding oxygen sublattice disorder and defect-mediated Al mobility.
  • Hydrogen suppresses Al migration but accelerates O diffusion in both phases. While enhanced O mobility facilitates metastable phase growth through defect propagation, the inhibition of Al migration prevents structural relaxation into the steady-state α-Al2O3 configuration. This kinetic imbalance perpetuates a disordered alumina matrix, favoring prolonged metastability.
These results reveal that hydrogen ingress from water vapor stabilizes metastable θ-Al2O3 by amplifying defect generation, altering vacancy dynamics, and disrupting atomic migration, which is critical for phase transitions. These findings provide atomic-scale insights into the degradation mechanisms of thermal barrier coatings in humid environments, establishing a theoretical foundation for the design of hydrogen- and oxidation-resistant coatings via defect engineering and hydrogen mitigation strategies.

Author Contributions

Conceptualization: B.Y. and X.G.; methodology: K.L.; software: K.L.; validation: W.S. and A.A.B.; formal analysis: K.L.; investigation: K.L.; resources: S.S.; data curation: W.S. and A.A.B.; writing—original draft preparation: K.L.; writing—review and editing: S.S., B.Y., and X.G.; supervision: S.S. and X.G.; funding acquisition: B.Y. and X.G. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 52265021 and 52465018), the Specialized Research Fund for the First-Class Disciplines of Education Bureau of Inner Mongolia (No. YLXKZX-NKD-038), and the Central Government in Guidance of Local Science and Technology Development (No. 2022ZY0074).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. (a) A (3 × 3 × 1) α-Al2O3 supercell; (b) a (1 × 4 × 2) θ-Al2O3 supercell. Al atoms in tetrahedral (green) and octahedral (blue) coordination are distinguished, while O atoms are shown in red.
Figure 1. (a) A (3 × 3 × 1) α-Al2O3 supercell; (b) a (1 × 4 × 2) θ-Al2O3 supercell. Al atoms in tetrahedral (green) and octahedral (blue) coordination are distinguished, while O atoms are shown in red.
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Figure 2. Atomic structure of α-Al2O3, highlighting octahedrally coordinated Al atoms (blue), the oxygen sublattice (red), and H atoms (yellow). Black arrows indicate lattice distortion trends.
Figure 2. Atomic structure of α-Al2O3, highlighting octahedrally coordinated Al atoms (blue), the oxygen sublattice (red), and H atoms (yellow). Black arrows indicate lattice distortion trends.
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Figure 3. Atomic structure of θ-Al2O3, showing tetrahedrally (green) and octahedrally (blue) coordinated Al atoms, the oxygen sublattice (red), and H atoms (yellow). Black arrows denote lattice distortion trends.
Figure 3. Atomic structure of θ-Al2O3, showing tetrahedrally (green) and octahedrally (blue) coordinated Al atoms, the oxygen sublattice (red), and H atoms (yellow). Black arrows denote lattice distortion trends.
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Figure 4. Energy changes in single and double Al/O vacancies in α-Al2O3 under undoped and H-doped conditions.
Figure 4. Energy changes in single and double Al/O vacancies in α-Al2O3 under undoped and H-doped conditions.
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Figure 5. Energy changes in single and double Al/O vacancies in θ-Al2O3 under undoped and H-doped conditions.
Figure 5. Energy changes in single and double Al/O vacancies in θ-Al2O3 under undoped and H-doped conditions.
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Figure 6. Migration energy barriers and pathways for (a) Al and (b) O in α-Al2O3, as well as (c) Al and (d) O in θ-Al2O3, comparing undoped and H-doped systems.
Figure 6. Migration energy barriers and pathways for (a) Al and (b) O in α-Al2O3, as well as (c) Al and (d) O in θ-Al2O3, comparing undoped and H-doped systems.
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Figure 7. Atomic-scale schematic of H+ interactions influencing θ-Al2O3 lattice growth.
Figure 7. Atomic-scale schematic of H+ interactions influencing θ-Al2O3 lattice growth.
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Table 1. Bulk modulus, shear modulus, and Young’s modulus of crystalline cells.
Table 1. Bulk modulus, shear modulus, and Young’s modulus of crystalline cells.
Phase Bulk Modulus (GPa)Shear Modulus (GPa)Young’s Modulus (GPa)
α-Al2O3Present model223.26165.75399.56
Reference220.63 [36]162.28 [36]390.98 [36]
θ-Al2O3Present model201.74142.67343.35
Reference199.04 [36]143.65 [36]347.38 [36]
Table 2. Vacancy generation energies for H-doped and -undoped α-Al2O3 and θ-Al2O3.
Table 2. Vacancy generation energies for H-doped and -undoped α-Al2O3 and θ-Al2O3.
PhaseVacancy E f o r m /eV
References
E f o r m /eV
Present Model
E f o r m H /eV
Present Model
δE/eV
α-Al2O3VO6.80 [37,38]6.734.56−2.17
VAl-oct12.13 [37,38]12.016.75−5.26
θ-Al2O3VO6.20 [39]6.113.29−2.82
VAl-oct-12.515.91−6.60
VAl-tet-12.095.14−6.95
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Lv, K.; Sun, S.; Yuan, B.; Guo, X.; Song, W.; Boiko, A.A. First-Principles Analysis of Phase Stability and Transformation Suppression for Hydrogen-Doped Alumina. Coatings 2025, 15, 545. https://doi.org/10.3390/coatings15050545

AMA Style

Lv K, Sun S, Yuan B, Guo X, Song W, Boiko AA. First-Principles Analysis of Phase Stability and Transformation Suppression for Hydrogen-Doped Alumina. Coatings. 2025; 15(5):545. https://doi.org/10.3390/coatings15050545

Chicago/Turabian Style

Lv, Kun, Shiyang Sun, Bo Yuan, Xiaofeng Guo, Weiao Song, and Andrei A. Boiko. 2025. "First-Principles Analysis of Phase Stability and Transformation Suppression for Hydrogen-Doped Alumina" Coatings 15, no. 5: 545. https://doi.org/10.3390/coatings15050545

APA Style

Lv, K., Sun, S., Yuan, B., Guo, X., Song, W., & Boiko, A. A. (2025). First-Principles Analysis of Phase Stability and Transformation Suppression for Hydrogen-Doped Alumina. Coatings, 15(5), 545. https://doi.org/10.3390/coatings15050545

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