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Article

Effects of Pressure on Hydrogen Diffusion Behaviors in Corundum

by
Shun-Feng Yan
1,2,
Lin Li
1,2,*,
Xiao Dong
3,
Xiao-Wei Li
4,
Mao-Wen Yuan
1,5 and
Sheng-Rong Li
1,5
1
State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, 29 Xueyuan Road, Beijing 100083, China
2
Institute of Earth Sciences, China University of Geosciences, 29 Xueyuan Road, Beijing 100083, China
3
Key Laboratory of Weak-Light Nonlinear Photonics, School of Physics, Nankai University, Tianjin 300071, China
4
School of Materials Science and Technology, China University of Geosciences, 29 Xueyuan Road, Beijing 100083, China
5
School of Earth Science and Resources, China University of Geosciences, 29 Xueyuan Road, Beijing 100083, China
*
Author to whom correspondence should be addressed.
Crystals 2025, 15(8), 672; https://doi.org/10.3390/cryst15080672
Submission received: 7 July 2025 / Revised: 17 July 2025 / Accepted: 20 July 2025 / Published: 23 July 2025
(This article belongs to the Section Inorganic Crystalline Materials)
Browse Figures
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Abstract

Hydrogen, as the smallest atom and a key component of water, can penetrate minerals in various forms (e.g., atoms, molecules), significantly influencing their properties. The hydrogen diffusion behavior in corundum (α-Al2O3) under high pressure was systematically investigated using the DFT + NEB method. The results indicate that H atoms tend to aggregate into H2 molecules within corundum under both ambient and high-pressure conditions. However, hydrogen predominantly migrates in its atomic form (H) under both low- and high-pressure environments. The energy barriers for H and H2 diffusion increase with pressure, and hydrogen diffusion weakens the chemical bonds nearby. Using the Arrhenius equation, we calculated the diffusion coefficient of H in corundum, which increases with temperature but decreases with pressure. On geological time scales, hydrogen diffusion is relatively slow, potentially resulting in a heterogeneous distribution of water in the lower mantle. These findings provide novel insights into hydrogen diffusion mechanisms in corundum under extreme conditions, with significant implications for hydrogen behavior in mantle minerals at high pressures.

1. Introduction

Hydrogen diffusion, both on the surface and within the interior of minerals, has garnered significant attention from researchers [1,2,3,4,5,6,7]. Numerous studies have investigated hydrogen diffusion on the surface of magnesium [8], periclase [2], quartz [3], corundum [4,5,6], and steel [9,10,11]. As the smallest atom, hydrogen can penetrate minerals in various forms (e.g., atomic, ionic, or molecular states), significantly influencing their structural, electrical, and optical properties [11,12,13,14,15,16,17,18,19,20]. The behavior of hydrogen is particularly critical in the context of Earth’s deep interior. Present as a component of water, hydrogen is widely distributed in the planet’s mantle and significantly affects the physical and chemical properties of mantle minerals [21], including the rheology [22], seismic wave velocities [23], phase transitions [24], and electrical conductivity [25,26].
In the mantle, corundum (α-Al2O3) is a potential host for hydrogen and can form through several geological processes. It is known to be a decomposition product of common hydrous minerals at high pressure and temperature [27,28,29,30,31]. Additionally, its primary component, Al2O3, is transported into the deep Earth via the subduction of oceanic crust. Mid-ocean ridge basalt (MORB), for instance, can contain up to 16 wt.% Al2O3 and acts as a significant carrier of this component into the Earth’s interior [32,33]. Subsequent high-pressure phase transformations within subducting slabs, particularly under alkali-depleted conditions, can lead to the formation of single-phase corundum [34,35]. The existence of corundum in the deep mantle is supported by direct evidence, as it has been discovered as inclusions in diamonds sourced from the lower mantle [36,37]. Given its formation pathways and its exceptional stability under extreme pressure (phase transitions only occur above 110 GPa [38]), corundum is a highly relevant mineral for studies of the deep Earth. Despite its geological importance, however, research on hydrogen in corundum has been limited. While early work focused on hydrogen dissolution and surface diffusion [4,5,6,39,40,41], limited attention has been given to the diffusion properties of hydrogen within the interior of corundum, particularly under the high-pressure, high-temperature conditions relevant to the mantle. Fundamental questions remain unanswered, such as the stability and aggregation state of hydrogen under such extreme conditions, and the quantitative relationship between pressure, temperature, and the diffusion coefficient.
In this study, the diffusion behavior of hydrogen in corundum under increasing pressure is comprehensively investigated using the first principles theory combined with the climbing image nudged elastic band (CI-NEB) method [42,43]. The results indicate that the energy barriers for both H atoms and H2 molecules migrating in corundum increase with pressure, owing to the narrowing diffusion channels as external pressure increases. Notably, the findings demonstrate that hydrogen tends to diffuse as individual H atoms rather than in the H2 molecular form, even under pressures up to 90 GPa. Additionally, hydrogen diffusion weakens nearby chemical bonds. The attempt frequency of H atoms in corundum was thoroughly explored as a function of temperature and pressure. Consequently, the precise diffusion coefficient of hydrogen in corundum under extreme conditions can be calculated using the Arrhenius equation [44,45]. This study provides valuable insights into hydrogen diffusion in corundum under high-pressure conditions and encourages further research into particle diffusion in minerals under extreme environments.

2. Computational Methods

The calculations of this work were performed using density functional theory (DFT) within the framework of the Vienna Ab Initio Simulation Package (VASP) v6.4.2 [46,47,48,49,50]. The project-augmented wave (PAW) method and the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) [51,52], both implemented in VASP, were employed for the pseudopotentials and exchange-correlation functionals. The pseudo-valence electron configurations of Al [s2p1], O [2s22p4], and H [1s1] were employed in all the calculations. An energy cutoff of 600 eV for the plane wave basis was applied for the geometry optimizations and property calculations of corundum systems containing both hydrogen atoms and H2 molecules. All atomic positions and the supercell size were optimized to equilibrium using the conjugate gradient algorithm, with the forces on the atoms reduced to less than 0.02 eV/Å in all directions [53,54]. The Brillouin zone integrations used a Γ-centered k-point grid for the 2 × 2 × 1 supercell of corundum crystals, containing 72 O atoms and 48 Al atoms [6,55]. Geometry optimizations were performed using a 9 × 9 × 4 Γ-centered k-point grid, while other calculations used a 4 × 4 × 3 k-point grid. The calculated lattice constants for bulk α-Al2O3 were 9.6116 Å for a and b, and 13.1122 Å for c. The pressures applied to the H-bearing corundum systems were uniform, meaning equal pressure was applied in all directions. The climbing image nudged elastic band (CI-NEB) method was used to optimize the highest intermediate image and accurately locate the saddle point [42,43], providing more precise transition states and migration energy barriers. This method has been successfully applied to various problems, including studies of particle diffusion in minerals. To estimate the energy barriers of H and H2 diffusion in corundum, three linear interpolation intermediate images were constructed between the initial and final positions of H and H2 along the diffusion pathways, and the CI-NEB algorithm was applied to each case. To further explore the electronic distribution around the hydrogen atom and H2 molecule, the electron localization function (ELF) for the H-bearing corundum system was calculated at both the energy minimum and saddle points. A quantitative charge distribution analysis in H-bearing corundum systems was performed using Bader charge analysis [56]. The attempt frequencies of hydrogen atoms in 2 × 2 × 1 supercells of corundum under varying pressures and temperatures, modeled as canonical ensembles (constant particle number N, volume V, and temperature T), were computed using ab initio molecular dynamics (AIMD) simulations in VASP. Each simulation ran for 6000 timesteps with a timestep of 0.5 fs, totaling 3 ps. To isolate the attempt frequency of hydrogen, all Al and O atoms were fixed, allowing only the H atom to move freely, thereby excluding interference from the atomic vibrations of Al and O atoms. Finally, the diffusion coefficient of hydrogen in corundum was calculated using the Arrhenius equation [44,45].

3. Results and Discussion

Firstly, various possible incorporation sites for hydrogen in corundum were tested, and the most stable site was identified as the center of an oxygen octahedron composed of six oxygen atoms, as shown in Figure 1. Subsequently, the formation energies of the hydrogen atoms or molecules incorporated into corundum were calculated using the following formula:
E f = E α − A l 2 O 3 : H − E α − A l 2 O 3 − E H
where E f , E α − A l 2 O 3 : H , E α − A l 2 O 3 , and E H represent the formation energy, the total energy of the hydrogen-bearing corundum system, the pristine corundum system, and hydrogen, respectively. The calculated formation energies for H (H2) entering into corundum at 0 GPa and 90 GPa are 0.85 eV (−2.23 eV) and 1.98 eV (−0.92 eV), respectively. This indicates that when hydrogen atoms enter corundum, they absorb heat or perform external work, whereas hydrogen molecules release heat upon entry. Additionally, we examined the effect of zero-point energy (ZPE) on the energy barrier for hydrogen diffusion in corundum. The results showed a ZPE correction of −0.1567 eV for a 1.0126 eV diffusion barrier at 0 GPa, and −0.2218 eV for a 1.7170 eV barrier at 90 GPa. For simplicity, this ZPE correction has not been included in the diffusion barriers reported in this study.

3.1. Hydrogen Atom Diffusion in Corundum

To investigate the diffusion behavior of hydrogen atoms in corundum, the climbing image nudged elastic band (CI-NEB) algorithm, combined with density functional theory (DFT), was employed to calculate the energy barrier for a single hydrogen atom (H) diffusing along the minimum energy pathway—i.e., the path of least resistance, which defines the true migration coordinate—in corundum at various pressures. The CI-NEB simulation model was applied to a corundum supercell containing a single hydrogen atom, as illustrated in Figure 1.
An illustration of the diffusion pathway and the diffusion energy barrier for a hydrogen atom (H) in corundum under 0 GPa is shown in Figure 2a–c. To identify the preferred migration path and form of hydrogen in corundum, we tested three potential migration paths from the center of one oxygen octahedron to the center of another. As seen in Figure 2c, two distinct diffusion paths for the H atom are evident: a blue path and a fuchsia path, with the green path being equivalent to the blue one. The H atom migrates with an energy barrier of 1.01 eV along the blue path and 1.76 eV along the fuchsia path at 0 GPa. These values are slightly lower than those calculated by Mao (1.27 eV), Wang (1.10 eV), and Belonoshko (1.24 eV) using the NEB method, but they are consistent with the results from Pan, who employed the CI-NEB method [4,40,57,58]. Subsequently, we calculated the energy barriers for H atom diffusion in corundum under pressures of 20 GPa, 40 GPa, 60 GPa, 80 GPa, and 100 GPa, as shown in Figure 2d. The results indicate that the energy barrier for H atom migration in corundum increases almost linearly (from 1.01 eV to 1.77 eV) as the pressure rises from 0 GPa to 100 GPa. This increase is attributed to the decreasing interatomic spacing in corundum with increasing pressure, which reduces the diameter of the migration channel along the minimum energy pathway, as shown by the black dotted line in Figure 2d. Consequently, the interaction strength between atoms increases with pressure, making it more difficult for the H atom to migrate in corundum, and leading to a progressively higher diffusion energy barrier.
The electronic properties of hydrogen diffusion in corundum can be analyzed through the partial density of states (PDOS), Bader charge analysis, and the ELF. Figure 3 presents the PDOS of H-bearing corundum (at the energy minimum and saddle point) under different pressures at 0 K. As shown in Figure 3c,e, there are electronic states near the Fermi level, indicating that H-bearing corundum exhibits some degree of metallicity. This characteristic remains present even under a pressure of 90 GPa, as illustrated in Figure 3d,f. Notably, compared with the PDOS of pristine corundum (see Figure 3a,b), the electronic states near the Fermi level in the H-bearing corundum system are mainly introduced by the incorporated hydrogen. Furthermore, the PDOS near the Fermi level is primarily contributed by the s orbital of the H atom and the p orbital of the O atoms (see Figure 3c–f), implying that H predominantly interacts with O.
The Bader charge analysis indicates that the H atom carries a charge of 1.23 e (1.39 e) and 1.22 e (1.44 e) under 0 GPa and 90 GPa in corundum at the energy minimum (and at the saddle point), respectively. Pressure induces charge transfer from the corundum lattice to the H atom. The two-dimensional (2D) ELF of H atom diffusion in corundum is displayed in Figure 4a,b. By comparing Figure 4a,b, it is evident that, as the H atom moves along the migration channel, the electrons (represented by the red and green colors) surrounding the H atom do not experience the same squeezing and deflection observed in other minerals [59]. Instead, the electrons consistently remain around the H atom, a property that persists even under high pressure.

3.2. Hydrogen Molecule Diffusion in Corrundum

In this section, we first investigated the stable configurations of two hydrogen atoms (H) and two hydrogen molecules (H2) in the corundum supercell under 0 GPa and 90 GPa, respectively. The computed total energies of different configurations, varying with the distance between two hydrogen atoms and molecules, are shown in the insets of Figure 5. Figure 5a,b illustrate that the configurations with smaller hydrogen atomic distances exhibit significantly lower total energies than those with larger distances, indicating that hydrogen atoms dispersed in corundum have a tendency to aggregate and form H2 molecules. Furthermore, Figure 5c,d demonstrate that the configurations where multiple H2 molecules occupy a single oxygen octahedron are unstable, whereas the most stable configuration occurs when a single H2 molecule occupies an oxygen octahedron, a property that persists even under high pressure. While the favorable formation energy of H2 provides a strong thermodynamic driving force for isolated H atoms to aggregate, the kinetics of this process are critically dependent on their diffusion barrier.
To further investigate the behavior of hydrogen molecule diffusion in corundum, we calculated the minimum energy pathways and energy barriers for H2 diffusion in corundum under various pressures using the CI-NEB method. Figure 6a,b illustrate the diffusion pathway and the corresponding energy barrier of 2.30 eV (3.20 eV) for H2 migration in corundum under 0 GPa. As pressure increases, the energy barrier for H2 migration also increases, rising from 2.30 eV (3.20 eV) at 0 GPa to 3.43 eV (5.89 eV) at 90 GPa. This increase is attributed to the decreasing interatomic spacing between Al and O atoms around the H atom at the saddle point as pressure increases, which hinders the movement of the H2 molecule and raises the energy barrier. A comparison between Figure 2 and Figure 6 reveals that the diffusion energy barriers for H2 molecules are higher than those for H atoms. Despite having the same diffusion pathways in corundum, hydrogen prefers to migrate in its atomic state, even under high pressures.
Figure 7a,c show the presence of electronic states near the Fermi level, indicating that H2-bearing corundum, like H-bearing corundum, exhibits metallic characteristics. This property remains under 90 GPa, as shown in Figure 7b,d. This behavior differs from that of periclase, another H2-bearing mineral in the lower mantle, where periclase containing H2 behaves as a semiconductor. The PDOS near the Fermi level is primarily contributed by the s orbital of H and the p orbital of O atoms (see Figure 7a–d), suggesting that H primarily interacts with O. The Bader charge analysis shows that the H2 molecule carries a charge of 2.27 e (2.40 e) at 0 GPa and 2.33 e (2.49 e) at 90 GPa at the energy minimum (at the saddle point), respectively (Figure 4c,d). Similar to H atoms, pressure induces charge transfer from the corundum lattice to H2. Figure 4c,d display the 2D ELF of H2 molecule diffusion in corundum under different pressures. By comparing Figure 4a,b, it is observed that pressure does not significantly restrict the range of electronic motion.

3.3. Diffusion Coefficient of Hydrogen in Corundum

The previous discussions did not consider the impact of temperature, although the diffusion behavior at finite temperatures provides valuable insights into hydrogen diffusion in corundum. Therefore, the diffusion coefficient of hydrogen in corundum at various temperatures is examined. To estimate this, the diffusion coefficient is calculated using the Arrhenius equation [44,45] as follows:
D T = a 2 ν e x p − Δ E k B T  
where a represents the migration distance, ν the attempt frequency, Δ E the energy barrier, k B the Boltzmann constant, and T the temperature. The migration distance a is measured as the distance between the initial and final migration sites. The energy barrier Δ E was computed using the CI-NEB method, as described earlier. The attempt frequency ν was determined from DFT-MD calculations [3,57,59]. We calculated the total energy of the H-bearing corundum system, modeled as a canonical ensemble, over varying timesteps under different temperatures and pressures, as shown in Supplementary Figure S1 and Figure S2, respectively.
The attempt frequency of H in corundum at a constant pressure of P = 0 GPa was evaluated across a temperature range from 500 K to 2000 K (see Supplementary Figure S1). As shown in Figure S1, H exhibits several vibrational modes in corundum. The attempt frequency was calculated by counting the periods of the lowest-energy vibrational mode over the total timesteps, as diffusion typically follows the lowest-energy pathway [57]. Consequently, the attempt frequency of H in corundum was obtained at 500 K ( 1.396 × 10 12 Hz), 1000 K ( 1.961 × 10 12 Hz), 1500 K ( 2.356 × 10 12 Hz), and 2000 K ( 2.595 × 10 12 Hz) (Table S1). These values indicate a linear increase in attempt frequency with temperature, as illustrated in Figure S3a.
Next, we investigated the variation in the attempt frequency of H in corundum with pressure (ranging from 0 GPa to 90 GPa) at a constant temperature of T = 1000 K. Based on Figure S2, the attempt frequency of H in corundum was calculated at 0 GPa ( 1.961 × 10 12 Hz), 30 GPa ( 2.148 × 10 12 Hz), 60 GPa ( 2.183 × 10 12 Hz), and 90 GPa ( 2.233 × 10 12 Hz). The results indicate that a sharp increase in attempt frequency occurs at lower pressures (below 30 GPa), followed by a more gradual rise at higher pressures (above 30 GPa), as shown in Figure S3b.
By applying the calculated attempt frequency to the Arrhenius formula, we can determine the diffusion coefficient (D) of hydrogen in corundum under specific temperature (T) and pressure (P) conditions. To validate our predictions, we compared them with available experimental and simulated data, as shown in Figure 8a. The atomic hydrogen diffusivity predicted in this work is consistent with the results calculated by Belonoshko [57], Mao [58], Wang [4], and Pan [40]. The slight discrepancies arise from the different methods used to calculate attempt frequency and activation energy. As shown in Figure 8b, the diffusion coefficient decreases gradually as pressure increases.

4. Discussion and Geological Implications

Alkaline elements in MORB tend to be lost during subduction, as they strongly partition into the melt depending on the hydration and carbonatization levels [62,63]. The remaining alkaline content in MORB further affects Al incorporation, with alkali-depleted conditions potentially stabilizing single-phase corundum [64,65]. At approximately 520 km depth, as davemaoite exsolves, majoritic garnet becomes enriched in Al, and its Al/Si ratio can reach a maximum [66]. As garnet destabilizes at around 670 km depth, additional Al-bearing phases form to accommodate excess Al. When alkaline elements are sufficiently depleted, the phase sequence in MORB changes, resulting in a transformation from garnet to bridgmanite and corundum [34]. Between 670 km and 710 km depth, portions of garnet gradually transform to the NAL phase and stishovite, while the remainder decomposes into bridgmanite [67]. Throughout this process, garnet remains the primary carrier of Al2O3. At the base of the transition zone, the Al2O3 content in garnet can reach approximately 20 wt.% [68]. High-temperature and high-pressure experiments on the MORB system indicate that small amounts of Al2O3 can also dissolve into davemaoite and stishovite, with contents reaching around 4 wt.% and 5 wt.% at the top of the upper mantle, respectively [35,68]. When garnet decomposes at approximately 27 GPa, the lower mantle is then composed of bridgmanite, davemaoite, stishovite, and other aluminum-bearing phases, with Al2O3 primarily entering the lattice of bridgmanite [69]. Studies on the MgSiO3-Al2O3 system demonstrate that Al2O3 solubility in bridgmanite increases with rising temperature and pressure [34,70]. Along a near-normal mantle geotherm, the Al2O3 solubility in bridgmanite rises from 13.6 mol% at 26.3 GPa to 16.0 mol% at 30 GPa [34]. Reducing the Na2O and K2O content in MORB to around 0.7 wt.% leads to the exsolution of 8.5 vol.% Al2O3 as a single phase at approximately 720 km depth; in colder subducting slabs, bridgmanite cannot incorporate all Al2O3, potentially resulting in aluminum-rich phases. Along a colder slab geotherm, the proportion of single-phase Al2O3 may increase to 11.5 vol.% in alkali-depleted MORB at 740 km depth [35]. Consequently, MORB at this depth consists of 17.4 vol.% stishovite, 24.6 vol.% davemaoite, 6.4 vol.% NAL phase, 40.1 vol.% bridgmanite, and 11.5 vol.% corundum [35].
This complex sequence of phase transformations demonstrates that single-phase corundum can indeed exist as a stable phase in specific regions of subducting slabs in the lower mantle. Therefore, the mobility of hydrogen within this phase is a key parameter for understanding the deep water cycle. Hydrous minerals in subducted oceanic crust may transport substantial amounts of water into Earth’s deep interior, potentially reaching as far as the core–mantle boundary [71]. Additionally, the low D/H ratio in lavas from Baffin Island and Iceland suggests the presence of primordial hydrogen reservoirs in the lower mantle [72]. Experimental and observational studies have further indicated a heterogeneous distribution of water in the mantle transition zone [73,74,75]. To evaluate the impact of hydrogen diffusivity on this distribution, the hydrogen diffusion lengths in corundum were calculated using the diffusion coefficients determined in this study, based on the mantle geotherm (Figure 9) [76]. Assuming a mantle convection velocity of 5 cm per year, the estimated timescale for a complete mantle convection cycle is approximately 100–500 million years [25,77,78]. The calculated hydrogen diffusion lengths in corundum show a maximum value of approximately 5.4 km, a distance reached only under the most favorable shallow mantle conditions. This maximum length is largely independent of water content or initial hydrogen incorporation mechanisms. Moreover, hydrogen diffusion may slow further when coupled with cation vacancies [25], resulting in even shorter diffusion lengths.
Consequently, water transported into the lower mantle by subducted slabs and stored in stable phases like corundum is likely to remain locally confined. This slow diffusion provides a powerful microscopic mechanism supporting the hypothesis of a heterogeneous distribution of water throughout the Earth’s lower mantle. However, other factors affecting hydrogen diffusion in corundum, such as grain boundary diffusion and compositional variations, warrant further investigation to validate these conclusions. The limited experimental data on corundum’s water content under mantle conditions also complicates efforts to estimate hydrogen’s contribution to the lower mantle’s electrical conductivity via the Nernst–Einstein equation [25,26]. Thus, additional studies, particularly those aimed at obtaining experimental data, are needed to accurately quantify this effect.

5. Conclusions

In this study, the stability and diffusion behavior of hydrogen (both atomic H and molecular H2) in corundum were systematically investigated under conditions relevant to the Earth’s mantle using first principles calculations. Our main conclusions are as follows:
  • Energetically, isolated hydrogen atoms are unstable within the corundum lattice and have a strong thermodynamic driving force to aggregate and form H2 molecules.
  • Kinetically, however, the diffusion energy barrier for atomic H (e.g., 1.01 eV at 0 GPa) is significantly lower than that for a H2 molecule (2.30 eV at 0 GPa). This indicates that hydrogen’s primary migration mechanism within corundum is as individual atoms, not molecules.
  • The diffusion energy barrier for atomic H increases systematically with pressure, rising from 1.01 eV at 0 GPa to 1.77 eV at 100 GPa. This effect acts to inhibit diffusion.
  • The overall diffusion coefficient, calculated using the Arrhenius equation, incorporates the competing effects of pressure and temperature. Our results show that the diffusion coefficient increases with temperature but decreases with pressure.
  • Under deep mantle geotherm conditions, the effect of high pressure is dominant, resulting in a very low diffusion coefficient. Consequently, even under the most favorable shallow mantle conditions, the maximum diffusion length over a 100–500 million-year mantle convection cycle is estimated to be approximately 5.4 km. This limited diffusion provides strong microscopic support for the hypothesis of a heterogeneous distribution of water in the lower mantle.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/cryst15080672/s1, Figure S1: Attempt frequency of H in corundum varies with increasing temperature. (1 timestep = 0.5 fs; 500 K (a), 1000 K (b), 1500 K (c), and 2000 K (d)); Figure S2: Attempt frequency of H in corundum varies with increasing pressure. (1 timestep = 0.5 fs; 0 GPa (a), 30 GPa (b), 60 GPa (c), and 90 GPa (d)); Figure S3: (a) Attempt frequency of H in corundum varies with temperature under a constant pressure of 0 GPa. (b) Attempt frequency of H in corundum varies with pressure at a constant temperature of 1000 K; Table S1: Diffusion ratios of H in corundum at different temperatures and pressures.

Author Contributions

Conceptualization, L.L. and S.-F.Y.; Data curation, S.-F.Y.; Formal analysis, S.-F.Y. and L.L.; Investigation, L.L. and S.-F.Y.; Methodology, S.-F.Y.; Project administration, L.L.; Resources, L.L.; Supervision, L.L.; Validation, L.L.; Visualization, S.-F.Y.; Writing—original draft, S.-F.Y.; Writing—review and editing, L.L., X.D., X.-W.L., M.-W.Y. and S.-R.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (U2444208, 91962101, 41603063, 41802044, 4160030283), and this work was supported by the High-performance Computing Platform of China University of Geosciences, Beijing.

Data Availability Statement

The data that support the findings of this study are publicly available on Zenodo under the title “Effects of pressure on hydrogen diffusion behaviors in corundum”. The data can be accessed via the following DOI: [https://doi.org/10.5281/zenodo.14474701].

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Crystals 15 00672 g001
Figure 1. Simulation model of a single hydrogen within a corundum 2 × 2 × 1 supercell.
Figure 1. Simulation model of a single hydrogen within a corundum 2 × 2 × 1 supercell.
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Figure 2. (a,b) The energy barrier and migration pathway of the H atom in corundum at 0 GPa; (c) possible migration pathways of H atoms; (d) the energy barrier of H atom migration in corundum and the interatomic distance between Al and O atoms.
Figure 2. (a,b) The energy barrier and migration pathway of the H atom in corundum at 0 GPa; (c) possible migration pathways of H atoms; (d) the energy barrier of H atom migration in corundum and the interatomic distance between Al and O atoms.
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Figure 3. The partial density of states (PDOS) of pristine corundum under 0 GPa (a) and 90 GPa (b). The PDOS of the H atom at the energy minimum under 0 GPa (c) and 90 GPa (d). The PDOS of the H atom at the saddle point under 0 GPa (e) and 90 GPa (f). The vertical dashed line represents the Fermi level.
Figure 3. The partial density of states (PDOS) of pristine corundum under 0 GPa (a) and 90 GPa (b). The PDOS of the H atom at the energy minimum under 0 GPa (c) and 90 GPa (d). The PDOS of the H atom at the saddle point under 0 GPa (e) and 90 GPa (f). The vertical dashed line represents the Fermi level.
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Figure 4. (a,b) The two-dimensional (2D) electron localization function (ELF) of the H atom at the energy minimum and saddle point under 0 GPa and 90 GPa, respectively; (c,d) the 2D ELF of the H2 molecule at the energy minimum and saddle point under 0 GPa and 90 GPa, respectively.
Figure 4. (a,b) The two-dimensional (2D) electron localization function (ELF) of the H atom at the energy minimum and saddle point under 0 GPa and 90 GPa, respectively; (c,d) the 2D ELF of the H2 molecule at the energy minimum and saddle point under 0 GPa and 90 GPa, respectively.
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Figure 5. Total energies as a function of the distance between two H atoms under 0 GPa (a) and 90 GPa (b), and between two H2 molecules under 0 GPa (c) and 90 GPa (d).
Figure 5. Total energies as a function of the distance between two H atoms under 0 GPa (a) and 90 GPa (b), and between two H2 molecules under 0 GPa (c) and 90 GPa (d).
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Figure 6. (a,b) The energy barrier and migration pathway of H2 in corundum at 0 GPa; (c,d) the energy barrier and migration pathway of H2 in corundum at 90 GPa.
Figure 6. (a,b) The energy barrier and migration pathway of H2 in corundum at 0 GPa; (c,d) the energy barrier and migration pathway of H2 in corundum at 90 GPa.
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Figure 7. The PDOS of H2 at the energy minimum under 0 GPa (a) and 90 GPa (b). The PDOS of H2 at the saddle point under 0 GPa (c) and 90 GPa (d). The vertical dashed line represents the Fermi level.
Figure 7. The PDOS of H2 at the energy minimum under 0 GPa (a) and 90 GPa (b). The PDOS of H2 at the saddle point under 0 GPa (c) and 90 GPa (d). The vertical dashed line represents the Fermi level.
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Figure 8. (a) The diffusivity of hydrogen in corundum as a function of temperature at a constant pressure of 0 GPa (For comparison, data from Wang et al. [4], Ramírez et al. [16], Pan et al. [40], Belonoshko et al. [57], Mao et al. [58], Fowler et al. [60], and Kronenberg et al. [61] were replotted from their respective publications). (b) The diffusivity of hydrogen in corundum as a function of pressure at a constant temperature of 1000 K.
Figure 8. (a) The diffusivity of hydrogen in corundum as a function of temperature at a constant pressure of 0 GPa (For comparison, data from Wang et al. [4], Ramírez et al. [16], Pan et al. [40], Belonoshko et al. [57], Mao et al. [58], Fowler et al. [60], and Kronenberg et al. [61] were replotted from their respective publications). (b) The diffusivity of hydrogen in corundum as a function of pressure at a constant temperature of 1000 K.
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Figure 9. Hydrogen diffusion time scales (t) as a function of hydrogen diffusion length scales. The left and right boundaries of the shaded area correspond to the maximum and minimum values of the diffusion range obtained from the simulation.
Figure 9. Hydrogen diffusion time scales (t) as a function of hydrogen diffusion length scales. The left and right boundaries of the shaded area correspond to the maximum and minimum values of the diffusion range obtained from the simulation.
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Yan, S.-F.; Li, L.; Dong, X.; Li, X.-W.; Yuan, M.-W.; Li, S.-R. Effects of Pressure on Hydrogen Diffusion Behaviors in Corundum. Crystals 2025, 15, 672. https://doi.org/10.3390/cryst15080672

AMA Style

Yan S-F, Li L, Dong X, Li X-W, Yuan M-W, Li S-R. Effects of Pressure on Hydrogen Diffusion Behaviors in Corundum. Crystals. 2025; 15(8):672. https://doi.org/10.3390/cryst15080672

Chicago/Turabian Style

Yan, Shun-Feng, Lin Li, Xiao Dong, Xiao-Wei Li, Mao-Wen Yuan, and Sheng-Rong Li. 2025. "Effects of Pressure on Hydrogen Diffusion Behaviors in Corundum" Crystals 15, no. 8: 672. https://doi.org/10.3390/cryst15080672

APA Style

Yan, S.-F., Li, L., Dong, X., Li, X.-W., Yuan, M.-W., & Li, S.-R. (2025). Effects of Pressure on Hydrogen Diffusion Behaviors in Corundum. Crystals, 15(8), 672. https://doi.org/10.3390/cryst15080672

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