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α-Al2O3 (0001) interface: A first-principles study
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Hydrogen diffusion mechanism on ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface: A first-principles study L.Y. Wang a , F. Sun a,∗ , Q.L. Zhou b , D.M. Liao a , Y.Z. Jia a , L.H. Xue a , H.P. Li a , Y.W. Yan a a b
State Key Laboratory of Material Processing and Die & Mould technology, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China Faculty of Science, Shizuoka University, Shizuoka 422-8529, Japan
h i g h l i g h t s • The ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface structural model was established. • The adsorption sites and adsorption energy of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface were calculated by density functional theory, and transition states of adsorption sites were determined based on transition-state search.
• The hydrogen resistance mechanism of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface was discovered by first-principles.
a r t i c l e
i n f o
Article history: Received 30 October 2016 Received in revised form 7 May 2017 Accepted 8 May 2017 Available online xxx Keywords: ␣-AlPO4 ␣-Al2 O3 Interface First-principles Tritium permeation barriers
a b s t r a c t ␣-AlPO4 (0001)/␣-Al2 O3 (0001) fabricated by selective laser sintering could improve the performance at protection against H permeation compared with that of single phase ␣-Al2 O3 and ␣-AlPO4 . In this study, the possible interfacial structures, thermodynamics and kinetics of hydrogen diffusion in heterojunction ␣-AlPO4 (0001)/␣-Al2 O3 (0001) coating were investigated based on the density functional theory. The adsorption energy and the adsorption sites are calculated in order to obtain the most stable configuration. The hydrogen isotopic diffusion in heterojunction ␣-AlPO4 (0001)/␣-Al2 O3 (0001) is also compared with that in ␣-Al2 O3 (0001) or ␣-AlPO4 (0001) surface. The interfacial binding illustrates that hydrogen is more difficult to diffuse through the grain compare with ␣-Al2 O3 (0001) or ␣-AlPO4 (0001). Due to the higher saddle point energy of hydrogen migration and potential well, the hydrogen resistivity property of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) is better than the single phase materials. The interface of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) is predicted to be effective at suppressing hydrogen permeation. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Operating of radioactive tritium, optimizing of tritium balance and controlling tritium inventory play crucial roles in fusion reactors similar to the International Thermonuclear Experimental Reactor (ITER). The utilization of a coating, namely, hydrogen permeation barrier (HPB), deposited on structural material of steel is an effective way to hinder tritium migration [1]. The hydrogen permeation barrier is one of the key technological developments of fusion reactor cladding, and is an important safeguard to reach the safety tritium radioactive environmental standards [2]. There are several materials posing as formidable candidates for tritium permeation barrier (TPB) coatings, such as the BN [3], Cr2 O3 [4], ZrO2 [5], Er2 O3 [6] and Y2 O3 [7]. Among all of the HPB materials, Al2 O3
∗ Corresponding author. E-mail address: [email protected] (F. Sun).
[8–14] has received the most widespread attention. Owing to low permeability, low conductivity, structural stability, corrosion resistance, the feasibility of the process, and so on, the ␣-Al2 O3 coating was carried out earlier and has become one of the tritium candidate coating materials of fusion reactors [15,16]. Tritium barrier effect of the ␣-Al2 O3 coating was corroborated by the experiment, and its mechanism was discovered. For hydrogen isotopes permeation through HPB material, the hydrogen isotopes could be absorbed on the surface of the upstream side and firstly dissociated into atoms, then dissolved into the material, followed by diffusing through the material, and finally recombining into molecules on the downstream side [17,18], which is calculated based on first-principles. First-principles is widely used in the H diffusion and obtains the H site. Many researchers have obtained the properties and mechanisms of HPB through first-principles. Hydrogen sites are calculated in previous density functional theory (DFT)-local density approximation (LDA) at a tetrahedral site in bulk FeAl [19]. Johnson
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et al. have calculated the hydrogen site on the FeAl (110) surface by GGA-PBE (Perdew-Burke-Ernzerh), while hydrogen adsorbs on top of Al atoms of the FeAl (100) surface [20]. Zhang et al. [21] utilized PW91 (Perdew-Wang)-GGA (generalized gradient approximation) to carry out first-principles total energy calculations in ␣-Al2 O3 /FeAl, and revealed the mechanism of hydrogen diffusion in the interfacial slab. Next, thin ceramic coatings, such as SiO2 , act as TPB material to suppress tritium permeation through structural materials [22]. The ␣-AlPO4 crystal structure is derived from the SiO2 . The investigation of ␣-AlPO4 , whose tritium simulation has not been reported, could reveal the effect of tritium resistance to the tetrahedral crystal. Moreover, the hydrogen isotope diffusion mechanism from the ␣-Al2 O3 to ␣-AlPO4 is unknown. The diffusion of hydrogen isotopes and stability will depend on the structure of the oxide interface, and the lattice mismatch degree between the components further affects the performance of HPB [21]. Therefore, the diffusion of tritium in ␣-Al2 O3 and ␣-AlPO4 interface region, which is also lacking in a clear structure, is distinct from that in single phase ␣-Al2 O3 and ␣-AlPO4 . The simulation can reveal the diffusion mechanism of tritium to ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface and predict the new material of HPB. It is reasonable to do theoretical studies for diffusion of hydrogen in ␣-AlPO4 (0001)/␣Al2 O3 (0001). In the present paper, the structure of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface was established and relaxed. Macroscopic experiments have found that hydrogen isotopic permeation through such aluminum rich coating based HPB is predominantly controlled by hydrogen diffusion in bulk [23,24]. Thus it is reasonable to use hydrogen atoms instead of tritium atoms for simulation. Based on the interface structure, composite interfacial adsorption sites and the adsorption energy were also calculated by first-principles calculation. Utilizing transition-state search method by Dmol3, the diffusion process of H atoms from ␣-AlPO4 (0001) into the ␣-Al2 O3 (0001) were then also well-studied in this paper.
2. Computational method and model 2.1. Method Dmol3 [16] program package in Materials Studio 8 of Accelrys Inc. by first-principles was used to calculate total energy in the PW91 [25] -GGA. The parameters used in the ␣-Al2 O3 calculation [26] were selected most likely on account of the lack of reports on hydrogen isotope penetration to ␣-AlPO4 . The double numerical quality basis set with polarization functions (DNP) [27] had to be adapted, and the semi-core pseudopotential [28] could be utilized. Spin-polarized and Monkhorst-Pack mesh [29] k-points of 3 × 3 × 1 for bulk and surface calculations were selected. All calculations were utilized a convergence tolerance of energy of 2.0 × 10−4 Ha/atom (1 Ha = 27.21 eV), a maximum force of 0.004 Ha/Å, and a maximum displacement of 0.005 Å, allowing the energy of the model to converge. Maximum SCF cycles were turned into 200. The cut-off energy were 300 eV. The three potentials chosen to optimize the structure of ␣AlPO4 include GGA, LDA, and PBE. The result demonstrates that the PW91-GGA is the best suitable potential to approach the experiment result. Lattice constants were a = b = 4.949 Å, c = 10.945 Å for ␣-AlPO4 which is consistent with the experimental value a = b = 4.944 Å, and c = 10.946 Å. The optimized lattice constants for the bulk ␣-Al2 O3 were a = b = 4.806 Å and c = 13.133 Å which were the same parameters to the experimental value. Adsorption energy is defined as: Eads = E[slab+H] − (E[slab] + E[H] ) where E[slab+H] , E[slab] , and E[H] are the calculated total energy of the H atom on the ␣-AlPO4 (1000)/␣Al2 O3 (0001) slab, a clean ␣-AlPO4 (1000)/␣-Al2 O3 (0001) slab and
a gas-phase H atom. With the definition, negative values of Eads signifies adsorption is more stable than the corresponding clean surface and H atom. The complete linear synchronous transit/quadratic synchronous transit (LST/QST) method is used to locate the transition states (TS) for hydrogen dissociation and hydrogen diffusion. Frequencies of hydrogen are determined by all critical points identified on the potential energy surface (PES) to determine minima and transition states.
2.2. Established and relaxed geometric structures The ␣-Al2 O3 belongs to the hexagonal close pack (hcp). The O atoms in the unit cell are the cubic close-packed structure on ␣-Al2 O3 (0001). Among the numerous ␣-Al2 O3 crystal planes, ␣Al2 O3 (0001) is the most stable juxtaposed with ␣-Al2 O3 (1–102) and ␣-Al2 O3 (11–20) [30]. The lattice constants of ␣-Al2 O3 (0001) are a = b = 4.754 Å, c = 12.988 Å compared with the experimental values (a = b = 4.759 Å, c = 12.992 Å [31]). ␣-AlPO4 has a hexagonal structure whose close-packed plane is (0001). The crystal structure of ␣-AlPO4 (0001) whose lattice constants are a = b = 4.944 Å, c = 10.946 Å is shown in Fig. 1. In crystallography, lattice mismatch degree is defined as: ı = (aˇ − a˛ )/a˛ Where a␣ , aˇ refers to the lattice constant. With the calculation, ␣-AlPO4 (0001) and ␣-Al2 O3 (0001) have small lattice mismatch degree with 2.795% (less than 5%). It implies that this interface is a coherent interface [32]. (2 × 2) Supercell flat slab model was used to simulate the interface configuration. To simulate the actual surface, it is necessary to add a sufficiently large vacuum in the direction perpendicular to the surface of the ␣-AlPO4 . Interaction of the adjacent unit cell can be ignored when the vacuum layer spaced between the alumina surfaces equals to 15 Å [21]. Therefore, the interfacial lattice constants are a = b = 9.698 Å, c = 40.000 Å. As the structure shown in Fig. 1(A), a possible mechanism contributing to the instability of the structure is the existence of a separate oxygen atom at the interface. With the addition of an Al atom, the total energy of the interface declined by 11.94 eV compared with the sum of original structure’s energy and single Al atomic energy. Consequently, Al atoms were added to relax all geometric structures. For the cyclical principle, 13 kinds of supercell flat slab models were established, having six possible configurations, as shown in Fig. 1(B). The final geometric structure of the ␣-Al2 O3 (0001)/␣-AlPO4 (0001) slab is shown in Fig. 2. Two slabs are made of 22 layers. The ␣-AlPO4 (0001) surface was modeled by a slab consisting of 10 layers, whereas ␣-Al2 O3 (0001) surfaces were modeled by a slab composed of 12 layers (i.e., four O layers). Compared with others, the structure, as shown in Fig. 1(B) (b), was thought as the general construction in the material because it is the most representative structure. As shown in Fig. 2, the O5-Al3-O4 bond angle is 137.135◦ in the optimized structure which has smaller repulsive force compared with it in the original structure. In the original structure, the distances of Al3-O4, Al3-O5, Al3-O6 and Al3-O7 are 2.192 Å, 1.978 Å, 1.727 Å and 1.850 Å, respectively. With the relaxed geometric calculation by Dmol3, the distances of Al3-O4, Al3-O5, Al3-O6 and Al3-O7 are 1.812 Å, 2.012 Å, 1.787 Å and 1.826 Å, respectively. The interatomic distances (Al-O) in the interface region of both slabs are very close to corresponding experimental values (1.86-1.97 Å [26]). The result considers that proper binding between ␣-AlPO4 (0001) and ␣-Al2 O3 (0001) was obtained, providing support to the real relevance of the models.
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Fig. 1. Established geometric structures of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface. (A) One of the original structure of interface without Al atom. (B) Six possible structures of interface with the addition of an Al atom.
Fig. 3. Potential energy curve of hydrogen at various positions of the ␣-AlPO4 (0001)/Al2 O3 (0001) interface. A, B, C, D, E, F, G, H, and I are the nine stable adsorption sites.
Fig. 2. Relaxed structure of ␣-Al2 O3 (0001)/␣-AlPO4 (0001) and adsorption sites and hydrogen atom diffusion roads in magnified view.
3. Result and discussion 3.1. Interface effect on stability of hydrogen H was placed on the surface sites and at the interstitial sites in the interface of ␣-AlPO4 (0001)/␣-Al2 O3 (0001). The atomic configurations for H-occupied sites are shown in Fig. 1 of Electronic Supplementary information. The potential energy curve of hydrogen at various positions are displayed in Fig. 3. The stable adsorption
sites are indicated in Fig. 2. H atom was located at 0.5 Å (less than the bond length of the H O bond) above each site, and was then relaxed to observe whether the H atom could exist around the adsorbed atoms. For an isolated hydrogen atom, the top site of Al1 is an unstable adsorption site, and the top sites of Al2 and Al3 are metastable adsorption sites. Due to the distance between A-site and P1 being 2.981 Å, the location of A-site is similar to it in ␣-AlPO4 (0001). The adsorption energies of H atoms in A, B, and C is −0.26 eV, −0.78 eV, and −1.23 eV respectively. In single phase ␣-AlPO4 (0001), as shown in Fig. 2 of Electronic Supplementary information, homologous D-site and Esite are the same. The adsorption energies of H atoms in D and E are −1.98 eV and −2.55 eV, respectively. Because the Al1-O4-Al3-O3 structure is different from Al1-O3-Al2-O5, the adsorption energies of D-site and E-site have several differences.
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Fig. 4. Potential energy diagrams of H diffusion inside ␣-AlPO4 (0001)/␣-Al2 O3 (0001) in two paths. (a) The first path, (b) The second path.
At the interfacial surface, F-site located in the middle of Al2 and Al3 is the most stable adsorption site of both slabs. The distances between the hydrogen atom and Al2 and Al3 are 1.753 Å, and 1.803 Å, respectively, with the H O5 bond length surpassing the experiments. Therefore, the H atom which had been placed in the F-site only forms the bond with two Al atoms. The adsorption energy of the F-site is about −3.28 eV. When they have placed above O5, O6, Al2, and Al3, H atoms are all transited to F-site through the geometric calculation. Obviously, F-site is potential well to the H atom. As for part of the interface of ␣-Al2 O3 (0001), the adsorption sites G, H and I are stable adsorption sites. The adsorption energies are −1.44 eV, −0.67 eV, and −1.40 eV, respectively. G-site appeared above O7 and near Al2, which are stable adsorption sites on the same site of single phase ␣-Al2 O3 (0001). The Al2 atom and the Al3 atom translate upward when the H atom is located in the H-site. Finally, it can be determined in Fig. 3 that the adsorption energy of H atom gradually descends in the ␣-AlPO4 (0001) slab along with the reduction in distance of H from the surface. Relative to H on the ␣-AlPO4 part, hydrogen stability significantly increases at the interface and then decreases. This demonstrates that the H atom
from the ␣-AlPO4 to the interface region should be significantly exothermic, and it is endothermic for H entering into the Al2 O3 part. Hydrogen atoms in the ␣-Al2 O3 (0001) part is more stabilize than those in ␣-AlPO4 (0001). The internal adsorption energy of ␣Al2 O3 (0001) is near −2 eV [33], which is lower than the energy of G-site, H-site, and I-site. Therefore, in the interface, the adsorption energies of H atom are higher than in interior ␣-Al2 O3 . 3.2. Interface effect on H atom diffusion In ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface region, the migration of H atom into the ␣-Al2 O3 (0001) from ␣-AlPO4 (0001) can be shown in Fig. 2. The potential energy surface of H diffusion in ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface are shown in Fig. 4. Moreover, the corresponding sites of the initial, transition and final structures are also shown in Fig. 4. In the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface, 14 transition states, from TS1 to TS14, of H atom diffusion process were calculated. It is difficult for H atoms to overcome the energy barriers of C → TS5 → D (2.52 eV) and C → TS6 → E (1.95 eV), compared with the obstacles of B → TS3 → D (0.84 eV) and B → TS4 → E (1.34 eV).
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Although C-site is a stable adsorption site of the interface, it was also not included in migration paths. As shown in Fig. 4, there are only two possible ways for H atom permeation of the interface. Firstly, the first path of the hydrogen atom is A → TS1 → B → TS3 → D → TS7 → F → TS12 → I. It is relatively easy for the hydrogen atom to pass through the ␣-AlPO4 (0001) part. H atom migration barriers from A-site to D-site (A → TS1 → B → TS3 → D) are 0.22 eV and 1.35 eV, respectively. H atom in the D-site then rotates around the F-site, and then jumps to the I-site. This process is analogous to the H diffusion in the ␣-Al2 O3 (0001). Energy barriers for H atom to diffuse through D → TS7 → F and F → TS12 → I are 0.40 eV and 2.91 eV, respectively. H diffusion through the bulk of ␣-AlPO4 (0001) part of the slab is possible, but the highest barrier (2.91 eV) of the surface-to-subsurface path must be overcome. That is to say, the rate of F → TS12 → I diffusion of H atoms determines the H diffusion rate in the interface region. Secondly, the second path of H atom diffusion is A → TS1 → B → TS4 → E → TS10 → G → TS14 → H. For H migration in the ␣-AlPO4 (0001) (A → TS1 → B → TS4 → E) side, the transition structure TS1 and TS4 with barriers about 0.22 eV and 0.84 eV were calculated. Next, the H atoms in the E-site transfer to G-site, then jump to H-site. This process is extensively different from the rotate-jump process in a pure ␣-Al2 O3 (0001) slab. The E → TS10 → G determines the diffusion rate of H atom in the ␣-Al2 O3 side which is higher than the greatest barrier in the first path. For the path G → TS14 → H, meaning that the H atoms transfer to the interior ␣-Al2 O3 , the energy barrier for H atom is 1.73 eV. Finally, the diffusion behavior of hydrogen atoms of ␣-AlPO4 (0001) part of the interface is similar to the single phase ␣-AlPO4 (0001), which is shown in Fig. 2 of Electronic Supplementary information. However, H diffusion in ␣-Al2 O3 (0001) part of the interface is different when it is in ␣-Al2 O3 (0001). Therefore, the paths of the H atom are distorted in the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface. The activation energies of H diffusion in ␣-AlPO4 (0001) and ␣-Al2 O3 (0001) are 0.67 eV (shown in Fig. 1 of Electronic Supplementary information) and 1.58 eV [26], while the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface is 2.91 eV. The potential well of H atom in the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface is larger than in ␣-AlPO4 (0001) and ␣-Al2 O3 (0001). A small amount of H atom can pass through the interface. Accordingly, the performance of barriers of H diffusion in ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface is preferable in the ␣-Al2 O3 (0001) and the ␣-AlPO4 (0001).
4. Conclusion The structure of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) slab with two coherent interfacial regions was established. Thermodynamics and kinetics of hydrogen diffusion in two slabs were investigated by using density functional theory. Potential energy pathways were predicted. The results show that diffusion behavior of hydrogen atoms in the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface is similar to the single phase ␣-AlPO4 material. The activation energy is 2.91 eV in the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface, while the single phase ␣-AlPO4 (0001) and ␣-Al2 O3 (0001) are 0.67 eV and 1.58 eV. There is less atom can pass through the interface. Accordingly, the performance of barriers of H diffusion in ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface is preferable in the ␣-Al2 O3 (0001) and the ␣-AlPO4 (0001).
Acknowledgements This work is supported by National Magnetic Confinement Fusion Science Programs (Grant No. 2013GB110005) and the Pro-
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Hydrogen diffusion mechanism on ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface: A first-principles study L.Y. Wang a , F. Sun a,∗ , Q.L. Zhou b , D.M. Liao a , Y.Z. Jia a , L.H. Xue a , H.P. Li a , Y.W. Yan a a b
State Key Laboratory of Material Processing and Die & Mould technology, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China Faculty of Science, Shizuoka University, Shizuoka 422-8529, Japan
h i g h l i g h t s • The ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface structural model was established. • The adsorption sites and adsorption energy of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface were calculated by density functional theory, and transition states of adsorption sites were determined based on transition-state search.
• The hydrogen resistance mechanism of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface was discovered by first-principles.
a r t i c l e
i n f o
Article history: Received 30 October 2016 Received in revised form 7 May 2017 Accepted 8 May 2017 Available online xxx Keywords: ␣-AlPO4 ␣-Al2 O3 Interface First-principles Tritium permeation barriers
a b s t r a c t ␣-AlPO4 (0001)/␣-Al2 O3 (0001) fabricated by selective laser sintering could improve the performance at protection against H permeation compared with that of single phase ␣-Al2 O3 and ␣-AlPO4 . In this study, the possible interfacial structures, thermodynamics and kinetics of hydrogen diffusion in heterojunction ␣-AlPO4 (0001)/␣-Al2 O3 (0001) coating were investigated based on the density functional theory. The adsorption energy and the adsorption sites are calculated in order to obtain the most stable configuration. The hydrogen isotopic diffusion in heterojunction ␣-AlPO4 (0001)/␣-Al2 O3 (0001) is also compared with that in ␣-Al2 O3 (0001) or ␣-AlPO4 (0001) surface. The interfacial binding illustrates that hydrogen is more difficult to diffuse through the grain compare with ␣-Al2 O3 (0001) or ␣-AlPO4 (0001). Due to the higher saddle point energy of hydrogen migration and potential well, the hydrogen resistivity property of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) is better than the single phase materials. The interface of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) is predicted to be effective at suppressing hydrogen permeation. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Operating of radioactive tritium, optimizing of tritium balance and controlling tritium inventory play crucial roles in fusion reactors similar to the International Thermonuclear Experimental Reactor (ITER). The utilization of a coating, namely, hydrogen permeation barrier (HPB), deposited on structural material of steel is an effective way to hinder tritium migration [1]. The hydrogen permeation barrier is one of the key technological developments of fusion reactor cladding, and is an important safeguard to reach the safety tritium radioactive environmental standards [2]. There are several materials posing as formidable candidates for tritium permeation barrier (TPB) coatings, such as the BN [3], Cr2 O3 [4], ZrO2 [5], Er2 O3 [6] and Y2 O3 [7]. Among all of the HPB materials, Al2 O3
∗ Corresponding author. E-mail address: [email protected] (F. Sun).
[8–14] has received the most widespread attention. Owing to low permeability, low conductivity, structural stability, corrosion resistance, the feasibility of the process, and so on, the ␣-Al2 O3 coating was carried out earlier and has become one of the tritium candidate coating materials of fusion reactors [15,16]. Tritium barrier effect of the ␣-Al2 O3 coating was corroborated by the experiment, and its mechanism was discovered. For hydrogen isotopes permeation through HPB material, the hydrogen isotopes could be absorbed on the surface of the upstream side and firstly dissociated into atoms, then dissolved into the material, followed by diffusing through the material, and finally recombining into molecules on the downstream side [17,18], which is calculated based on first-principles. First-principles is widely used in the H diffusion and obtains the H site. Many researchers have obtained the properties and mechanisms of HPB through first-principles. Hydrogen sites are calculated in previous density functional theory (DFT)-local density approximation (LDA) at a tetrahedral site in bulk FeAl [19]. Johnson
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et al. have calculated the hydrogen site on the FeAl (110) surface by GGA-PBE (Perdew-Burke-Ernzerh), while hydrogen adsorbs on top of Al atoms of the FeAl (100) surface [20]. Zhang et al. [21] utilized PW91 (Perdew-Wang)-GGA (generalized gradient approximation) to carry out first-principles total energy calculations in ␣-Al2 O3 /FeAl, and revealed the mechanism of hydrogen diffusion in the interfacial slab. Next, thin ceramic coatings, such as SiO2 , act as TPB material to suppress tritium permeation through structural materials [22]. The ␣-AlPO4 crystal structure is derived from the SiO2 . The investigation of ␣-AlPO4 , whose tritium simulation has not been reported, could reveal the effect of tritium resistance to the tetrahedral crystal. Moreover, the hydrogen isotope diffusion mechanism from the ␣-Al2 O3 to ␣-AlPO4 is unknown. The diffusion of hydrogen isotopes and stability will depend on the structure of the oxide interface, and the lattice mismatch degree between the components further affects the performance of HPB [21]. Therefore, the diffusion of tritium in ␣-Al2 O3 and ␣-AlPO4 interface region, which is also lacking in a clear structure, is distinct from that in single phase ␣-Al2 O3 and ␣-AlPO4 . The simulation can reveal the diffusion mechanism of tritium to ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface and predict the new material of HPB. It is reasonable to do theoretical studies for diffusion of hydrogen in ␣-AlPO4 (0001)/␣Al2 O3 (0001). In the present paper, the structure of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface was established and relaxed. Macroscopic experiments have found that hydrogen isotopic permeation through such aluminum rich coating based HPB is predominantly controlled by hydrogen diffusion in bulk [23,24]. Thus it is reasonable to use hydrogen atoms instead of tritium atoms for simulation. Based on the interface structure, composite interfacial adsorption sites and the adsorption energy were also calculated by first-principles calculation. Utilizing transition-state search method by Dmol3, the diffusion process of H atoms from ␣-AlPO4 (0001) into the ␣-Al2 O3 (0001) were then also well-studied in this paper.
2. Computational method and model 2.1. Method Dmol3 [16] program package in Materials Studio 8 of Accelrys Inc. by first-principles was used to calculate total energy in the PW91 [25] -GGA. The parameters used in the ␣-Al2 O3 calculation [26] were selected most likely on account of the lack of reports on hydrogen isotope penetration to ␣-AlPO4 . The double numerical quality basis set with polarization functions (DNP) [27] had to be adapted, and the semi-core pseudopotential [28] could be utilized. Spin-polarized and Monkhorst-Pack mesh [29] k-points of 3 × 3 × 1 for bulk and surface calculations were selected. All calculations were utilized a convergence tolerance of energy of 2.0 × 10−4 Ha/atom (1 Ha = 27.21 eV), a maximum force of 0.004 Ha/Å, and a maximum displacement of 0.005 Å, allowing the energy of the model to converge. Maximum SCF cycles were turned into 200. The cut-off energy were 300 eV. The three potentials chosen to optimize the structure of ␣AlPO4 include GGA, LDA, and PBE. The result demonstrates that the PW91-GGA is the best suitable potential to approach the experiment result. Lattice constants were a = b = 4.949 Å, c = 10.945 Å for ␣-AlPO4 which is consistent with the experimental value a = b = 4.944 Å, and c = 10.946 Å. The optimized lattice constants for the bulk ␣-Al2 O3 were a = b = 4.806 Å and c = 13.133 Å which were the same parameters to the experimental value. Adsorption energy is defined as: Eads = E[slab+H] − (E[slab] + E[H] ) where E[slab+H] , E[slab] , and E[H] are the calculated total energy of the H atom on the ␣-AlPO4 (1000)/␣Al2 O3 (0001) slab, a clean ␣-AlPO4 (1000)/␣-Al2 O3 (0001) slab and
a gas-phase H atom. With the definition, negative values of Eads signifies adsorption is more stable than the corresponding clean surface and H atom. The complete linear synchronous transit/quadratic synchronous transit (LST/QST) method is used to locate the transition states (TS) for hydrogen dissociation and hydrogen diffusion. Frequencies of hydrogen are determined by all critical points identified on the potential energy surface (PES) to determine minima and transition states.
2.2. Established and relaxed geometric structures The ␣-Al2 O3 belongs to the hexagonal close pack (hcp). The O atoms in the unit cell are the cubic close-packed structure on ␣-Al2 O3 (0001). Among the numerous ␣-Al2 O3 crystal planes, ␣Al2 O3 (0001) is the most stable juxtaposed with ␣-Al2 O3 (1–102) and ␣-Al2 O3 (11–20) [30]. The lattice constants of ␣-Al2 O3 (0001) are a = b = 4.754 Å, c = 12.988 Å compared with the experimental values (a = b = 4.759 Å, c = 12.992 Å [31]). ␣-AlPO4 has a hexagonal structure whose close-packed plane is (0001). The crystal structure of ␣-AlPO4 (0001) whose lattice constants are a = b = 4.944 Å, c = 10.946 Å is shown in Fig. 1. In crystallography, lattice mismatch degree is defined as: ı = (aˇ − a˛ )/a˛ Where a␣ , aˇ refers to the lattice constant. With the calculation, ␣-AlPO4 (0001) and ␣-Al2 O3 (0001) have small lattice mismatch degree with 2.795% (less than 5%). It implies that this interface is a coherent interface [32]. (2 × 2) Supercell flat slab model was used to simulate the interface configuration. To simulate the actual surface, it is necessary to add a sufficiently large vacuum in the direction perpendicular to the surface of the ␣-AlPO4 . Interaction of the adjacent unit cell can be ignored when the vacuum layer spaced between the alumina surfaces equals to 15 Å [21]. Therefore, the interfacial lattice constants are a = b = 9.698 Å, c = 40.000 Å. As the structure shown in Fig. 1(A), a possible mechanism contributing to the instability of the structure is the existence of a separate oxygen atom at the interface. With the addition of an Al atom, the total energy of the interface declined by 11.94 eV compared with the sum of original structure’s energy and single Al atomic energy. Consequently, Al atoms were added to relax all geometric structures. For the cyclical principle, 13 kinds of supercell flat slab models were established, having six possible configurations, as shown in Fig. 1(B). The final geometric structure of the ␣-Al2 O3 (0001)/␣-AlPO4 (0001) slab is shown in Fig. 2. Two slabs are made of 22 layers. The ␣-AlPO4 (0001) surface was modeled by a slab consisting of 10 layers, whereas ␣-Al2 O3 (0001) surfaces were modeled by a slab composed of 12 layers (i.e., four O layers). Compared with others, the structure, as shown in Fig. 1(B) (b), was thought as the general construction in the material because it is the most representative structure. As shown in Fig. 2, the O5-Al3-O4 bond angle is 137.135◦ in the optimized structure which has smaller repulsive force compared with it in the original structure. In the original structure, the distances of Al3-O4, Al3-O5, Al3-O6 and Al3-O7 are 2.192 Å, 1.978 Å, 1.727 Å and 1.850 Å, respectively. With the relaxed geometric calculation by Dmol3, the distances of Al3-O4, Al3-O5, Al3-O6 and Al3-O7 are 1.812 Å, 2.012 Å, 1.787 Å and 1.826 Å, respectively. The interatomic distances (Al-O) in the interface region of both slabs are very close to corresponding experimental values (1.86-1.97 Å [26]). The result considers that proper binding between ␣-AlPO4 (0001) and ␣-Al2 O3 (0001) was obtained, providing support to the real relevance of the models.
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Fig. 1. Established geometric structures of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface. (A) One of the original structure of interface without Al atom. (B) Six possible structures of interface with the addition of an Al atom.
Fig. 3. Potential energy curve of hydrogen at various positions of the ␣-AlPO4 (0001)/Al2 O3 (0001) interface. A, B, C, D, E, F, G, H, and I are the nine stable adsorption sites.
Fig. 2. Relaxed structure of ␣-Al2 O3 (0001)/␣-AlPO4 (0001) and adsorption sites and hydrogen atom diffusion roads in magnified view.
3. Result and discussion 3.1. Interface effect on stability of hydrogen H was placed on the surface sites and at the interstitial sites in the interface of ␣-AlPO4 (0001)/␣-Al2 O3 (0001). The atomic configurations for H-occupied sites are shown in Fig. 1 of Electronic Supplementary information. The potential energy curve of hydrogen at various positions are displayed in Fig. 3. The stable adsorption
sites are indicated in Fig. 2. H atom was located at 0.5 Å (less than the bond length of the H O bond) above each site, and was then relaxed to observe whether the H atom could exist around the adsorbed atoms. For an isolated hydrogen atom, the top site of Al1 is an unstable adsorption site, and the top sites of Al2 and Al3 are metastable adsorption sites. Due to the distance between A-site and P1 being 2.981 Å, the location of A-site is similar to it in ␣-AlPO4 (0001). The adsorption energies of H atoms in A, B, and C is −0.26 eV, −0.78 eV, and −1.23 eV respectively. In single phase ␣-AlPO4 (0001), as shown in Fig. 2 of Electronic Supplementary information, homologous D-site and Esite are the same. The adsorption energies of H atoms in D and E are −1.98 eV and −2.55 eV, respectively. Because the Al1-O4-Al3-O3 structure is different from Al1-O3-Al2-O5, the adsorption energies of D-site and E-site have several differences.
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Fig. 4. Potential energy diagrams of H diffusion inside ␣-AlPO4 (0001)/␣-Al2 O3 (0001) in two paths. (a) The first path, (b) The second path.
At the interfacial surface, F-site located in the middle of Al2 and Al3 is the most stable adsorption site of both slabs. The distances between the hydrogen atom and Al2 and Al3 are 1.753 Å, and 1.803 Å, respectively, with the H O5 bond length surpassing the experiments. Therefore, the H atom which had been placed in the F-site only forms the bond with two Al atoms. The adsorption energy of the F-site is about −3.28 eV. When they have placed above O5, O6, Al2, and Al3, H atoms are all transited to F-site through the geometric calculation. Obviously, F-site is potential well to the H atom. As for part of the interface of ␣-Al2 O3 (0001), the adsorption sites G, H and I are stable adsorption sites. The adsorption energies are −1.44 eV, −0.67 eV, and −1.40 eV, respectively. G-site appeared above O7 and near Al2, which are stable adsorption sites on the same site of single phase ␣-Al2 O3 (0001). The Al2 atom and the Al3 atom translate upward when the H atom is located in the H-site. Finally, it can be determined in Fig. 3 that the adsorption energy of H atom gradually descends in the ␣-AlPO4 (0001) slab along with the reduction in distance of H from the surface. Relative to H on the ␣-AlPO4 part, hydrogen stability significantly increases at the interface and then decreases. This demonstrates that the H atom
from the ␣-AlPO4 to the interface region should be significantly exothermic, and it is endothermic for H entering into the Al2 O3 part. Hydrogen atoms in the ␣-Al2 O3 (0001) part is more stabilize than those in ␣-AlPO4 (0001). The internal adsorption energy of ␣Al2 O3 (0001) is near −2 eV [33], which is lower than the energy of G-site, H-site, and I-site. Therefore, in the interface, the adsorption energies of H atom are higher than in interior ␣-Al2 O3 . 3.2. Interface effect on H atom diffusion In ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface region, the migration of H atom into the ␣-Al2 O3 (0001) from ␣-AlPO4 (0001) can be shown in Fig. 2. The potential energy surface of H diffusion in ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface are shown in Fig. 4. Moreover, the corresponding sites of the initial, transition and final structures are also shown in Fig. 4. In the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface, 14 transition states, from TS1 to TS14, of H atom diffusion process were calculated. It is difficult for H atoms to overcome the energy barriers of C → TS5 → D (2.52 eV) and C → TS6 → E (1.95 eV), compared with the obstacles of B → TS3 → D (0.84 eV) and B → TS4 → E (1.34 eV).
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Although C-site is a stable adsorption site of the interface, it was also not included in migration paths. As shown in Fig. 4, there are only two possible ways for H atom permeation of the interface. Firstly, the first path of the hydrogen atom is A → TS1 → B → TS3 → D → TS7 → F → TS12 → I. It is relatively easy for the hydrogen atom to pass through the ␣-AlPO4 (0001) part. H atom migration barriers from A-site to D-site (A → TS1 → B → TS3 → D) are 0.22 eV and 1.35 eV, respectively. H atom in the D-site then rotates around the F-site, and then jumps to the I-site. This process is analogous to the H diffusion in the ␣-Al2 O3 (0001). Energy barriers for H atom to diffuse through D → TS7 → F and F → TS12 → I are 0.40 eV and 2.91 eV, respectively. H diffusion through the bulk of ␣-AlPO4 (0001) part of the slab is possible, but the highest barrier (2.91 eV) of the surface-to-subsurface path must be overcome. That is to say, the rate of F → TS12 → I diffusion of H atoms determines the H diffusion rate in the interface region. Secondly, the second path of H atom diffusion is A → TS1 → B → TS4 → E → TS10 → G → TS14 → H. For H migration in the ␣-AlPO4 (0001) (A → TS1 → B → TS4 → E) side, the transition structure TS1 and TS4 with barriers about 0.22 eV and 0.84 eV were calculated. Next, the H atoms in the E-site transfer to G-site, then jump to H-site. This process is extensively different from the rotate-jump process in a pure ␣-Al2 O3 (0001) slab. The E → TS10 → G determines the diffusion rate of H atom in the ␣-Al2 O3 side which is higher than the greatest barrier in the first path. For the path G → TS14 → H, meaning that the H atoms transfer to the interior ␣-Al2 O3 , the energy barrier for H atom is 1.73 eV. Finally, the diffusion behavior of hydrogen atoms of ␣-AlPO4 (0001) part of the interface is similar to the single phase ␣-AlPO4 (0001), which is shown in Fig. 2 of Electronic Supplementary information. However, H diffusion in ␣-Al2 O3 (0001) part of the interface is different when it is in ␣-Al2 O3 (0001). Therefore, the paths of the H atom are distorted in the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface. The activation energies of H diffusion in ␣-AlPO4 (0001) and ␣-Al2 O3 (0001) are 0.67 eV (shown in Fig. 1 of Electronic Supplementary information) and 1.58 eV [26], while the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface is 2.91 eV. The potential well of H atom in the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface is larger than in ␣-AlPO4 (0001) and ␣-Al2 O3 (0001). A small amount of H atom can pass through the interface. Accordingly, the performance of barriers of H diffusion in ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface is preferable in the ␣-Al2 O3 (0001) and the ␣-AlPO4 (0001).
4. Conclusion The structure of ␣-AlPO4 (0001)/␣-Al2 O3 (0001) slab with two coherent interfacial regions was established. Thermodynamics and kinetics of hydrogen diffusion in two slabs were investigated by using density functional theory. Potential energy pathways were predicted. The results show that diffusion behavior of hydrogen atoms in the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface is similar to the single phase ␣-AlPO4 material. The activation energy is 2.91 eV in the ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface, while the single phase ␣-AlPO4 (0001) and ␣-Al2 O3 (0001) are 0.67 eV and 1.58 eV. There is less atom can pass through the interface. Accordingly, the performance of barriers of H diffusion in ␣-AlPO4 (0001)/␣-Al2 O3 (0001) interface is preferable in the ␣-Al2 O3 (0001) and the ␣-AlPO4 (0001).
Acknowledgements This work is supported by National Magnetic Confinement Fusion Science Programs (Grant No. 2013GB110005) and the Pro-
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