Cr Effect on Hydrogen Interactions with Intrinsic Point Defects and

Article pubs.acs.org/JPCC

Cr Effect on Hydrogen Interactions with Intrinsic Point Defects and Hydrogen Diffusion in α‑Al2O3 as Tritium Permeation Barriers Xin Xiang, Guikai Zhang, Feilong Yang, Xiaolin Wang,* Tao Tang, and Yan Shi Institute of Materials, China Academy of Engineering Physics, Mianyang 621908, People’s Republic of China ABSTRACT: Hydrogen transport in the outer Al2O3 scale is the rate-limiting step for H-permeation resistance of FeAl/ Al2O3-type aluminide tritium permeation barriers (TPBs) in fusion reactors. With first-principle calculations, the effects of Cr, a main impurity element in the Al2O3 scale, on intrinsic point defect formation, hydrogen interactions with intrinsic point defects, and hydrogen diffusion in α-Al2O3 have been investigated under the working conditions of aluminide TPBs. It is found that Cr addition is favorable for the formation of VO, yet unfavorable for VAl formation in α-Al2O3. Compared with the α-Al2O3−H case, Cr is beneficial for the formation of H-related defects in α-Al2O3, whereas it is unfavorable for the Hi trapping ability of VAl and VO. HO− will dominate among Hi−, VAl3−, VO0, and [VAl3−−H+]2−, and only one step of Hi reorientation will be involved for the Hi diffusion in Cr-doped α-Al2O3. Hi is the dominant diffusion species in both pure and Crdoped α-Al2O3, whereas the activation energy of H diffusion in Cr-doped α-Al2O3 is sharply reduced, which is unfavorable for Hpermeation resistance of aluminide TPBs. The Cr effect on hydrogen behaviors in α-Al2O3 can be attributed to the chemically unstable electron structure of Cr3+ and a relatively stronger bonding interaction between H and Cr than that between H and Al or O atoms.

1. INTRODUCTION The feasibility of tritium self-sufficiency and energy extraction will be tested in the test blanket module (TBM) in the international thermonuclear experimental reactor (ITER) program.1−3 However, this effort may encounter frustration because of the tritium permeation into and through structural materials in TBMs, which can lead to D/T fuel loss, hydrogen/ helium embrittlement, and environmental contamination in fusion reactors.4,5 A widely adopted resolution is to prepare a thin coating layer as a tritium permeation barrier (TPB) on the outer surface and/or inner wall of structural materials in the blanket and auxiliary tritium handling systems.6−8 For the commonly used FeCr base structural materials, the most promising choice of TBM TPBs is a complex aluminide coating, typically FeAl/Al2O3 for its high tritium permeation reduction factor (PRF), low thermal mismatch, metallurgical bonding, self-healing, and excellent compatibility.9−11 It is known that the hydrogen permeation in materials involves six processes of absorption, dissociation, dissolution, diffusion, recombination, and desorption.8,12 Obviously, the performance of TPBs depends on the coating integrity, coating materials, and interface features of the coating/substrate. As for FeAl/Al2O3 TPBs, the main functional component for hydrogen resistance is the outer Al2O3 scale rather than the inner transition FeAl layer, since the hydrogen PRF of Al2O3 under convenient service conditions is much higher than that of FeAl,4 which has also been verified theoretically recently.13 Therefore, the transport of hydrogen in Al2O3 is definitely the rate-limiting step for hydrogen permeation in aluminide TPBs. However, the property of atomic transport in Al2O3, both in the © 2016 American Chemical Society

bulk and on the surface, is strongly dependent on the defect chemistry, including the impurity chemistry of Al2O3.14,15 The knowledge of hydrogen interactions with defects (intrinsic or extrinsic defects, i.e., impurities) in Al2O3 is thus essential in scientific and technologic interests for aluminide TPBs. The latest first-principle study predicted that H will have a strong interaction with intrinsic point defects, especially the vacancy-type defects in α-Al2O3, and the introduced H exists mainly in the form of Hi+ rather than [VAl3−−H+]2− and HO+, for which Hi+ is the dominant diffusion species, contributing to the transport of hydrogen in α-Al2O3.14 However, an impurity, even with a concentration of parts per million magnitude, will dominate the defect chemistry of α-Al2O3.16,17 It is thus anticipated that the hydrogen interactions with intrinsic point defects and hydrogen diffusion in α-Al2O3 will be significantly affected by impurities. As for the typical aluminide TPBs, the preparation process commonly involves two steps of aluminization and oxidation.5 The former is to form an FeAl transition layer via interdiffusion between Al atoms from a certain Al source and Fe atoms from steel substrates, and the latter is to form an Al2O3 film on the transition layer by selective oxidation.5 During interdiffusion, other alloying elements, especially Cr (7−22 wt %), from the substrate will also be involved to form FeAl layers of solid solutions or intermetallics, such as (Fe,Cr)2Al5/(Fe,Cr)Al3, (Fe,Cr)Al/(Fe,Cr)3Al, (Fe,Cr,Ni)2Al5/(Fe,Cr,Ni)Al3, and Received: April 9, 2016 Revised: April 19, 2016 Published: April 19, 2016 9535

DOI: 10.1021/acs.jpcc.6b03628 J. Phys. Chem. C 2016, 120, 9535−9544

Article

The Journal of Physical Chemistry C

work. Using a 3 × 3 × 1 k-point sampling, the relaxed crystal constants (a = b = 4.821 Å, c = 13.105 Å) of corundumstructured α-Al2O3 agreed well with the previous experimental values (a = b = 4.759 Å, c = 12.991 Å)37 and theoretical results.38 The obtained band gap was 6.18 eV, considerably smaller than the experimental value (8.80 eV),37 the reason for which is often attributed to the common underestimation of the band gap for metal oxides by the first-principle method.17,38 The formation energy and binding energy are defined by the following equations:38,39

(Fe,Cr,Ni,Mn)2Al5/(Fe,Cr,Ni,Mn)Al3.18,19 In the presence of Cr, it is observed experimentally that the formation, surface topography, compactness, composition, and crystal type of Al2O3 scales formed on such FeAl-type layers are significantly affected during the following oxidation step,20−22 forming Al2O3-rich scales., i.e., solid solutions or mixed oxide scales of Cr2O3 and Al2O3, although the former takes up a rather small proportion in the Al2O3 scale.23,24 Especially, Cr is beneficial for the formation of α-Al2O3,20,22,25 suggesting that Cr is favorable for aluminide TPBs in some aspect, since α-Al2O3 is much more H-permeation-resistive than any other metastable Al2O3 phase.26 However, it is widely recognized that Cr in corundum can alter the physical, chemical, electronic, and optical properties of this material.27 The famous example is that the transparent or colorless pure corundum will turn red in color after Cr doping.28,29 Therefore, it can be envisioned that the hydrogen behavior in α-Al2O3 would be affected by the Cr presence. H-permeation experiments have suggested that the purer the Al2O3 film formed on the FeAl layer, the higher the tritium PRF for aluminide TPBs,30 indicating that the Cr presence is unfavorable. Thus, for the concerned H-permeation resistance, a controversy emerges for the Cr effect on aluminide TPBs; that is, Cr has a great influence on aluminide TPBs, while whether Cr is favorable or unfavorable for the Hpermeation resistance has not been systematically clarified, which is of paramount importance to the preparation and application of aluminide TPBs. Hence, in this regard, characterization of Cr-related defects appears essential, and how Cr-related defects affect the reaction mechanism of molecular and atomic H in aluminide TPBs needs to be clarified. In this work, therefore, the first-principle method is employed to investigate the influence of Cr doping on the formation of intrinsic point defects and H-related defects, hydrogen interactions with intrinsic point defects, and hydrogen diffusion in α-Al2O3, giving considerable insights into the detailed mechanisms governing H transport in aluminide TPBs. The results are anticipated to be instructive for the selection, development, and optimization for the preparation technique, and also meaningful for studies on the oxidation and tritium permeation behaviors of aluminide TPBs. To our best knowledge, no similar studies have been devoted to such work on aluminide TPBs before.

f tot tot Edef (X ) = Edef − Eperf +

∑ Δniμi + qEF i

b f f f Edef (XY ) = Edef (X ) + Edef (Y ) − Edef (XY )

(1) (2)

Efdef(X)

where is the formation energy of defect species X and Ebdef(XY) is the binding energy of defect XY, which could be considered as a combination of defect species X and Y. Etot def and Etot are the total energies of the crystal lattices with and perf without defect, respectively. Δni is the added (negative) or removed (positive) number of atom species i in the crystal lattice. μi is the atomic chemical potential of element i (O, Al, H, or Cr in this work). The atomic potentials of Al and O are constrained by the equilibrium condition (2μAl + 3μO = μAl2O3; μAl2O3 is the chemical potential of the Al2O3 molecule) and will be dependent on the working conditions. As for aluminide TPBs, they often work under the conditions of over 773 K with exposure to H2 (D2, T2) of ordinary or high pressure,14,40 which could be considered as O-deficient (relatively Al-rich) in a hydrogen environment. In this work, only the working atmosphere (O-deficient and H-rich) of aluminide TPBs was considered. Thus, under the common O-deficient and H-rich service conditions, μAl is determined to be the total energy of the Al unit cell, i.e., μAl = μmetal Al , yielding μO = (μAl2O3 − 2μAl)/3. By the same method, the atomic potentials of introduced H and Cr can be determined as μH = μH2/2 and μCr = μmetal Cr , respectively. q is the charge state of defect X, varying from neutral to fully ionized states, i.e., −3 to 0 for VAl, 0 to +2 for VO, and −1 to +1 for Hi etc., which is used as a jellium background charge in this work. EF is the Fermi level within the band gap (0 ≈ Eg) of α-Al2O3. Since the GGA calculations usually underestimate the band gap value Eg of metal oxides as compared to the experimental data, resulting in the underestimation of the formation energies,41 the formation energies were thus corrected by directly substituting the calculated Eg with the experimental value of 8.8 eV in the present work, as done in previous studies.14,35,36,42 On the other hand, considering the small Cr concentration (0.4 atom %) and the recognized underestimation of the band gap by GGA calculations,41 the Cr effect on the band gap of α-Al2O3 was intentionally neglected in this work. Consequently, as shown in eq 1, the formation energy of a certain charged defect in αAl2O3 (with and without Cr doping) under a fixed O condition is linearly dependent on the Fermi level, and thus, the variation of the defect formation energy within the band gap (0−8.8 eV) could be plotted. For a defect species in various charge states, different formation energy plots can be drawn in the same manner. At a given Fermi level, the charged defect with the smallest formation energy is energetically most favorable. Accordingly, the defect formation energies in various charge states in α-Al2O3 as a function of the Fermi level EF under a certain O condition could be clearly established.

2. COMPUTATIONAL METHOD AND MODEL 2.1. Method. All the first-principle calculations in this work were conducted with the DMol331 module in the Materials Studio of Accelrys Inc. The generalized gradient approximation (GGA) parametrized in Perdew−Wang (PW91) was employed to treat the exchange-correlation potential.32 The all-electron framework33 was utilized to do the core treatment, and the double numerical quality basis set with polarization functions (DNP)34 was determined as the basis set with the basis file of 3.5. Values of 0.008 Ha and 4.3 Å were used to deal with the orbital occupancy and cutoff, respectively. The convergence tolerances of energy, force, and displacement used were the same as those in our previous work.35,36 Since α-Al2O3 is a nonmagnetic material, and the electronic structures were not especially concerned in this work, non spin polarization was adopted for all the calculations. Moreover, after plenty of tests, non spin polarization treatments provide an energy deviation within 2 meV/atom by contrast with spin polarization, which is sufficiently reasonable for the following calculations in this 9536


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3. RESULTS AND DISCUSSION 3.1. Cr Effect on Intrinsic Point Defects in α-Al2O3. To investigate the influence of Cr on the hydrogen interactions with intrinsic point defects in α-Al2O3, one Al atom in the αAl2O3 supercell was first substituted with a Cr3+, as shown in Figure 1. The propensity of α-Al2O3 doped with Cr3+ can be related to the isostructural characteristics of α-Al2O3 and Cr2O3, since Cr3+ is isovalent with Al3+, and the crystal ionic radius of Cr3+ (0.755 Å) is analogous with that of Al3+ (0.675 Å),45 leading to similar unit cell sizes of the corresponding metal oxides (4.9307 and 4.7602 Å, respectively),45 which is favorable for isomorphic Cr substitution in α-Al2O3, as theoretically revealed recently.36 The variations of the formation energies of vacancy-type isolated intrinsic point defects in various charge states in αAl2O3 with EF before and after Cr doping are shown in Figure 2. In this figure, only results under the common service

The protocol of complete linear synchronous transit/ quadratic synchronous transit (LST/QST)43 was employed to determine the migration barriers of the H-related defects in αAl2O3 before and after Cr doping. On the basis of the nudged elastic band (NEB) method,44 a rough minimum energy pathway between the stable initial and final structures was mapped out. Thereafter, a maximum of 20 images was interpolated to obtain a complete energy pathway. Frequencies were calculated at all critical points on the potential energy surface to identify the minima and transition states for the diffusion of H-related defects. 2.2. Model. A 36-layer corundum-structured 2 × 2 × 2 αAl2O3 supercell was built for defect calculations in this work. The Brillouin zone was changed with a 2 × 2 × 1 k-point mesh. After full optimization with the crystal lattice and atomic positions, the crystal lattice of the optimized supercell was constrained, and all atoms except for those in both the upper and bottom 10 layers were allowed to relax during defect formation and migration calculations. One point defect was created by introducing (interstitial), removing (vacancy), or substituting (substituent) an atom in the nearby geometry center of the optimized and constrained α-Al2O3 supercell to eliminate possible defect self-interactions. The situation would be a little different after Cr addition. Specifically, a Cr atom was first located in the nearby geometry center of the supercell. Thereafter, a point defect was generated within different atomic distances (1 NN to 8 NN; NN stands for the nearest neighbor) from the Cr atom in the supercell. After geometry optimization, the minimum total energy of the point defect containing the supercell was selected to determine the most stable site for each defect species (intrinsic point defect and H-related defect included) in α-Al2O3, as shown in Figure 1. According to our previous work,35 in an O-deficient environment, VAl and VO are relatively easier to form than other intrinsic point defects in αAl2O3. Therefore, only vacancy-type defects were considered in the following calculations.

Figure 2. Formation energies of vacancy-type intrinsic point defects in various charge states before and after Cr doping in α-Al2O3 as a function of the Fermi level under the condition of O deficiency.

conditions of aluminide TPBs, i.e., O-deficient with the most stable charge states of each vacancy species, are exhibited. The charge states of vacancy defects remain the same after Cr doping. However, the proportion of each charge state varies. For instance, the +1-charged VO takes up a larger ratio within the whole range of EF, while the −3-charged VAl gains a smaller one after Cr doping. Moreover, the −1, −2, and −3 charge states of VAl will shift to the higher Fermi level. Significant changes also occur for the formation energies of each vacancy in Cr-doped α-Al2O3. The formation energy of VO decreases by about 1.5−1.8 eV within the whole EF range after Cr doping. As for VAl, the formation energy will also be reduced when EF locates near the top (0−2.6 eV) of the valence band, and then will be increased in the higher EF range (2.6−8.8 eV). In view of the formation energy, it thus can be concluded that the Cr addition is favorable for the formation of VO, yet unfavorable for VAl formation in α-Al2O3. Therefore, Cr has a significant influence on vacancy-type intrinsic point defects in α-Al2O3, which may consequently exert some impact on the hydrogen interactions with intrinsic point defects and hydrogen transport in α-Al2O3. 3.2. Cr Effect on Hydrogen-Related Defects in α-Al2O3. The formation energies of H-related defects and vacancy-type defects in various charge states in α-Al2O3 before and after Cr doping as a function of the Fermi level under O-deficient and

Figure 1. Side view of the Cr-containing 2 × 2 × 2 α-Al2O3 supercell (only the relaxed layers are shown). The gray ball depicts the Cr atom, and red and purple balls denote oxygen and aluminum atoms, respectively. The letters A and B indicate the most stable vacancy sites of Al and O atoms after Cr doping, respectively, and A′ and B′ separately represent possible Al and O vacancy sites accommodating H atoms, while the letter C (C′) indicates an interstitial site of H. 9537


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Figure 3. Formation energies of H-related defects and vacancy-type defects in various charge states (a) before and (b) after Cr doping in α-Al2O3 as a function of the Fermi level under O-deficient and H-rich conditions.

Figure 4. Local atomic configurations of equilibrium-state H-related defects (a) Hi+, (b, e) [VAl3−−H+]2−, (c) HO+, (d) Hi−, and (f) HO− in pure and a Cr-doped α-Al2O3 supercell. The white, red, purple, and gray balls depict H, O, Al, and Cr atoms, respectively, and the blue circles denote VAl in the supercell.

Al2O3. By contrast, the formation energy of Hi+ will be slightly reduced by Cr addition, while that of Hi− will be significantly decreased, up to about 2.3 eV. Obviously, Cr addition has a great influence on the formation and existing form of Hi in αAl2O3. A situation similar to that of Hi is presented for the case of H accommodation at a VO site, as shown in Figure 3. After geometry optimization, the H atom remains at the VO site, whether Cr exists or not, indicating a H substituent at the VO site forms in α-Al2O3 (Figure 4), which is labeled as HO in this work. In pure α-Al2O3, only +1- and −1-charged HO sites are present in the whole range of the Fermi level; that is, the negative U behavior47−49 also exists for HO, consistent with the recent theoretical predications,14 while the neutral HO0 emerges and takes up a large proportion after Cr doping. Furthermore, the share of HO+ decreases dramatically in Cr-doped α-Al2O3, while that of HO− gets a relatively small increase. On the other hand, the formation energy of HO+ will be reduced by about 1.4 eV, and that of HO− will be lowered by up to about 5.4 eV,

H-rich conditions are plotted in Figure 3, and only the most stable charge states of each defect species are exhibited in this figure. After geometry optimization, the H atom remains within the same octahedral interstitial site in both pure and Cr-doped α-Al2O3, forming a H interstitial (Hi), as shown in Figure 4. On the other hand, it can be seen from Figure 3a that only +1- and −1-charged interstitial H atoms are present in the whole range of the Fermi level, and the neutral state, i.e., Hi0, is not a stable defect formed in α-Al2O3, in agreement with previous results.14,46 This phenomenon is known as negative U behavior in a strong electron−phonon coupling system, such as GaAs, ZrO2, and TiO2 etc.47−49 However, the neutral Hi emerges in α-Al2O3 after Cr doping, although the proportion of Hi0 is much smaller than that of Hi+ and Hi−, as shown in Figure 3b. Therefore, the doped Cr may have some impact on the electron−phonon interactions in α-Al2O3. Moreover, the relative ratio of Hi+ to Hi− in the whole EF range changes from slightly larger than 1 to fairly smaller than 1, indicating that the −1-charged state will dominate for Hi in Cr-doped α9538


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Table 1. Formation Energies (EF, eV) of H-Related and Vacancy-Type Defects of Equilibrium States in α-Al2O3 before and after Cr Doping under O-Deficient and H-Rich Conditions HO+ undoped Cr-doped

HO−

2.11

Hi+

Hi−

[VAl3−−H+]2−

VO0

VAl3−

0.30

2.11 1.56

2.78 1.04

2.13 3.43

2.47 −0.36

stability is HO+ = [VAl3−−H+]2− > Hi+ (Figure 3a), while it is Hi+ > [VAl3−-H+]2− > HO+ in ref 14. The difference between the present work and ref 14 may result from the different supercells utilized; for the latter the 2 × 2 × 2 α-Al2O3 supercell was built on the basis of the optimized α-Al2O3 crystal lattice (a = b = 4.806 Å, c = 13.133 Å),14 yet a 2 × 2 × 2 α-Al2O3 supercell was directly built and then optimized in this work (a = 4.822 Å, b = 4.823 Å, c = 13.105 Å), though the lattice constants in both works are in good agreement with the experimental values.37 After Cr doping, the equilibrium states of H-related defects in α-Al2O3 are changed to HO−, [VAl3−−H+]2−, and Hi−, and the relative stability is HO− > Hi+ > [VAl3−−H+]2−, shown in Figure 3b. Therefore, the equilibrium charge states and relative stability of H-related defects in α-Al2O3 are significantly affected by Cr doping. Following to eq 1, the formation energies of H-related defects at the respective determined equilibrium Fermi energies before and after Cr doping in α-Al2O3 are listed in Table 1. As a reference, the energy of a free H2 molecule was provided, labeled as a horizontally short dashed line in Figure 3. From Table 1, all the H-related defects in pure α-Al2O3 have positive formation energies, i.e., higher than that of the free H2 molecule. That is, the H-related defects are not thermodynamically stable, which is favorable for aluminide TPBs resisting H permeation. Moreover, the difference of formation energies for these three types of defects is small, indicating the coexistence of the H-related defects in α-Al2O3. However, the formation energy of each H-related defect in α-Al2O3 will be greatly reduced by Cr. Especially for the most stable HO− defect, the formation energy is negative, which means that HO− is thermodynamically stable in Cr-doped α-Al2O3. Furthermore, the formation energy difference among these three H-related defects increases after Cr doping, with a maximum of 1.92 eV ([VAl3−−H+]2− relative to HO−), and a minimum of 0.66 eV (Hi− relative to HO−). Therefore, HO− will dominate, and Hi− will also take up a considerable proportion, while [VAl3−−H+]2− will only share a very small percentage in Cr-doped α-Al2O3. In a word, Cr is beneficial for the formation of H-related defects, i.e., HO, Hi, and [VAl−H] in α-Al2O3. 3.3. Cr Effect on Hydrogen Interactions with Intrinsic Point Defects in α-Al2O3. Following eq 2, the stabilities of Hrelated defects in α-Al2O3 before and after Cr doping are further characterized by binding energies (listed in Table 2), for which a positive binding energy means an attractive interaction and a negative one indicates a repulsive interaction existing among single defects composing a defect complex.14 For pure α-Al2O3, under O-deficient and H-rich conditions, at the equilibrium Fermi level of 4.12 eV, the occupation of H+ at a VO0 site enables the formation of HO+, and the binding energy of 3.14 eV between H+ and VO0 is positive, indicating that an attractive interaction exists for H+ and VO; that is, H+ will be easily trapped by VO0. After Cr doping, the stable charge state for Hi at the Fermi level of 5.02 eV changes to −1, and thus, the accommodation of H− at a VO0 site results in the formation of HO−. However, the binding energy between H− and VO0 is significantly reduced to 1.70 eV, indicating that the attractive

resulting from the obvious decrease of the VO formation energy by Cr addition, as shown in Figure 2. Therefore, the formation and existing form of HO will be greatly influenced by Cr in αAl2O3. As for the case of H accommodation at a VAl site, unlike HO, the H atom stays away from the VAl site, yet bonds to one of the six nearest O neighbors of VAl, forming a [VAl−H+]q complex in both pure and Cr-containing α-Al2O3 (Figure 4). As shown in Figure 3, hydrogenation of VAl by H+ enables charge states of −2, −1, 0, and +1, with the most energetically favorable −2-charged state, i.e., [VAl3−−H+]2−, before and after Cr doping, consistent with the previous theoretical predictions.14,46 However, the proportion of [VAl3−−H+]2− will be reduced, and the formation energy will be increased by 0−1.3 eV in the high level of EF (≥2.4 eV) by Cr addition, also resulting from the increase of the VAl formation energy by Cr (Figure 2). Obviously, the formation and energetics of [VAl−H] will be evidently influenced by Cr in α-Al2O3. Interestingly, the equilibrium Fermi energy (denoted as a vertical dashed line in Figure 3) of α-Al2O3 has a significant shift before and after Cr doping, as shown in Figure 3. For the insulating system of pure α-Al2O3, the equilibrium Fermi energy EF can be chosen at the midpoint of Eg,50 i.e., 4.4 eV. Nevertheless, in the presence of an impurity, depending on the nature of the impurity species, the equilibrium Fermi energy will change, which can be determined via the positively charged defect and negatively charged defect of the lowest formation energies,14,50 since defects with the lowest formation energies have the highest concentrations and are dominant in the system.51 As seen in Figure 3a, with the chosen atomic chemical potentials, HO+ and [VAl3−−H+]2− have the lowest formation energies among the charged defects for a wide range of Fermi levels in H-containing α-Al2O3, for which the corresponding formation energy lines intersect at EF = 4.12 eV. The equilibrium Fermi energy can thus be determined at EF = 4.12 eV, 0.28 eV closer to the valence band by contrast with pure α-Al2O3. On the other hand, in Cr- and H-containing αAl2O3, HO+ definitely has the lowest formation energy among all the positively charged defects for a wide range of Fermi levels, and [VAl3−−H+]2− has a relatively wider range of Fermi levels than other negatively charged defects, i.e., HO−, Hi−, and VAl3−, as shown in Figure 3b. However, HO+ is not the most stable form for HO at a Fermi level larger than 3.2 eV. Therefore, the variation tendency of the HO+ formation energy with a high Fermi level (EF ≥ 3.2 eV) was plotted, shown as a blue dotted line in Figure 3b, which intersects the [VAl3−− H+]2− line at EF = 5.02 eV. Consequently, the equilibrium Fermi energy is also determined at EF = 5.02 eV, 0.62 eV closer to the conduction band by contrast with pure α-Al2O3; that is, a shift of 0.9 eV occurs in H-containing α-Al2O3 before and after Cr doping. With the determined equilibrium Fermi energies, the equilibrium states of H-related defects in pure α-Al2O3 are HO+, [VAl3−−H+]2−, and Hi+, consistent with the recent theoretical results.14 However, the results for the relative stability of these defects are different. In this work, the relative 9539


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known that the bulk hydrogen diffusion is one of the six processes of hydrogen permeation in materials, and the hydrogen diffusion is realized by the migration of H-related defects.8,14 Thus, the migration processes of equilibrium-state H-related defects in α-Al2O3 before (Hi+, HO+, [VAl3−−H+]2−) and after (Hi−, HO−, [VAl3−−H+]2−) Cr doping are investigated in this work. For Hi in α-Al2O3, only the diffusion from an octahedral interstitial site to an adjacent one (e.g., C → C′ in Cr-doped αAl2O3, as illustrated in Figure 1) was considered, which will contribute to the H transport in the material, and the migration energies are listed in Table 3. It can be seen that the migration

Table 2. Binding Energy (Eb) and Atomic Distance (dO−H) between the Introduced H Atom and the Nearest O Atom for Each H-Related Defect of the Equilibrium State in αAl2O3 before and after Cr Doping under O-Deficient and HRich Conditions Eb (eV) H-related defect +

HO H O− [VAl3−−H+]2− Hi+ Hi−

undoped

dO−H (Å)

Cr-doped

undoped

Cr-doped

0.995 1.006

0.995

3.14 1.70 3.30

3.32

2.041

Table 3. Migration Energy (Em) and Activation Energy (Q) for the Self-Diffusion of Each Equilibrium-State H-Related Defect in α-Al2O3 before and after Cr Doping under ODeficient and H-Rich Conditions

interaction of H with VO in α-Al2O3 is weakened by Cr, though H− will still be trapped by VO0. For the [VAl3−−H+]2− complex, the binding energies between + H and VAl3− at the respective equilibrium Fermi energies in αAl2O3 before and after Cr doping are almost the same, yet still larger than that of HO, as shown in Table 2. The doped Cr thus has a slight influence on the large attractive interaction of H+ with VAl3− in α-Al2O3, which can also be revealed from the atomic distance (dO−H) between the H atom and the nearest O atom in the system. In this case, H+ bonds to one of the six nearest O neighbors of VAl3−, and the H−O distance remains unchanged, i.e., 0.995 Å, slightly larger than the experimental H−O bond length of H2O,52 both before and after Cr doping. As for Hi+ in pure α-Al2O3, it will bond to an O atom with a bond length of 1.006 Å, while a 2-fold larger distance (2.041 Å) will be present in Cr-doped α-Al2O3 (Table 2). Obviously, a repulsive interaction exists between Hi− and a neighboring O atom after Cr doping, totally different from the attractive interaction of Hi+ with an O neighbor in pure α-Al2O3. The reason must originate from the Coulomb interaction variation between the negatively charged O atom and Hi, since the equilibrium charge state of Hi will be changed by Cr addition in α-Al2O3. The positive binding energies of HO+, HO−, and [VAl3−− + 2− H ] suggest that Hi will be trapped by VO0 and VAl3− in αAl2O3, whether Cr doping exists or not (Table 2). However, a positive binding energy does not guarantee the ready formation of a defect complex, and should be greater than the largest formation energy of the constituent defects of the complex.39 In pure α-Al2O3, the binding energy of HO+ is larger than the formation energies of its constituents, i.e., Hi+ and VO0, indicating that HO+ will be readily formed in α-Al2O3, as shown in Tables 1 and 2. Moreover, the formation energies of HO+, Hi+, and VO0 are in the same level (Table 1); that is, they may coexist in α-Al2O3, though HO+ possesses a relatively larger concentration. A similar situation is also presented for [VAl3−− H+]2− in pure α-Al2O3. After Cr doping, it can be judged that HO− will be readily formed in α-Al2O3, yet HO− will be dominant among HO−, Hi−, and VO0. However, the binding energy of [VAl3−−H+]2− is relatively smaller than that of VAl3− in Cr-doped α-Al2O3 (Tables 1 and 2). Consequently, [VAl3−− H+]2− may coexist with VAl3− in α-Al2O3 after Cr doping, though the latter has a much higher formation energy. Therefore, Hi+, VAl3−, and VO0 are likely to coexist with [VAl3−−H+]2− and HO+ in pure α-Al2O3, while HO− will dominate among Hi−, VAl3−, VO0, and [VAl3−−H+]2− in Crdoped α-Al2O3. 3.4. Cr Effect on the Diffusion Barriers and Activation Energies of Hydrogen-Related Defects in α-Al2O3. It is 0

Cr-undoped Em (eV) Q (eV)

Cr-doped

Hi+

[VAl3−−H+]2−

HO+

Hi−

[VAl3−−H+]2−

H O−

1.96 4.43

5.88 7.99

6.93 9.04

1.10 1.40

6.92 8.48

6.97 6.61

energy of Hi in α-Al2O3 will be greatly reduced from 1.96 to 1.10 eV by Cr. The two energies are both less than 2.0 eV, and such small migration barriers enable the Hi migration in αAl2O3 under convenient circumstances, whether Cr is present or not. Combined with the calculated formation energy (Table 1) and migration energy (Table 3), the activation energy for the self-diffusion of each H-related defect in α-Al2O3 can be obtained by the sum of the two energies,39 as shown in Table 3. According to this table, the activation energy of self-diffusion for Hi in α-Al2O3 will be dramatically decreased as a result of Cr addition. Obviously, Cr is beneficial for the Hi diffusion in αAl2O3, which will be unfavorable for aluminide TPBs resisting H permeation. As for the H-related defect complexes, i.e., [VAl3−−H+]2−, HO+, and HO− in α-Al2O3, the self-diffusion path from the most stable vacancy site to a possible adjacent one is selected (e.g., A → A′ for [VAl3−−H+]2−, and B → B′ for HO− in Cr-doped αAl2O3, as shown in Figure 1). Subsequently, the corresponding migration energies and activation energies for self-diffusion are calculated, also listed in Table 3. The results show that the minimum migration energy for [VAl3−−H+]2− in α-Al2O3 is 5.88 eV, much smaller than that for HO+. However, after Cr doping, both the migration energies increase, up to nearly 7.0 eV. Such high migration barriers indicate that the direct diffusion of [VAl3−−H+]2−, HO+, or HO− is nearly unlikely to occur in αAl2O3 under convenient circumstances. Interestingly, the selfdiffusion activation energy for [VAl3−−H+]2− in α-Al2O3 will be increased by Cr, yet that for HO will be reduced remarkably, possibly resulting from the significant decrease of the HO− formation energy in Cr-doped α-Al2O3. On the other hand, the stability of H-related defect complexes in α-Al2O3 can be further characterized by their dissociation energies, estimated by the sum of the binding energy of the defect complex and migration energy of Hi.39 Combined with the results from Tables 2 and 3, the dissociation energies of [VAl3−−H+]2− and HO+ in pure α-Al2O3 are 5.27 and 5.09 eV, respectively, which will be greatly reduced to 4.40 and 2.80 eV after Cr doping. Anyway, these dissociation energies of [VAl−H] and HO complexes are smaller than the corresponding migration energies, indicating that these H-related defect complexes in 9540


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Figure 5. Energy profiles for the migrations of (a) Hi+ in pure α-Al2O3 and (b) Hi− in Cr-doped α-Al2O3. The local configurations and bonding states of Hi are shown at the critical points of the energy profiles.

Figure 6. (a) Density of states for an equilibrium-state H-related-defect-containing α-Al2O3 supercell and (b) partial density of states for equilibriumstate Hi and the nearest O atom before and after Cr doping. The valence-band maxima are set at 0 eV, and extra levels for Cr-doped α-Al2O3 (compared with pure α-Al2O3) are denoted by blue arrows.

α-Al2O3, the Hi− migration will be the rate-limiting step for Hi− diffusion for its much higher energy in the activation energy (Table 1 and 3). On the other hand, the decrease of the binding energies of H-related defect complexes by Cr (shown in Table 2) suggests that the trapping ability of H by vacancy-type defects in α-Al2O3 is lowered by Cr addition, increasing the H mobility and decreasing the activation energy of H migration. Therefore, from these points, Cr is beneficial for the H diffusion in α-Al2O3, which will be unfavorable for aluminide TPBs resisting H permeation. To explore the Cr effect on the H diffusion in detail, the processes of Hi diffusion in α-Al2O3 before and after Cr doping are investigated, as shown in Figure 5. In these figures, the local configurations and bonding states of Hi at the critical points of the energy profiles are also shown. It can be seen that, during the Hi+ diffusion in pure α-Al2O3, complex variations will emerge for the bonding state of Hi+: (1) Hi+ bonds to a single O atom, and the H−O bond is reoriented and stretched (initial state (IS) to state 2). (2) Hi+ bonds to one more O atom from another O layer within the same octahedral interstitial site, forming the transition state, i.e., state 3. (3) The initial H−O bond is broken, and Hi+ bonds to an adjacent Al atom besides the O atom from the new layer (states 4 and 5). (4) The H−Al bond is broken, and Hi+ only bonds to the O atom from the new layer. Then the H−O bond is reoriented (states 6−11),

α-Al2O3 are likely to dissociate at high temperatures to release the trapped H, contributing to the H transport in the material, maybe in the form of Hi, other than via the direct diffusion of complexes. The propensity will be further enhanced by Cr doping. In a word, the stability and self-diffusion process of Hrelated defect complexes in α-Al2O3 are significantly affected by Cr. By further contrast in Table 3, it is clear that Hi has the lowest migration energy and self-diffusion activation energy among H-related defects in α-Al2O3, both before and after Cr doping. Moreover, as stated above, the H-related defect complexes in α-Al2O3 are unlikely to diffuse directly. Therefore, Hi+ and Hi− are the dominant diffusion species in pure and Crdoped α-Al2O3 under the working conditions of aluminide TPBs, respectively. The calculated diffusion activation energy of Hi+ in pure α-Al2O3 is 4.43 eV, on the same level as the previously reported theoretical prediction14 and experimental result.47 After Cr doping, the diffusion activation energy of Hi− in α-Al2O3 is reduced to 1.40 eV. Such a small energy enables the Hi− diffusion under convenient circumstances. Moreover, by comparison, the formation energy of Hi+ in pure α-Al2O3 is higher than the migration energy (shown in Tables 1 and 3), suggesting that the formation energy is actually the key term in the activation energy; that is, the Hi+ formation is the ratelimiting step for Hi+ diffusion in pure α-Al2O3. As for Cr-doped 9541


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The Journal of Physical Chemistry C and eventually hops to the final state (FS), as shown in Figure 5a. Therefore, two steps are involved in the Hi+ diffusion in pure α-Al2O3: (1) the screw motion of Hi+ from the initial bonded O atom to another O atom from a new O layer within the same octahedral interstitial site, in which the breaking and re-forming of the H−O bond accompanied by the forming and breaking of the H−Al bond occur (IS to state 10), and (2) the hopping of Hi+ from one bonded O atom to an adjacent O atom in the same O layer yet in a different but adjacent octahedral interstitial site, in which only the breaking and reforming of the H−O bond take place (state 10 to FS). The first step of Hi+ diffusion is a little different from the previously reported results14 in which the forming and breaking of the H− Al bond were not revealed. By contrast, the process of Hi− diffusion in Cr-doped α-Al2O3 is much simpler than Hi+ diffusion in pure α-Al2O3, as shown in Figure 5b. Only one step is involved, that is, the reorientation of the H−Cr bond from one octahedral interstitial site to an adjacent one, without any breaking, forming, or re-forming of any other H-related bonds (i.e., H−O and H−Al bonds), resulting in a much lower activation energy consumed than that in pure α-Al2O3, as shown in Table 3. During the Hi− diffusion, Hi− bonds to and rotates around the Cr substituent all the time. The transition state will form when Hi− rotates to the O layer between the two adjacent octahedral interstitial sites. Therefore, it is easy to understand the greater readiness of H diffusion in Cr-doped α-Al2O3 than that in pure α-Al2O3; that is, Cr is beneficial for H diffusion in α-Al2O3, which in turn is unfavorable for the H-permeation resistance of aluminide TPBs, consistent with the results obtained from Table 3. The Cr effect on hydrogen interactions with intrinsic point defects in α-Al2O3 can be related to the electronic structures of these defects. As a typical example, calculated densities of states (DOS) for equilibrium-state H-related-defect-containing αAl2O3 before and after Cr doping are shown in Figure 6a. It can be seen that the overall DOS profile for each type of H-relateddefect-containing Cr-doped α-Al2O3 is quite similar to that of pure α-Al2O3. However, after Cr doping, the DOS spectra are shifted to the lower energy range, up to about 5.4 eV. Moreover, extra levels can be observed at around conduction band edges of the band gap, denoted as blue arrows in Figure 6a. Obviously, Cr exerts some influence on the electronic structures of H-related defects, resulting in the variations of hydrogen interactions with intrinsic point defects in α-Al2O3. Take Hi as an example; calculated partial densities of states (PDOS) for equilibrium-state Hi and the nearest O atom before and after Cr doping are shown in Figure 6b. From this figure, in pure α-Al2O3, the H s state ranges from −19.7 to −16.8 eV, from −8.6 to −1.1 eV, and from 5.2 to 9.2 eV, with two main peaks located at −7.9 and 8.2 eV, and the s and p states of the nearest O atom of Hi mainly locate in such energy ranges, indicating that H mainly interacts with O, which can also be revealed in Figure 5a. However, after Cr doping, great changes occur for the overall PDOS profiles of the H s, O s, and O p states. The H s state shifts to the lower energy range, and the energy interval of the two main peaks shrinks from 16.0 to 4.6 eV. For the nearest O atom of Hi, the O s state booms in a rather low energy range (−23.4 to −19.5 eV), and the O p state also shifts to a lower energy range, accompanied by a significant variation of the PDOS profile. The more important case is that the PDOS overlapping for H and O atoms is greatly reduced after Cr doping, leading to a weak interaction between the two atoms, as shown in Table 2. On the contrary, the s, p,

and d states of the Cr atom mainly locate in energy ranges similar to that of the H s state, indicating that a strong interaction exists for H and Cr atoms, which can be observed in Figure 5b. On the other hand, it is known that the electron arrangement of Cr3+ is 1s22s22p63s23p63d3, and the three outer electrons are not chemically stable, which can be partly shared with Hi, resulting in the formation of Hi− and a strong bonding interaction between H and Cr in Cr-doped α-Al2O3 (Figure 6b). Hence, Cr3+ acts as an electron donor in the process of H diffusion. Moreover, both the lattice Al3+ and O2− ions in pure α-Al2O3 have closed electron shells, and thus, the electrons are more chemically stable than that of Cr3+. Consequently, weaker interactions between H and the lattice atoms, especially O, will take place, as shown in Figure 6b. However, the relatively stronger bonding interaction of Hi with the Cr atom does not mean extra activation energy will be consumed for the H diffusion in Cr-containing α-Al2O3, since no H-related bonds will break, form, or re-form as happens in pure α-Al2O3, resulting in the greater readiness of H diffusion in Cr-doped αAl2O3, which is unfavorable for the H-permeation resistance of aluminide TPBs, as also revealed in Table 3 and Figure 5.

4. CONCLUSIONS Cr is definitely present in the outer Al2O3 scale in aluminide TPBs, and thus, the effects of Cr on hydrogen interactions with intrinsic point defects and hydrogen diffusion in α-Al2O3 under the common working conditions of aluminide TPBs, i.e., Odeficient and H-rich conditions, have been investigated on the basis of first-principle calculations. The results obtained can be summarized as follows: (1) Cr is favorable for the formation of VO, yet unfavorable for VAl formation in α-Al2O3. (2) The formation, existing form, charge state, and relative stability of H-related defects, i.e., Hi, HO, and [VAl−H], will be greatly influenced by Cr, and Cr is beneficial for the formation of H-related defects in α-Al2O3. (3) Hi will be trapped by VO and VAl in α-Al2O3, which will be weakened to different extents by Cr. Moreover, H-related defects are likely to coexist with intrinsic point defects in pure α-Al2O3, while HO− will dominate after Cr doping. (4) Hi is the dominant diffusion species in both pure and Crdoped α-Al2O3, and Cr is beneficial for the H diffusion in αAl2O3, which will be unfavorable for H-permeation resistance of aluminide TPBs. Two steps of screw motion and hopping are involved for the Hi diffusion in pure α-Al2O3, in which the forming and breaking of the H−Al bond and/or the breaking, forming, and re-forming of the H−O bond occur, while only one step of reorientation of the H−Cr bond is involved, contributing to the greater readiness of H diffusion in Cr-doped α-Al2O3. (5) The Cr effect on hydrogen interactions with intrinsic point defects and H diffusion in α-Al2O3 can be attributed to the chemically unstable electron structure of Cr3+ and a relatively stronger bonding interaction between H and Cr than that between H and crystal Al and O atoms.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 86-816-3626483. Notes

The authors declare no competing financial interest. 9542


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(19) Cheng, W. J.; Wang, C. J. Effect of Chromium on the Formation of Intermetallic Phases in Hot-Dipped Aluminide Cr-Mo Steels. Appl. Surf. Sci. 2013, 277, 139−145. (20) Fazio, C.; Stein-Fechner, K.; Serra, E.; Glasbrenner, H.; Benamati, G. Investigation on the Suitability of Plasma Sprayed FeCr-Al Coatings as Tritium Permeation Barrier. J. Nucl. Mater. 1999, 273, 233−238. (21) Zhang, G. K.; Chen, C. A.; Luo, D. L.; Wang, X. L. An Advance Process of Aluminum Rich Coating as Tritium Permeation Barrier on 321 Steel Workpiece. Fusion Eng. Des. 2012, 87, 1370−1375. (22) Stein-Fechner, K.; Konys, J.; Wedemeyer, O. Investigations on the Transformation Behavior of the Intermetallic Phase (Fe,Cr)2Al5 Formed on MANET II Steel by Aluminizing. J. Nucl. Mater. 1997, 249, 33−38. (23) Yang, H. G.; Zhan, Q.; Zhao, W. W.; Yuan, X. M.; Hu, Y.; Han, Z. B. Study of An Iron-Aluminide and Alumina Tritium Barrier Coating. J. Nucl. Mater. 2011, 417, 1237−1240. (24) Zhan, Q.; Yang, H. G.; Zhao, W. W.; Yuan, X. M.; Hu, Y. Characterization of the Alumina Film with Cerium Doped on the IronAluminide Diffusion Coating. J. Nucl. Mater. 2013, 442, S603−S606. (25) Kitajima, Y.; Hayashi, S.; Nishimoto, T.; Narita, T.; Ukai, S. Acceleration of Metastable to Alpha Transformation of Al2O3 Scale on Fe-Al Alloy by Pure-Metal Coatings at 900 °C. Oxid. Met. 2011, 75, 41−56. (26) Levchuk, D.; Koch, F.; Maier, H.; Bolt, H. Deuterium Permeation through Eurofer and α-Alumina Coated Eurofer. J. Nucl. Mater. 2004, 328, 103−106. (27) Deer, W. A.; Howie, R. A.; Zussman, J. An Introduction to the Rock-Forming Minerals, 2nd ed.; Prentice Hall: Upper Saddle River, NJ, 1996. (28) Gaudry, E.; Cabaret, D.; Sainctavit, P.; Brouder, C.; Mauri, F.; Goulon, J.; Rogalev, A. Structural Relaxations around Ti, Cr and Fe Impurities in α-Al2O3 Probed by X-ray Absorption Near-Edge Structure Combined with First-Principles Calculations. J. Phys.: Condens. Matter 2005, 17, 5467−5480. (29) Hine, N. D. M.; Frensch, K.; Finnis, M. W.; Foulkes, W. M. C.; Heuer, A. H. Point Defects and Diffusion in Al2O3. Presented at the International Conference on QMC in the Apuan Alps V, Vallico Sotto, Tuscany, Italy, July 25 to Aug 1, 2009. (30) Forcey, K. S.; Ross, D. K.; Simpson, J. C. B.; Evans, D. S.; Whitaker, A. G. The Use of Aluminising on 317 Austenitic and 1.4914 Martensitic Steels for the Reduction of Tritium Leakage from the Net Blanket. J. Nucl. Mater. 1989, 161, 108−116. (31) Delley, B. From Molecules to Solids with the DMol3 Approach. J. Chem. Phys. 2000, 113, 7756−7764. (32) White, J. A.; Bird, D. M. Implementation of Gradient-Corrected Exchange-Correlation Potentials in Car-Parrinello Total-Energy Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 4954. (33) Delley, B. An All-Electron Numerical Method for Solving the Local Density Functional for Polyatomic Molecules. J. Chem. Phys. 1990, 92, 508−517. (34) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. (35) Xiang, X.; Zhang, G. K.; Wang, X. L.; Tang, T.; Shi, Y. A New Perspective on the Process of Intrinsic Point Defects in α-Al2O3. Phys. Chem. Chem. Phys. 2015, 17, 29134−29141. (36) Xiang, X.; Zhang, G. K.; Yang, F. L.; Peng, X. X.; Tang, T.; Shi, Y.; Wang, X. L. An Insight to the Role of Cr in the Process of Intrinsic Point Defects in α-Al2O3. Phys. Chem. Chem. Phys. 2016, 18, 6734− 6741. (37) Kurita, T.; Uchida, K.; Oshiyama, A. Atomic and Electronic Structures of α-Al2O3 Surfaces. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 155319. (38) Matsunaga, K.; Tanaka, T.; Yamamoto, T.; Ikuhara, Y. FirstPrinciples Calculations of Intrinsic Defects in Al2O3. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 085110. (39) Varley, J. B.; Peelaers, H.; Janotti, A.; Van de Walle, C. G. Hydrogenated Cation Vacancies in Semiconducting Oxides. J. Phys.: Condens. Matter 2011, 23, 334212.

ACKNOWLEDGMENTS This work is supported by the National Magnetic Confinement Fusion Science Program (Grant No. 2013GB110006B) and the National Natural Science Foundation of China (Grant Nos. 21471137 and 11275175).

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REFERENCES

(1) Sawan, M. E.; Abdou, M. A. Physics and Technology Conditions for Attaining Tritium Self-Sufficiency for the DT Fuel Cycle. Fusion Eng. Des. 2006, 81, 1131−1144. (2) El-Guebaly, L. A.; Malang, S. Toward the Ultimate Goal of Tritium Self-Sufficiency: Technical Issues and Requirements Imposed on ARIES Advanced Power Plants. Fusion Eng. Des. 2009, 84, 2072− 2083. (3) Zheng, S.; King, D. B.; Garzotti, L.; Surrey, E.; Todd, T. N. Fusion Reactor Start-up without An External Tritium Source. Fusion Eng. Des. 2016, 103, 13−20. (4) Hollenberg, G. W.; Simonen, E. P.; Kalinin, G.; Terlain, A. Tritium/Hydrogen Barrier Development. Fusion Eng. Des. 1995, 28, 190−208. (5) Xiang, X.; Wang, X. L.; Zhang, G. K.; Tang, T.; Lai, X. C. Preparation Technique and Alloying Effect of Aluminide Coatings as Tritium Permeation Barriers: A Review. Int. J. Hydrogen Energy 2015, 40, 3697−3707. (6) Aiello, A.; Ciampichetti, A.; Benamati, G. An Overview on Tritium Permeation Barrier Development for WCLL Blanket Concept. J. Nucl. Mater. 2004, 329−333, 1398−1402. (7) Konys, J.; Aiello, A.; Benamati, G.; Giancarli, L. Status of Tritium Permeation Barrier Development in the EU. Fusion Sci. Technol. 2005, 47, 844−850. (8) Causey, R. A.; Karnesky, R. A.; San Marchi, C. Tritium Barriers and Tritium Diffusion in Fusion Reactors. Compr. Nucl. Mater. 2012, 4, 511−549. (9) Kumar, E. R.; Danani, C.; Sandeep, I.; Chakrapani, Ch.; Pragash, N. R.; Chaudhari, V.; Rotti, C.; Raole, P. M.; Alphonsa, J.; Deshpande, S. P. Preliminary Design of Indian Test Blanket Module for ITER. Fusion Eng. Des. 2008, 83, 1169−1172. (10) Luo, D. L.; Song, J. F.; Huang, G. Q.; Chen, C. A.; Huang, Z. Y.; Deng, X. J.; Qin, C.; Qian, X. J.; Zhang, G. K. Progress of China’s TBM Tritium Technology. Fusion Eng. Des. 2012, 87, 1261−1267. (11) Wong, C.P. C.; Salavy, J. F.; Kim, Y.; Kirillov, I.; Kumar, E. R.; Morley, N. B.; Tanaka, S.; Wu, Y. C. Overview of Liquid Metal TBM Concepts and Programs. Fusion Eng. Des. 2008, 83, 850−857. (12) Mao, W.; Chikada, T.; Suzuki, A.; Terai, T.; Matsuzaki, H. Hydrogen Isotope Dissolution, Diffusion, and Permeation in Er2O3. J. Power Sources 2016, 303, 168−174. (13) Zhang, G. K.; Wang, X. L.; Yang, F. L.; Shi, Y.; Song, J. F.; Lai, X. C. Energetics and Diffusion of Hydrogen in Hydrogen Permeation Barrier of α-Al2O3/FeAl with Two Different Interfaces. Int. J. Hydrogen Energy 2013, 38, 7550−7560. (14) Zhang, G. K.; Lu, Y. J.; Wang, X. L. Hydrogen Interactions with Intrinsic Point Defects in Hydrogen Permeation Barrier of α-Al2O3: A First-Principles Study. Phys. Chem. Chem. Phys. 2014, 16, 17523− 17530. (15) Heuer, A. H.; Nakagawa, T.; Azar, M. Z.; Hovis, D. B.; Smialek, J. L.; Gleeson, B.; Hine, N. D. M.; Guhl, H.; Lee, H. S.; Tangney, P.; et al. On the Growth of Al2O3 Scales. Acta Mater. 2013, 61, 6670− 6683. (16) Lagerlöf, K. P. D.; Grimes, R. W. The Defect Chemistry of Sapphire (α-Al2O3). Acta Mater. 1998, 46, 5689−5700. (17) Hine, N. D. M.; Frensch, K.; Foulkes, W. M. C.; Finnis, M. W. Supercell Size Scaling of Density Functional Theory Formation Energies of Charged Defects. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 024112. (18) Sánchez, L.; Bolívar, F. J.; Hierro, M. P.; Pérez, F. J. Temperature Dependence of the Oxide Growth on Aluminized 9− 12%Cr Ferritic-Martensitic Steels Exposed to Water Vapour Oxidation. Thin Solid Films 2009, 517, 3292−3298. 9543


Article

The Journal of Physical Chemistry C (40) Huang, Q. Y.; Wu, Y. C.; Li, J. G.; Wan, F. R.; Chen, J. L.; Luo, G. N.; Liu, X.; Chen, J. M.; Xu, Z. Y.; Zhou, X. G.; et al. Status and Strategy of Fusion Materials Development in China. J. Nucl. Mater. 2009, 386−388, 400−404. (41) Zhang, S. B.; Wei, S. H.; Zunger, A.; Katayama-Yoshida, H. Defect Physics of the CuInSe2 Chalcopyrite Semiconductor. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 9642. (42) Zhang, S. B.; Wei, S. H.; Zunger, A. Intrinsic n-Type versus pType Doping Asymmetry and the Defect Physics of ZnO. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 63, 075205. (43) Fischer, S.; Karplus, M. Conjugate Peak Refinement: An Algorithm for Finding Reaction Paths and Accurate Transition States in Systems with Many Degrees of Freedom. Chem. Phys. Lett. 1992, 194, 252−261. (44) Henkelman, G.; Jonsson, H. Improved Tangent Estimate in the Nudged Elastic Band Method for Finding Minimum Energy Paths and Saddle Points. J. Chem. Phys. 2000, 113, 9978−9985. (45) Baltrusaitis, J.; Hatch, C.; Orlando, R. Electronic Properties and Reactivity of Simulated Fe3+ and Cr3+ Substituted α-Al2O3(0001) Surface. J. Phys. Chem. C 2012, 116, 18847−18856. (46) Ramírez, R.; Colera, I.; González, R.; Chen, Y.; Kokta, M. R. Hydrogen-Isotope Transport Induced by An Electric Field in α-Al2O3 Single Crystals. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, 014302. (47) Syzgantseva, O. A.; Calatayud, M.; Minot, C. Revealing the Surface Reactivity of Zirconia by Periodic DFT Calculations. J. Phys. Chem. C 2012, 116, 6636−6644. (48) Bonapasta, A. A. Evidence of the Negative-U Behavior of H in GaAs from An Investigation of H and As Antisites. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58, 10378. (49) Padilha, A. C.; Rocha, A.; Raebiger, H.; Dalpian, G. Negative U Behavior of TiO2‑x Magnéli and Corundum Phases. Presented at the APS March Meeting, San Antonio, TX, March 2−6, 2015. (50) Kílíc, C.; Zunger, A. Origins of Coexistence of Conductivity and Transparency in SnO2. Phys. Rev. Lett. 2002, 88, 095501. (51) Van de Walle, C. G. Theory of Hydrogen-Related Levels in Semiconductors and Oxides. Electron Dev. Meeting, IEDM Technical Dig. IEEE Int. 2005, 400−403. (52) Aldstadt, J. H., III; Bootsma, H. A.; Ammerman, J. L. Chemical Properties of Water. Encyclopedia of Inland Waters 2009, 139−147.

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