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Mechanism for adsorption, dissociation and diffusionof hydrogen in hydrogen permeation barrier of a-Al2O3:A density functional theory study

Guikai Zhang a,b,*, Xiaolin Wang a,b, Yifu Xiong a, Yan Shi a, Jiangfeng Song a, Deli Luo a

aChina Academy of Engineering Physics, Mianyang 621900, ChinabCollege of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230031, China

a r t i c l e i n f o

Article history:

Received 19 July 2012

Received in revised form

23 October 2012

Accepted 28 October 2012

Available online 20 November 2012

Keywords:

Hydrogen adsorption

Hydrogen diffusion

DFT

a-Al2O3

Hydrogen permeation barrier

* Corresponding author. China Academy of Enfax: þ86 816 3625900.

E-mail address: Gkzhang712@163.com (G0360-3199/$ e see front matter Copyright ªhttp://dx.doi.org/10.1016/j.ijhydene.2012.10.1

a b s t r a c t

Toward understanding physical interaction of hydrogen isotopes with a-Al2O3 barrier,

adsorption, dissociation and diffusion of hydrogen in a-Al2O3(0001) slab have been inves-

tigated by density functional theory (DFT) and rate theory. H2 molecule, with parallel

configuration, preferentially absorbs on a top Al atom site of first atomic layer on

a-Al2O3(0001) surface, while H atom strongly bonds at a top O atom site of the second

atomic layer, H atoms recombine into molecules on top Al atom sites of the third atomic

layer. The barrier for H2 exothermic dissociation on surface is 0.79 eV. The potential energy

pathways of H diffusion in a-Al2O3 are studied, predicting that H atom diffusion prefer-

entially occurs via surface path rather than bulk path involving elementary reorientation

and hopping steps. The surface-to-subsurface diffusion is significantly endothermic except

for the surface and subsurface-to-bulk path. Mechanism, in well agreement with experi-

mental result, of a-Al2O3 resisting hydrogen permeation has proposed.

Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

1. Introduction [4,5], TiN/TiC [6] and SiC [7], etc, have shown resistance of

In fusion reactor like ITER, structural materials, such as

Eurofer97, 316L and F82H steel generally have high perme-

ability of hydrogen isotopes in the operational temperature

range [1e3]. Thus suppression of the hydrogen isotopes

permeation through wall of duct is an interesting issue to

safely operate radioactive tritium, optimize the tritium

balance and minimize hydrogen embrittlement of container.

The use of a layer namely hydrogen permeation barrier

deposited on structural materials is efficacious way to reduce

the hydrogen isotopes, especially tritium, penetration.

Hydrogen permeation barriers, such as aluminum rich coating

gineering Physics, P.O. Bo

. Zhang).2012, Hydrogen Energy P08

hydrogen isotopic permeability. The best solution is identified

in aluminum rich coating with Al2O3 scale on their surface [8].

Such aluminum rich coating based barriers on steel, con-

sisting of an outer Al2O3 layer and an inner Al-rich interme-

tallic layer, are usually formed by aluminization of the steel

with hot dip process, as well as with various pack-

cementation, vacuum plasma spray and electrodeposition of

aluminum, followed by oxidation [8e12]. The inner Al-rich

intermetallic layer is made up of mixed Fe3Al and FeAl.

Nickel, Cr, and mixed-aluminides are also formed. The outer

layer often has a mixed oxide scale that is rich in Al2O3 [16].

However, different processes lead to the oxide scales of

x 919-71, Mianyang 621900, Sichuan, China. Tel.: þ86 816 3626726;

ublications, LLC. Published by Elsevier Ltd. All rights reserved.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 1 5 7e1 1 6 51158

differing composition, thickness and defect density, and

permeation reduction factors (PRF) of barriers vary between 10

and 10,000with a wide range of scatter. The barrier containing

a clean Al2O3 scale often has the greatest PRF, especially with

a-Al2O3 scale [13e15]. What are attributed to the greatest PRF

and how they operate during hydrogen isotopes permeation

through the a-Al2O3 barrier?

For hydrogen isotopes to permeate through the hydrogen

permeation barrier, the hydrogen isotopesmust absorb on the

surface, dissociate into atoms, dissolve into the barrier,

diffuse through the barrier, and then recombine into mole-

cules on the downstream side. The resistance performance of

the barrier depends on the barrier integrity as well as the

physical interaction of the barrier material with hydrogen

isotopes. Vast present publications, however, are fusing on

processes and hydrogen isotopic permeation efficiency eval-

uation, to enhance the integrity of the Al2O3 barrier. Only

relatively few studies have devoted to the understanding of

the physical interaction of Al2O3 with hydrogen isotopes,

which are important from the fundamental standpoint of

resisting mechanism of hydrogen isotopic permeation, but

also from the technological viewpoint of improving processes

for the Al2O3 barrier.

To describe distinct physics of the interactions between

hydrogen isotopes and barrier material, Hollenberg et al.,

considering such hydrogen isotopic behaviors with barriers

and dependence of the permeation rate on the hydrogen

isotope partial pressure, proposed composite diffusionmodel,

area defect model and surface desorption model [15,17]. It is

concluded from these models that hydrogen permeation is

controlled by the hydrogenmolecule dissociate rate on barrier

surface or by the hydrogen atom diffusion rate in barrier.

Unfortunately, these models have revealed the rate-

controlling mechanism for permeation, but not how

hydrogen isotopes adsorb, dissociate, dissolve into the a-Al2O3

barrier, diffuse through the barrier, and recombine into

molecules, which are urgent to be studied both experimen-

tally and theoretically. While less information is available

regarding the H atom or molecule on surface or into bulk of a-

Al2O3.

Experimentally, Toofanet al. have found that thestructureof

a-Al2O3(0001) layer, with single domain O- or Al-terminated

surface, gives a poor agreement with observation [18]. Barth

et al. have reported that a-Al2O3 interaction with H2 or H2O can

generate hydrogen clusters by scanning atomic force micro-

scope [19]. Previous DFT-generanzed gradient approximation

(GGA) calculations predicted that the terminated atoms of a-

Al2O3(0001) surface have a great relationshipwith environment:

the single Al atom terminated surface is stable surface,whereas

theO-terminatedsurfacebecomesstablewhenfilledwithH [20].

More recent DFT-GGA calculations predicted that H atom sits at

O atop site onto a-Al2O3(0001) surface, andH atom cluster forms

in the regime of higher H coverages [21]. Belonoshko et.al, with

molecule dynamic calculations, derived hydrogen diffusivity in

a-Al2O3 as D(T ) ¼ 21.73 � 10�8exp(1.24 eV/kBT ) m2/s [22].

In presentwork, a-Al2O3 slab is applied to offermicroscopic

insight into mechanisms for adsorption, dissociation and

diffusion of hydrogen into the a-Al2O3 barrier by a combina-

tion of DFT calculations, path techniques and vibrational

frequencies, enabling a direct determination of the rate

limiting processes to identify mechanism of purity a-Al2O3

resisting hydrogen isotopic permeation. a-Al2O3 is of special

interest because of effective hydrogen isotopic permeation

reduction and anti-corrosion behavior. To the best of our

knowledge, no similar publication has devoted to such work

on the a-Al2O3 barrier.

2. Computational method and model

2.1. Method

All present calculations are performed with DFT plane wave

method utilizing the Cambridge Serial Total Energy Package

(CASTEP) [23] in the Materials studio of Accelry Inc. The

ultrasoft pseudopotential [24] in conjunctionwith the Perdew-

Wang (PW91) [25] functional within GGA, is applied. The

Brillouin zone is sampled with the Monkhorst-Pack grid [26].

The calculations are carried out using the 3 � 3 � 3 and

3 � 3 � 1 Monkhorst-Pack mesh k-points for bulk and surface

calculations, respectively. Cutoff energy is set to be 400 eV,

which converges total energies to within 2 meV/atom. The

convergence criteria for the structure optimization and energy

calculation are set to (a) an SCF tolerance of 2.0 � 10�6 eV/

atom, (b) an energy tolerance of 2.0 � 10�3 eV/atom, (c)

a maximum force tolerance of 0.02 eV/�A, and (d) a maximum

displacement tolerance of 5.0 � 10�4 eV, giving energies

computationally converging to within 2 meV/atom.

The complete linear synchronous transit/quadratic

synchronous transit (LST/QST) method is used to locate the

transition states (TS) for the H2 dissociation on surface and the

hydrogen diffusion in slab. Frequencies are calculated at all

critical points identified on the potential energy surface to

identify minima and transition states. For a local energy

minimum, all frequencies are real, whereas for a transition

state, a single imaginary frequency appears, thus identifying

the position on the potential energy surface as a saddle point,

i.e., a transition state. If more than one imaginary frequency is

found for a saddle point, the path found does not go through

true TS and then we search for other paths.

2.2. Model

The primitive cell of a-Al2O3 is rhombohedra. Since the O

atoms approximately form a hexagonal close packed (hcp)

lattice with Al atoms occupying 2/3 of the octahedrally coor-

dinated interstitial positions, the conventional hexagonal cell

is used to, throughout this paper, describe the structure [27].

The structure has a �OeAleAleOeAleAl- stacking sequence

in the (0001) direction, with 2.2 �A between the O planes in the

bulk configuration. Thus, three (0001) surface terminations

are obtainable by cleaving the bulk structure: single Al atom

terminated (Al-I), O atoms terminated (O-I) and two Al atoms

terminated (Al-II) a-Al2O3(0001) surface. The surface is

modeled using a slab geometry with (2 � 2) surface unit cells

and periodic boundary conditions in all three dimensions. A

total amount of 12 layers are used in the slab (i.e., four O

layers), out of which the six bottom layers are frozen in their

bulk position. The top most six layers are allowed to relax in

all calculations. The vacuum depth separating the slab in the

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 1 5 7e1 1 6 5 1159

(0001) direction is 15 �A. Test calculations show that increasing

the number of free layers to 12 while keeping six frozen layers

alters surface energy by < 0.2 eV.

The optimized bulk a-Al2O3 lattice parameters for a, b and c

are 4.806, 4.806 and 13.133 �A, which are in good agreement

with the experimental values (a ¼ b ¼ 4.759 �A and c ¼ 12.990 �A

[28]) and the results of other DFT calculations [29,30].

According the definition of surface energy [29], calculated

surface energies of Al-I, O-I and Al-II termination surface are

1.53, 6.05, and 6.15 J/m2, respectively. The Al-I termination

surface, thus, is believed to be the most stable one, in satis-

factory agreement with computationally values [29,30].

Therefore, we use this surface for all subsequent calculations

in this paper.

In this study, the adsorption energy is defined as

DEads ¼ E[slabþadsorbate] � (E[slab] þ E[adsorbate]), where

E[slab þ adsorbate], E[slab], and E[adsorbate] are the calculated total

energy of adsorbed species on the a-Al2O3(0001) surface,

a clean a-Al2O3(0001) surface and a gas-phase molecule or

atom, respectively. With this definition, negative values of

DEads denote adsorption that is more stable than the corre-

sponding clean surface and gas phase H2.

Fig. 1 e The top (a) and side (b) view of a 2 3 2 primitive cell

of a-Al2O3(0001) surface, Letters indicate possible

adsorption sites for atomic and molecular hydrogen on

surface and bulk. Red and purple balls depict oxygen and

aluminum atoms. (For interpretation of the references to

colour in this figure legend, the reader is referred to the

web version of this article.)

Table 1 e Adsorption energies and bond lengths for Hatom on a-Al2O3(0001) surface.

Adsorption site DEads, (eV) d (Al2O3-H) (�A)

A �2.18 1.62

B �2.35 0.98

C e e

D e e

E �1.43 1.05

3. Results and discussion

3.1. Atomic hydrogen adsorption on clean a-Al2O3(0001) surface

Fig. 1 shows the attempted adsorption sites on the Al-I

terminated surface. Position D is on top of an Al atom in the

fourth atomic layer and corresponds to the Al position in

subsurface a-Al2O3. Position A and C is on top of Al atom of the

first (top) and third atomic layer, respectively, while position

B, E, F and G is on top of O atom of the second, fifth, eighth and

eleventh atomic layer. The calculated adsorption energies for

H in the different positions are shown in Table 1. As

mentioned above, the first atomic layer contains four Al atoms

resulting in H atom surface coverage of 0.25 ML upon

adsorption of one H atom.

The only stable adsorption site for the H atom on the

surface is the surface position B, with an adsorption energy of

�2.35 eV. Results from adsorption attempts in positions A and

E indicate that these positions are saddle points. Hence, weak

forces act on the adatoms in the exact adsorption positions,

but a slight perturbation causes the adatoms to move to the

position B seemingly without barrier. The adsorption energies

in the saddle points A and E are �2.18 and �1.43 eV, respec-

tively, indicating that the activation barrier for H adatom

surface diffusion between surface sites on surface is of the

order of 0.18 eV (assuming diffusion via site A), while that for

the H diffusion from surface to subsurface is 0.92 eV

(assuming diffusion via site E). Moreover, the existence of

energetically less favorable sites in bulk a-Al2O3 relative to the

surface indicate that resistant role to hydrogen permeation

may take place at the surface. However, to fully elucidate the

barrier height, more careful investigations would be neces-

sary. Adsorption in position C or D, i.e., the top of Al atoms in

subsurface, is unstable and the adatoms spontaneously move

to or away surface positions during the energy minimization

process.

We also examined coadsorption of two H atoms to identify

final states for H2 dissociation. Table 2 lists the adsorption

energies for these coadsorption calculations. The initial and

final sites identified in Table 2 indicate the initial placement of

the H atoms and their final location after optimization. Four

different initial geometries converge to, upon optimization,

adsorb on the Al top atom (A) and the O top atom (B, B0 and B00,as shown in Fig. 1) with same adsorption energy of �7.05 eV.

The AB, AB0 and AB00 distances are 2.685, 2.907 and 4.061 �A,

Table 2 e Adsorption energies for two coadsorbed H atoms on a-Al2O3(0001) surface.

Initial sites AB AC AD AE BC BD BE CD CE DE BB0 BB00

Final sites AB AB0 AB00 AE C AB0 BE C AB e BB0 BB00

DEads (eV) �7.05 �7.05 �7.05 �6.05 0.41 �7.05 �4.25 0.31 �6.30 e �5.33 �4.19

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 1 5 7e1 1 6 51160

respectively. However, the AB00 distance is too large to be

reasonable final configurations for dissociation, although it is

presumably accessible via surface diffusion following disso-

ciation. Thus the AB and AB0 configurations are used as the

end points in the H2 dissociation study.

The CE configuration, having a low adsorption energy of

�6.30 eV, also converges to AB configuration. One of H atoms,

however, adsorbs on bottom of O atom, not on top.

Note that the sum of binding energies for H atom on the

site A and B from Table 1 is �4.53 eV, which is considerably

less than the �7.05 eV value obtained for coadsorption on the

AB site. The reason for the enhanced binding appears to be

due to cooperative effects and can be understood by frontier

orbital theory [31]. The adsorption of an H atom at the site A

changes the frontier orbitals, having some anti-bonding

character, of the surface, while a second H on the site B only

involves bonding orbitals (Fig. 2). Thus, coadsorption on the

site AB should exhibit the larger binding energy than the sum

of the isolated binding energies.

In view of BC and CD geometry, they converge to the same

final configuration, site C, which is the most unstable config-

uration having positive adsorption energies. This means that

the formation of H2 molecule having HeH bond length of

0.75 �A, in agreement with H2 molecule bond length of 0.74 �A

[32]. We can conclude that hydrogen atoms recombine into H2

molecules at the positions C on a-Al2O3(0001) surface, even

though the kinetic barrier for this process is unknown.

3.2. Molecular hydrogen adsorption on clean a-Al2O3(0001) surface

For the adsorption of H2, we have investigated both end-on

(with the HeH bond is normal to the a-Al2O3(0001) surface)

and side-on (with the HeHbond is parallel to the a-Al2O3(0001)

surface) coordinations of the molecule to various adsorption

sites on the a-Al2O3(0001) surface. For the end-on configura-

tion, the optimized geometries and adsorption energies of the

H2 on a-Al2O3(0001) surface have been summarized in Table 3.

Fig. 2 e Charge density difference plot in a plane

perpendicular to the surface for two hydrogen atoms

coadsorption at site AB.

The calculated HeH bond lengths in five different adsorption

sites are about 2e3% longer than that in the gas phase. Among

all of the calculated adsorption configurations of H2 on the a-

Al2O3(0001) surface, the adsorption energies of H2 in most

adsorbed sites vary with in �0.05 to �0.02 eV, indicating that

the adsorption of H2 on the a-Al2O3(0001) surfacewith the end-

on configuration belongs to physisorption. The side-on coor-

dination results are shown in Table 4. We found that H2 can

absorb stably on the A site with the calculated adsorption

energy of �0.12 eV. In summary, it is found that the adsorp-

tion of H2 molecule on the a-Al2O3(0001) surface favors the top

Al site of the first atomic layer with the side-on configuration.

This configuration is used as the initial point in the H2 disso-

ciation study.

It is well-known that DFT can not give reliable energies for

weakly bound systems [33], therefore, the absolute energies

for these physisorbed molecules are not likely to be accurate.

This is not a severe difficulty for our purposes, since a change

in these physisorption energies will not have a large effect on

the quantity of interest to us, namely the dissociation barrier.

For example, an error in the H2 binding energy of a factor of 2

would change the dissociation barrier by less than 0.05 eV

[33,34].

3.3. Dissociation of H2 on clean a-Al2O3(0001) surface

We have computed the dissociation pathways for H2 starting

from H2 adsorbed at the site A, and ending at two H atoms

coadsorbed at either the AB or AB’ site. The calculated disso-

ciation path (A / TS / AB) is plotted in Fig. 3. The dissocia-

tion energy barrier computed directly from the data is 0.79 eV,

that for dissociation pathway (A / TS / AB0) proceeds in

a similar fashion but with a higher energy barrier of 0.90 eV,

Therefore, The hydrogenmolecules can easily dissociate from

the Al top site (site A) to the Al top site and the O top site (site

B). Dissociation adsorption of H2 is predicted to be exothermic

for two pathways. The reversed path, AB/ TS/ A, proceeds

in a endothermic fashion with a higher energy barrier of

0.92 eV, suggesting that it is definitely easier for H2 dissocia-

tion on clean a-Al2O3(0001) surface than hydrogen atoms

recombination.

The initial physisorbed state is gas-like in that the HeH

bond length is calculated to be 0.75�A, which is the same as the

DFT optimized gas-phase bond length. The distance between

the H atom and the nearest surface atom is 2.23 �A. In the

transition state, the HeH bond length is 1.06 �A and the

distance between the two different H atoms and the nearest

surface Al atom and O atom is 1.73 and 1.26 �A, respectively.

The coadsorbed state is the AB configuration from Table 2 and

is characterized by AleH bond with a bond length of 1.58 �A,

which is smaller than the AleH bond in the AlH3 molecule of

1.72 �A [35], and OeH bond with a bond length of 0.97 �A, which

Table 3 e End-on adsorption energies and bond lengthsof H2 on a-Al2O3(0001) surface.

Adsorptionsite

DEads(eV)

d1 (Al2O3eH2)(�A)

d2 (Al2O3eH2)(�A)

d(HeH)(�A)

A �0.02 2.23 2.23 0.75

B e e e e

C �0.04 3.19 3.89 0.76

D �0.05 3.50 4.00 0.75

E e e e e

Fig. 3 e Potential energy diagram of H2 dissociation on a-

Al2O3(0001) surface. The insert figures are the top and side

view of the physisorbed simulation model, the transition

simulation model, and the AB simulation model.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 1 5 7e1 1 6 5 1161

is slightly longer than the OeH bond in the H2O molecule of

0.95 �A [36].

3.4. H diffusion in a-Al2O3(0001) slab

The dissociative adsorption of hydrogen results in two H

atoms adsorbed on the surface, and the H atoms may migrate

on surface and diffuse into bulk. As shown in Fig. 1, positions

A, B, and C correspond to the atom positions of a-Al2O3

surface, D and E corresponds to the atom position of subsur-

face a-Al2O3. Thus, the possible surface path of H diffusion is

A / B or B / A, while possible path from surface-to-

subsurface is A / E and A / B / E.

The potential energy surface (PES) for H-atommigration on

the a-Al2O3(0001) surface is shown in Fig. 4. We found that the

diffusion from the site A to the site B (A / TS1 / B) entails

a energy barrier of 0.72 eV, the reversed path, B / TS1 / A,

proceeds in a similar fashion but with a higher energy barrier

of 0.90 eV. In the transition state, the HeO bond length is

1.49 �A and 1.46 �A, respectively.

The potential energy surface for H-atom migration from

surface to subsurface by the B/E path is shown in Fig. 4. For

the H atom adsorbing at the site B, H atom diffusion process

involves two steps: (1) the reorientation step in which

hydrogen atom remains bonded to the same oxygen atom at

site the B (B/ TS2/ BK, BK site is the bottom of O atom in the

second layer) and (2) the hopping step in which breaking and

reforming of OeH bond takes place (BK / TS3 / E). The

barrier for the reorientation step is relatively high (1.58 eV),

that for the hopping, on the other hand, is 0.53 eV (Fig. 4).

Unlike for A / B/ E path, we found a one-step minimum

energy path for the H atom diffusion from the site A to the site

E (A / TS1 / E) entails a much higher energy barrier of

4.39 eV. The potential energy surface for the A / E path is

shown in Fig. 5.

As shown in Figs. 4 and 5, the surface-to-subsurface

diffusion barriers for both paths on a-Al2O3 are large,

Table 4 e Side-on adsorption energies and bond lengthsof H2 on a-Al2O3(0001) surface.

Adsorptionsite

DEads(eV)

d1 (Al2O3eH2)(�A)

d2 (Al2O3eH)(�A)

d (HeH)(�A)

A �0.12 2.23 2.23 0.75

B e e e e

C e e e e

D e e e e

E e e e e

>1.58 eV, but the outward barriers are also fairly large,

>0.81 eV. So it is energetically more favorable for H to be on

surface. Encouragingly, a significant energy barrier exists for

the H diffusion. We conclude that a-Al2O3 surface could be

especially effective in inhibiting H uptake. In addition,

Hydrogen diffusion from surface to subsurface is predicted to

be significantly endothermic on both paths except for surface

path A / TS1 / B.

As shown in Fig. 4, the H atom can further migrate in the

bulk a-Al2O3 from the E site to the O atoms in the bulk by the

path: E / TS4/ EK / TS5/ F / TS6 / FK / TS7 / G (Site

EK, FK and GK are bottom site of the fourth, eighth and eleventh

O atomic layer, respectively.), which only have to overcome

relatively small barriers of 0.68, 0.45, 0.46, and 1.22 eV,

respectively. The low barriers indicate that H canmigrate into

bulk a-Al2O3 via the H atom reorientation on one O atom layer

followed by H atom hopping to another O atoms layer.

We can conclude, therefore, that the most favorable

diffusion path of H atoms is the surface path (A / TS1 / B).

Favorable bulk diffusion path is B / TS2 / Bk / TS3 /

E/ TS4/ Ek / TS5/ F/ TS6/ Fk / TS7/ G, in which H

migrates in the bulk a-Al2O3 via the H atom reorientation on

one O atom layer followed by the H atomhopping to another O

atom layer. Hydrogen diffusion from subsurface to bulk is

slightly exothermic.

As mentioned above, H diffusion into the bulk a-Al2O3 is

also possible but the H atom reorientation barrier of 1.58 eV at

subsurface must first be overcome. This is an extremely high

barrier, comparing with apparent H diffusion barriers, such as

Eurofer97 with a 0.25 eV barrier [1], F82H steel with a 0.13 eV

barrier [3,15] and 316L steel with a 0.54 eV barrier [6,37], in

structural materials and the H2 dissociation barrier of 0.79 eV,

which illustrates that the a-Al2O3 with high H diffusion barrier

can prevent hydrogen permeation. In other words, the very

high H diffusion barrier for the reorientation step of the site B

on a-Al2O3 (0001) surface creates a strong diffusivity limitation

for overall hydrogen permeation through a-Al2O3 coated

structural materials. However, these discussions only

consider activation energies, one part of kinetic, for H2

Fig. 4 e A / B / E path PES of H diffusion on the a-Al2O3(0001) surface and inside bulk a-Al2O3. The insert figures are side

views of the initial simulation model, the transition simulation models, and end simulation model.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 1 5 7e1 1 6 51162

dissociation and H diffusion on a-Al2O3. Overall investigations

of the limitation for the hydrogen permeation pathway in a-

Al2O3 should be jointly viewedwith prefactors, another part of

kinetic, which will be discussed in next section.

In addition, the highest barrier for reorientation step at the

site B, an elementary diffusion step, is higher than the

apparent hydrogen diffusivity of 1.32 eV [0.83 eV] for single

crystal a-Al2O3[a-Al2O3 ceramics] [15,38], indicating that

micro-defects, such as vacancies, impurity, dislocations and

grain boundaries would play an important role on diffusion. A

complex simulation models, thus, are clearly needed for

identification in the future.

Fig. 5 e A / E path PES of H diffusion into a-Al2O3(0001) subsu

simulation model, the transition simulation model, and end sim

3.5. Kinetics for H2 molecule dissociation and H atomdiffusion

On the basis of the framework of Transition State Theory

(TST) [39], within a harmonic approximation, the vibrational

properties of solid can be expressed in terms of the N normal

modesfZuigNi of the system at the potential minimum, and the

(N�1) normal modesfZu�i gN�1

i at the saddle point. The activa-

tion energy can be expressed as

DE ¼ Vm þ 1

2

XN�1

i¼1

Zu�i �

1

2

XN

i¼1

Zui (1)

rface. The insert figures are side views of the initial

ulation model.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 1 5 7e1 1 6 5 1163

, which is a sum of the classical migration barrier (Vm) and

avibrational zero-point energy (ZPE ) correction. Theprefactor,

vqm0 ¼ kBT

h

YN

i¼1

�1� e�Zui=kBT

�

YN�1

i¼1

�1� e�Zu�

i=kBT

�; (2)

is often interpreted as a characteristic “attempt frequency”.

Where, Vm is the difference in potential energy between the

saddle-point and minimum configurations. h, kB and T is

Planck’s constant, Boltzmann constant and the absolute

temperature, respectively.

In Fig. 4, H atom bulk diffusion process involves one limi-

tation step that is the reorientation step at the site B with

a relatively high energy barrier of 1.58 eV. As we known, the

vibrational frequencies of a hydrogen defect drastically

change as the system approaches either of the transition

states. At the saddle point of the reorientation step,wefind, for

hydrogen, two real modes at 1517.34 cm�1 and 3418.67 cm�1

and one imaginary (unstable) mode at 721.18 cm�1. Here, it is

one of the OeH wag modes that become unstable, accompa-

nied by a slight hardening of the stretch mode and a corre-

sponding softening of the remaining wag mode.

At the saddle point of the hopping step from the site B to

the site E with a 0.53 eV barrier (Fig. 4), we instead find two real

modes at 1402.1 cm�1 and 1823.55 cm�1 and one imaginary

mode at 476.68 cm�1. It is the high frequency OeH stretch

mode that gradually softens and becomes unstable.

The differences in vibrational ZPE, evaluated using eq. (1),

between the transition states and the initial state are given in

Table 5. In the approximation, changes of all atomic

frequencies during a transition are considered. This gives

a negative contribution and would lower the migration

barriers for hydrogen reorientation and hopping by �0.04 and

�0.10 eV, respectively.

The harmonic approximation should only be expected to

work well at sufficiently low temperatures, where all modes

can be considered harmonic (excluding possible quantum

effects at very low temperatures), but several studies have

shown that it is often applicable even at rather high temper-

atures and in highly complex systems [33,39]. Thus, calculated

prefactors, using eq. (2), of hydrogen reorientation and

hopping varyingwith temperature are given in Table 5. For the

reorientation step, this gives an effective frequency that

roughly corresponds to the missing wag mode, but for the

hopping step, the result is considerably smaller than that of

themissing stretchmodewhich is a direct consequence of the

Table 5 e Over-barrier hydrogen reorientation andhopping in a-Al2O3: Vibrational zero-point energy (ZPE)correction to the migration barrier, correspondingprefactors vqm

0 at different temperature.

Step ZPE (eV) vqm0 (ps�1)

300 K 773 K 873 K 1273 K

Reorientation �0.04 13.67 38.83 42.15 51.34

Hopping �0.10 5.79 8.88 9.25 10.50

hardening of the OeH wag modes that occur for the strongly

hydrogen-bonded saddle-point configuration [40]. Both pre-

factors decrease with decreasing temperatures.

For H2 dissociation, the barrier computed directly is

0.79 eV. We find two real modes at 1698.86 cm�1 and

1901.130 cm�1 and one imaginarymode at 1168.35 cm�1. Zero-

point energy correction computed within the harmonic

approximation increases this value to 0.80 eV. The H2 mole-

cule and surface atoms that are allowed to relax during the

optimization are used for the finite difference calculations in

the zero-point energy calculation. The reaction rate per-site

for H2 dissociation can be expressed as [39]

rH2¼ 2h2

εrotP

kBTð2pmkBTÞ3=2e�DE=kBT

YN�1

i¼1

�1� e�Zu�

i=kBT

�(3)

Where εrot ¼ 7.55meV [39] is the rotational constant for H2, P is

the pressure of gaseous H2, and m is the mass of a hydrogen

molecule. The estimated reaction rates computed from eq. (3)

are shown in Table 6. H2 dissociation rate on clean a-

Al2O3(0001) surface is slow, especially at room temperature,

and sharply increaseswithH2 gases pressure and temperature

increasing.

3.6. How a-Al2O3 resist hydrogen isotopic permeation?

We approximate the overall diffusivity of H in a-Al2O3 by only

considering the path, B / TS2 / BK, with the highest barrier

of 1.58 eV, and corresponding prefactors of H atom are shown

in Table 5.

As a combination of comparing the reorientation rates,

a product of prefactor vqm0 ande�DE=kBT, of H atom diffusion into

bulk a-Al2O3 with H2 dissociation rates on a-Al2O3 surface, the

H2 dissociation rate, with magnitude varying from 10�7 to

10�4(Table 6), is much higher than the H atom reorientation

rate varying from 10�9 to 10�6 in the temperature range of

773e873 K at 100e500 kPa that is the typical environment of

hydrogen-permeation-barrier operation. A conclusion to be

drawn, thus, is that hydrogen permeation is mainly inhibited

by hydrogen atom diffusion into bulk a-Al2O3 rather than

hydrogenmolecule dissociate on clear a-Al2O3 surface in such

environment. On the other hand, the H2 dissociation rate

becomes lower than the reorientation rate as the pressure

decreased below 1 kPa, which is symptomatic of hydrogen

permeationmainly inhibited by hydrogenmolecule dissociate

on clear a-Al2O3 surface. These results taken as a group

predict that hydrogen permeation is inhibited by hydrogen

atom diffusion into bulk a-Al2O3, a result of the highest H

Table 6 e H2 dissociation rate on a-Al2O3 surface varyingwith pressure and temperature.

Hydrogenpressure(kPa)

rH2 (ps�1 site�1)

300 K 773 K 873 K 1273 K

100 2.30 � 10�25 3.30 � 10�7 9.50 � 10�5 8.01 � 103

500 1.15 � 10�24 1.65 � 10�6 4.75 � 10�4 4.00 � 102

1000 2.30 � 10�24 3.30 � 10�6 9.50 � 10�4 8.01 � 102

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 1 5 7e1 1 6 51164

atom reorientation barrier at the first O atomic layer, at

100e500 kPa for 773e873 K, whereas that is limited by H2

dissociation from the site A to coadsorption the site AB (Fig. 1)

on surface as hydrogen gases pressure below 1 kPa.

Experimental evidences support ours prediction results.

According Sievert’s law [15], hydrogen transport in metals

with hydrogen permeation barrier can be understood by

examining the hydrogen pressure dependence of permeation.

Diffusion-controlled permeation through coating on metals is

proportional to the square root of the hydrogen partial pres-

sure. Linear pressure dependence is symptomatic of perme-

ation limited by hydrogen absorption or recombination.

McGuire et al. [41] reported that the Al2O3/FeAl coating

modified the Sievert’s law dependence of uncoated stainless

steel (0.5) to an exponent of 1 in the region of 0.2e1 kPa at

773 K. Perujo et al. [42] found a 0.5 pressure exponent above

20 kPa similar to Forcey et al. [43], and a singular dependence

below 20 kPa on a MANET steel similar to McGuire [41].

Identifying the key reason for a-Al2O3 resisting hydrogen

permeation to be the highest barrier for surface-to-subsurface

H atom diffusion allows us to propose a strategy for increasing

resistance efficiency of hydrogen isotopic permeation: by

forming strong hydrogen-bonded to either O atoms or Al

atoms on surface that can sharply increase stability of

adsorption hydrogen on the a-Al2O3 surface. This hypothesis

will be evaluated in a future paper.

4. Conclusions

The adsorption, dissociation and diffusion of hydrogen in

pure a-Al2O3(0001) slab have been studied by DFT with PW91

functional, and then the kinetics for hydrogen dissociation

and diffusion are predicted on the basis of the framework

of TST.

Firstly, we have studied adsorption of H2 and H on the

clean a-Al2O3(0001) surface and have identified several ener-

getically favorable binding sites. H2 molecule, with parallel

configuration, is found to preferentially absorb on the top Al

atom site (site A) of the first layer on a-Al2O3(0001) surface

with the adsorption energy of �0.12 eV. H atom bound at the

top of O atom site (site B) in the second layer has adsorption

energy of �2.35 eV, while coadsorption of two H atoms

strongly absorb on site A and B. Hydrogen atoms recombine

into molecule at the top of Al atoms in the third layer.

The potential energy pathways of H diffusion and H2

dissociation on pure a-Al2O3 have identified. The barrier for H2

dissociation on a-Al2O3(0001) surface is about 0.79 eV, with

a corresponding recombination barrier of 0.92 eV. The most

favorable diffusion path of H atoms is the surface path

(A / TS1 / B), with the adsorption energy of 0.72 eV. H atom

bulk diffusion process involves two steps on every O atomic

layer of a-Al2O3: (1) the reorientation step in which hydrogen

atom remains bonded to same O atom and (2) the hopping

step in which breaking and reforming of OeH bond takes

place. Favorable path from surface to subsurface is

B / TS2 / Bk / TS3 / E / TS4 / Ek, in which the high

barrier of 1.58 eV for the path B-TS2-Bkmust first be overcome,

and then H further migrate into bulk a-Al2O3 with path

Ek / TS5 / F / TS6 / Fk / TS7 / G, which only have to

overcome relatively small barriers of 0.68, 0.45, 0.46 and

1.22 eV, respectively. The surface-to-subsurface diffusion is

significantly endothermic except for surface and subsurface-

to-bulk path.

Finally, to identify mechanisms of purity a-Al2O3 resisting

hydrogen isotopes permeation, the kinetics for hydrogen

dissociation and diffusion are predicted. Hydrogen perme-

ation through a-Al2O3 is mainly inhibited by hydrogen atom

diffusion into bulk a-Al2O3, a result of the highest H atom

reorientation barrier at the first O atomic layer of a-Al2O3

surface, at 100e500 kPa for 773e873 K, whereas that is limited

by H2 dissociation from site A to coadsorption site A and B on

surface as hydrogen gases pressure decreased below 1 kPa.

Of course, we have simulated the behavior of H interacting

with perfect crystals, and actual dissociation and diffusivity

would be affected by micr-defects in real material, suggesting

that how defects change such hydrogen behaviors are urgent

to study in the future.

Acknowledgments

We thank Prof. Bingyun Ao, Dr. Chongyu Shen and Dr. Kun

Cao formany helpful discussions. Thisworkwas supported by

National Magnetic Confinement Fusion Science Program

(2010GB112000) and National Nature Science Foundation of

China (11275175).

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