J. Plasma Fusion Res. SERIES, Vol. 11 (2015)

Dependence of surface orientation of erbium oxide on hydrogen behaviors
Wei MAOa , Takumi CHIKADAb, Akihiro SUZUKIc, Takayuki TERAId, Hiroyuki MATSUZAKIaThe University Museum, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japanb
Deparment of Chemistry, Graduate School of Science, Shizuoka University,
836 Ohya Suruga-ku Shizuoka 422-8529, Japanc
Nuclear Professional School, School of Engineering, The University of Tokyo,
2-22, Shirakata-shirane, Tokai, Naka, Ibaraki 319-1188, Japand
Department of Nuclear Engineering and Management, School of Engineering, The University of Tokyo,
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
D(Received: 17 September 2014 / Accepted: 19 January 2015)

Erbium oxide is used as tritium permeation barrier in fusion blanket systems, where a hydrogen isotope is adsorbed on thesurface, diffusion from the surface, etc. In this article, based on first-principles calculations, we examine the effect of
surface orientation on the H behaviors in cubic Er2O3 surfaces. It was found that the comparative stability of (110), (111),
and (001) surfaces is predicted to be: (111) > (110) > (001). The behaviors of H adsorption and penetration in cubic Er 2O3(110) and (111) surfaces are predicted to be somewhat different from those in cubic Er 2O3 (001) surface. Consequently, we
conclude that the surface orientation dependence of the surface properties should be noted in terms of H adsorption andpenetration in Er2O3 surfaces.
Keywords: Er2O3 surfaces, density-functional theory, H adsorption, H penetration

diffusion, and trapping. As recently reported in Refs. [8,9],
density functional theory (DFT) calculations have become
a valuable tool to elucidate the structures and determine thedynamics of interstitial H in metals, alloys and ceramics,
and are used to successfully predict the microscopic
behavior of H in oxides such as Cr2O3, TiO2, SiO2 andAl2O3 [10-13]. Therefore, it is essential to apply DFT
calculations to the studies on the interaction between
atomic hydrogen and Er2O3 surfaces.
Interest in the adsorption and penetration ofhydrogen atoms in Er2O3 surfaces stems mainly from its
relevance in TPB coatings. Cubic (001), (110) and (111)
surfaces of Er2O3 were studied based on the experimental
results of X-ray diffraction measurement [7,14]. On thebasis that one must understand clean surfaces before one
can understand how they interact with their environment,
we have placed emphasis on those surfaces regarding tosurface structure and electronic properties of Er2O3.
Subsequently, we discussed H adsorption and penetrationin the surfaces via DFT calculations. We provide
computational details in Sec. II and then present anddiscuss our results in Sec. III. Finally, we summarize ourwork in Sec. IV.

1. Introduction

One of the key components of deuterium(D)-tritium (T) fuelling cycle in fusion blanket systems isthe tritium recovery in which tritium permeation barrier(TPB) plays an important role in containing and handling
D and T within the reactor building and controllinghydrogen isotope release to the environment without
incurring exorbitant costs [1,2]. As to barrier materials,
erbium oxide (Er2O3) attracts much attention in theapplication of TPB due to high permeation reduction
factor (PRF), good compatibility with liquid lithium, highthermodynamics stability at high temperatures and in airand high electrical resistivity [3-7]. In addition, Er2O3 has
one of the lowest Gibbs free energy of formation among
all binary oxide ceramics [5,6]. As a result, Er2O3 hasbeen selected as one of the candidate materials for TPB
coatings.
Suppressing H isotope permeation in TPB coatings
explains the importance of interaction between atomic
hydrogen and erbium oxide [7], and hence much work is
required to be devoted to both experimental and theoreticalstudies of the interaction. In the interaction, it is necessary
to understand the thermodynamics and kinetics ofhydrogen adsorption on Er2O3 surfaces and subsequenthydrogen behavior in bulk Er2O3, including penetration,

2. Computational details

author’s e-mail: mao@nuclear.jp

30©2015 by The Japan Society of Plasma
Science and Nuclear Fusion Research

W. Mao et al., Dependence of Surface Orientation of Erbium Oxide on Hydrogen Behaviors

The computational simulations performed in thisstudy were done using spin-polarized DFT calculations as
implemented in the Vienna Ab Initio Simulation Package(VASP) and the Generalized Gradient Approximation(GGA) of Perdew and Wang (PW91) [15] for electron
exchange and correlation. The kinetic energy cutoff forthe planewave basis set is set to 500.0 eV for all DFT
calculations: increasing the cutoff resulted in variations in
the total energy of < 2 meV/atom (0.192 kJ͑ mol-1/atom).
The surface and the adsorbate-systems have been
simulated using a slab model, which includes 12-16
stoichiometric layers relaxed and unrelaxed and a vacuum
region (>1.0 nm). The slabs are tested when increasing
one stoichiometric layer results in variations of surface
energy less than 0.05 J/m2. Periodic boundary conditions
are used, with the one electron pseudo-orbitals expanded
over a plane wave basis set. The K-meshes are obtained
from Monkhorst-Pack scheme [16].
The sampling of the Brillouin zone is performed
using k-meshes of 4×4×1 for (1×1) surface unit cell. For
the bulk Er2O3 consisting of 32 Er and 48 O atoms, weuse a mesh size of 4×4×4 for k-point sampling. These
above k-meshes have been tested to be converged to < 1
meV/atom (0.096 kJ͑ mol-1/atom). Atomic relaxations
are performed regarding to a conjugate gradientalogirithm [17] and the force on each atom is converged
to be less than 1 meV/nm (0.096 kJ͑ mol-1/nm). During
the optimization both the adsorbate (H) and the Er&O
atoms in the top 3-6 stoichiometric layer of the slab areallowed to relax while the remaining Er&O atoms of theslab are frozen at bulk optimized configurations. In
addition, dipole corrections originally introduced by
Neugebauer and Scheffler [18] are included in order tocorrect for the errors introduced by the use of periodic
boundary conditions. Thus, the adsorption energy (Eads)of adsorbate H considering dipole correction can becalculated as [19]( Eads ) d >E (S) Hod  E (S)  NE ( H)@ / N(1)
where E(S)Ѝd refers to the energy of the system when Hatom is d distance apart from the Er2O3 surface, and E(S)is the energy of the Er2O3 surface, and E(H) is the energy
of ground state isolated H atom/H2 molecule with spinpolarization. H diffusion from the surface to the solutesite in the bulk is calculated using climbing image nudged
elastic band (CINEB) method [20] as implemented in
DFT calculations.
To gain further understanding of the interaction
between the H atom and the cubic Er2O3 (001) surface,
we have presented the charge density plot calculated
including the dipole correction. Consideration of quantum
effects [21] is important at low temperature for lightspecies such as atomic H. Therefore, zero-point-energy(ZPE) corrections have been considered at thehigh-symmetry adsorption sites by summing up thezero-point vibrational energies of the H`s normal mode,
i.e. ZPE 1 2 ¦ hvi , where vi is the real normal mode
frequency [21,22].

3. Results and discussions

3.1. Bulk Er2O3
In the unit of cubic Er2O3, it belongs to space groupIa3 and has 32 Er atoms occupying the 8a and 24dequipoints and 48 O atoms occupying 48 e equipoints.
The lattice constant of 1.0545 nm derived by DFT
calculations and fitting with Birch-Murnaghan 3rd-orderequation of state (EOS) [23] corresponds well with theexperimental data of 1.05431 nm [5]. The corresponding
bulk modulus has also been calculated using the above
euqtion as Bo = 148.0 GPa, in good agreement with theexperimental result Bo = 140.7 GPa [6,24] within adeviation of 5%. The electronic density of states (DOS)of bulk Er2O3 has been calculated using GGA, as shownin Fig. 1. The highest occupied valence band exhibits
mainly O 2p features while the lowest unoccupied
conduction band mainly consists of Er 5d electrons. Thissuggests that strong ionic characteristics with weakcovalency exist in Er-O bonding in bulk Er2O3.

Fig. 1. Total electronic density of states (DOS) of cubic Er 2O3,(b) partial DOS of Er atoms of cubic Er2O3 and (c) partial DOS
of O atoms of cubic Er2O3. The dash line corresponds to the
Fermi energy levels in the Er2O3 bulk.

In addition, band structures of Er 2O3 are calculated at
45 regularly spaced k points in the irreducible portion of
Brillouin zone (BZ) by straightforward matrix
diagonalization. calculated band structures along thehigh-symmetry axes of the BZ for Er2O3 are shown in Fig. 2.
The calculated direct GGA gap of 4.01 eV at ǻ isunderestimated compared with the experimental data of 5.30
eV [25]. As is well known, this discrepancy stems from the
GGA in the density-functional theory. However, the large
band gap estimated apparently suggests that Er2O3 is a good
insulator.

31

W. Mao et al., Dependence of Surface Orientation of Erbium Oxide on Hydrogen Behaviors

value of 9.1910-3 kJ/m2 for stoichiometric Er2O3 (001)surface. Other non-stoichiometric surfaces, such as(110)-O rich, (111)-O rich, and (111)-Er rich surfaces, areunstable due to variations of surface energies dependingon the chemical potential/field of oxygen atoms.
Consequently, it is considered that the stability of
low-index cubic (001) and (110) surfaces mainly depends
on the ratio of Er:O at room temperature, in good
agreement with that of Er2O3 (001) surface [19]. In otherwords, the stoichiometric (111), (001), and (110) surfaces
are the most stable surfaces because surface energy is
independence of the chemical field of oxygen at room
temperature. This basically corresponds to the results of
XRD examinations that the (111), (001), and (110)orientations are found in the same coatings of Er 2O3[3,14,27,28]. In addition, the density of states (DOS) of
stoichiometric Er2O3 (110) and (111) surfaces arepresented in Fig. 4. It was found that band gaps between
conduction bands and valence bands are small in both
Er2O3 (110) and (111) surfaces. The two surfaces are
predicted to be some metallic character, similar to that of
Er2O3 (001) surface [19].

Fig. 2. Calculated band structures of Er2O3.

3.2. Surface structural and electronic properties
As reported in Ref. [26], surface energy has
become one of the critical parameters determining thestability of surface terminations. To obtain surface energy
from DFT calculations, we use a supercell (slab)
approach at T = P = 0. For Er 2O3 surfaces, it can becalculated as
slab
bulk
V 2Etot
 N Er Etot
 (2 N O  3N Er )PO / 2 A (2)slab
where E tot refers to the total energy of the slab supercell,bulk
is the energy for bulk Er2O3 per formula unit (f.u.),
Etot
and A is the surface area. NEr and NO represent numbersof Er atoms and O atoms in the slab, respectively.
Therefore, the (NO1.5NEr) are excessive oxygen beyond
stoichiometric Er2O3 units in the slab. PO is the chemical
potential of oxygen and defined as the variation of the O
chemical field between one O2 molecule and one Er2O3
formula unit.
According to Eq. (2), we have calculated surface
energy for Er2O3 (110) and (111) surfaces with different
surface terminations, as shown in Fig. 3. After relaxation,
the surface energies of 3.0410-3 kJ/m2 and 6.0110-3
kJ/m2 are derived for stoichiometric Er2O3 (111) and(110) surfaces respectively, somewhat lower than the

(A)

(B)

Fig. 4. (A) Density of states (DOS) of the isolated cubic Er 2O3(110) surface slab, and (B) DOS of the isolated cubic Er 2O3(111) surface slab: (a) DOS of the isolated cubic Er 2O3 (110)and (111) surfaces, (b) partial DOS of Er atoms of the isolated
cubic Er2O3 (110) and (111) surfaces, and (c) partial DOS of O
atoms of the isolated cubic Er2O3 (110) and (111) surfaces. The
Fermi energy levels are represented as the vertical dash line ineach diagram.

Fig. 3. Surface energies for various surfaces of cubic Er2O3
versus chemical potential of oxygen. (001) surface is terminatedby single Er atom layer while (111) and (110) surfaces are
terminated by a mixed layer with Er and O atoms. (110)-O richand (111)-O rich surfaces are terminated by single Er atom layer
while (111)-Er rich surface is terminated by single O atom
layer.

32

W. Mao et al., Dependence of Surface Orientation of Erbium Oxide on Hydrogen Behaviors

3.3. Hydrogen adsorption on Er2O3 surfaces
After analyzing surface structural and electronic
properties of stoichiometric Er 2O3 (110) and (111)
surfaces, we studied several possibly high-symmetry sites
on those surfaces for H adsorption. These sites are on topof Er atom, Er-Er bridge, Er-O bridge, O atom, andfourfold hollow position surrounded by fourneighbouring O atoms. It was found that the fourfold
hollow position is the most stable adsorption site due tothe largest adsorption energy. More emphasis is therefore
placed on the most stable adsorption site (e.g. A position).
H adsorption energies at the A site on the (110) and (111)
surfaces were calculated using Eq.(2), as shown in Table
1. It was found that adsorption energies on the moststable site (A) of Er2O3 (110) and (111) surfaces are -2.01
eV/H (-1.92 eV/H with ZPE corrections) and -2.67 eV/H(-2.56 eV/H with ZPE corrections), somewhat lower thanthat (-3.12 eV (-2.99 eV/H with ZPE corrections)) on
Er2O3 (001) surface [19].
(a)The large adsorption energies verify the strong
covalent of H-O bonds and weak H-Er interactions. Thisis also confirmed by the results of LDOS (in Fig. 6) andcharge density (in Fig. 7) of Er2O3 (110) and (111)
surfaces in comparison with those of Er2O3 (001) surface[19], in which metallic character of H-Er interactions isvery weak due to negligible variations of conduction
bands and Er charge densities, as indicated in Fig. 6 andFig. 7. Consequently, H adsorption on Er2O3 (110) and(111) surfaces are not a physisorption but chemisorption
at the expense of the formation of H-O covalent bonds.
Although the mechanism of H adsorption on Er2O3 (110)and (111) surfaces is the same as that on Er2O3 (001)surface, the large deviations of adsorption energy among
them results in the dependence of surface orientation andH adsorption.
(A)

(B)

(b)

Fig. 5. Stable adsorption site (A) and solution site (L2) for H
adsorption and penetration on (a) cubic Er2O3 (110) surface and(b) cubic Er2O3 (111) surface.
Table 1

Fig. 6. Total density of states (DOS) of (A) the isolated cubic
Er2O3 (110) and (B) the isolated cubic Er2O3 (111) surface slabs
after H adsorption. Partial DOS of Er atoms and O atoms of theHydrogen adsorption energy in the stable adsorption

two isolated cubic surface slabs after H adsorption are indicatedsite (A) on Er2O3 (110) and (111) surfaces. The hydrogen

along with DOS using the small Fig. (a), Fig. (b), and Fig. (c)adsorption energy on Er2O3 (001) surface is attached in

respectively. The Fermi energy levels are represented as thecomparison with those on Er2O3 (110) and (111) surfaces.

vertical dash line in each diagram.

Values in parentheses are ZPE corrected.
Surface

Adsorption energy (eV/H)(110)-2.67 (-2.56)(111)-2.01 (-1.92)(001)-3.12 (-2.99)
33

W. Mao et al., Dependence of Surface Orientation of Erbium Oxide on Hydrogen Behaviors

constructed by substituting D/T mass for hydrogen massin the H pseudopotential. The total potential energies
were therefore calculated for H, D and T, respectively.
From the DFT calculations, we found that the differenceof total potential energies, at the critical sites between
interstitial H, D and T atoms was less than 10-4 eV interms of perfect and imperfect Er2O3. Although H, D and
T atoms possess different normal mode frequencies [22],
(a)

(A)

(B))

Fig. 7. Charge densities of (A) cubic Er2O3 (110) surface and (B)(b)

cubic Er2O3 (111) surface after H adsorption. H atom strongly
bonds with O atoms while it weakly interacts with Er atoms byelectron transfer.

3.4. Hydrogen penetration from Er2O3 surfaces
After analyzing H adsorption on Er2O3 (110) and(111) surfaces, we also studied the process of H penetrationfrom those surfaces, using the models in Fig. 5. A site isdetermined as the most stable adsorption position. Figure 5
shows a possible high-symmetry solution site (bulk site),
L2, located at tetrahedral site (TS). As TS position isenergetically favorable for H penetration, we studied H
penetration in terms of penetration energies and penetration
pathways from A to L2 site. With CINEB method, thepenetration energies of 1.6 eV (1.58 eV with ZPE
corrections) and 2.4 eV (2.36 eV with ZPE corrections) aredefined for cubic Er2O3 (110) and (111) surfaces
respectively, as shown in Fig. 8. The penetration energy
from the (110) surface is close to that from the (001)surface [29], but somewhat lower than that from the (111)
surface. Therefore, it is considered that the behavior of H
penetration depends on surface orientations of cubic Er2O3.

Fig. 8. Energy profile for H adsorption and penetration on (a)Er2O3 (110) surface with a penetration energy of 1.6 eV, and (b)Er2O3 (111) surface with a penetration energy of 2.4 eV. The
penetration energies are calculated by CINEB using 12 images,
and ZPE corrections are not included in the profile of potential
energies.

ZPE corrections of H/D/T adsorption energies,
penetration and diffusion energy barriers verify the same
fact that the deviation of the energies is less than 0.05 eV
between H, D and T atoms. Consequently, it is consideredthat the isotope effect would be ignored within 0.05 eV.
This neglect approach is reasonable because H/D/T atom
is much lighter than the oxygen and erbium atoms.

3.5. Quantum effects on H behaviors in Er2O3 surfaces
Quantum effects on H behaviors in Er2O3 wereconsidered in terms of zero-point energy (ZPE)
corrections and H isotope effect. Considering an isotope
effect of hydrogen, we substituted deuterium/tritium forhydrogen to simulate its behaviors in Er2O3 surface via
DFT calculations. The pseudopotential for H, D and T isdifferent due to their distinguished mass (mH:mD:mT=1:2:3), in which the pseudopotential of D/T is

4. Conclusions
The main findings of this study can be summarized asfollows:
1) The native structural and electronic properties of cubic
Er2O3 surfaces are studied. It was found that both
surface energies and electronic structures of the34

W. Mao et al., Dependence of Surface Orientation of Erbium Oxide on Hydrogen Behaviors

surface mainly depend on the ratio of Er:O.
2) Considering quantum effects, H behaviors (e.g.
adsorption, penetration) in cubic Er2O3 surfaces areinvestigated in terms of density of states, adsorptionenergy, penetration energy, etc.
3) From the comparisons of surface properties of (110),(111), and (001) surfaces of cubic Er2O3, it isconsidered that the effect of surface orientations on
surface properties should be noted in terms of H
adsorption energy and penetration energy. The
comparative ability of H adsorption on Er2O3 surfaces
is predicted to be: (111) < (110) < (001). In addition, H
penetration from (111) surface is predicted to be much
more difficult than that from (110) and (001) surfaces.

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As H adsorption and penetration play an importantrole in the surface effects of erbium oxide, the dependenceof surface orientation on H behaviors will provide afundamental understanding of the microscopic behaviorsof H on the basal plane of erbia in the process of H
permeation.
Acknowledgments
This work was supported in part by GoNERI, the Global
Center of Excellence (G-COE) Program of the Nuclear
Education and Research Initiative of the Japan Society for
the Promotion of Sciences (JSPS).

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