J. Plasma Fusion Res. SERIES, Vol. 10 (2013)

Experimental and computational studies on tritium permeation mechanism
in erbium oxide
Wei Mao1),*, Takumi Chikada1), Akihiro Suzuki2), Takayuki Terai1) and Kenji Yamaguchi3)1) Department of Nuclear Engineering and Management, School of Engineering, The University of Tokyo, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113-8656, Japan.
2) Nuclear Professional School, School of Engineering, The University of Tokyo, 2-22, Shirakata-shirane, Tokai, Naka,
Ibaraki 319-1188, Japan.
3) Quantum Beam Science Directorate, Japan Atomic Energy Agency, 2-4 Shirakata-shirane, Tokai, Naka, Ibaraki
319-1195, Japan.
(Received: 10 May 2012 / Accepted: 3 October 2012)

A tritium permeation barrier (TPB) is much required in fusion blankets to reduce the loss of fuel and minimize
radiological hazard. However, the detailed mechanism of tritium permeation through TPB coatings has not yet beenclarified because of their complicated crystal structures. To understand the microscopic mechanism, we have not only
prepared and characterized nanostructured ceramic Er2O3 thin films, but also studied the energetics and mobility ofinterstitial deuterium in cubic bulk Er2O3 using ab initio density-functional calculations. The estimated diffusion activationenergy (Ea) of interstitial deuterium is somewhat higher than the diffusion energy barrier observed experimentally at 873 K.
This result shows that grain boundary structures existing in the TPB of Er2O3 significantly lower the diffusion barrier andchange the diffusion pathway. Transport of hydrogen and its isotopes through the Er 2O3 coatings are likely to be dominatedby grain boundaries rather than by grains.
 
Keywords: Hydrogen isotope permeation measurement, Erbium oxide, Density functional theory calculations,
Nudged elastic band

ceramics [6]. Recently, Er2O3 is attracting more and more
attentions in the application of TPB coatings for fusion
systems.
Up to now, we have made rapid progress in the
fabrication of TPB coatings by different methods such as
sputtering deposition (SD) [7] and metal-organic
decomposition (MOD) [8], but complex crystal structuresand many surface defects still exist in the coatings, whichmake it difficult to investigate the detailed mechanism ofhydrogen isotope permeation. At present, a high-quality
ceramic Er2O3 thin film with nanostructures is
successfully synthesized by arc source plasma assisted
deposition (ASPAD). The ceramic shows grain boundary
structures which are regarded as large defects in terms of
permeation of hydrogen isotopes. Consequently, we place
more and more emphasis on investigating hydrogenisotope behavior in this nanostructured thin film becauseof its slightly simpler structures compared to those
prepared by SD and MOD methods.
In addition to experimental studies, ab-initio
calculations based on density functional theory (DFT)
have been applied to complement the established

1. Introduction

There is no doubt that the environmental andeconomic acceptability of presently conceived D-T
fueled fusion power plants will be dependent on theability to contain and handle tritium within the reactor
building and to control tritium releases to theenvironment without incurring into exorbitant costs [1, 2].
The problems of tritium leakage have been studied since1970`s [3], and tritium permeation barrier (TPB) coating
has been one of the most important subjects in thedevelopment of liquid lithium blanket for fusion systems.
As to coating materials, a great many ceramics such as
Y3Al2O12, CaO, MgO, AlN (aluminum nitride), Al2O3,
Y2O3 and Er2O3 were initially considered potentiallyeligible. Of these Er2O3 was selected as one of the most
preferable candidate materials for TPB coatings becauseof its high permeation reduction factor (PRF) [4], highthermodynamic stability at high temperatures and in air,
good compatibility with liquid Li, and high electricalresistivity [5]. Additionally, Er2O3 has one of the lowest
Gibbs free energy of formation among all binary oxide
author’s e-mail: mao@nuclear.jp

27©2013 by The Japan Society of Plasma
Science and Nuclear Fusion Research

W. Mao et al., Experimental and Computational Studies on Tritium Permeation Mechanism in Erbium Oxide> direction. That is, it possesses two vacancies (16c) at
the corners of the oxygen cube, as shown in Fig. 1.
Ab initio density-functional calculations are used toinvestigate the diffusion behavior of interstitial deuteriumin bulk Er2O3. We employ Vienna ab initio Simulation
Package (VASP) for our total energy and DFT
calculations. All calculations were performed using thefull-potential
frozen-core
all-electron
projected
augmented wave (PAW) method within the Generalized
Gradient Approximation (GGA) of Perdew and Wang
(PW91), as implemented in VASP [12]. The cut-offenergy of plane wave was set to 500.0 eV. According to
the Monkhorst-Pack scheme [13], we performed the tests
with the k-point grid of 2x2x2 in the integration over the
Brillouin zone. In the initial configuration of the crystal
lattice, we have chosen the experimental cubic structureof Er2O3 unit cell with a = 1.0543 nm, 32 erbium atoms(occupying the 8a and 24d equipoints) and 48 oxygen
atoms (occupying 48e equipoints). We conducted abinitio DFT calculations in the unit cell of Er2O3 for thegeometry optimization of lattice parameters and atom
positions. The geometry relaxations were terminatedwhen residual forces on each atom and energy changes
on each atom were less than 0.001 eV/Å and 1x10-5 eV,
respectively. All calculations below referring tointerstitial D were performed by inserting an individual D
into the cell optimized by DFT methods. It is worth
noting that the parameters of cut-off energies and k-point
meshes were tested under the convergence criteria ofenergy changes on each atom less than 0.001 eV, andfound sufficient to give reliable convergent results in the
ab initio DFT calculations.

experimental methods to investigate the energetics andmobility of atomic deuterium (D) in cubic bulk Er2O3. In
recent years, DFT calculations have become a very
valuable tool to elucidate the structures and determine thedynamics of interstitial H in metals, alloys, ceramics andother solids such as heterogeneous catalysts [9]. It isreported that DFT can be used to predict the precise
mechanism of H diffusion or reaction events incondensed phases [10]. It is, therefore, essential to apply
DFT calculations to the diffusion of hydrogen and its
isotopes in Er2O3 for the verification of experimental data.
As a result, a comparison between diffusion experiments
and DFT simulations can provide useful information on
the mechanism of hydrogen isotope permeation.
In this study, the objective is to compare thediffusion activation energies of interstitial D derived by
DFT calculations with the diffusion energy barriers
obtained from the experiments, and to study the
relationship between the microstructure and hydrogenisotope behavior in Er2O3 for the mechanism of tritium
permeation.

2. Methodology
2.1. Preparation and characterization of Er2O3 coatings
A mirror polished disk-shaped substrate of 20 mm
in diameter and 0.5 mm in thickness was coated by arc
source plasma assisted deposition (ASPAD), described inRef. [7]. The substrate materials were made from reduced
activation ferritic/martensitic (RAFM) steels, including
JLF-1 ( 0.10% C; 0.05% Si; 0.45% Mn; 0.003% P;
0.002% S; 0.003% Al; 8.85% Cr; 1.99% W; 0.20% V;
0.080% Ta; 0.0231% N; 0.0002% B; < 0.01% Ni; <0.05% Cu; <0.001% Mo; < 0.002% Nb; balance Fe) andF82H (7.65% Cr; 2.00% W; 0.50% Mn; 0.20% V; 0.04%
Ta; 0.10% Si; 0.10% C; balance Fe) steels. Er2O3 coating
about 1.3ȣm thick was deposited on one side of thesubstrate. Subsequently, deuterium permeation throughthe coated sample was carried out in the temperature
range 573-973 K at driving pressures of 103-105 Pa [7].
2.2 Ab initio density-functional calculations in bulk
Er2O3
At room temperature, Er2O3 exhibits cubic rareearth bixbyite (C phase, space group Ia3) structure with alarge complex unit cell comprising 16 Er2O3 sequioxide
units with an experimental lattice parameter of 1.0543
nm [11]. In this structure, the O anions approximately
occupy three-quarters of all the tetrahedral interstices
while the Er cations lie in a face centred cubic
arrangement. Apart from rotation symmetry, the bixbyite
structure is different from that of the fluorite in missing
one-fourth of the sites in the anion sublattice in the < 111

Fig. 1. Cubic bixbyite structure of Er2O3 unit cell. The cell is
subdivided into eight small units, in which tetrahedral
vacancies (16c) are virtually depicted as obtained from acomparison between the bixbyite and fluorite structures.

3. Results and discussions

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W. Mao et al., Experimental and Computational Studies on Tritium Permeation Mechanism in Erbium Oxide

3.1 Microstructures of Er2O3 coatings
Er2O3 coatings of 1.3 ȣ m in thickness wereprepared using JLF-1 substrate and the ASPAD method.
The coatings were found to possess a high-quality grainboundary nanostructure, as shown in Fig. 2. This grainboundary is regarded as the largest defect because ofalmost complete absence of other defects such asvacancies and dislocations. The average grain size of thecoatings is about 200 nm.

3.2 Calculations of Er2O3 lattice constant
As initial configuration we have selected theexperimental cubic structure of Er2O3 with a lattice
constant of 1.0543 nm. The lattice parameter corresponds
to a volume of 1.1719 nm3. After relaxations of thestructure with a different lattice constant approaching theexperimental one (forces on atoms are less than 0.001
eV/Å), we obtained the cubic unit cell with a series ofvalues of lattice constant and corresponding volume as afunction of total energy shown in Fig. 4. After fitting with
Birch-Murnaghan 3rd-order equation of state (EOS) [15],we obtained the balanced volume of 1.1727 nm3
corresponding to the lowest total energy and the optimized
lattice constant equal to 1.0545 nm, in good agreementwith the experimental ones [11].

Fig. 2. STEM image of the Er2O3 coating fabricated by arc
sputtering plasma assisted deposition (ASPAD) at room
temperature and annealed at 973 K.

Given no change of grain sizes with instantincrease of temperatures, the relationship between grain
size and deuterium permeation flux was investigated in
the Er2O3 coatings by permeation measurements carriedout at 773, 873, and 973 K, as shown in Fig. 3. The
average grain sizes of the coatings as deposited, after themeasurements at 773, 873, and 973 K are 20, 90, 250,
and 280 nm, respectively. Apparently, the deuterium
permeation flux decreases with increasing grain size
when the temperatures are kept constant, in good
agreement with previous results [14]. In other words, adecrease of grain sizes results in an increase of thepermeation flux of deuterium through the Er2O3 coatings.

Fig. 4. Total energy configurations as a function of volume in theunit cell of Er2O3. The configurations are performed by ab initio
calculations and Birch-Murnaghan 3rd-order EOS fitting.

3.3 Individual D atom in bulk Er2O3
In the lattice model described in Section 2.2, wetheoretically occupied the initial positions of tetrahedral
vacancies in the oxygen anion sublattice, based on acomparison of the fluorite and bixbyite structures. Afterrelaxing the cell consisting of two primitive units, we
introduced an individual neutral hydrogen atom into the
cubic bixbyite structure to simulate dilute loadings ofinterstitial D, and calculate directly its motion by DFT.
Considering a great number of interstitial sites (thetetrahedral vacancies of oxygen anion are included) in the
structure, we found that D binding energy is mainly
dependent on the type of the surrounding atoms, especiallythe nearest neighboring ones. The binding energy of aninterstitial D atom in host lattice can be defined as follows:

Fig. 3. Grain size dependence of deuterium permeation flux
through the 1.3ȣm thick Er2O3 coatings. The grain sizes of thecoatings were estimated by TEM images. The permeation
measurements were carried out at a pressure of 8.00 x 10-4 Pa. In
the figure, X is the permeation flux-grain size point in the plot,
and the red rash arrows represent the change at constanttemperatures of 773, 873, and 973 K.

Ebind

E( D / S )  E( S )  E( D )(1)where E(D/S) and E(S) are the total energy of the system withand without an interstitial D atom, respectively. E(D) is theenergy of D atoms in free space with spin polarization.
With regard to the DFT calculations, the D binding energy

29

W. Mao et al., Experimental and Computational Studies on Tritium Permeation Mechanism in Erbium Oxide

in the tetrahedral vacancies of oxygen anion sublatticewere found to be strongest among the interstitial sites,
equal to - 10 kJ/mol representing an exothermic reaction.
This indicates that an individual interstitial deuterium atom
is easily trapped in the tetrahedral vacancies. In otherwords, the tetrahedral interstitial site of oxygen anion
sublattice belongs to the local minima position surroundedby the interstitials filled with O anions.
It is worthwhile to look into the effect of spinpolarization because the total energy goes down 14~18
kJ/mol when a deuterium atom is inserted into theinterstitial site of the tetrahedral. We therefore include spinpolarization in the present computational scheme andapply it to an individual H2 molecule. The calculated
binding energy / cohesive energy and bond length of H2
are 4.55 eV and 0.740 Å, corresponding well to theexperimentally obtained values of 4.48 eV and 0.741 Å
[16], respectively. Such calculations confirm the fact thatthe computational scheme considering spin polarization isreliable and sufficient to give fully converging results.

The overall minimum energy pathway (MEP)
shown in Figure 5 indicates another new local minima
position (C) and barriers (A-C*, C-B*) along the pathconnecting the initial local minima position (A) and its
crystallographic equivalent position (B). The migration
barriers from A to C and from C to B are 41.5 kJ/mol(0.43 eV) and 39.6 kJ/mol (0.41 eV), respectively.
Furthermore, we have as well calculated a migration
barrier of 157.3 kJ/mol (1.63 eV) in the minimum energy
pathway of deuterium diffusion along the direction fromC to C`s crystallographic equivalent site. The maximum(157.3 kJ/mol) in the MEPs corresponds to the position
where D diffuses through the highest number of bondmaking/breaking events in Er2O3, in which thecorresponding activated state locates the O-layer at thesite equidistant from O anions.
3.5 Relationship between diffusion and permeation ofhydrogen and its isotopes through erbium oxide
The permeability of hydrogen isotopes is generally
defined as the steady state diffusional transport of atoms
through a material supporting a pressure difference.
According to the theory reported in the paper of Marchi
et al. [18], the permeability and diffusivity of hydrogenisotopes through single-layer material can be expressedin the general form as follows:

3.4 Diffusion behavior of deuterium in bulk Er2O3
To investigate the diffusion behavior of deuterium inbulk Er2O3, we employed the DFT calculations to examine
trapping binding sites, diffusion pathways and diffusion
activation energies for an individual D atom hopping fromone local minima position to its nearest neighboring site.
The diffusion activation energies (Ea) were determined by
the energy difference between the local minima position
and the activated state site. The hopping distance between
the two energy minima in the bulk Er2O3 was measured tobe 3.787 Å. The activated states were found by the nudged
elastic band (NEB) [17] method using nine images as wellas the symmetry consideration, in which forces on atoms
are zero and any infinitesimal change of deuterium initialcoordinate causes a finite change of atomic coordinates.
The identical position of the activated states lies in the Er
layer at the point equidistant from Er cations, derived by
the above two methods.

E)
)
(2)
RT
ED
)
D D0 exp( (3) 
RT
where Φ (mol/m/s/Pa1/2) and D (m2/s) are thepermeability and diffusivity of hydrogen, respectively. R(8.314 J/mol/K) is the gas constant; T (K) is the sample
temperature; and EΦ (J/mol) and ED (J/mol) are theactivation energy of permeation and diffusion ofhydrogen and its isotopes, respectively. Φ0 and D0 are thecorresponding coefficients of diffusion and permeation.
Equations (2) and (3) indicate that diffusivity canrepresent permeability to a large extent since they are
similar in magnitude over a wide range of temperaturesin the transport of hydrogen and its isotope atoms
through the material.
According to Ref. [14], the permeation flux understeady-state conditions through a single layer barrier canbe expressed as
1
P2
J KD
(4)
d
where J is the permeation flux per unit area of material of
thickness d (m); K is the Sieverts` constant and P thedriving pressure of hydrogen and its isotopes. Since Φ =KD, Eq. (4) in combination with Eq. (2) gives therelationship between the permeation flux (J) and theactivation energy (ED) of diffusion under steady-state
conditions, i.e.
)

Fig. 5. Energy versus reaction coordinate obtained by the NEB
method in bulk Er2O3. The initial separation distance between the
two local minima sites is 3.787 Å.

30) 0 exp( W. Mao et al., Experimental and Computational Studies on Tritium Permeation Mechanism in Erbium Oxide

J1)P 2 / d) o exp( E D  ES 12)P / dRTcorrespondingly. Actually, GB’s existing in Er2O3
coatings degrade the grain sizes due to loss of bulk areaand lead to an increase of permeation flux, in good
agreement with the experimental data given in Fig. 3. It
is intuitively considered that diffusion and permeation ofhydrogen and its isotopes through erbium oxide are likely
to occur predominately through grain boundaries rather
than grains. In addition, it is worth noting that theactivation energy obtained in the deuterium permeation isstill large and high concentration to that derived by the
DFT calculations. This suggests that the Er2O3 coatings
prepared by the ASPAD method possess highperformance as required for TPB coatings. As shown in
Fig. 3, the growth of grain size enhances the ability of thecoatings to suppress deuterium diffusion and permeation.
As the grains become very large, the permeability of
deuterium will decrease because of the absence of grainboundaries. That is, the activation energy is maximized
when the Er2O3 coatings become a perfect crystal without
any grain boundary as assumed in the DFT calculations.

(5)
where Es (J/mol) is the heat of solution of hydrogenatoms in the single-layer material or oxide with athickness of d (m), and EΦ is defined as the sum of ES
and ED. It is obvious that diffusion plays an importantrole in the process of permeation of hydrogen and its
isotopes based on the relationship of permeation flux J
and diffusion activation energy ED given in Eq. (5). With
the aim of understanding the mechanism of permeation itis therefore reasonable to study first the diffusion
behavior of hydrogen and its isotopes through erbiumoxide.
In experiments on the permeation of deuterium, thediffusion activation energy was estimated from an
Arrhenius plot of temperature versus diffusivity, D being
obtained by measuring the time-lag tl (s) with relationshiptl (s) = d2/6D, as described in [19]. The measured
activation energy of approximate 20.0 kJ/mol [14] is ofsimilar order of magnitude with the D diffusion energy
barrier of 157.3 kJ/mol evaluated by the NEB method as
implement in ab initio DFT calculations. The
discrepancy in activation energies is partly attributed to
the fact that nanostructured Er2O3 thin films were used in
the experiments while bulk Er2O3 was adopted in thecomputational simulations. Although the Er2O3 thin films
were prepared by the ASPAD method with the aim ofachieving good performance as TPB coatings, they hadvery large defects, i.e. grain boundaries (GB`s) within thenanostructure as revealed by Fig. 1. A GB represents anenvironment where the symmetry of a crystal isterminated. Apart from the diffusion of hydrogen and its
isotopes through the bulk of erbia, diffusion is likely tooccurs also via the large defect GB`s.
In order to elucidate the hydrogen behavior in
erbium oxide, we purposely conducted ab initio DFT
calculations in the bulk Er2O3 assuming an ideal crystal
structure. The volume and geometry relaxations in thecalculations show that an individual interstitial D prefers
to bind in the tetrahedral interstitial sites of O anion
sublattice (local minima). MEP found by the NEB
method shows the diffusion pathway of deuterium
hopping from one local minima to the nearest
neighboring one. Most important, the maximum energy
difference between the minimum site and the estimatedtransition state (saddle point) determined in this way is
157.3 kJ/mol, and somewhat higher than theexperimental value of 20.0 kJ/mol. This indicates that at
the grain boundary the activation energy for hydrogenisotope (deuterium) diffusion decreases because of thedifferent diffusion pathway as predicted by MEP. In otherwords, the diffusivity of deuterium will be increased if
we introduce GB into the perfect bulk Er2O3. On thebasis of Eq. (5), which relates the permeation flux J tothe diffusivity D, the permeability will increase

4. Conclusions

In this study, the mechanism of tritium permeation
through Er2O3 has been investigated by the experimental
measurements and the computational simulations. We
have prepared Er2O3 coatings of 1.3ȣm in thickness by
the ASPAD method and characterized the coatings via
deuterium permeation measurements. From theexperiments, we concluded that a grain boundary
nanostructure exists in the Er2O3 coating and estimatedthe diffusion activation energy to be 20.0 kJ/mol.
Additionally, ab initio DFT calculations based ontransition state theory were carried out for interstitial
deuterium in an ideal supercell assuming cubic bixbyite
Er2O3. Calculated and fitted lattice constants of Er2O3
showed good agreement with the experimental data. Also
the minimum energy sites, diffusion pathways anddiffusion activation barriers for an individual D atom
were found by MEP calculations. The local minima
position is found located in the tetrahedral interstitial siteof oxygen anion sublattice. The results indicate that thepreferred hopping path of individual D atoms is from one
local minima position to its nearest neighboring site. The
maximum diffusion activation energy resulting from the
MEP calculation is 157.3 kJ/mol and higher than thatobtained experimentally (20.0 kJ/mol). This discrepancy is
attributed to grain boundary structures found in the Er2O3
coatings. GB`s lead to pathways of hydrogen diffusion
different from MEP derived by DFT calculations. They
provide useful information on tritium permeation
mechanism in erbium oxide. Additionally, it appears that
diffusion and permeation of hydrogen and its isotopes
through the Er2O3 coatings will probably take placethrough grain boundaries rather than grains. This

31

W. Mao et al., Experimental and Computational Studies on Tritium Permeation Mechanism in Erbium Oxide

conclusion is drawn from i) the comparison of theactivation energy between diffusion experiments and DFT
simulations ii) the interdependence of hydrogen and its
isotope diffusion and permeation, and iii) the relationshipbetween the permeation flux and grain size during themeasurement of deuterium permeation.

Acknowledgements

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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