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 e n e r g y 3 7 ( 2 0 1 2 ) 8 0 3 3 e8 0 4 2
Available online at www.sciencedirect.com
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Hydrogen energetics and charge transfer in the Ni/LaNbO4
interface from DFT calculations
K. Hadidi a,*, T. Norby b, O.M. Løvvik a,c, A.E. Gunnæs a
a
Department of Physics, University of Oslo, FERMiO, Gaustadalleen 21, NO-0349 Oslo, Norway
Department of Chemistry, University of Oslo, FERMiO, Gaustadalleen 21, NO-0349 Oslo, Norway
c
SINTEF Materials and Chemistry, Forskningsveien 1, NO-0314 Oslo, Norway
b
article info
abstract
Article history:
Calculations based on density functional theory have been used to simulate interface
Received 30 July 2011
structures between the tetragonal and monoclinic phases of LaNbO4 (LN) and Ni. Schottky
Received in revised form
barrier heights were calculated using the interface electronic structure; they were 3.0 and
7 October 2011
1.8 eV for p- and n-type barriers. The hydrogen interstitials were found to be significantly
Accepted 4 November 2011
higher stable in the LN part of the interface than in bulk LN. Also, the potential energy
Available online 14 December 2011
curve of hydrogen diffusion from Ni into LN exhibited a deep well of around 2 eV, located in
the gap region between two components. The stability of H atom in the gap region and
Keywords:
interfacial layers of LN is explained by metal-induced gap states and indicates that there
LaNbO4
will be an accumulation of hydrogen in this area. It was shown that hydrogen is ionized
Ni
when enters from Ni to the LN interfacial layer, approaching to the O atoms and that the
DFT
electron lost from hydrogen resides in the interface states, located in the band gap of LN.
Hydrogen
Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
reserved.
Fuel cell
Interface
1.
Introduction
Proton conducting fuel cells (PCFCs) have received much
attention related to their potential utilization in solid oxide
fuel cell (SOFC) technology [1]. In PCFC operation, details of the
physical phenomena of the pathway of hydrogen (proton),
starting with a H2 molecule at the anode side and ending with
protons in the electrolyte and water at the cathode side, are
still largely unknown. In this regard, characterization of the
metaleoxide interface structure as a part of the hydrogen
(proton) pathway appears essential.
The application of lanthanum niobate (LaNbO4) based
ceramics as high temperature proton conducting electrolyte
in PCFCs has recently been discussed in the literature [2].
Acceptor doped LaNbO4 (LN) displays a proton conductivity of
nearly 0.001 S cm1 at 900 C [3]. The preference for this
compound to other state-of-the-art proton conductors with
higher conductivity, such as Ba- and Sr-based perovskites is
due to its chemical stability under realistic operational
conditions. LN transforms from the monoclinic fergusonite
phase (m-LN) to a tetragonal schelite structure (t-LN) within
the temperature range of 490 Ce525 C [4]. In a LN based
PCFC, Ni is often chosen as anode, where it will assumingly do
the job as current collector and catalyze dissociative adsorption of H2 since the most stable LN surface is not receptive
toward H atoms [5].
In the present work, Ni and the two polymorphs of LN were
employed as components to simulate two different interface
structures; tetragonal (t-) and monoclinic (m-) interface
models. The interfacial region (IR) can be considered as
* Corresponding author.
E-mail address: kianoosh.hadidi@fys.uio.no (K. Hadidi).
0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijhydene.2011.11.032
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a transition region, which begins from the gap region and can
extend to a few layers of each component. The characteristics
of the interfacial region are neither purely metallic nor oxide
like. In our work, the whole super cell represents the interfacial region. The fundamental properties of the interfacial
region, such as interface dipole or Schottky barrier originate
from its chemical bonds [6,7], which depend on the type of
surfaces that meet, as well as the lattice mismatch between
the constituents. As shown subsequently, we do not expect
the binding configuration at the m-interface to be different
from that in the t-interface. Hence, more comprehensive
analyses, including Schottky barrier estimation, hydrogen
interstitials energetics, and charge transfer across the IR were
performed for the m-interface only. In some cases calculations
were compared to the conventional bulk models of LN and Ni
(referred to as Ni or LN bulk in the text).
Various options can be applied to simulate an interface
structure, related to all the possible surface terminations of
two materials being accommodated with each other. Many of
the physical properties can be affected by the choice of
surfaces. In this study, the LN (010) and Ni (100) surfaces were
chosen to generate interface structures, due to the low surface
energies of these surfaces and the possibility to create relatively small atomistic models. The quantitative results clearly
depend on this choice, so any numbers presented in this study
should be interpreted with care. Nevertheless, many of the
results are qualitative of nature, and should give considerable
insight into the detailed mechanisms governing hydrogen
transport and membrane performance. Also, some of the
results should be applicable for metaleoxide interfaces in
general.
2.
Methodology
2.1.
Computational details
Band structure density functional theory (DFT) through the
Vienna ab initio simulation package (VASP) [8,9] was implemented to perform the present calculations. The generalized
gradient approximation within the PerdeweBurkee
Ernzerhofscheme (PBE-GGA) [9,10] was utilized to account for
the exchange-correlation corrections. We used soft potentials,
which describe the valence electronic orbitals as 5s25p66s25d1
for La, 4p65s24d3 for Nb, 2s22p4 for O and 4s23d8 for Ni. The
projected augmented wave (PAW) [11,12] method was
employed to consider the core shell electrons. Cut-off energy of
500 eV was found to be sufficient to achieve numerical
convergence of relative electronic energies within 0.001 eV. A
similar accuracy was obtained by using a maximum distance of
0.25 Å1 between the k points; this was achieved with a grid of
5 2 5 points for the interface structure. The experimental
covalent radii of 1.69, 1.37, 0.73 and 1.21 Å were applied for La,
Nb, O and Ni, respectively, to calculate the local density of
states (LDOS). For ionic optimization, a conjugate gradient
algorithm [13] was utilized in most of the cases unless the
primary configuration of atomic geometries was close to the
local minimum. In that case we used the residual minimization
scheme with direct inversion in the iterative subspace (RMMDIIS) [14]. The residual forces were less than 0.05 eV Å1 when
all geometries were relaxed. All calculations were performed
with spin polarization. We applied Bader analysis [15] to
understand the charge transfer between different species in
the interface structure. In this method, the space of the
molecular system is divided into atomic volumes according to
their charge densities, such that the gradient of the electron
density vanishes at every point on the dividing surfaces.
One of the challenging issues when designing the atomistic
interface model is to satisfy the periodic boundary conditions
of two materials with different lattice parameters at the same
time. A variety of methods have been discussed in the literature [16]: (1) incoherent interfacial region; to keep the lattice
parameters of both materials in their equilibrium state. The
misfit can be adjusted when extending the interface super cell
along the interfacial plane. Since the size of the super cell
needed for this adjustment is directly dependent on the misfit
ratio of two lattice parameters, there is in some cases no
rational limitation for the super cell extension. Due to the
system size limitation of DFT based methods; this is not
feasible in our case. (2) Coherent interfacial region; to
accommodate the lattice parameters of two materials,
straining the smaller lattice into ‘tensile coherent boundary
conditions’ or compressing the larger lattice into ‘compressive
coherent boundary conditions’. It is also possible to change
both lattice parameters to achieve the coherency. (3) Semicoherent interfacial region; local coherency and misfit dislocations alternating along the interfacial plane.
The coherent method (2) offers the possibility of using
smaller unit cell for calculations and the tensile coherent
method is superior to the compressive coherent one from its
smaller overestimation of the work of adhesion and interfacial
energy [16]. In the present work, we implemented the tensile
coherent method to construct the atomistic interface model
between Ni and LN. Therefore, the lattice parameters of Ni
parallel to the (010) surface were strained to be adjusted to those
of LN. It was kept fixed at the bulk value (as relaxed by DFT)
along the normal of the interfacial plane. Subsequently, ionic
relaxation of the interface structure was used to minimize the
induced strain.There is a possibility that some strain remained
perpendicular to the interface plane due to the change in
volume of the Ni phase, but this was not investigated further.
2.2.
Construction methodology
It is important to select appropriate surface terminations of the
two interface components. This selection will be based on the
following considerations: which are the most abundant
surfaces in reality, how large will be the calculation expenses,
and how can the lattice mismatch be minimized. The (010)
surface is the most stable among low index surfaces of LN [5],
and should thus be the most abundant under real conditions.
Furthermore, the surface unit cell of LN (010) is the smallest
available of this compound, giving the opportunity to create an
atomistic model with fewer atoms.
Fig. 1 is an illustration of a 2 2 1 super cell of Ni along
with the (010) surface of t- and m-LN. The PBE-GGA optimized
lattice parameters of Ni and LN bulk unit cells are tabulated in
Table 1. As shown in Fig. 1, the diagonal of the Ni unit cell face
(specified at the (100) surface) with a value of 4.98 Å is comparable to the (010) surface dimensions (5.56 and 5.20 Å in m-LN
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 e n e r g y 3 7 ( 2 0 1 2 ) 8 0 3 3 e8 0 4 2
8035
Fig. 1 e (a) The 2 3 2 3 1 unit cell of fcc Ni. The lattice distances applied to create the Ni/LN interface are specified by darker
balls. (b) The (010) monoclinic LN surface and (c) the (010) surface of tetragonal LN seen from above.
and 5.45 Å in t-LN). Hence, the Ni (100) surface can be aligned to
the (010) surface of both the LN phases. The lattice misfit can be
obtained by:
d¼
aLN pffiffiffi
2aNið100Þ
aLN
(1)
where a designates the PBE-GGA relaxed lattice parameters. In
m-LN, the two lattice constants parallel to the interfacial plane
are slightly different. The lattice mismatch will then be 10%
and 5% along the [001] and [100] directions of the interfacial
plane, respectively. For the tetragonal phase of LN, the lattice
misfit is 7.6%. These values are rather large, and add considerable uncertainty to our calculations. As mentioned previously, however, this gives the opportunity to achieve
qualitative results with a relatively small unit cell size.
In order to accommodate Ni atoms properly at the LN
surface, the most stable sites for Ni adsorption at the LN (010)
surface were calculated. Adsorption energy was defined for
this purpose as
Eadsorp ¼ ENi=LNslab ELNslab ENi
(2)
Here, ELN-slab and ENi are total electronic energies of the
clean LN slab and bulk Ni, respectively, and ENi=LNslab is the
Table 1 e The experimental [32,33] and calculated lattice
parameters of fcc Ni and LaNbO4. a, b and g are structural
angles.
This work
Parameters a
t-LN
m-LN
Ni
b
c
a
Experiment
b
LN slab energy including a Ni ad-atom. The calculated H
adsorption energies for the sites specified in Fig. 2a are
plotted in Fig. 2b. The most stable Ni atoms are found
between surface Nb and La atoms (the sites labeled “O2O3”
and “Nb1Nb3” in Fig. 2b). This insight was used to position
the Ni component on LN when creating the interface
models. Although these calculations were only performed
for the monoclinic structure, it is reasonable to believe that
the results are valid also for t-LN. The interatomic
distances are not very different in the two LN phases, so
the stability of Ni binding should not rely significantly on
the LN phase.
The thickness of the interface models is another parameter
to determine. We used a 5 layers Ni slab in combination with
a 3 layers LN slab; one layer of LN is here defined to consist of
a stoichiometric amount of La, Nb, and O, and is thus a larger
entity than the single-atom layers of Ni. This gave a thickness
of 7.04 and 7.08 Å for the Ni and LN components, so that the
unrelaxed interface models were in total 18.00 Å thick,
including gap region.
a
g
b
c
b
5.45 5.45 11.76 90 90
90 5.40 5.40 11.67 90
5.58 11.67 5.26 90 90.65 90 5.56 11.52 5.20 94.1
3.53 3.53 3.53 90 90
90 3.52 3.52 3.52 e
3.
Results
3.1.
Relaxed geometric structures
As shown in Fig. 3, the geometric structures of the m- and tinterface are very similar. The relaxed structures exhibit
a significant distortion of the Ni part induced by the lattice
mismatch. The relaxed interatomic distances are tabulated
in Table 2 and compared to the corresponding experimental
interatomic distances [17]. The range of the interatomic
distance within the first coordination shell is a measure of
local distortions of the lattice. We see from Table 2 that this
range is significantly more extended for the NieNi and NieO
interatomic distances than for any other pairs of atoms; this
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Fig. 2 e (a) The most stable Ni adsorption sites at the (010) surface of monoclinic LN. Surface atoms are specified with labels.
(b) Calculated adsorption energies as a function of height above the surface for a Ni atom at different sites on the 2 3 2 (010)
LN surface. In order to specify the initial Ni interstitial sites, legend of each plot shows the surface atoms, which surround
a Ni ad-atom.
is due to the tensile distortion of the Ni component. It is also
clear that the bond length distributions in the Ni component
for both m- and t-interface structures are quite similar.
Compared to the bulks of m- and t-LN, all optimized
minimum interatomic distances in the LN component of the
interface structures have been increased. The minimum
variation is 0.01 Å for LaeNb in the m-interface, and the
maximum change is 0.17 Å, which belongs to the NbeNb
interatomic distance of the t-interface. It is interesting to see
that the interatomic distances between Ni and LN (NieO,
NieLa, NieNb) of both m- and t-interface models are very
similar to corresponding experimental values; within
approximately 0.1 Å. This suggests that proper binding
between Ni and LN has been obtained, and gives support to
the physical relevance of our atomistic models.
It is important to note that, even if the distortions of the
Ni component are too large to be of any relevance to the
bulk part of a physical system, it is not unreasonable to
assume that such distortions may occur locally at the
interfacial region in real systems. Even if a semi-coherent
situation (with dislocations in addition to coherent
regions) or even an amorphous Ni component is much more
likely to occur in reality, a local distribution of NieNi and
NieO distances similar to that of our interface model is
likely to exist.
The real excess of energy, related to the formation of an
interface is defined according to the chemical potentials of
constituents [18]:
g ¼ Ginter X
mi N i
(3)
i
where G is the total Gibbs free energy of the interface model,
mi the chemical potential and Ni the number of atoms of the
components. This energy comprises both chemical and
elastic contributions g ¼ ðEe1 þ Ech Þ. From ab initio calculations in T ¼ 0 K the chemical part of interfacial energy is
defined as:
g¼
ENi=LN nNi EBNi nLN EBLN
2A
(4)
Here, A is the surface unit cell area and ENi/LN is the total
electronic energy of the interface structure (Ginter) from DFT
calculations, and EBX is the bulk energy of compound X. The
latter is multiplied by the number of layers of this
compound in the interface structure, nx. The chemical
interfacial energies for the monoclinic and tetragonal
Fig. 3 e Side view of a part of the Ni/LN interface models: (a) unrelaxed tetragonal, (b) relaxed tetragonal, (c) unrelaxed
monoclinic, and (d) relaxed monoclinic (Ni atoms are specified with white color).
8037
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Table 2 e Interatomic distances (Å) for the monoclinic and tetragonal interface models within the first coordinate shell,
from DFT calculations compared to the experimental values [17]. The maximum and minimum values are reported when
there is a distribution of this quantity.
Atoms
Interatomic distances
monoclinic interface
La-Ni
Nb-Ni
O-Ni
Ni-Ni
Nb-O
Nb-La
La-O
Nb-Nb
tetragonal interface
Unrelaxed
Relaxed
Unrelaxed
Relaxed
2.72
2.88
2.42e2.96
2.55e2.79
1.77e1.93
3.59
2.27
3.37
3.05
2.85
2.14e2.9
2.37e2.87
1.86e1.96
3.7 3
2.36
3.58
2.12
2.2
1.94e2.96
2.61,2.72
1.84e1.94
3.85
2.36
3.92
2.96
2.63
2.09e2.98
2.38e2.91
1.84e1.94
3.84
2.38
3.83
interface super cell have been calculated as 2.85 and 2.82 J/
m2, respectively. The difference between the interfacial
energies can be attributed to the increase of lattice
mismatch in the monoclinic structure compared to the
tetragonal one.
3.2.
Electronic structure
Fig. 4 illustrates the total (DOS) and local density of states
(LDOS) of the m-interface model, compared to the DOS of
bulk Ni and LN. In metalesemiconductor (MS) interfaces
(although LN with an experimental band gap of 4.8 eV is an
insulator, it can also be regarded as a wide band gap semiconductor), the Fermi level of oxide is generally aligned with
metal. When the DOS in bulk LN and Ni are compared with
that of the interface model, the interface electronic structure
is seen to be dominated by metallic states; as an example,
there is no band gap in the interface structure. Likewise, the
LDOS projected on LN atoms at the interfacial layer (the
neighbor layer of Ni) exhibit spin polarization; this is clearly
visible in the Nb p orbital, shown in the inset of Fig. 4. The
valence bands further exhibit hybridization between the s
and p orbitals of the LN elements and Ni. There is also a small
overlap between the d orbitals of Ni, La and Nb in the valence
band region. The orbital overlap between LN elements and Ni
presented in the LDOS of interface model confirms that
chemical bonds have been formed between Ni and LN
components. Similar bonds are seen at the t-interface (not
shown here).
The electronic states appearing in the band gap of the
interface model can be interpreted as metal-induced gap
states (MIGS). These states are also demonstrated in LDOS
projected on the LN elements. MIGS are due to the relaxation of metal electronic wave functions to the semiconductor at the interface [19,20]. These energy states
decay exponentially in deeper layers of the semiconductor.
Recent studies have suggested that the Schottky barrier
height (SBH) [21] does not strongly depend on the
metal work-function since the Fermi level may be pinned
by the MIGS [22].
The SBH is a potential barrier at the metalesemiconductor
interface, serving as a rectifying factor for charge transport
across the IR. The p- and n-type SBHs are defined as:
Experimental
2.92 in all La-Ni compositions
2.69-2.79 (Ni6Nb6O)
2.08-2.95 (La2(NiO4
2.48 (fcc Ni)
1.86 (m-LN), 1.89 (t-LN)
3.74 (m-LN), 3.85 (t-LN)
2.48 (m-LN), 2.52 (t-LN)
3.60 (m-LN), 4 (t-LN)
Fp ¼ Ef VBT
(5)
Fn ¼ CBM Ef ¼ Eg Fp
(6)
Here, Fp and Fn are the SBHs for holes and electrons,
respectively, Ef is the Fermi level of the interface structure,
CBM and VBT are the conduction band minimum and valence
band top of the LN component, and Eg is the LN band gap. To
find the LN component VBT, the valence band minimum
(VBM) of LN bulk was adjusted with the VBM of the interface
structure. Since DFT at the GGA level tends to underestimate
band gaps, the experimental LN band gap value of 4.8 eV was
used to calculate the n-type SBH. We obtained Fn ¼ 1.8 eV and
Fp ¼ 3 eV for our interface model (the calculated band gap
from DFT calculation is w3.6 eV [5,23]). This means that
electrons in the LN conduction band, at the interfacial region
will tend to move toward and into Ni.
3.3.
Stability of hydrogen in the interface model
It is interesting to study the potential energy of a hydrogen
atom when it moves through the interface structure from the
Ni component to the LN component. Dissociative hydrogen
adsorption at the surfaces of Ni and its diffusion pathway
through the bulk have been thoroughly discussed in the
literature previously [24,25], and are therefore not the topics of
this study. We have placed H at interstitial sites according to
Fig. 5a, which should provide a representative selection of
sites through the interfacial region. The relaxed H positions
are shown in Fig. 5b.
We report here the binding energy Ebin of H in the interface
model, which is defined as
Ebin ¼ EInterfaceþH EInterface 1=2EðH2 Þ
(7)
The formation energy of H2 from H atoms was found to be
E(H2) ¼ 4.52 eV, which agrees reasonably with experimental
values [26]. Similar calculations were also performed for bulk
Ni and LN for comparison with the interface, and to compare
with previously reported results in the literature. As shown in
Table 3, our results for the binding energy of H in bulk Ni
compare very well with those previously reported by Wimmer
et al. [27].
In the Ni component of interface model, H was placed at
tetrahedral sites (Nos. 3 and 5) and octahedral sites (Nos. 4 and
8038
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Fig. 4 e DOS and LDOS of the m-interface structure. LDOS are projected on atoms in the interfacial layers of LN and Ni at the
IR. Contributions are shown for O (wine dashes), La (solid black lines), Ni (green dots), and Nb (solid, bright gray, filled areas).
The orbital is specified by a label at each plot. The region of the LN band gap in the interface electronic structure, which is
filled by the metal-induced gap states is determined by two parallel arrows in the LDOS (p and s orbitals). To clarify the spin
polarization of (refer to the text) energy states, the p orbitals of La and Nb are also shown separately in an inset. The DOSs of
bulk LN and Ni are shown in the lowest panel. (For interpretation of the references to color in this figure legend, the reader is
referred to the web version of this article.)
6). Sites 3 and 4 can be considered as subsurface sites, while
sites 5 and 6 placed in the middle of Ni component should be
similar to bulk sites (see Fig. 5). The calculated binding energies should, however, not be expected to be the same as the
corresponding energies in bulk Ni due to the large tensile
distortion of the Ni component. The interatomic NieH
distances show unique values in bulk Ni: 1.8 Å for the octahedral site and 1.6 Å for the tetrahedral site. The H positions
are then symmetrical, at least in the low-density regime. In
contrast, these distances exhibit a range of values in the
interface models (Table 3). This is due to the loss of symmetry
induced by the tensile stress. Hence, the calculated Ebin also
exhibits a range of values in the interface model. When
comparing with the previously reported results in literature,
Ebin is higher (less stable) in the Ni component than in
subsurface Ni, while it is lower (more stable) than in bulk Ni.
8039
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Fig. 5 e Positions of hydrogen interstitial sites in the monoclinic interface model before (a) and after (b) relaxation. The
starting points for the hydrogen sites in the LN part were between La and Nb (sites 10 and 13), La and La (site 12), and Nb and
Nb (site 11). Sites 2, 7, 8, and 14 were between LN and Ni (gap region). In the Ni component, octahedral sites (4 and 6) and
tetrahedral sites (3 and 5) were chosen. In (b), the relaxed H positions are shown together with the unrelaxed positions of
the other interface atoms, to clearly exhibit how H atoms have moved during relaxation. In (c), the corresponding relaxed H
positions in the bulk LN model are presented. The initial H sites are not shown since H atoms are not significantly displaced
due to the relaxation in this case.
This is most pronounced for the subsurface tetrahedral site,
which in the interface structure has stability rather like that of
the octahedral site than of the subsurface tetrahedral site in
pure Ni. This is due to the stressed Ni lattice close to the
interface, which has led to tetrahedral sites with NieH interatomic distances, approaching those of the octahedral site
(Table 3).
The calculated H binding energies and the interatomic
distances between H and its nearest neighbors in both the LN
component and bulk are similarly listed in Table 4. The initial
and relaxed H sites are shown in Fig. 5. From this table, we see
that the relaxed interatomic distance between hydrogen and
oxygen atoms is between 0.98 and 1.00 Å in the LN component. This is equal to the distance found for adsorbed H atom
at the (010) LN surface [5] and is the typical OeH bond length in
solid compositions when H atom has a formal charge of þ1
[28]. The same OeH bond length can be seen in the two most
stable H binding sites (10 and 13) of bulk LN as well.
The distance between H and La is slightly larger in the LN
component than in bulk LN. This is also the case for the NbeH
distances when only the most stable sites are regarded. The
explanation of this must be a larger freedom of ionic
displacements in the interface models close to the interface
plane (the plane between LN and Ni). This is illustrated in
Fig. 6, where the relaxed interface model is compared to the
situation when H is placed at site 11. In the H-included model,
the minimum interatomic distance for LaeNb is increased by
up to 0.7 Ǻ, while the LaeLa and NbeNb interatomic distances
are increased by 1.0 Ǻ. The NbeNi distance is similarly
extended by 0.33 Ǻ, while La and Ni become 0.7 Ǻ closer. All Habsorbed interface models exhibit similar geometric
relaxations.
The large relaxations are accompanied by significantly
lower H binding energy (more stability) in the LN component
compared to the LN bulk. The binding energies are listed in
Table 4 and schematically presented in Fig. 7 across the
Table 3 e Interatomic distances (Å) and binding energies of hydrogen (eV/atom) in the Ni component of the interface
model in comparison with corresponding calculated and experimental values for Ni bulk. For the Ni component, the H
sites are numbered according to Fig. 5.
Ni component
Ni Bulk
Literature[24,27]
Subsurface
Bulk
Subsurface
Site
3-tetra
4-octa
5-tetra
6-octa
Ni-H
Eb
1.63e1.7
0.197
1.72e1.9
0.2
1.48e1.58
0.349
1.58e1.98
0.179
This work
Bulk
Bulk
Tetra
Octa
Tetra
Octa
Tetra
Octa
e
0.51
e
0.2
1.58
0.33
1.77
0.075
1.6
0.34
1.8
0.07
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Table 4 e Interatomicdistances (Å) between the relaxed H interstitial and its nearest neighbors in the first coordination
shell as well as H binding energies (Eb) in eV/atom, at the LN component, gap region and LN bulk. The specified H sites have
been described in Fig. 5. yini and yre represent the y coordinates of H before and after ionic relaxation, according to the
coordinate system of interface model in Fig. 5.
Site
LaeH (Å)
NbeH (Å)
NieH (Å)
OeH (Å)
yini (Å)
yre (Å)
Eb
LN component
12
13
11
10
2.7
2.66
e
1.00
5.22
5.98
0.01
2.7
2.66
e
0.98
5.4
6.02
0.19
2.68
2.55
e
0.98
5.16
6.26
0.38
2.6
2.63
e
0.98
6.36
6.72
0.41
LN bulk
8
e
2.64
2.38
1.00
7.66
8.32
0.38
7
14
1.58
2.68
2.68
1.44
e
e
e
e
1.7
e
e
e
8.3
9.02
1.44
6.59
8.17
0.32
9.53
9.35
1.6
interface. The subsurface sites of the LN component (all sites
in the LN component, shown in Fig. 5b), exhibit a H binding
energy of around 1.8 eV more stable than in bulk LN (the
leftmost points of Fig. 7). This is most readily explained by
MIGS offering electronic states in the band gap, thus
increasing the stability of H in the LN component.
Furthermore, hydrogen atoms in the LN component relax
toward the interfacial plane. This is quantified in Table 4,
Fig. 6 e Relaxed interatomic distances between selected
metal atoms in the LN component in (a) the perfect
interface model and (b) the interface model when a H
interstitial has been included in site 11.
2
12
13
11
10
15
2.31
1.24
e
e
e
e
3.05
2.46
1.92
e
1.00
e
e
2.16
e
2.12
e
1.22
e
e
2.76
2.64
2.46
e
0.98
e
e
1.77
2.03
e
1.27
e
e
2.29
comparing the y coordinate (refer to Fig. 3) of the relaxed
hydrogen positions with that of the initial positions. Such
a directed relaxation of H interstitials occurs neither in bulk
LN nor Ni component (Fig. 5). As mentioned above, hydrogen
interstitials attain much lower energies and higher stability in
the LN component than in bulk, which is related to the
influence of MIGS. Since these gap states exponentially
reduces through the oxide part of the interface structure; H
atoms in the LN component are more stabilized close to the
interfacial plane.
The gap region between LN and Ni components is extended
perpendicular to the interfacial plane as 2.44 Å, when
considering the nearest Ni and O atoms. In this region, we find
that the NieH distances in sites 2, 7, and 14 (1.44e1.7 Å) are
Fig. 7 e Potential energy curve of hydrogen at various
interstitial positions in the interfacial region (red
diamonds) compared to corresponding energies in bulk LN
from the present work (green crosses) and in the Ni
subsurface and bulk [24,27] (green squares). The H binding
energy is defined in Section 3.3. Solid lines specify the
borders of Ni and LN interfacial surfaces, considering sites
2 and 8. Sites 10 and 3 are at the interfacial layers of LN and
Ni components. (For interpretation of the references to
color in this figure legend, the reader is referred to the web
version of this article.)
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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 e n e r g y 3 7 ( 2 0 1 2 ) 8 0 3 3 e8 0 4 2
Table 5 e The calculated charge of the hydrogen atom when placed at different sites (refer to the Fig. 5 for definition of the
sites) as well as the charge of the Ni and LN interfacial layers when including H atom in these sites. The nearest atoms to
the H interstitial are listed in the “Neighbors” row.
Site
H-Neighbors
H charge
Ni charge
LN charge
12
11
10
14
8
7
2
4
3
6
Nb,La,O
þ1
0
1
Nb,O,La
þ1.0
þ0.1
1.1
La,Nb,O
þ1.00
þ0.01
1.01
La,Ni,Nb
0.39
þ0.72
0.33
Ni,Nb,O
þ1.0
0.1
0.9
Ni
0.3
þ0.7
0.4
Ni
0.31
þ0.70
0.40
Ni
0.28
þ0.70
0.42
Ni
0.37
þ0.80
0.52
Ni
0.28
þ0.72
0.43
comparable with what is found for H adsorption at the (100)
surface of pure Ni (1.84 Å for the most stable site at the (100) Ni
surface [24]). Likewise, the OeH and NbeH distances at site 8
are very close to the corresponding distances at the pure LN
(010) surface [5]. In this respect, these sites can be considered
to be on the interfacial LN and Ni surfaces, respectively.
The stability of hydrogen atoms still increases, when
moving to the gap region in the interface model. At the
interfacial surface of LN (site 8), the binding energy is
0.38 eV; this is around 1.5 eV more stable than the adsorption energy of H on the pure LN (010) surface [5]. At the most
stable site on the interfacial surface of Ni (site 2), there is still
a significant effect of the MIGS stabilization; here, the binding
energy is 1.6 eV, which is 1.1 eV below the adsorption energy
on the pure Ni (100) surface (approximately 0.5 eV [29]). The
stabilization rapidly disappears when we enter Ni; the
subsurface site is stabilized by 0.3 eV compared to pure Ni,
while the remaining sites are virtually unchanged. A deep
potential well can thus be seen, localized between the Ni and
LN components, bonded to the Ni interfacial surface (Fig. 7).
The consequence of this is that any available hydrogen
atoms will be trapped near the interfacial plane (Fig. 7), where
the potential energy of hydrogen is very low. In addition,
hydrogen will be accumulated in the region of LN close to the
interface plane, due to the significant stabilization of
Fig. 8 e The sum of Bader charges for each layer (each layer
is specified by black dots for Ni and black squares for LN) of
the Ni and LN components, relative to the atomic states.
The interfacial layers for LN and Ni (on both sides of each
component) were adjusted at the first and last points of the
plots, to present the charge transfer between LN and Ni
interfacial layers which shown to be from Ni to LN. This
makes the interfacial dipole which is demonstrated by
arrows.
hydrogen relative to bulk LN. We believe that this is a general
phenomenon in all metal/oxide interfaces, since it relies on
the existence of MIGS which are commonly found in this kind
of interfaces.
3.4.
Charge transfer
Charge transfer to and from H atoms through the interface
structure was investigated through the Bader analysis. For
these calculations, we used the same relaxed H positions as
specified in the previous section (Fig. 5b). The results of these
calculations are summarized in Table 5. When H is in contact
with Ni, charge transfer is from Ni to H in all cases, where the
NieH distance is less than 2 Ǻ. This can be justified by the
electronegativity of Ni being slightly lower than that of H.
When H is within or at the LN component, it is ionized into
a proton bonded to an oxide ion with a bond length of 0.98 Å,
as expected [28].
Fig. 8 presents a plot of the integrated charge per layer
across the LN and Ni components in the perfect interface
model. The total average charge of the Ni layers displays
a periodic behavior, due to the charge screening effects on the
different metal layers. The Ni and LN interfacial layers (leftmost and rightmost in the plot) exhibit an average positive
and negative charge respectively, which indicates a charge
transfer from Ni to the LN component at the interface. This is
due to the chemical bonds between metal and semiconductor;
thus the binding configuration is responsible for the formation
of the interface dipole [7,30,31]. The existence of chemical
bonds between the Ni and LN components was affirmed in the
previous sections. Due to the incoherency between components at the IR and a variety of surface terminations meeting
each other, the bond configuration will certainly vary in
polycrystalline materials. In this respect, there will be several
different local dipole values at the IR and only an effective
average dipole can be measured for the whole structure.
We have shown in Section 3.3 that the significant stability
of H atom in the IR is grounded in the presence of MIGS. The
electron of ionized H will thus be placed in these gap states
close to the Fermi level since the O valence bands are already
filled. In the operation of a fuel cell, these electrons can be
delocalized and enter to the conduction band to feed an
external electronic current in the circuit connected to the Ni
electrode.
4.
Conclusions
We have constructed two atomistic interface models between
the Ni (100) surface and the (010) surface of LaNbO4 (LN) in its
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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 e n e r g y 3 7 ( 2 0 1 2 ) 8 0 3 3 e8 0 4 2
tetragonal and monoclinic phases. Local density of states
confirmed the formation of chemical bonds between Ni and
LN elements. In the interfacial region (IR), the calculated ntype Schottky barrier height (SBH) was found to be 1.8 eV,
indicating that at the IR, the LN conduction band electrons will
migrate to the Ni part.
The potential energy of hydrogen across the interfacial
region displayed a deep potential well of around 2 eV between
the LN and Ni components, with H primarily bonded to Ni. It is
induced by metal-induced gap states (MIGS), stabilizing H at
a site resembling adsorption sites on the pure Ni surface.
These very stable interstitial sites will lead to hydrogen trapped at the interfacial plane. In addition, stabilization of
hydrogen or hydrogen ionized to protons in a larger region
within LN close to the interface plane will lead to further
accumulation in the interfacial region.
Bader charge analysis demonstrated that a dipole is
formed at the interface, due to charge transfer from Ni to the
LN component; this is a result of chemical binding between
the two components. Furthermore, it was shown that H
donates its electron at the LN interfacial layer, and thus
becomes a proton bonded with an oxide ion. The electrons lost
from H atoms reside in the MIGS, placed in the band gap of LN
close to the Fermi level. Regarding the significant value of the
n-type SBH, these electrons will migrate to the Ni part where
they, for instance, make up the current flowing when the Ni
part is connected as an electrode in a fuel cell.
Acknowledgment
The authors would like to thank the NOTUR consortium for
computational resources and the Research Council of Norway
for funding (NANOMAT project NANIONET 182065/S10).
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