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 ) 6 6 7 4 e6 6 8 5
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Atomistic study of LaNbO4; surface properties and hydrogen
adsorption
K. Hadidi a, R. Hancke b, T. Norby b, A.E. Gunnæs a, O.M. Løvvik a,c,*
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:
We have calculated fundamental properties of pure and hydrogen-covered (010), (101),
Received 29 November 2011
(100) and (001) surfaces of the low temperature monoclinic phase of LaNbO4 (LN). The (010)
Received in revised form
surface was the most stable one, exhibiting electronic structure and local geometric
13 January 2012
configurations similar to bulk. As the first stage of proton migration into the electrolyte, the
Accepted 17 January 2012
ability of LN surfaces to split H2 molecules was probed indirectly by calculating the
Available online 15 February 2012
adsorption energy of H atoms on two of the LN surfaces. H adsorption on the (010) surface
was found to be strongly endothermic, and thus cannot contribute much in splitting H2.
Keywords:
The adsorption energy on the relatively unstable (101) surface was on the other hand
LaNbO4
approximately 0.6 eV, in the right range for surface H2 to be catalyzed beneficially. H
Density functional theory
adsorption on this surface was induced by surface states in the band gap of the clean
Surface energy
surface. Since the unstable (101) surface is not abundant, the rate of dissociative adsorption
Hydrogen adsorption
of H2 on the LN surface can be anticipated to be very low. Application of the energies to
simple adsorption isotherm calculations for typical proton conducting fuel cells (PCFCs)
operating temperatures correspondingly showed very low H coverage, and it is not expected that LaNbO4 surfaces can contribute much to the H2 activation reaction of a PCFC
anode.
Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
reserved.
1.
Introduction
Ceramic ion conducting materials find potential applications
in many important energy conversion technologies such as
fuel cells. In solid oxide fuel cells (SOFCs) depending on the
type of ions responsible for the charge transport (e.g. oxide
ions or protons) and on the general properties of the electrolyte, a variety of fuel cell operating conditions and functions
can be obtained. In principle, proton conducting fuel cells
(PCFCs) can provide more efficient fuel utilization than oxide
ion conducting solid oxide fuel cells, since water is produced
at the cathode side so that the fuel is not diluted at the anode
side. Furthermore, water vapor production at the anode side
of the SOFCs reduces the cell voltage and can also cause metal
components in the anode to oxidize [1].
Perovskite-structured doped barium cerates are state of
the art proton conducting electrolytes with excellent proton
conductivities in the order of 0.01 S cm1 [2e5]. The application of these compounds suffers, however, from their
decomposition by reaction with acidic gases such as CO2. The
efficiency of Ba zirconates is also affected by their high grain
boundary resistance. More recent proton conducting
* Corresponding author. SINTEF Materials and Chemistry, Forskningsveien 1, NO-0314 Oslo, Norway.
E-mail address: o.m.lovvik@fys.uio.no (O.M. Løvvik).
0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijhydene.2012.01.065
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 ) 6 6 7 4 e6 6 8 5
materials are the rare-earth ortho-niobates and tantalates [6].
The highest proton conductivity in this class has been reported for acceptor-doped LaNbO4 (LN); w0.001 S cm1 at
950 C in wet atmospheres [7]. Despite this moderate proton
transport, LN is still of interest as a model electrolyte in proton
conducting solid oxide fuel cells due to its chemical stability
towards CO2 under operating conditions and has been investigated with respect to thermodynamics and mobility of
protons, dopants and defects [8e11]. A number of other
advantageous properties besides proton transport are also
found in LN, such as blue and ultraviolet emission when being
excited by X-Ray radiation [12]. It also exhibits dielectric
microwave properties which have been associated with the
ferroelasticity of LN in its monoclinic phase [13,14].
In order to have proton transport through PCFCs the
hydrogen molecule should be adsorbed dissociatively at
a surface. This can occur at the surfaces of heterogeneous
catalysts such as Pt or Ni through the anode, where H2 enters
to the fuel cell operational system. To increase the functionality of the anodes, they are made in the form of cermets
containing Ni and a ceramic phase which is the same as the
implemented electrolyte. Therefor it is also interesting to
investigate the interaction of H2 in gas phase directly with the
surface of the proton conducting membrane. Furthermore,
a thorough understanding of the oxide surfaces and their
interaction with hydrogen is essential to analyze the physical
phenomena taking place, when hydrogen moves at the
electrolyte-electrode and electrolyte-gas interfaces and also
the triple phase boundary of an electrode. We have investigated such issues in a recent paper [15].
In the present work we have calculated the detailed electronic and geometric properties of the perfect, low index (001),
(010), (100) and (101) surfaces of LN. Also, the ability of the (010)
and (101) surfaces to dissociate and adsorb H2, as a model
system of oxide surface interactions in a PCFC, has been
investigated. The possibility for hydrogen to donate its electron locally when interacting with surfaces of LN grains were
also clarified. To support the interpretation of our studies,
simple thermodynamic considerations were applied to
quantify the hydrogen coverage at finite temperatures.
LN has a monoclinic fergusonite type structure at low
temperature and transforms into a tetragonal scheelite type
structure between 490 C and 525 C [16]. Although it is in the
tetragonal state at typical operating temperatures, we chose
to study the monoclinic phase (Fig. 1) in order to remain
consistent with the calculations which were performed at 0 K.
We expect that the results should not deviate much from
those of the tetragonal phase since the surface properties are
primarily determined by the local bonding configurations at
the surface, which are similar in both polymorphs.
All calculations were performed on perfect LN surfaces.
However, acceptor doped materials are usually used as electrolyte in PCFCs in order to increase the mobility of protons.
This results in oxygen vacancies as structural defects with the
potential to affect the electronic and geometric structure of
the electrolyte even near the surface. This is beyond the scope
of this study, but we nevertheless believe that our calculations
are highly relevant for the first part of the process in which
hydrogen gas is transported to the LN surface and converted
to protons.
6675
Fig. 1 e The bulk structure of LaNbO4. Yellow (bright), green
(dark), and orange (small) balls designate Nb, La, and O
atoms, respectively. The shaded surface specifies the (100)
plane and the dashed contour presents one layer of the
structure including one formula unit. Four oxygen atoms
participate in a tetrahedral construction with Nb at the
center; this has been shown as a shaded tetrahedron in the
figure. (For interpretation of the references to color in this
figure legend, the reader is referred to the web version of
this article.)
2.
Computational method
The computations were based on plane wave density functional theory using the Vienna ab-initio simulation package
(VASP) [17,18]. In all calculations, we utilized the generalized
gradient approximation within the PerdeweBurkeeErnzerhof
(PBE-GGA) scheme [18,19]. The projector augmented wave
(PAW) method was employed to treat the core regions [20,21].
To set the partial occupancies [22e24] for density of states
(DOS) and highly accurate total energy calculations we used
the tetrahedron method with Blöchl corrections [25,26];
otherwise Gaussian smearing was employed [27]. Close to the
local minimum, geometry optimization was implemented
using the residual minimization scheme with direct inversion
in the iterative subspace (RMM-DIIS) [28], whereas the conjugate gradient algorithm [29] was chosen when relaxation
started from a position far from the local minimum. The
relaxation procedure was applied to the bulk structure and
slabs until the forces on all unconstrained atoms were less
than 0.05 eV/Å. Soft potentials [20,21], which only treat the
electrons in the outermost shells as valence electrons, were
utilized for all calculations after confirming that the results
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did not change significantly when including additional
valence electrons. Thus the valence electrons were
5s25p66s25d1 for La, 4p65s24d3 for Nb and 2s22p4 for O. The
numerical parameters were chosen to obtain convergence of
the total energy within 1 meV per unit cell. A MonkhorstePack
k-point grid with minimum density corresponding to a k-point
distance of 0.16 Å1 and a cutoff energy equal to 850 eV were
found to be necessary to evaluate the total electronic energy
within 1 meV per unit cell. In the vacuum direction of slabs
only the gamma point was used. Since the calculated forces
converged to within 0.1 eV/Å using a cutoff energy of 450 eV,
we applied this value to relax the structures. LN is nonmagnetic in the ground state, so no spin-polarization was taken
into account in the bulk calculations. It was also clarified, that
spin-polarization does not affect on the calculated energies
for the slabs. To calculate local density of states, empirical
covalent radii of 1.69, 1.37 and 0.73 Å were chosen as
WignereSeitz radii for La, Nb and O, respectively [30]. To
ensure that the electron density of slabs tails off to zero in the
vacuum and that the top of one slab has negligible effect on
the bottom of the next, a vacuum layer of at least 10 Å was
applied to make the slab structures.
To quantify zero point energy corrections of the adsorbed
H atoms, the Hessian matrix was calculated and diagonalized
to find the normal modes and energies for localized vibrations
of hydrogen ad-atoms in the most stable binding sites. The
Hessian matrix for the BorneOppenheimer potential energy
surface was estimated numerically using a finite difference
approximation. Hydrogen atoms were then moved around the
local minimum with a displacement of 0.1 Å in each direction.
All the other atoms in the slabs model were constrained at
their positions.
We used the conventional bulk unit cell [31] with four
formula units in our calculations (Fig. 1). In the slab models,
each layer contained one formula unit in the (010) plane, while
the slabs in the (101), (001), and (100) planes contained two
formula units per layer (Fig. 2). All the results presented in this
work were produced with slabs containing the correct stoichiometry, that is, without adding or removing oxygen at the
surface. Tests of slabs with excess oxygen did not show
improved stability and were not considered any further.
3.
Results
3.1.
Bulk geometric structure
The experimental lattice parameters and atomic coordinates
presented by Tsunekawa et al. [31] were utilized for the
initialization of the structural relaxation. The bulk unit cell was
relaxed with respect to ionic positions and cell size and shape
simultaneously. The resulting calculated lattice parameters
and atomic sites accompanied by previously published GGA
based results of Kuwabara et al. [11] are shown in Table 1. In
comparison with the experimental values, the calculated
lattice constants are overestimated by 1.2, 1.3 and 0.4% and the
monoclinic g angle is underestimated by 0.5%. As a result, the
cell volume is overestimated by almost 3%, compared to a corresponding 4% overestimation of the cell volume in the
preceding calculations. Furthermore, all errors in the atomic
coordinates are less than 2%, as compared to 3% of the previously reported values. The modest discrepancy between the
two sets of DFT results can be ascribed to differences in
numerical parameters, numerical noise or different starting
geometries. Since the DFT calculations are valid at 0 K and the
experiments are taken at room temperature, we can expect
that the discrepancy between theory and experiment is
somewhat larger if temperature were taken into account.
Fig. 2 e Upper panels: Side view of 4 layers relaxed slabs representing the specified surfaces. The surface direction is
upwards in the paper plane. Lower panels: Top view of the same slabs. The atoms are represented in the same manner as in
Fig. 1.
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0.8
O2,16f
This work
Kuwabara
et al.b
5.20
11.52
5.56
94.09
332.99
0.62292
0.1036
0.2376, 0.0334,
0.0564
0. 1460, 0.2042,
0.4888
5.26
11.67
5.58
93.65
343.51
0.629
0.105
0.241, 0.033,
0.055
0.145, 0.205,
0.491
5.38
11.69
5.49
91.20
345.52
0.626
0.118
0.246, 0.037,
0.080
0.157, 0.209,
0.495
a Ref. [31].
b Ref. [11].
3.2.
displacement (Å)
a (Å)
b (Å)
c (Å)
a(degrees)
Volume (Å3)
La,4e (0,y,0.25)
Nb,4e(0,y,0.25)
O1,16f
Experimental
(293 K)a
101 - 4layer
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
Extending coordinate (Å)
0.3
010 - 4 layers
displacement (Å)
Table 1 e Equilibrium lattice constants, volume and
atomic coordinates for monoclinic LaNbO4 (space group
I2/c).
0.2
0.1
Slab geometric structure
To make the slab models, we used the relaxed bulk unit cell as
the starting point; this we call the bulk cut slabs (Fig. 2). When
relaxing the surfaces there are three possibilities. One is to
relax a number of layers on one side and keep the remaining
layers fixed at the bulk positions. This approach defines an
asymmetric slab [32]; layers on one side are relaxed to mimic
the surface, while layers on the other side are kept fixed to
mimic continuation into the bulk. An important potential
problem of an asymmetric slab model is that this may generate
an electrostatic dipole. Another alternative is to describe the
surface using a symmetric model where atoms in the middle
layers are fixed at their bulk geometries and the layers above
and below are allowed to relax. This avoids the formation of
artificial dipoles, but makes it necessary to include a relatively
large number of layers; this can be computationally intensive
for complicated structures like that of LaNbO4. The third
option, which was chosen in this work, is to allow all atoms in
the slab to be relaxed. This has many features common with
the second approach above, except the restriction on the
middle atoms. This can also serve as a test of whether we have
included a sufficient number of layers in the slab models: If this
is the case, we expect that the middle layers are very close to
the bulk geometry after relaxation. This is illustrated for the
(010) and (101) four layers slabs in Fig. 3. It can be seen that for
both these slabs, very small displacements occur in the middle
of slabs, whereupon four layers are sufficient to evaluate
surface properties in these surfaces.
Although LN is known to be an ionic oxide, the studied
surfaces are nonpolar and also neutral since each slab layer is
stoichiometric and the number of cations and anions in both
terminations of the slabs is the same. The force minimizations could not be completed for the (001) and (100) surfaces,
as significant forces always remained despite various efforts
to relax the structures. As shown in the next section, these
surfaces are considerably less stable than the two others,
when using un-relaxed surface structures to assess the
surface stability. This instability explains the difficulty to
converge the forces for the (100) and (001) surfaces.
0
0
5
10
15
Extending coordinate (Å)
Fig. 3 e Displacement of atoms due to relaxation of the slab
models, shown here as a function of the slab depth (the
“extending coordinate” is perpendicular to the slab plane)
for a four layers slab of the (010) surface (lower panel) and
a four layers slab of the (101) surface (upper panel). The
minimum atomic displacements in the middle represent
typical bulk behavior.
The relaxed interatomic distances are summarized in
Table 2. The small unit cell size of the slabs does not allow any
surface reconstructions, so this possibility cannot be excluded
by our study. Some variations in the interatomic distances do
occur, as shown in Table 2, but they cannot be taken as
reconstructions. We first note that all the minimum interatomic distances between metal and oxygen atoms in the
slabs are smaller than those in the bulk. Inspecting the relaxed
slab structures reveals that these short bonds are all placed
between the surface oxygen atoms and surface-subsurface
metal atoms. At the same time, we can see an increase of
the bond lengths between the subsurface metal and oxygen
atoms. Surface oxygen atoms have lost some of their bonds,
and therefore strengthen their bonds with the remaining
surface-subsurface metal atoms; at the same time the oxygen
bonds with the subsurface metal atoms are elongated.
Predictably, this change of interatomic distances is more
pronounced in the less stable surfaces. As an example, the
difference between maximum and minimum distances of
LaeO is 13% for the most stable (010) surface, as compared to
4% in the bulk. This difference is increased to 27% for the less
stable (101) surface. Similarly, the spread of the other interatomic distances is significantly larger for the (101) surface
than for the (010) surface. In most of the cases the spread is
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Table 2 e Interatomic distances in Å for the relaxed bulk unit cell and slabs of monoclinic LaNbO4. The minimum and
maximum distances within the first coordination shells are listed.
Minimum
LaeO
NbeO
LaeNb
LaeLa
NbeNb
LaeO
NbeO
LaeNb
LaeLa
NbeNb
2.476
2.320
2.124
1.879
1.850
1.810
3.727
3.730
3.470
3.973
3.988
3.657
3.607
3.696
3.330
2.547
2.621
2.702
1.940
1.930
1.963
3.971
3.967
3.963
4.004
3.995
4.057
4.384
4.151
4.112
smallest in the bulk, but in some cases it is even smaller for
the (010) surface. These results are consistent with the surface
energy calculations of the next section, showing that the (010)
surface is the most stable one.
The minimum LaeO bond at the (101) surface is 14%
smaller than that of the bulk. This reflects a very strong
interaction between oxygen and lanthanum at this surface
which we will return to when presenting density of states
(DOS) calculations.
3.3.
Surface stability
Surface energies (s) were calculated by comparing the total
energy of the slab with the bulk energy multiplied with the
number of layers in the slab through the relationship:
s¼
1
EN NEBulk
2A Slab
(1)
Here ENSlab is the energy of a slab with N layers, A is the
surface area, and EBulk is the bulk energy [33,34]. It has been
shown that Eq. (1) diverges linearly as N increases when EBulk
is taken from a true bulk calculation. The solution to this
problem is to utilize a linear fit method in which the quantity
EBulk is calculated from a linear fit to the slabs’ cohesive
energies versus N. To make sure that we could obtain
convergence using this method, the variation of computed
surface energies s versus the number of layers for relaxed
(101) and (010) and un-relaxed (001) and (100) surfaces was
plotted in Fig. 4. It is evident that the energies are relatively
well converged already at three layers, the very unstable (100)
surface being an exception. We also note that many of the
slabs exhibit an oscillating behavior, with odd and even
numbers of layers converging to different values. A notable
example of this is the (010) slab, which converges to 0.76 and
0.63 J/m2 for the even- and odd-numbered slabs, respectively.
The explanation of this behavior is the different symmetry of
every second layer, leading to different geometrical configurations of odd and even numbered layers.
Calculated surface energies for different layers of relaxed
and un-relaxed slabs are summarized in Table 3. As is also
shown in Fig. 4, these values establish the (010) surface as the
most stable one with the lowest surface energy. Since the (100)
and (001) surfaces are nonpolar and neutral, their considerable instability can be attributed to a large number of dangling
bonds.
From Table 3 it can be also concluded that the change in
surface energies due to geometry optimization is larger for the
less stable (101) surface (34e40%) than for the (010) surface
(1e25%). Since the relaxation process was successful only for
the two more stable surfaces, we chose them for the following
analysis.
3.4.
bulk
Electronic structure of the LN clean surfaces and
The total density of states of the tetragonal and monoclinic
phases of LN has previously been calculated for the bulk by
Arai et al. [35]. The calculated total (DOS) and local (LDOS)
density of states of the LN bulk and the (010) and (101) four
layers slabs are shown in Fig. 5. The LDOS of slabs were
projected on the surface and subsurface atoms and only the
most important valence orbitals have been included. The
energy is defined relative to the Fermi level, which by default
is placed at the valence band maximum. We have shifted the
energy of the (101) slab so that the conduction band
minimum matches that of LN bulk; this makes it easier to
compare the DOS plots.
The band gap of the relaxed bulk unit cell was here found
to be 3.6 eV, which agrees reasonably well with 3.8 eV found by
Arai et al. Compared to the experimental value (4.8 eV), the
calculated band gap is considerably underestimated, which is
typical for standard DFT calculations at the GGA level. Our aim
in this paper is primarily to compare the electronic structure
of surfaces to that of the bulk, so the absolute value of the
band gap is not crucial.
001
100
re-010
re-101
4
Surface Energy (eV)
Bulk
(010)
(101)
Maximum
3
2
1
0
0
2
4
6
8
Number of layers
Fig. 4 e Convergence behavior of the surface energies for
different surfaces of lanthanum niobate. In the [010]
direction the surface energy converges to different values
for odd and even layers. Refer to the text for the method of
calculating the surface energy. The (010) and (101) surfaces
are relaxed, while the others are kept fixed at the bulk cut
structure.
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Table 3 e The calculated surface energy s of low index surfaces of monoclinic LaNbO4 in J/m2.
s (J/m2)
Relaxed (010)
Relaxed (101)
Un-relaxed (101)
Un-relaxed (010)
Un-relaxed (001)
Un-relaxed (100)
2 layers
3 layers
4 layers
5 layers
6 layers
7 layers
0.74
0.64
e
0.54
2.04
3.95
2.13
0.76
1.3
0.70
1.98
3.74
2.27
0.63
1.2
0.62
1.96
3.4
2.19
0.76
1.3
0.91
1.92
2.92
2.16
0.63
e
0.84
e
e
e
0.75
1.94
3.35
2.63
A comparison of the band gap for the (010) slab and the
bulk shows that they are virtually the same, while the band
gap is slightly decreased for the (101) surface due to a new
band. This sharp, strong and non-dispersed band is located at
the upper 0.5 eV of the valence band. Note that the energy
levels of this surface were 0.5 eV shifted as explained in the
figure caption.
The surface LDOS plots show that the energy bands above
3.5 eV of the conduction band for bulk and the (010) slab,
primarily consist of Nb 4d with a contribution of La 4f and 5d.
There are also traces of La 6s and Nb 5s orbitals in the
conduction band, but to a much smaller degree. The band
close to the Fermi level of the (101) surface which is responsible for the band gap reduction as discussed above is constructed from overlap of La s and d with O p orbitals. In order
to interpret this special band, the density of states of O p and
La s and d orbitals projected at the (101) subsurface sites were
also plotted. The density of these energy states is slightly
reduced for the La s and d orbitals, while a significant reduction is seen for the O p orbital. The reduced DOS of this band
when going from the surface to the subsurface combined with
its presence at the band gap of the (101) surface strongly
suggest that these states are surface states.
A pure surface state is generally located in a projected band
gap and its wave function decays exponentially to zero in the
bulk. In the case of semiconductors, such states are usually
due to dangling covalent bonds at the surface [36]. The relaxed
interatomic distances within the (101) surface (Table 2) affirm
stronger bonding between surface oxygen atoms and
lanthanum atoms located both at the surface and in the
subsurface layer. Hence, La d and s and O p orbitals participate
to construct the surface states.
Turning to the valence bands, they extend continuously
from the Fermi level down to 4 eV for both the (010) surface
(101) slab
bulk
La-s,subsurface
(010) slab
La-s, surface
0.1
La-d, surface
0.4
0.0
O-p,surface
O-p, subsurface
4
0
Nb-d, surface
6
La-f, surface
3
0
(States/eV.cell)
LDOS (states/eV.atom)
0.0
0.8 La-d, subsurface
Nb-s, surface
0.2
0.0
-5 -4 -3 -2 -1
0
1
Energy (eV)
2
3
4
5
80
0
DOS
-5 -4 -3 -2 -1
0
1
2
3
4
5
Energy (eV)
Fig. 5 e Comparison between the electronic structure of the (010) and (101) slabs and bulk. Local density of states was
projected onto the top-most atoms, except the O 2p and La s and d orbitals which also have been plotted for the subsurface
of (101) slab either. The latter plots have been specified by “subsurface” in their labels. The Fermi levels of bulk and the (010)
surface are shown by the vertical dotted line, while that of the (101) surface is shown by vertical solid line. The energy levels
of the (101) surface were shifted by 0.5 eV to match the conduction band levels of this surface with those of the bulk.
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and bulk. Nb s and d as well as La s and d orbitals participate in
the valence bands below 1 eV. The O p states contribute to
the entire valence bands.
The very unstable (100) and (001) surfaces could not be
relaxed. Thus the DOS of these surfaces have not been
included, since geometry optimization is essential for
a precise calculation of density of states. But it can be
mentioned that the band gaps for these un-relaxed
surfaces completely disappeared due to appearance of the
surface states. This confirms a large number of dangling
bonds at these surfaces (as already remarked in Section
3.3), which means that these surfaces will likely not exist in
reality.
3.5.
Hydrogen adsorption
As demonstrated in Section 3.2, a four-layer slab is sufficient
to reliably assess surface properties for the (010) and (101)
surfaces. Hence hydrogen adsorption calculations were performed using these slab models. At each stage, One H atom
was placed on the 1 1 surface model, which corresponds to
the one monolayer H coverage. The limited size of the surface
unit cell can lead to repulsion between the periodically
distributed hydrogen atoms; we therefore repeated some of
our calculations using a larger surface unit cell, which
approaches a lower H coverage. The dimensions of the surface
models and also the results of calculations are shown in Table
4. The adsorption energy of a H atom from the gas phase is
defined as:
Eads ¼ EH=slab Eslab 1
EH ðgÞ
2 2
(2)
where EH/slab and Eslab are the total energies of the slab models
with and without the H adsorbate, respectively and EH2 ðgÞ is the
calculated total electronic energy of a hydrogen molecule. For
H2, the binding energy defined as EðgÞ 2E (subtracting the
energy of H atoms) was found to be 4.52 eV from our calculations. It is somewhat higher than the experimental value of
4.75 eV but comparable with typical results from GGA based
calculations [37]. Since the LaNbO4 surfaces display quite
complicated structures, we considered a large number of
possible adsorption sites, depicted in Fig. 6. Adsorption energies were calculated moving H atom in steps of 0.2 Å from the
surface to the vacuum, thus creating a 3D potential energy
surface (PES). The minimum of this PES was used as input to
a relaxation of all degrees of freedom, including the LN atoms.
This was done to avoid ending up in a local minimum, and is
expected to be a robust procedure to search for the global
minimum of an adsorbate on such a complicated surface.
The widths of the potential energy curves of adsorbed H
atoms are quite different; one can thus expect significant
effects from the vibrational energies of the very light
hydrogen atom. We therefore calculated zero point energy
(ZPE) corrections of the most stable sites in order to provide
more realistic adsorption energies. By adding two terms to Eq.
(2), the contribution of vibrational energies in the H adsorption
energy can be obtained:
Eads ¼ EH=slab Eslab 1
1 ZPE
EH ðgÞ þ EZPE
E
H=slab 2 2
2 H2
(3)
ZPE
Here, the additional terms EZPE
H=slab and ð1=2ÞEH2 are zero point
energies of the adsorbed H atom and gas phase H2 molecule,
respectively. The ground state vibrational energy for H2 (g)
was evaluated to be 0.55 eV, which agrees well with the
experimental value (0.516 eV) [38,39]. The zero point corrections for the H adsorbate at the (010) and (101) surfaces were
found to be 0.32 and 0.337 eV, respectively, which shows the
significance of ZPE corrections for this sort of calculations
(Table 4).
From Fig. 7, we find that the most stable site for H at the
(010) surface is above the surface oxygen atoms (the labels 6
and 7 in Fig. 6). The optimal adsorption energy of H above
a (010) surface oxygen atom is approximately 2.1 eV. This
value decreases by almost 1.2 eV when all the atoms of the
surface are allowed to relax (Table 4). The final adsorption
energy with ZPE correction for the most stable site of this
surface is 1.5 eV, which clearly signifies that H adsorption is
not stable at the pure and perfect (010) surface. This is probably an effect of the high stability of this surface, which gives
poor possibilities for bonding interactions. The most stable
position of H at this surface is illustrated in Fig. 8.
For the (101) surface, the most stable sites are above the two
oxygen atoms labeled 1 and 3 and also the interstitial site
between O8 and La2 (Fig. 6). From the (101) surface density of
states, the surface energy levels within the band gap are due to
hybridization of the O p and La d states. These states participate significantly in the charge density distribution at the solidvacuum interface and also contribute to physical processes at
the surface. We can therefore expect that the most stable sites
lie in the vicinity of the O and La atoms responsible for the
surface states (for instance between O8 and La2 in Fig. 6). After
force minimization of the H adsorbed surface model, the lowest
adsorption energy was found for hydrogen, residing in the
binding site between the topmost surface O and subsurface La
(labeled as “O3” and “subsurface” in Fig. 8).
We see from Table 4 that the most stable site on the (101)
surface exhibits negative adsorption energy (0.96 eV) when
the ZPE corrections have not been applied. This value is
Table 4 e Characteristics of hydrogen adsorbed at the most stable sites of the rigid (Ri) and relaxed (Re) (010) and (101)
surfaces. The hydrogen height above the surface (h) and surface unit cell dimensions are given in Å, and the energies are
shown in eV/atom.
Surface
(101)
(010)
O2 O2-like (010) surface
Surface unit cell size (Å)
H (Å)
Eads, Ri-surface (eV)
Eads, Re-surface (eV)
Eads þ ZPE (eV)
7.92, 11.67
5.56, 5.2
7.92, 7.43
1.89
1.48
1.48
1.94
2.08
3.33
0.96
1.175
1.167
0.64
1.512
1.456
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6681
Fig. 6 e Top view of the 2 3 2 (010) and 1 3 1 (101) surfaces of LaNbO4. The surface atoms are signed with numerical labels.
Interstitial sites at the surface as well as sites above the topmost metal and oxygen atoms were chosen as the possible
adsorption sites. The labels of the interstitial sites, shown in the figure, designate the surrounding surface atoms.
increased to 0.41 eV when applying the ZPE correction, but
still remains negative. The difference between the H binding
energies for the most stable sites of the (101) and (010) surfaces
is more than 2 eV, which clearly demonstrates that adsorption
can be strongly affected by surface (in-)stability.
As already mentioned, we checked the effect of the surface
unit cell size by repeating some of the calculations with
a larger unit cell model for the (010) surface. We chose to study
the O2 O2-like surface unit cell with 48 atoms including one
surface H atom, which gives a hydrogen coverage 1/2 monolayer. From Table 4, we find that the change of adsorption
energy arising from the limited surface unit cell size is in the
order of 102 eV. We can thus safely neglect such
contributions to our results. This conclusion can be extended
to the (101) surface, since the size of the (101) surface unit cell
is larger than that in the O2 O2-like (010) surface model.
The nearest neighbors of hydrogen adsorbate at the (010)
and (101) surfaces are tabulated in Table 5. It is shown that the
interatomic distance between adsorbed H and nearest surface
O is 0.98 Ǻ for both the (010) and (101) surfaces of LN. This is
a typical value for the OeH bond length in solids where the H
atom has a formal charge of þ1.
Since in this study the application of LN as a proton conducting membrane is emphasized, it would be interesting to
investigate where the electron of adsorbed hydrogen atom is
located. The DOS plots in Fig. 9 present how the Fermi levels of
Fig. 7 e Hydrogen adsorption energy as a function of height above surface. This height was measured from the lower
surface metal atom (Nb in the case of the (101) surface and La for the (010) surface). Adsorption sites with high energies are
not shown. The red squares designate the final energy for the most stable site after geometry optimization of the surface.
(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
6682
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Fig. 8 e The relaxed (010) and (101) surfaces of LN including the most stable H at its optimized sites.
the clean (010) and (101) surfaces move from the VBM, next to
the CBM when H is adsorbed. As clearly exhibited in the insets
of the hydrogenated slabs, the conduction band has a tail
around 0.1 eV into the valence band. The band which causes
the conduction band to stretch below the Fermi level can be
attributed to the H electron added to the LN electronic
structure.
To clarify the localization of the H electron we performed
band decomposed calculations in the relevant range of energies across the Fermi level. Fig. 10 presents the spatial distribution of the charge density in the mentioned energy range
for the (010) and (101) surfaces. The delocalization of the H
electron is evident from this figure. We see that for the less
stable (101) surface with a stable hydrogen atom, the hydrogen
atom has donated its electron completely. For the most stable
(010) surface, the unstable H atom has conversely a partial
share of its delocalized electron. This band can thus be
regarded as a possible contribution to an external electronic
circuit, forming the basis of a proton conducting fuel cell. It
can be also concluded that hydrogenation of the LN surfaces
can result in electron conductivity at these surfaces.
In order to investigate the influence of surface hydrogenation on the surface stability, we have compared the change
of energy per unit of surface area for the clean slab models
when adsorbing one monolayer hydrogen atom at the
surface:
DEsurface ¼
EH=slab Eslab
A
(4)
Table 5 e The interatomic distances d in Ǻ between
adsorbed H and its nearest neighbors at the most stable
sites of the fully covered (010) and (101) surfaces.
d (Å)
(101), O3 top
(010), O6 top
OeH
LaeH
NbeH
0.973
2.791
3.260
0.972
3.188
2.616
Although this is not a complete calculation of the adsorbent surface energy, it may provide useful insight into the
final H adsorption, since it quantifies the surface stability
after H adsorption. Our calculations concluded that
DEsurface ¼ 0.076 and 0.046 eV/Å2 for the hydrogen covered
(010) and (101) surfaces, respectively. The difference between
the stability of the two surfaces is thus significantly reduced
upon hydrogen adsorption, but the (010) surface is still the
most stable one.
3.6.
Entropy consideration
Under real operating conditions, the effect of temperature
and entropy on dissociative hydrogen adsorption may be
estimated by applying a simple Langmuir adsorption
isotherm [40]:
1
DSads DHads
P2H2 exp
2R
2RT
qH ¼
1
DSads DHads
2
1 þ PH2 exp
2R
2RT
(5)
Here qH and DSads designate the surface hydrogen atom
coverage and the standard change in entropy by dissociative
hydrogen adsorption, respectively. DHads is the standard
change in enthalpy upon adsorption, and is in this case equal
to the calculated Eads. DSads is defined as the difference
between the molar entropy of gaseous H2 at a standard pressure of 1 bar and the total molar entropy of two adsorbed
hydrogen atoms: DSads ¼ 2SH;ads SH2 ðgÞ . For chemisorption e
which we consider here e the adsorbed H atoms are expected
to be localized and immobile, and the only important contribution to SH,ads is that associated with vibrational motion.
Furthermore, given the small change in SH2 ðgÞ with temperature (between 500 and 800 C, SH2 ðgÞ goes from 160 to
170 J mol1 K1 [41]), and restricting ourselves to low H
coverage, we can assume that DSads is independent of both
coverage and temperature.
6683
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DOS ( states/eV cell)
100
200
clean (010) slab
50
100
0
-5
60
DOS ( states/eV cell)
clean (101) slab
-4
-3
-2
-1
0
1
2
3
4
5
0
-5
120
-4
-3
-2
-1
-0.2 -0.1 0.0 0.1 0.2
-6
-5
-4
2
3
4
5
-0.2 -0.1 0.0 0.1 0.2
0
-7
1
H-adsorbed (101) slab
H-adsorbed (010) slab
-8
0
-3
-2
-1
0
1
Energy (eV)
2
0
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
Energy (eV)
Fig. 9 e The electronic structure of the clean and H adsorbed (010) and (101) slabs. In order to demonstrate density of states
around the Fermi level, they are shown in the insets within a limited range of energy next to the Fermi level.
DSads cannot easily be calculated without performing
tedious phonon calculations beyond the scope of this work.
We can nevertheless estimate numerical values of DSads by
using a general guiding rule shown to be valid for both
dissociative and non-dissociative adsorption: 41:8 DSads 51:0 0:0014,DHads [42], where DSads and DHads are given in
J mol1 K1 and kJ mol1, respectively. Inserting the calculated
adsorption enthalpy for the (101) surface of 59.8 kJ mol1
Fig. 10 e Side view of the isosurfaces from the band decomposed charge density calculations for the H adsorbed (101) (left
side) and (010) (right side) surfaces across the Fermi level. Isosurface levels for the (101) and (010) surfaces correspond to
0.0002 e/Å3 and 0.001 e/Å3.
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(0.64 eV), the adsorption entropy should then be less negative than 135 J mol1 K1. The guiding rule requires
exothermic adsorption energies, and does thus not apply for
the (010) surface which has an endothermic enthalpy of
adsorption. In Fig. 11 the coverage on the (101) surface at 1 atm
H2 is plotted as a function of temperature for two different
values of DSads, arbitrarily chosen within the window
permitted by the guiding rule. The coverage is plotted on
a logarithmic scale in order to get a better picture of the
temperature dependency of the coverage when it approaches
zero. The hydrogen coverage decreases with increasing
temperature and a more negative adsorption entropy. As an
example, DSads ¼ 120 J mol1 K1 would result in a coverage
between 0.5 and 0.08 at temperatures relevant for fuel cell
operation, i.e. 500e800 C.
4.
Discussion
We have demonstrated that the LN (010) surface, which is
the most stable one, is repulsive towards hydrogen adsorption. The less stable (101) surface can on the other hand
adsorb H exothermically. The H adsorption energy at this
surface is comparable to what is found for good heterogeneous hydrogenation catalysts [43]. If this trend is general,
we can expect that even less stable surfaces like the (100) or
(001) surfaces exhibit yet stronger hydrogen receptivity. We
should keep in mind that the surfaces with high stability are
more abundant than the less stable ones, which means that
the number of sites with hydrogen adsorption energy
beneficial for hydrogen splitting is probably very low. This
result can be generalized since the order of stability was
found not to be affected by hydrogenation of the surfaces;
the less stable but more recipient surface remained at
a higher energy level than the most stable one. All in all, this
suggests that when hydrogen atoms are oxidized to protons
log θ
1
0.1
ΔSads = -120 J mol K
-1
-1
on the anode of a fuel cell with LN-based electrolyte, the
hydrogen gas would proceed through surfaces of an electron
conducting material (e.g. Ni) rather than through the surface
of the LN ceramic component. Similarly, a hydrogen pump
or steam electrolyzer would have to distribute the hydrogen
atoms reduced from protons through the surface of the
electron conducting material in order for efficient dehydrogenation to take place.
5.
Conclusions
We have predicted the surface energy of different lowindex surfaces of monoclinic lanthanum niobate (LN)
based on density functional theory calculations. The lowest
surface energy was found to be 0.63 J/m2, for the (010)
surface. This was supported by small variation of the
electronic structure and of the relaxed interatomic
distances at the (010) surface compared to the bulk. In
comparison, the less stable (101) surface with a surface
energy of 1.3 J/m2 was significantly modified relative to the
bulk, when relaxing the slab model. It was furthermore
shown that surface states located in the band gap of this
surface contributed to making the surface more reactive.
These states consisted of O p orbitals with a small contribution of La d and s orbitals. Consequently, the most stable
binding site for hydrogen at the (101) surface was found in
the neighborhood of the uppermost O and subsurface La
atoms. The calculated energy for splitting and adsorbing of
H2 was 0.64 eV at the most receptive site of the (101)
surface. The corresponding adsorption energy for the most
stable (010) surface was 1.5 eV; this surface is thus not
accessible for H. The distance between the H adsorbate and
surface O is 0.98 Å on both the LN surfaces we studied,
which closely resembles the typical OeH bond length in
bulk materials where H has a formal charge of þ1. This
strongly indicates that the H atoms are ionized to protons
already at the LN surface. It is also shown that the hydrogen’s electron is delocalized and consequently has the
possibility to take part in an external electronic circuit
which is required for proton conducting fuel cells. Since
the (101) surface has significantly higher surface energy
than the (010) one, the overall accessible surface area for
hydrogen interaction will exhibit a very small share of (101)
and similar surfaces. We can therefore expect that in the
anode cermet of LN-based electrolyte proton conducting
fuel cells, the average LN surface is incapable of efficient
splitting of hydrogen molecule from the gas phase.
ΔSads = - 80 J mol K
-1
400
-1
800
1200
T (K)
Fig. 11 e A logarithmic plot of the H coverage q estimated
theoretically on the (101) surface of monoclinic LaNbO4 as
a function of temperature with DSads of L120 and
L80 J molL1 KL1. These values represent the lower and
upper limits of DSads, so the real values would be in
between the two curves.
Acknowledgment
The authors would like to thank the Norwegian Research
Council for financial support and the NOTUR consortium for
computational resources. This study was a part of the
NANIONET project under the NANOMAT program; Project
number: 182065/S10.
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