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 5 ( 2 0 1 0 ) 1 6 8 1 – 1 6 9 2
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An ab initio study of dissociative adsorption of H2
on FeTi surfaces
A. Izanlou, M.K. Aydinol*
Metallurgical and Materials Engineering Department, Middle East Technical University, Ankara 06531, Turkey
a r t i c l e i n f o
Article history:
Received 25 September 2009
Received in revised form
14 December 2009
Accepted 20 December 2009
Available online 8 January 2010
Keywords:
FeTi
Hydrogen storage
Dissociative adsorption
Ab initio study
* Corresponding author. Tel.: þ90 (312) 210 2E-mail address: [email protected] (M.K.
0360-3199/$ – see front matter ª 2009 Profesdoi:10.1016/j.ijhydene.2009.12.136
a b s t r a c t
Dissociative adsorption of H2 on clean FeTi (001), (110) and (111) surfaces is investigated via
ab initio pseudopotential-plane wave method. Adsorption energies of H atom and H2
molecule on Fe and Ti terminated (001) and (111) and FeTi (110) surfaces are calculated on
high symmetry adsorption sites. It is shown that, top site is the most stable site for hori-
zontal H2 molecule adsorption on (001) and (111) surfaces for both terminations. The most
favorable site for H atom adsorption on these surfaces however, is the bridge site. In (110)
surface, the 3-fold hollow site which is composed of a long Ti–Ti bridge and an Fe atom,
(Ti–Ti)L–Fe, and again a 3-fold hollow site this time composed of a short Ti–Ti bridge and an
Fe atom, (Ti–Ti)S–Fe, are the most stable sites for H2 and H adsorption, respectively. With
the analysis of the above favorable adsorption sites, probable dissociation paths for H2
molecule over these surfaces are proposed. Activation energies of these dissociations are
also determined with the use of the dynamics of the H2 relaxation and climbing image
nudged elastic band method. It is found that H2 dissociation on (110) and Fe terminated
(111) surfaces has no activation energy barrier. On other surfaces however, activation
energies are calculated to be 0.178 and 0.190 eV per H2 molecule for Fe and Ti terminated
(001) surfaces respectively, and 1.164 eV for Ti terminated (111) surface.
ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
1. Introduction One of the concerns about the successful control of
Hydrogen is a handy energy carrier and can be used in
a variety of ways. In future, it could potentially replace
petroleum products in the long term. Unlike fossil fuels, it is
an environmentally friendly, non-polluting fuel. The
management of hydrogen as energy source on a sizable
scale involves five basic issues: production, storage and
transport, application, safety and economy. Chemical
decomposition of hydrocarbons and water [1], hydrogen
production from water using nuclear energy [2], wind
energy [3], solar energy [4] and thermomechanical biomass
processing [5] are some common ways of hydrogen gas
production.
523; fax: þ90 (312) 210 25Aydinol).sor T. Nejat Veziroglu. Pu
hydrogen as energy source is generally associated with its
storage and transportation. These problems are more and less
related to the lightness and chemical activity of free hydrogen.
An alternative and promising means of storing hydrogen is in
hydride compounds. Certain metals and their alloys, such as
magnesium-nickel, lanthanum-nickel and iron-titanium are
capable of absorbing hydrogen gas to form chemical
compounds referred to as hydrides. This kind of hydrogen
storing method avoids having to contain large volumes of
hydrogen as gas or to maintain special pressures and
temperatures needed for storing hydrogen as a compressed
gas or as a liquid. On the other hand, research and develop-
ment efforts are still required to investigate lighter hydrides or
18.
blished by Elsevier Ltd. All rights reserved.
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 5 ( 2 0 1 0 ) 1 6 8 1 – 1 6 9 21682
hydrides with even larger storage capacities which could lead
to convenient use of hydrogen for different applications. Pant
and Gupta [6] present following properties for the metal
hydride to be an optimum hydrogen storage material; high
hydrogen capacity per unit mass and unit volume, low
dissociation temperature, moderate dissociation pressure,
low heat of formation to minimize the energy necessary for
hydrogen release and low heat dissipation during the
exothermic hydride formation, reversibility for limited energy
loss during charge and discharge of hydrogen, fast kinetics,
high stability against moisture for a long cycle life, cyclic
stability, low cost of recycling and charging infrastructures
and high safety.
Adsorption of hydrogen on a surface is the first step for its
storage in a hydride compound. In this regard, many
researchers have studied hydrogen adsorption, dissociation
and diffusion on metallic surfaces, mostly using theoretical
methods. Among these metals, Mg for its suitable properties is
the subject of many studies for hydrogen storage. Pozzo and
Alfe [7] studied the effect of doping transition metal elements
on hydrogen dissociation on Mg (0001) surface. Their calcu-
lations show that doping the surface with transition metals on
the left of the periodic table eliminates the barrier for the
dissociation of the molecule, but the H atoms bind very
strongly to the transition metal, while transition metals on the
right of the periodic table do not bind H, but unfortunately
they do not reduce the barrier to dissociate H2 significantly.
Fedorov et al. [8] investigated theoretically the chemical
dissociation of hydrogen molecules on the (0001) surface of
Mg, on the given surface with adjoined individual Ti atoms,
and on the surface of a one-layer titanium cluster on the given
surface of magnesium. They have found that, dissociation of
hydrogen at solitary titanium atoms, as well as on the surface
of a Ti cluster, is facilitated to a considerable extent as
compared to pure magnesium. This improving behavior of Ti
on Mg (0001) surface was also claimed by Du et al. [9] using
nudged elastic band method (NEB) for calculating the activa-
tion energy of hydrogen dissociation on the surface of Ti-
doped Mg (0001). Kecik and Aydinol [10] worked on the
adsorption characteristics of hydrogen on Mg (0001) surface
using ab initio molecular dynamics. Among thirty four
selected elements, they found that, most of the transition
metal elements (from Ti to Ni in 3d and from Zr to Pd in 4d
series) were found to be beneficial dopants enabling the
hydrogen dissociation and adsorption. Especially, elements
such as Co, Mn and Fe in 3d series were found to be quite
effective.
The intermetallic compound FeTi reacts with hydrogen to
form, in succession, hydrides of the approximate composi-
tions FeTiH and FeTiH2. Hydrogen capacity of FeTi is around
1.9 wt% and its constituent elements are inexpensive [11].
Reilly and Wiswall [12] have measured dissociation pressure
of over 1 atm at 273 K for both hydrides. However, the acti-
vation process of FeTi is troublesome due to formation of an
oxide layer. Various researchers have studied the effect of
alloying elements experimentally [12–16] and theoretically on
improving the properties of FeTi related to its hydrogen
adsorption. Among theoretical studies, Kinaci and Aydinol
[17] found that the insertion of the hydrogen into the bulk FeTi
structure causes an increased electron density in the orbitals
of Fe which were oriented towards hydrogen atoms, indi-
cating stronger Fe–H chemical bond rather than Ti–H bond.
They also identified a new hydride phase which is less stable
than the experimentally observed ones, having four hydrogen
atoms per chemical formula. In another study, Lee et al. [18]
calculated the changes in the electronic structure in different
FeTi surfaces due to hydrogen absorption. Similarly, Kulkova
et al. [19] studied adsorption of hydrogen on the (001) and (110)
FeTi surface covered by palladium monolayer using the full
potential linearized augmented plane wave method within
the local density approximation. They have found that
adsorption is easier for Pd coated (001) surface rather than
clean one. However, no difference was seen between Pd
coated (110) surface and its clean form. Heller et al. [20]
investigated H adsorption kinetics of FeTi film coated by Ni
which is not as expensive as Pd. They have concluded that Ni
does not limit the hydrogen adsorption rate once the surface
is clean. However, the Ni surface is sensitive to contamina-
tion, as for instance by CO adsorbed from air. Therefore, one of
the major concerns in hydrogen storage in solid hydrides is
the ease of hydrogen adsorption reaction taking place at the
particle surface. Even if there may be a strong thermodynamic
affinity for this reaction, many times it is limited by kinetic
reasons [21,22]. One of the major kinetic barrier is at the
dissociation stage of the H2 molecule over the surface[23–25].
Therefore in practical applications catalysts are used
[13–16,26]. For this reason understanding of the surface states
and adsorption sites for H2 molecules and dissociated H atoms
is crucial.
In this study, surface characteristics of Iron–Titanium alloy
have been studied and hydrogen adsorption behavior of pure
surfaces was determined via ab initio pseudopotential-plane
wave method within the projector augmented wave (PAW)
scheme to density functional theory (DFT).
2. Computational details
In this study, all calculations were performed in a plane wave
basis set using the projector augmented wave (PAW) method
[27] within the formalism of density functional theory as
implemented in the VASP program [28–30]. In the calculations,
PAW potentials [31] were used, where exchange-correlation
functional with the generalized gradient approximation (GGA)
is in PBE form [32].
Initially, bulk calculations in FeTi, FeTiH and FeTiH2
structures were performed for several test purposes.
Following bulk calculations, simulation cells having free
surfaces of three different crystallographic planes; (001), (110)
and (111) in the FeTi structure were set up. Considering the
constituent elements Fe and Ti, (001) and (111) can have two
different terminations. Therefore a total of five different
surface structures were studied. Over these surfaces, H2 and H
adsorption sites were determined and probable dissociation
paths for the H2 molecule were postulated by the analysis of
the calculated adsorption energies. Furthermore, with the use
of climbing image nudged elastic band method and relaxation
dynamics, activation energies of the dissociation H2 of mole-
cule over these surfaces were determined.
Table 1 – Calculated crystal structure parameters and formation energies of the hydrides. Experimental data is given inparenthesis. Crystal structure data for FeTi, FeTiH and FeTiH2 are due to [35], [34] and [33] respectively. Experimentalformation energy data are from [12].
Compound Space Group Wyckoff Positions Lattice Parameters (A) Formation EnergykJ/mole of H2
Fe Ti H a b c
FeTi 221 1a 1b – 2.945 (2.972) – – –
FeTiH 17 2c 2d 2a 2.889 (2.956) 4.529 (4.543) 4.264 (4.388) 25.28 (28.1)
FeTiH2 65 4i 4 h 2aþ2cþ4e 6.957 (7.029) 6.071 (6.233) 2.769 (2.835) 26.86 (31–33.7)
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2.1. Bulk calculations
FeTi adopts the CsCl structure which has the symmetry of the
Pm3m (221) space group. Hydrides of this intermetallic,
however adopt an orthorhombic crystal structure. The crystal
structure details of the compounds are given in Table 1. After
setting up the simulation cells in the bulk sense with periodic
boundary conditions, the cell volume and the atomic positions
are allowed to relax to find the minimum energy configuration.
During these calculations, sampling in the reciprocal space
(k-point grid size) and spin polarization effect were considered
to attain a few meV convergency. It was found that, 24 � 24 �24, 20� 20� 20 and 16� 16� 24 gamma centered grid of k-point
sampling is adequate for FeTi, FeTiH and FeTiH2 structures,
respectively. Expectedly, since Fe is a magnetic element, the
total energies of the compounds changes with respect to spin
polarization. However in the calculated formation energies the
difference was found to be less than 5 meV. Therefore spin
polarization was not considered in further calculations. The
formation energies of the hydrides were calculated consid-
ering the below generic hydrogenation reaction:
2n
FeTiþH2/2n
FeTiHn (1)
as;
DEf ¼2n
EFeTiHn �2n
EFeTi � EH2(2)
The coefficients of the reaction were normalized to define the
formation energy per 1 mol of H2 gas, so as to simplify
Fig. 1 – High symmetry sites for adsorption on (a) Fe and (b) Ti
spheres represent Fe and Ti atoms respectively.
comparison. The energy of H2 is approximated to the energy of
an H2 molecule in vacuum at zero Kelvin, thus entropy term is
neglected. The calculated crystal structure parameters and
formation energies of the compounds are given in Table 1,
comparatively with the available experimental data [12,33–35].
As can be seen, the disagreement between the calculated and
the experimental lattice parameters is at maximum 2.6%,
which is quite acceptable in ab initio calculations. The agree-
ment in the formation energy of the compounds is fairly good,
where the discrepancy is approximately 10–15%.
2.2. Surface calculations
Three different crystallographic surfaces, (001), (110) and (111)
were considered to be studied for hydrogen adsorption. Slabs
of FeTi consisting of 3 � 3 surface unit cells were created with
8, 7 and 12 atomic layers for (001), (110) and (111) surfaces,
respectively. The position of atoms in the surface structures
was set according to the relaxed coordinates in bulk FeTi. In
the cells, a 15 A thick vacuum layer was put along the z-
direction so as to mimic the free surface. The cell volume and
the two very bottom atomic layers were fixed during the
calculations to impose the bulk condition as going down
below the surface. Whereas the rest of the top lying atoms
were allowed to relax fully until 1 meV convergency is
obtained in the total energy. In all surface calculations,
a gamma centered grid of 3 � 3 � 3 k-point set was used cor-
responding to 6 k-points in the irreducible Brillouin zone,
together with a first order Methfessel-Paxton [36] smearing of
width s¼ 0.2 eV. In the expansion of the plane-wave basis set,
terminated (001) surfaces. Brown (dark) and blue (light)
Fig. 2 – High symmetry sites for adsorption on (a) Fe and (b) Ti terminated (111) surfaces.
Fig. 3 – High symmetry sites for adsorption on (110)
surface. In case of three-fold hollow sites, the related
triangles are shown with solid black lines.
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 5 ( 2 0 1 0 ) 1 6 8 1 – 1 6 9 21684
a kinetic energy cutoff of 280 eV was used. The over all
convergency in the total energy is about 1 meV per unit cell.
In order to determine the most probable path for the
dissociation of the H2 molecule, the adsorption energies of the
H atom and the H2 molecule were calculated for many high
symmetry sites on the studied surfaces, where the details of
calculations are same as above. Since the calculations were
performed on 3 � 3 surface cell the adsorption of the species
corresponds to 0.11 monolayer coverage. In both Fe and Ti
terminated (001) surfaces, the high symmetry adsorption sites
are top, bridge and four-fold hollow positions, see Fig. 1. In
(111) surface similarly, there are top, bridge, three-fold FCC
hollow and three-fold HCP hollow sites as can be seen from
Fig. 2. The number of high symmetry sites are numerous in
(110) surface, see Fig. 3. They are Fe top, Ti top, Fe–Fe bridge,
Ti–Ti bridge and Fe-Ti bridge. Then there are four three-fold
sites which are (Ti–Ti)L–Fe, (Ti–Ti)S–Fe, (Fe–Fe)L–Ti and (Fe–
Fe)S–Ti. Since H2 is a linear molecule, it can be positioned at
these high symmetry sites in different ways. Namely, vertical
in which the H–H axis is perpendicular and horizontal where
the H–H axis is parallel to the surface plane. Moreover in
horizontal configuration, there is one more degree of freedom
which considers the alignment of the H–H axis of the molecule
over the surface. Different alignments over all studied
surfaces were labeled accordingly as given in Table 2.
Afterwards, an atom of H and vertically and horizontally
aligned molecule of H2 (having two hydrogen atoms separated
by equilibrium distance, calculated to be 0.7548 A) were put on
these sites at 1.5 A above the surface. The previously relaxed
surface layers at the pure state were then allowed to reposi-
tion so as to obtain the minimum energy configuration. In
order to avoid the motion of the adsorbed atom or the mole-
cule from the given site symmetry to an energetically more
favorable nearby position however, the hydrogen molecule or
atom is not allowed to relax in the x–y plane. Adsorption
energy then can be calculated considering the following
adsorption reaction,
FeTiðhklÞ þHn/FeTiðhklÞHn;ads (3)
as,
DEads ¼ EFeTiðhklÞHn;ads� EFeTiðhklÞ � EHn (4)
where, EFeTiðhklÞHn;adsis the total energy of the system with
adsorbed Hn, EFeTiðhklÞ is the total energy of the FeTi (hkl) slab
without any adsorbed species and EHn is the total energy of the
free atom or molecule. With this definition, negative values of
DEads denote adsorption that is more stable than the corre-
sponding clean surface and the free atom or molecule.
After the evaluation of a probable dissociation path, one
also needs to find the activation energy along that path, so
that kinetics of the dissociation reaction can be predicted. The
nudged elastic band (NEB) method, widely used for locating
transition states, is an efficient method for finding the
minimum energy path (MEP) between a given initial and final
state of a reaction [37–39]. An initial path is constructed and
represented by a discrete set of images of the system con-
necting the initial and final states. Adjacent images are con-
nected by springs, mimicking by elastic band and the tangent
of the path is estimated on each image. An optimization of the
band, mainly the minimization of the forces acting on images,
brings the band to the MEP.
The MEP can be used to estimate the activation energy
barrier for transitions between the initial and final states. Any
maximum along the MEP is a saddle point on the potential
surface, and the energy of the highest saddle point gives the
activation energy of the reaction. It is important to ensure that
the highest saddle point is found. It is quite common to have
MEPs with one or more intermediate minima and the saddle
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 5 ( 2 0 1 0 ) 1 6 8 1 – 1 6 9 2 1685
point closest to the initial state may not be the highest saddle
point for the transition [37].
The climbing image NEB (CI-NEB) method constitutes
a small modification to the NEB method [38]. Information
about the shape of the MEP is retained, but a rigorous
convergence to a saddle point is obtained. With the climbing
image scheme, the highest energy image climbs uphill to the
saddle point. This image does not feel the spring forces along
the band, but the true force at this image along the tangent is
inverted. In this way, the image tries to maximize its energy
along the band, and minimize in all other directions. When
this image converges, it will be at the exact saddle point [38].
In this study, we used CI-NEB method to calculate the MEP
for the dissociation of hydrogen molecule and determined
Table 2 – Calculated adsorption energies of H atom and H2 mo
Adsorption Site
(001) Fe terminated surface
Top
Bridge
4-fold Hollow
(001) Ti terminated surface
Top
Bridge
4-fold Hollow
the activation energy of the dissociation process. In these
calculations however, a smaller k-point grid, 3 � 3 � 1 is
employed to reduce computational cost.
3. Results and discussions
Quantifying the structure of surfaces, and particularly of
adsorbates on surfaces, relaxation is a key step to understand
many aspects of the behavior of surfaces including the elec-
tronic structure and the associated chemical properties. The
outermost atomic layers of a solid generally have layer
spacing which differs from that of the underlying bulk as
a consequence of the termination of the solid. Typically the
lecule over all studied surfaces of FeTi.
Adsorption Energy (eV)
H2 (horizontal) H2 (vertical) H
[1:] �0.463
�0.013 �2.128
[2:] �0.462
[1:] �0.074
0.008 �2.863
[2:] �0.011
[1:] �0.013
�0.010 �2.755
[2:] �0.017
[1:] �0.917
�0.379 �2.832
[2:] �0.913
[1:] �0.842
�0.420 �3.526
[2:] �0.391
[1:] �0.412
�0.418 �3.434
[2:] �0.409
(continued on next page)
Table 2 (continued )
Adsorption Site Adsorption Energy (eV)
H2 (horizontal) H2 (vertical) H
(111) Fe terminated surface
Top
[1:] �0.379
�0.035 �2.220
[2:] �2.231
Bridge
[1:] �1.676
0.002 �4.504
[2:] 0.056
FCC Hollow
[1:] �0.104
0.019 �4.498
[2:] �0.104
HCP Hollow
[1:] �0.184
0.002 �2.540
[2:] �0.183
(111) Ti terminated surface
Top
[1:] �0.151
0.004 �1.853
[2:] �0.151
Bridge
[1:] �0.022
�0.001 �3.140
[2:] �0.012
FCC Hollow
[1:] 0.017
�0.001 �2.414
[2:] �0.008
HCP Hollow
[1:] �0.006
0.007 �3.032
[2:] �0.011
(continued on next page)
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 5 ( 2 0 1 0 ) 1 6 8 1 – 1 6 9 21686
(continued )
Adsorption Site Adsorption Energy (eV)
H2 (horizontal) H2 (vertical) H
(110) surface
Fe Top
[1:] �0.470
�0.019 �2.831
[2:] �0.527
[3:] �0.562
Ti Top
[1:] �0.195
�0.007 �1.547
[2:] �0.176
[3:] �0.161
Fe–Ti Bridge
[1:] �0.182
0.023 �2.957
[2:] 0.015
Fe–Fe Bridge
[1:] 0.140
�0.009 �3.124
[2:] 0.095
Ti–Ti Bridge
[1:] �0.137
�0.007 �2.759
[2:] �0.008
3-fold (Fe–Fe)S–Ti Hollow
[1:] �0.095
�0.006 �2.510
[2:] �0.048
3-fold (Fe–Fe)L–Ti Hollow
[1:] �0.081
0.028 �2.261
[2:] �0.114
3-fold (Ti–Ti)S–Fe Hollow
[1:] �0.055
0.172 �3.268
[2:] �0.355
3-fold (Ti–Ti)L–Fe Hollow
[1:] �0.384
0.125 �2.887
[2:] �0.599
Table 3 – The clean surface interlayer distance relaxations of surfaces from bulk values.
Surface 6d12 6d23 6d34 6d45 6d56 6d67 6d78
(001) Fe terminated �18.2 7.7 �6.5 4.4 �3.6 – –
(001) Ti terminated �7.9 4.9 �2.1 1.4 �2.6 – –
(110) Fe–Fe spacing �8.0 1.2 �0.8 �0.3 – – –
(110) Ti–Ti spacing 0.3 0.7 0.4 0.5 – – –
(111) Fe terminated �30.2 �5.0 �3.1 4.6 �2.6 4.5 �1.3
(111) Ti terminated 1.7 �20.6 0.1 4.1 1.9 1.7 �2.4
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 5 ( 2 0 1 0 ) 1 6 8 1 – 1 6 9 21688
outermost layer spacing is contracted, the second layer
spacing expanded and so on, although the amplitude of this
relaxation damps rapidly with depth.
The clean surface interlayer distance relaxations of clean
surface from the bulk values are shown in Table 3 for all
studied surfaces of FeTi. Here, 6dnm corresponds to the
difference in the distance between nth and mth layer in bulk
and relaxed calculations in percentage. Therefore the negative
values indicate contraction in layer spacing, while positive
numbers show expansion with respect to the bulk layer
separations. Here, n ¼ 1 represents the surface layer, n ¼ 2
relates to the sub-surface layer and so on.
Results obtained from (001) surfaces in both terminations,
show a perfect order in relaxation values. The topmost layer
spacing shows a contraction of about 18% for Fe terminated
and 8% for Ti terminated surfaces. The next layer spacing
shows an expansion for both termination and this contrac-
tion–expansion cycle can be seen till the last relaxed layer. On
the other hand, the absolute amount of change in layer
spacing decreases as going down into the slab. Only the last
interlayer distance in Ti terminated (001) surface expresses an
exception. Comparing layer spacing between identically
numbered layers in Fe and Ti terminated (001) surface, it is
clear that the amount of contraction and expansion is about
two times bigger in Fe terminated (001) surface rather than Ti
terminated one. Therefore as a result, in case of (001) surface,
the Fe terminated one shows more relaxation.
The (110) crystallographic plane is composed of both Fe and
Ti atoms. During relaxation of the surface structure having
(110) symmetry, it was recognized that Fe and Ti atoms in the
same layer behave differently in a coordinated manner. In
a way, each layer dissociated into two, forming Fe and Ti only
sub-layers. In all layers of this structure, Ti–Ti spacing show
very little expansion, while the topmost Fe-layer spacing
experiences considerable amount of contraction, therefore
the top layer becomes Ti terminated. Nevertheless, the abso-
lute amounts of these changes are smaller than that of (001)
surface in both terminations.
Relaxation in the (111) surface is somewhat similar to the
relaxation phenomena observed in other surfaces. Especially
the outermost Fe-layer spacing, whether the top layer in Fe
terminated or the layer below the top in Ti terminated (111)
surfaces, show considerable contraction while Ti-layer
spacing express less expansion.
It is also found that, the reconstruction (atomic rear-
rangements within the plane) in pure surfaces of FeTi does not
occur, which is expected since the lateral order in FeTi
surfaces is not destroyed by any impurity atom or vacancy.
The calculated adsorption energies of horizontal and
vertical hydrogen molecule and hydrogen atom, for all labeled
positions are shown in Table 2. Between horizontal and
vertical hydrogen molecule adsorption, it is clear that in
almost all of the identical high symmetry adsorption sites, the
adsorption energy of vertical molecules are higher than that of
the horizontal alignment. Therefore as a result, H2 is more
likely to be adsorbed on all studied FeTi surfaces rather hori-
zontally than vertically.
Here, two sites show exception. In Ti terminated (001)
surface, the 4-fold hollow site is a little more favorable for
vertical molecule adsorption rather than the horizontal one.
However, for this surface symmetry the lowest energy
adsorption site is the top site (either [1:] or [2:] alignment)
where H2 lies horizontal. The other exception is on (110)
surface, Fe–Fe bridge site where the adsorption energies of
two horizontal molecules are positive which means this site
cannot adsorb a horizontal molecule. The vertical molecule is
therefore the least energy position for this site. But again it
cannot be considered as an adsorption site for the hydrogen
molecule compared to other low energy sites on this surface.
In case of atomic hydrogen adsorption on (001) surface, as
it can be seen from Table 2 for both Fe and Ti terminated
surfaces, the bridge site is the most favorable site. For
hydrogen molecule however, the top site is the most likeable
for adsorption. A very small difference of the order of 1 meV
exists between different alignments of hydrogen molecule on
the top site of both Fe and Ti terminated (001) surface. In both
situations the top [1:] site is slightly more favorable rather
than top [2:] site. It suggests that on this surface the molecule
alignment does not affect the adsorption of hydrogen mole-
cule notably. In Fe terminated (001) surface, after relaxation, H
atom on the bridge site moved downwards and its distance to
surface decreased from 1.5 to 0.46 A. At the same time, the two
Fe atoms of the bridge separated from each other and bridge
length was increased by 12.5%. At the H atom adsorbed
surface, no other appreciable relaxation and reconstruction
were seen. Meanwhile, H2 molecule on Fe top [1:] site moved
very slightly upwards. No obvious relaxation or reconstruc-
tion happened here. In Ti terminated (001) surface, H on the
bridge site stayed nearly at its position above the surface at
about 1.5 A. This time however, the two bridge Ti atoms
moved towards H atom and the distance between each Ti and
H was decreased about 10%. H2 molecule on Ti top [1:] site,
likewise moved upwards but quite considerably compared to
H atom. Its distance to surface is now about 2.2 A. The top Ti
atom is also elevated from the surface by 0.24 A. Meanwhile
the four nearest neighbor Ti atoms in surface layer moved
slightly towards the top Ti atom and decreased their distance
by 3%. Considering both favorable adsorption sites for atomic
and molecular hydrogen, a clearly reasonable path of
hydrogen molecule dissociation on (001) surface can be
Fig. 4 – Dissociation path for the H2 molecule over either Fe
or Ti terminated (001) surfaces.
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 5 ( 2 0 1 0 ) 1 6 8 1 – 1 6 9 2 1689
revealed. In both terminations the hydrogen molecule is
adsorbed on the top site of surface atoms and aligned pref-
erably along [1:] direction. After overcoming the probable
activation energy for dissociation, the hydrogen atoms within
the molecule begin to separate and the distance between
them increases. Meanwhile the movement of the departing
atoms would be along the initial molecule axis, where the
separated atoms are directly brought to the favorable bridge
sites for atomic hydrogen as depicted in Fig. 4. The minimum
energy path (MEP) for the dissociation of the hydrogen mole-
cule over Fe and Ti terminated (001) surfaces were calculated
using the CI-NEB method and the corresponding activation
energies were determined, see Fig. 5. In CI-NEB calculations,
initially four equally spaced images were constructed
between the initial and final states. The initial and final states
of the dissociation are assumed to be as given in Fig. 4. As can
be seen, for the initial state, top [1:] site for H2 molecule and for
the final state, adjacent bridge sites for the hydrogen atoms
are the most stable adsorption sites. This time however, for
the determination of precise initial and final states, the two
separate H atoms at the bridge sites or the H2 molecule at the
top site are allowed to relax in all directions. In the minimum
energy configuration of the initial states for both cases, we did
Fig. 5 – Minimum energy path (MEP) for the dissociation of H2 m
surfaces.
not observe the dissociation of the molecule during the
dynamics of relaxation, indicating nonzero activation energy
for the dissociation process. Along the dissociation pathway,
the H–H bond length starts to increase from its equilibrium
value to a final value of 3.1 A and 2.8 A for Fe and Ti cases
respectively. Whereas, the Fe–Fe and Ti–Ti bridge length in
both cases initially decreases slightly, then upon further
dissociation it increases again. The activation energy for the
dissociative adsorption of hydrogen was determined to be
0.178 and 0.190 eV per molecule of H2 for Fe and Ti terminated
(001) surfaces respectively. From the adsorption rate
measurements made in activated samples of FeTi powders
[40] however, it was concluded that the activation energy for
adsorption is zero. This experimental finding therefore, indi-
cates a more favorable dissociation path, probably in another
crystallographic surface of FeTi.
In Fe terminated (111) surface, bridge and FCC hollow sites
are the most favorable for atomic hydrogen adsorption.
Although the bridge site is slightly more stable, the large
difference between these two sites and other two, top and HCP
hollow, confirms taking both of these sites as favorable
adsorption sites for hydrogen atom adsorption. After relaxa-
tion, H atom on the bridge site went closer to the surface and
decreased its distance to the surface to 0.9 A. In addition,
considerable reconstruction happened on this surface. The
two Fe bridge atoms were attracted to the adsorbed H, so that
the distance between each bridge Fe and H decreased by 32%.
The top [2:] site for horizontal H2 molecule is the most stable
adsorption site with a very negative value in the order of eV.
Here, unlike the (001) surface the rotation of hydrogen mole-
cule on top site seems to change the adsorption energy seri-
ously. Analyzing the dynamics of the relaxation behavior of
this special site (top [2:]), one can see that the underlying
layers play a great role. In the case that each hydrogen atom in
the molecule points to unlike metal atoms at the sub-layers (Ti
in the second and Fe in the third layer as in top [2:] site which
constitutes a horizontal mirror symmetry with the H2 axis), H2
is pulled by the surface strongly in a tilted fashion, thus an
energetically stable and more favorable adsorption site
appears. While in the top [1:] position, there is vertical mirror
symmetry, so either side of the molecule experiences the
same electronic field. In this case, the molecule just moves
a little far away from the surface, which leads to a less
favorable adsorption site. The bridge [1:] site has the same
olecule over (a) Fe terminated and (b) Ti terminated (001)
Fig. 6 – Dissociation path for the H2 molecule over Fe terminated (111) surface. (a) First and (b) second probable paths.
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 5 ( 2 0 1 0 ) 1 6 8 1 – 1 6 9 21690
horizontal mirror symmetry as mentioned, which again gives
rise to considerably low adsorption energy. In these two sites,
top [2:] and bridge [1:], the tilting of the molecule is so appre-
ciable that the H2 molecule would have dissociated if not had
been restricted. We can then, represent two paths for
hydrogen dissociation on this surface. In the first suggestion,
Fig. 6(a), the hydrogen molecule starts to dissociate on the top
[2:] site and both hydrogen atoms follow a path, which leads
them to two nearest bridge sites. Although this travelling line
is not along the molecule axis, expresses a reasonable atom
migration path. Secondly, one of the hydrogen atoms travels
along the molecule axis until it reaches the FCC hollow site,
while the other atom goes to the nearest bridge site, Fig. 6(b).
For the determination of precise initial state and the probable
activation energy along the second suggested path, we put an
unrestricted H2 molecule over the Fe top [2:] site and allowed it
to relax. H2 molecule indeed dissociated readily, indicating
a zero activation energy process. CI-NEB calculation on this
surface therefore was not performed. The dissociation
happened in a linear fashion and the separated H atoms
moved to none of the exact high symmetry sites above, but the
projection of each hydrogen atom on the surface is as such
that, one is 0.7 A away from the FCC hollow and the other is 1
A away from the HCP hollow position. While they are at 0.1 A
and 1 A distance from the surface respectively. Here, inter-
estingly relaxation and reconstruction of surface slab is
negligible.
In Ti terminated (111) surface, favorable adsorption sites
for atomic hydrogen came out to be bridge and HCP hollow
sites. Again the bridge site shows itself a better adsorption
Fig. 7 – Dissociation path for the H2 molecule over Ti termina
point. Top site is the best site for molecule adsorption.
However here, unlike the Fe terminated (111) surface, the
adsorption energy is in the order of meV rather than eV and
there is not a difference between top [1:] and [2:] cases. After
relaxation, H on the bridge site moved downwards and
became a surface atom. Meanwhile, the two bridge Ti atoms
moved away from each other by 4.6%. No further obvious
relaxation and reconstruction were happened. H2 molecule on
top [1:] site of (111) Ti terminated surface, moved about 0.6 A
upwards and stayed horizontally. Except for a little contrac-
tion in surface slab, no other relaxation and reconstruction
were observed. At this surface, two dissociation paths can be
suggested: in the first one the hydrogen molecule begin to
dissociate from top [1:] site along its axis until the two
hydrogen atoms reach two bridge sites, Fig. 7(a). This mech-
anism is more like the dissociation on (001) surface. In the
second condition, dissociation starts from top [2:] site. The
hydrogen atom which is near an HCP hollow site, finds its way
directly to that site while the other one reaches the nearest
bridge site, Fig. 7(b). Considering the dissociation pathway
proposed in Fig. 7(a), the CI-NEB calculation resulted in an
activation energy of 1.164 eV per H2 to be present in the MEP.
In (110) surface, the best sites for adsorbing hydrogen atom
seem to be 3-fold (Ti–Ti)S–Fe hollow and Fe–Fe bridge sites.
The former site is more desirable since it has lower adsorption
energy. H atom on the 3-fold (Ti–Ti)S–Fe hollow site, after
relaxation, went closer to the surface and decreased its
distance to about 1 A. No obvious relaxation and reconstruc-
tion happened here. Unlike the other surfaces of FeTi which
have been studied earlier, here the top site is not the most
ted (111) surface. (a) First and (b) second probable paths.
Fig. 8 – Dissociation path for the H2 molecule over (110) surface. (a) First and (b) second probable paths.
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 5 ( 2 0 1 0 ) 1 6 8 1 – 1 6 9 2 1691
favorable point for hydrogen molecule adsorption, but the 3-
fold (Ti–Ti)L–Fe hollow [2:] site has the minimum adsorption
energy. Then comes the Fe top [3:] and Fe top [2:] sites. Like the
top site in Fe terminated (111) surface, the alignment of
hydrogen molecule changes the amount of adsorption energy
to some extent. By rotating from position top [1:] to top [3:], the
adsorption energy decreases by 10 meV. This is not quite valid
for the Ti top sites. Again like Ti terminated (111) surface, the
rotation of hydrogen molecule changes the adsorption energy
only slightly and the magnitude of the adsorption energy is
almost three times lower than that of Fe top sites. Considering
the molecule on its most desirable adsorption site, which is 3-
fold (Ti–Ti)L–Fe hollow [2:], one of the atom is almost already in
Fe–Fe bridge site. The other atom can go either to the far side
Fe–Fe bridge or Fe–Ti bridge or 3-fold (Ti–Ti)S–Fe site, Fig. 8(a).
The other dissociation path is a simple separation of both
hydrogen atoms along the molecule axis on opposite direc-
tions so that the molecule on its second favorable site, Fe top
[3:], dissociates into two atoms on their most likable 3-fold
(Ti–Ti)S–Fe hollow site, Fig. 8(b). The unrestricted initial state
calculation for H2 molecule on Fe top [3:] site again resulted in
prompt dissociation, bringing H atoms exactly to adjacent
(Ti–Ti)S–Fe hollow sites.
4. Conclusions
In this study, dissociation of hydrogen on three low index
surfaces of FeTi was investigated computationally using
density functional theory within generalized gradient
approximation. After performing several test calculations in
the bulk phases, adsorption energies of molecular and atomic
hydrogen on Fe and Ti terminated (001) and (111), and (110)
surfaces were calculated on high symmetry adsorption sites.
Later, probable dissociative adsorption paths for H2 molecule
were presented, upon which by CI-NEB calculations, their
activation energies were determined.
The most stable sites for the molecular hydrogen came out
to be top sites in (001) and (111) surfaces, whereas in (110)
surface top site is the second favorable. The most stable site
for H2 in (110) was found to be the 3-fold hollow site which is
composed of a long Ti–Ti bridge and an Fe atom. Calculated
adsorption energies for the top sites in Fe terminated (001), Ti
terminated (001), Fe terminated (111), Ti terminated (111)
surfaces and (Ti–Ti)L–Fe site in (110) surface were �0.463,
�0.917, �2.231, �0.151 and �0.599 eV/H2, respectively. Mean-
while, the most favorable adsorption sites for atomic
hydrogen were determined as bridge sites in all terminated
(001) and (111) surfaces. The adsorption energies were �2.863,
�3.526, �4.504 and �3.140 eV/H for Fe terminated (001), Ti
terminated (001), Fe terminated (111) and Ti terminated (111),
respectively. In (110) surface, 3-fold (Ti–Ti)S–Fe hollow site is
the most favorable site for hydrogen atom adsorption.
Considering molecular and atomic hydrogen adsorption
sites, the most likely paths of hydrogen molecule dissociation
on different surfaces of FeTi were predicted. Also, using CI-
NEB method, the dissociation reaction path and activation
energy for (001) surfaces was calculated. The activation
energies came out to be 0.178 and 0.190 eV for Fe and Ti
terminated (001) surfaces respectively, and 1.164 eV for Ti
terminated (111) surface. The dynamics of unrestricted H2
relaxation revealed that, there are zero activation energy
dissociation reaction pathways available on Fe terminated
(111) and (110) surfaces.
Acknowledgement
The numerical calculations reported in this paper were per-
formed at the ULAKBIM High Performance Computing Center
in TUBITAK, within the TR-Grid e-Infrastructure project.
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