an ab initio study of dissociative adsorption of h2 on...

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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.

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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)

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 1683

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.


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


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)


(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)


(continued )

Adsorption Site Adsorption Energy (eV)


(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


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.


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.


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.


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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