होम Applied Surface Science CO adsorption, dissociation and coupling formation mechanisms on Fe 2 C(001) surface

CO adsorption, dissociation and coupling formation mechanisms on Fe 2 C(001) surface

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Applied Surface Science
DOI:
10.1016/j.apsusc.2017.10.225
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March, 2018
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Applied Surface Science 434 (2018) 464–472

Contents lists available at ScienceDirect

Applied Surface Science
journal homepage: www.elsevier.com/locate/apsusc

Full Length Article

CO adsorption, dissociation and coupling formation mechanisms on
Fe2 C(001) surface
Xiaohu Yu a,∗ , Xuemei Zhang a , Yan Meng a , Yaoping Zhao a , Yuan Li a , Wei Xu a ,
Zhong Liu b,∗
a
Institute of Theoretical and Computational Chemistry, Shaanxi Key Laboratory of Catalysis, School of Chemical & Environment Sciences, Shaanxi
University of Technology, Hanzhong 723000, China
b
Key Laboratory of Salt Lake Resources and Chemistry, Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining 810008, China

a r t i c l e

i n f o

Article history:
Received 28 August 2017
Received in revised form 25 October 2017
Accepted 31 October 2017
Available online 1 November 2017
Keywords:
DFT
Iron carbide
Fischer-Tropsch synthesis
CO adsorption
Dissociation
Coupling

a b s t r a c t
By means of density functional theory calculations and atomic thermodynamics, we systematically investigated the CO adsorption on the Fe2 C(001) surface at different coverage. It has been found that CO prefers
to adsorb on the surface iron atom at low coverage (1–8 CO); CO prefers to adsorb at the bridge site of
Fe and C atoms at high coverage (9–12 CO). Eight CO molecules binding on the Fe2 C(001) surface is
favorable thermodynamically as indicated by the stepwise adsorption energy. The phase diagram shows
that addition of more CO molecules up to a number of 8 is thermodynamically favorable, and that the
incremental energy gained by adding one more CO molecule is almost constant up to 4 CO molecules,
decreases up to 8 CO molecules, after which it becomes thermodynamically unfavorable to add more
CO molecules. Probability distribution of different singe-CO adsorbed states on the Fe2 C(001) surface
as function of temperature shows that CO dissociation and coupling are least preferred, indicating that
carbide mechanism is not dominant in the iron-based Fis; cher-Tropsch synthesis reaction. The projected
density of states (PDOS) was used to analyze the CO adsorption mechanism.
© 2017 Elsevier B.V. All rights reserved.

1. Introduction
Iron carbide is an important active phase in iron-based catalysts in Fischer-Tropsch synthesis (FTs) process [1,2], which has
become increasingly important especially for liquid fuel production under the background of shortage of oil supply in the world. In
the process of FTs reactions, the iron-based catalyst is exposed to
the syngas (CO + H2 ) environment that maintains the stable existence of iron carbides [1,2]. It is well known that activation with
carbon monoxide and syngas in FTs typically results in complicated
conversion of Fe2 O3 to Fe3 O4 and, finally, to one or more iron carbides: CO adsorption on iron carbide surface hydrogenated by the
adsorbed hydrogen atom, followed by the coupling with CHx and
formed longer hydrocarbon. The initial step for CO adsorption on
the iron carbide surface has been widely investigated in experiments. However, there are few theoretical investigations aiming at
a comprehensive understanding the interaction between CO and
iron carbide surfaces [3–6].

∗ Corresponding authors.
E-mail addresses: yuxiaohu950203@126.com (X. Yu), liuzhong@isl.ac.cn (Z. Liu).
https://doi.org/10.1016/j.apsusc.2017.10.225
0169-4332/© 2017 Elsevier B.V. All rights reserved.

It was reported [7] that there exist Fe, Fe3 O4 , Fe4 C, Fe3 C, Fe2 C,
Fe5 C2 , Fe7 C3 in freshly activated or used Fe-based FTs catalysts, and
the phase formation and transformation of iron carbides usually
change with different temperature in fused catalysts. In addition,
it was found [8] that Fe2 C and Fe2.2 C phases are formed simultaneously at low temperature (115 ◦ C), however only the Fe2 C phase
is formed at 150–185 ◦ C; the Fe5 C2 phase is formed in the range
220–400 ◦ C; and stable the Fe3 C phase is formed at 450 ◦ C. However, there are only a few theoretical studies on the adsorption
of small molecules on Fe, Fe3 O4 , Fe4 C, Fe3 C and Fe5 C2 surfaces
[3–5,9–16] and no report on the Fe2 C surfaces. Cao et al. [3] reported
that CO prefers to adsorb on the three-fold iron site of (001), (110),
and (100) on the Fe5 C2 surfaces. Liao et al. [4] reported that CO
favors the three-fold site of (100) and the four-fold site of (001),
but the two-fold site and three-fold site of (010) at low coverage
for CO adsorption on the Fe3 C surfaces. Recently, Ramo and Jenkins
[5] studied the small molecules adsorption on the Fe3 C(010) surface and found that CO prefers to adsorb at bridge site of two iron
atoms which agrees well with Liao et al.’ results [4]. Deng et al. [6]
researched CO adsorption on the Fe4 C surfaces and found that CO
adsorbs at different sites of different surfaces. Huang et al. [17] studied CO adsorption on the magnetite (111) surface using standard
density functional theory (DFT) and it was found that the on-top

X. Yu et al. / Applied Surface Science 434 (2018) 464–472

465

Fig. 1. (a) Top and (b) Side views of the Fe2 C(001) surface. (iron atoms in blue, carbon atoms in grey). (For interpretation of the references to colour in this figure legend, the
reader is referred to the web version of this article.)

configurations are most stable on both Fetet1 and Feoct2 terminations. In addition, the CO adsorption on the Feoct2 termination is
more stable than on the Fetet1 termination. Yu et al. [18] systematically studied CO adsorption on the Fe3 O4 surfaces using DFT+U,
and found that more than one CO can bind on one surface iron atom
on both Fetet1 and Feoct2 terminations of Fe3 O4 (111) and A layer of
Fe3 O4 (110), only one CO can bind on one surface iron atom on other
surfaces, and different adsorption mechanisms can be explained by
spatial effect.
The orthorhombic Fe2 C phase was chosen in this work since its
stability is more stable than hexagonal Fe2 C by 0.16 eV on the basis
of former computed cohesive energies [19]. In addition, Fe2 C(001)
surface was selected to study the interaction with H2 molecules
since it is one of main facet of Fe2 C [19], and surface structures
and properties of Fe2 C have been predicted [19] theoretically. In
order to get the detailed mechanism for CO adsorption on Fe2 C
surfaces, extensive DFT calculations were carried out to investigate CO adsorption on the Fe2 C(001) surface at different coverage
in the present work. Boltzmann statistics was used to analyze the
probability distribution of different adsorption states of single CO
as function of temperature. The phase diagram of CO adsorption
on the Fe2 C(001) surface is analyzed using atomic thermodynamics. In addition, we discussed the overall trends of the adsorption
energy as a function of coverage and analyzed the CO adsorption
mechanisms using the projected density of states (PDOS).

ate a lattice constant (a = 4.651 Å, b = 4.258 Å. C = 2.801 Å) for bulk
Fe2 C, which agrees well with the experimental value (a = 4.704 Å,
b = 4.318 Å, c = 2.830 Å) [26] and former theoretical result [19].
2.2. Surface model
Top and side views of p(2 × 2) supercell of the Fe2 C(001) surface are shown in Fig. 1a. The four-layer slabs are used to describe
the Fe2 C(001) surface, with the top two layers and adsorbed CO
are allowed to fully relax, and two bottom layers are fixed in bulk
position. A 15 Å vacuum gap was used to separate from Fe2 C(001)
surface images which is periodically repeated in the z direction
perpendicular to the surface. In all calculations, the CO molecules
were adsorbed on one side of the Fe2 C(001) surface. The leading
dipole moment errors induced CO molecules adsorption on the
Fe2 C(001) surface were corrected by using dipole moment methods
as implemented in the VASP code [20–22].
For the Fe2 C(001) surface with n adsorbed CO molecules, we
defined the total CO adsorption energy as:
E(CO)n = E(nCO/Fe2 C(001)) − E(Fe2 C(001)) − nE(CO)]

where E(nCO/Fe2 C(001)), E(Fe2 C(001)) and E(CO) are the energies
of the adsorbed system, clean Fe2 C(001) surface, and an isolated CO
molecule in gas phase, respectively, and n is number of adsorbed
CO molecules. The stepwise adsorption energy is defined as:
E(CO) = E(CO)n − E(CO)n- 1 .

2. Method and surface model

(1)

(2)

The average adsorption energy is defined as:

2.1. Computational method

E = E(CO)n /n

All calculations were performed by using the frozen-core allelectron projector-augmented wave (PAW) method within spin
polarized DFT as implemented in the Vienna Ab-initio Simulation
Package (VASP) [20–22]. The exchange and correlation energies of
the electrons were described by the generalized gradient approximation (GGA) [23] functional parametrized by Perdew, Burke,
and Ernzerhof (PBE). A 400 eV cutoff energy was used to control the number of plane waves and a 645 eV cutoff energy was
used to control the number of the augmentation wavefunctions.
Projector-augmented-wave (PAW) potentials [24] with valence
configurations of 3p6 3d6 4s2 , 2s2 2p4 and 2s2 2p2 were used to
describe the Fe, O, and C atoms, respectively. The Brillouin zone
integrations were performed using Monkhorst-Pack (MP) grids
[25], and a Gaussian smearing ␴ was 0.2 eV. Structure optimizations
were conducted until the energy was smaller than 10−4 eV and the
Hellmann-Feynman force on each atom was less than 0.02 eV/Å.
For integration within the Brillouin zone, specific k-points were
selected using a 7 × 7 × 7 MP grid for the bulk Fe2 C and a 3 × 3 × 1
MP grid for Fe2 C(001) surface. These settings were able to gener-

From above definition, it is clear that a more negative adsorption energy indicates the stronger adsorption. A cubic unit cell of
10 × 10 × 10 Å3 was used to calculate CO, and the calculated bond
distance of CO molecule is 1.14 Å, which agrees well with previous
theoretical result (1.14 Å) [27] and the experimental result (1.13 Å)
[28].

(3)

3. Results and discussion
In this work, the CO adsorption was defined as CO molecule
binding on the surface iron atoms, the CO mixed adsorption was
defined as CO molecules binding on the surface iron and carbon
atoms, the CO coupling was defined as CO molecule binding on
the surface lattice carbon atom and forming a C CO-like structure,
and the CO dissociation was defined as CO molecule dissociates to
carbon and oxygen atoms binding on the Fe2 C(001) surface. The
total adsorption energies of the most stable CO adsorption, coupling, mixed and dissociation formation configurations are shown
in Table 1.

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X. Yu et al. / Applied Surface Science 434 (2018) 464–472

Table 1
The total adsorption energy (eV) of CO adsorption, mixed, dissociation and coupling on Fe2 C(001) surface (CO adsorption was defined as CO molecule binding on the surface
iron atoms, CO mixed adsorption was defined as CO molecules binding on the surface iron and carbon atoms, CO dissociation was defined as CO molecule dissociates to
carbon and oxygen atoms binding on Fe2 C(001) surface, and CO coupling was defined as CO molecule binding on the surface lattice carbon atom and forming a C CO–like
structure).

Fe2 C(001)

Fe2 C(001)

states

1 CO (eV)

2 CO (eV)

3 CO (eV)

4 CO (eV)

5 CO (eV)

6CO (eV)

adsorption
mixed
dissociation
coupling
states
adsorption
mixed

−1.99

−3.96
−2.97
−0.73
−2.20
8CO (eV)
−12.03
−11.79

−5.78
−4.82
−0.37
−3.19
9CO (eV)

−7.59
−6.59
0.18
−4.23
10CO (eV)

−8.81
−8.55

−10.16
−9.57

11CO (eV)

12CO (eV)

−12.13

−11.79

−11.50

−11.29

−0.22
−1.08
7CO (eV)
−11.10
−10.39

3.1. CO adsorption on Fe2 C(001)
For one CO molecule, adsorption, dissociation and coupling
configurations were computed. In the most stable adsorption configuration (Fig. 2a), tilted CO molecule adsorbs on the surface iron
atom with the Fe C bond length of 1.760 Å and the bond length of
C O changes from 1.140 to 1.173 Å with the total adsorption energy
of −1.99 eV. In the most stable coupling configuration (Fig. 2b), CO
molecule binds on surface carbon atom with Cs C bond length of
1.332 Å, and C O bond length changes from 1.140 to 1.186 Å; the
total adsorption energy is −1.08 eV. In the most stable dissociation configuration (Fig. 2c), the dissociated carbon atom binds at
the bridge site of two surface iron atoms with Fe-C bond lengths
of 1.762 Å and 1.760 Å, and the dissociated oxygen atom binds on
the bridge site of two surface iron atoms with Fe-O bond lengths of
1.796 and 1.795 Å; the total adsorption energy is −0.22 eV. Comparing the three CO binding modes, one can easily see that CO binding
on surface iron atom is most preferred and CO dissociation is least
favorable thermodynamically for one CO molecule.
For two CO molecules, adsorption, coupling, dissociation and
mixed configurations were computed. In the most stable adsorption configuration (Fig. 2d), the two tilted CO molecules adsorb
on two surface iron atoms with the total adsorption energy of
−3.96 eV. In the most stable coupling configuration (Fig. 2e), two
CO molecules adsorb on two surface carbon atoms, and the total
adsorption energy is −2.20 eV. In the most stable mixed adsorption and coupling configuration (Fig. 2f), one CO molecule adsorbs
on surface iron atom and another CO molecule binds on the surface carbon atom with the total adsorption energy of −2.97 eV. In
the most stable dissociation configuration (Fig. 2g), the two dissociated carbon atoms bind on two bridge sites of surface iron atoms
and the two dissociated oxygen atoms adsorb at two bridge sites
of surface iron and carbon atoms with the total adsorption energy
of −0.73 eV. It indicates that the two CO molecules prefer to adsorb
on two surface iron atoms thermodynamically and CO dissociation
is least favorable thermodynamically for two CO molecules.
For three CO molecules, adsorption, coupling, mixed and
dissociation configurations were computed. In the most stable
adsorption configuration (Fig. 2h), three CO molecules adsorb
on three surface iron atoms with the total adsorption energy of
−5.78 eV. In the most stable coupling configuration (Fig. 2i), three
CO molecules adsorb on three carbon atoms, and the total adsorption energy is −3.19 eV. In the most stable mixed adsorption and
coupling configuration (Fig. 2j), two CO molecules bind on two surface iron atoms and another CO molecule adsorbs at the bridge
site of surface iron and carbon atoms with the total adsorption
energy of −4.82 eV. In the most stable dissociation configuration
(Fig. 2k), three dissociated carbon atoms adsorb at three surface
bridge sites of iron atoms and three dissociated oxygen atoms bind
at three bridge sites of surface carbon and iron atoms, and the total
adsorption energy is −0.37 eV. It indicates that three CO molecules

adsorption is most preferred thermodynamically and dissociation
is least favorable thermodynamically for three CO molecules.
For four CO molecules, adsorption, coupling, mixed and dissociation configurations were computed. In the most stable adsorption
configuration (Fig. 2l), four CO molecules adsorb on four surface
iron atoms with the total adsorption energy of −7.59 eV. In the
most stable coupling configuration (Fig. 2m), four CO molecules
bind on four surface carbon atoms, and the total adsorption energy
is −4.23 eV. In the most stable mixed adsorption and coupling configuration (Fig. 2n), three CO molecules bind on three surface iron
atoms and another CO molecule adsorbs at the bridge site of surface
carbon and iron atoms, and the total adsorption energy is −6.59 eV.
In the most stable dissociation configuration (Fig. 2o), four dissociated C atoms adsorb at bridge sites of iron and iron atoms, and
four dissociated O atoms bind at bridge sites of iron and carbon
atoms with the total adsorption energy of 0.18 eV. Comparing three
adsorption modes, one can easily see that CO molecule adsorption is
most stable thermodynamically and dissociation is least favorable
thermodynamically for four CO molecules.
For five CO molecules, adsorption, and mixed configurations
were computed. In the most stable adsorption configuration
(Fig. 2p), five CO molecules adsorb on five surface iron atoms, and
the total adsorption energy is −8.81 eV. In the most stable mixed
configuration (Fig. 2q), four CO molecules adsorb on four surface
iron atoms and last CO molecule binds at the bridge site of surface Fe and C atoms, and the total adsorption energy is −8.55 eV. It
shows that five CO adsorption on the Fe2 C(001) surface is preferred
thermodynamically for five CO molecules.
For six CO molecules, adsorption, and mixed configurations
were computed. In the most stable adsorption configuration
(Fig. 2r), six CO molecules adsorb on six surface iron atoms with
the total adsorption energy of −10.16 eV. In the most stable mixed
configuration (Fig. 2s), five CO molecules adsorb on five surface iron
atoms and another CO molecule binds on the bridge site of iron and
carbon atoms, and the total adsorption energy is −9.57 eV. One can
clearly see that six CO adsorption is favorable thermodynamically
for six CO molecules.
For seven CO molecules, adsorption, and mixed configurations were computed. In the most stable adsorption configuration
(Fig. 2t), seven CO molecules bind on seven surface iron atoms with
the total adsorption energy of −11.10 eV. In the most stable mixed
configuration (Fig. 2u), six CO molecules bind on six surface iron
atoms and another CO molecule binds at bridge site of iron and
carbon atoms, and the total adsorption energy is −10.39 eV. It indicates that seven CO adsorption on the Fe2 C(001) surface is most
favorable thermodynamically for seven CO molecules.
For eight CO molecules, adsorption, and mixed configurations were computed. In the most stable adsorption configuration
(Fig. 2v), eight CO molecules adsorb on eight surface iron atoms
with the total adsorption energy of −12.03 eV. In the most stable
mixed configuration (Fig. 2w), five CO molecules adsorb on five surface iron atoms and two CO molecules bind at two bridge sites of

X. Yu et al. / Applied Surface Science 434 (2018) 464–472

467

Fig. 2. Configurations of the most preferred CO adsorption, coupling, mixed and dissociation on Fe2 C(001) surface at different coverage (carbon atoms in grey ball, iron atom
in blue, carbon and oxygen atoms of adsorbed CO in black and bigger red ball). (For interpretation of the references to colour in this figure legend, the reader is referred to
the web version of this article.)

iron and carbon atoms, and last CO molecule goes to the bridge site
of iron atoms, and the total adsorption energy is −11.79 eV. One
can see that eight CO adsorption is favorable thermodynamically
for eight CO molecules.
For nine to twelve molecules, only mixed configurations were
computed. The most stable nine CO mixed adsorption and coupling
configuration (Fig. 2x), seven CO molecules adsorb on seven surface iron atoms and one CO molecule goes to surface bridge site
of iron and carbon atoms, and last CO molecule adsorbs at bridge
site of surface iron atoms: the total adsorption energy is −12.13 eV
and the stepwise adsorption energy is −0.10 eV. It indicates that
nine CO molecules binding on the Fe2 C(001) surface is favorable
thermodynamically according negative value of stepwise adsorption energy. The most stable ten CO mixed adsorption and coupling
configuration (Fig. 2y), seven CO molecules adsorb on the surface
iron atoms and two CO molecules bind at two bridge sites of surface
iron and carbon atoms, and last CO molecule goes to the bridge site
of surface iron atoms: the total adsorption energy is −11.79 eV and
stepwise adsorption energy is 0.34 eV. It indicates that ten CO bind-

ing on the Fe2 C(001) surface is not favorable thermodynamically
according positive value of stepwise adsorption energy. The most
stable eleven CO adsorption is mixed adsorption and coupling configuration (Fig. 2z): four CO molecules adsorb on four surface iron
atoms and four CO molecules bind at bridge sites of surface iron
and carbon atoms, and last three CO molecules go to three bridge
sites of surface iron atoms: the total adsorption energy is −11.50 eV.
The most stable twelve CO adsorption (Fig. 2a’) is mixed adsorption
and coupling configuration: four CO molecules adsorb on the four
surface iron atoms and four CO molecules bind at four bridge sites
of surface carbon and iron atoms, and last four CO molecules go to
four bridge sites of surface iron atoms: the total adsorption energy
is −11.29 eV.
The total adsorption energy for one to twelve CO molecules most
stable adsorption is −1.99, −3.96, −5.78, −7.59, −8.81, −10.16,
−11.10, −12.03, −12.13, −11.79, −11.50 and −11.29 eV, while the
stepwise adsorption energy is −1.99, −1.97, −1.82, −1.81, −1.22,
−1.35, −0.94, −0.93, −0.10, 0.34, 0.29 and 0.21 eV, and corresponding average adsorption energy is −1.99, −1.98, −1.93, −1.89, −1.76,

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X. Yu et al. / Applied Surface Science 434 (2018) 464–472

Fig. 3. Projected density of states (PDOS) for the clean Fe2 C(001), free CO molecule,
and the most stable one CO adsorption on Fe2 C(001) surface.

−1.69, −1.58, −1.50, −1.35, −1.18, −1.05 and −0.94 eV, respectively. One can clearly see that eight CO binding on the Fe2 C(001)
surface is favorable thermodynamically according the stepwise
adsorption energy. From the average adsorption energy, twelve CO
binding on the Fe2 C(001) surface is favorable thermodynamically.
The total adsorption energy for one to four CO molecules dissociative adsorption is −0.22, −0.73, −0.37 and 0.18 eV, while the
stepwise adsorption energy is −0.22, −0.51, 0.36 and 0.55 eV, and
corresponding average adsorption energy is −0.22, −0.36, −0.19
and 0.09 eV, respectively. One can see that two CO dissociative
adsorption on the Fe2 C(001) surface is favorable thermodynamically according to negative value of the stepwise binding energy.
Comparing with different adsorption modes, one can clearly see
that CO adsorption is most preferred and dissociation is least preferred thermodynamically.
3.2. Electronic structures
There are exposed eight iron atoms and four carbon atoms on the
Fe2 C(001) surface. To shed light on the mechanism of CO adsorption on the Fe2 C(001) surface, the projected density of states (PDOS)
(Fig. 3) of free CO molecule, most stable adsorption on Fe-top, on
bridge site of Fe and C atoms, on C-top, and the iron and carbon
atoms in the first layer which CO adsorbed in the first layer, were
plotted to analysis. As discussed above, the tilted CO adsorption on
Fe-top is favorable for one CO molecule adsorption on the Fe2 C(001)
surface. For free CO molecule (Fig. 3a), it is well known that 3␴,
4 ␴, 1␲ and 5 ␴ come from the chemical bonding of CO, and 2
␲* comes from the antibonding of CO. Here chemical bonding 5 ␴
and antibonding 2␲* states mainly contribute to CO chemisorption
on metal atom. One can clearly see that the occupied 5␴ orbital is

below the Fermi level for free CO molecule, while the band of the
adsorbed CO shifts to lower energy (Fig. 3). The shifting of the 5␴
and 2␲* is primarily the result of the 5␴-d forward donation and
d-2␲* back-donation [3,18]. First the charge transfer from 5␴ of
adsorbed CO molecule to the d orbital of surface transiton metal
atoms leads to the shrinking of 5␴ near the Fermi level and the
significant stronger metal-C chemical bonding due to the bonding
nature of the 5␴ orbital. And then the charge transfer from the surface to the molecule leads to the broadening of 2␲* band with an
edge near the Fermi level and the significant elongation of the C O
bond due to the antibonding nature of the 2␲* orbital. From configuration of CO binding on the Fe2 C(001) surface, it can be found
that CO adsorption on Fe-top is mainly due to the bonding between
carbon atom of adsorbed CO molecule and surface Fe atom. While
for CO adsorption on C-top, the adsorption is mainly due to the
bonding between carbon atom of adsorbed CO and surface carbon
atom. For CO adsorption on bridge site of Fe and carbon atoms, the
adsorption is mainly due to the bonding between the carbon atom
of adsorbed CO and surface iron and carbon atoms. Compared to
the total DOS of a free and adsorbed CO molecule (3␴, 4 ␴, 1␲ and
5 ␴ for the C O bonds, and 2␲* for the C O antibonding), one can
easily see that the total DOS of the adsorbed CO molecule shifts to
lower energies (Fig. 3b–d). From Fig. 3c, apart from 3␴, 4 ␴ and 1␲
states shifting to lower energy, one can see that 5 ␴ state becomes
smaller and almost disappears, indicating there is charge transfer
from 5 ␴ state of adsorbed CO to the surface uncoordinated Fe atom.
It indicates that there is chemical bonding between carbon atom of
adsorbed CO molecule and surface Fe atom. The PDOS of Fe atom in
the first layer corresponding to 4 ␴ and 1␲ states becomes larger
and broader (Fig. 3c), this means that surface Fe atom derives charge
from adsorbed CO molecule. From CO coupling to surface carbon
atom (Fig. 3b), one can see that except 3␴, 4 ␴ and 1␲ states shift
to lower energy and there is new state around −15 eV which indicates formation of C C chemical bonding. Same to CO coupling the
surface carbon atom, there is new state around −14 eV which is
smaller than CO coupling with surface carbon atom for CO adsorption on bridge site of Fe and C atoms (Fig. 3d). It indictes that new
C C chemical bonding formed for CO binding on bridge site of Fe
and C atoms.
3.3. Probability distribution of different single-CO adsorbed states
on Fe2 C(001) surface
In order to derive the probability distribution of different single
CO adsorbed states on the Fe2 C(001) surface at different temperature, we draw the probability distribution plot as function
of temperature using Boltzmann statistics [29–31]. One can see
that adsorption energies derived from single CO adsorption on the
Fe2 C(001) surface show differences, indicating that the different
adsorption configurations may only coexist at high temperature.
According to Boltzmann statistics, each adsorption configuration
has a probability of occurrence, Pm , which is function of the temperature: Pm = 1/Zexp[-E/(KB T)], where Z is the canonical partition
function, and E is the adsorption energy of single CO adsorption
on Fe2 C(001) surface. One can easily derive the probability distribution plot of CO adsorption on the Fe2 C(001) surface at different
temperature (Fig. 4). The most stable CO adsorption on the top of Fe
is most preferred at 0 K (Fig. 4). The probability distribution of other
least stable configurations increases along higher temperature and
the probability distribution of most stable CO adsorption gradually
decreases. The probability distribution of second stable adsorbed
Fe–Fe bridge site will increase to 0.31 at 500 K. In addition, it can
be easily seen that the probability of CO coupling increases little
by little (Fig. 4). There is general rule: probability distribution of
different least stable adsorption states of single CO molecule gradually increases along the higher temperature. The different adsorbed

X. Yu et al. / Applied Surface Science 434 (2018) 464–472

469

Fig. 4. Probability distribution of different single-CO adsorbed states on Fe2 C(001) surface as function of temperature.

states of single CO can be exchangeable indicated by increasing
probability distribution of least adsorbed CO states at high temperature. However, one can clearly see that CO coupling with surface
carbon atom is very difficult as the probability of CO coupling is
only 1.5e−5 at 1000 K, in particular probability of CO dissociation
is only 7.2e−10 at 1000 K on the Fe2 C(001) surface. In addition, we
found that H2 is easy to adsorb on surface carbon atom to form CH2
species according our unpublished data and other former theoretical results [7,32]. It indicates that carbide mechanim may not be
the main reaction path in iron-based FTs, while the direct interaction of CO with CH2 may be the main reaction path in iron-based
FTs reaction.
3.4. Phase diagram of CO adsorption on Fe2 C(001) at given
conditions
It is well known that the effect of temperature and pressure on
the bulk [33], surface [34–36] and cluster [37–39] can be studied
by the atomic thermodynamics. In this work, phase diagram of CO
adsorption on the Fe2 C(001) surface as function of given conditions
was plotted to analyze the effect of temperature and CO pressure
on stable CO adsorption at different coverage [40,41]. The Gibbs
free energy (G) of nCO adsorption on the Fe2 C(001) surface was
defined as:





ads
GFe
C (T, P, nCO) = G nCO/Fe2 C (001) − G [Fe2 C (001)]
2

−nGCO (T, pCO )





(1)

where G nCO/Fe2 C (001) is the Gibbs free energy of Fe2 C(001)
surface with adsorbed CO molecules, G [Fe2 C (001)] is the Gibbs
free energy of clean Fe2 C(001) surface, GCO (T, pCO ) are the Gibbs
free energy of isolated CO molecules in gas phase, n is number of
adsorbed CO molecules, T is the temperature, and pCO is the partial
pressure of CO in the gas atmosphere. According above definition,
one can easily see that a more negative G indicates the more stable
adsorption structure.
Then the value of GCO (T, pCO ) can be expressed as:
total
+ CO (T, p0 ) + kB T ln(p/p0 )
GCO (T, pCO ) = ECO

(2)

total is the total enery of CO molecules including zero point
where ECO
vibration energy, CO (T, p0 ) term includes vibrational and rota-

tional contributions for CO gas, and can be taken from tables of
thermodynamic data [42]. The last term kB Tln(p/p0 ) is the contribution of temperature and CO partial pressure to the CO chemical
potential and kB is the Boltzmann constant. One can easily see that
the last term kB Tln(p/p0 ) contribution to solid surfaces can be negligible since their large mass differences compared to the large
contribution of vibration to gases. Thus, the DFT calculated total
energy can be applied to instead of the Gibbs free energies of solid
surface. Now the Eq. (1) can be rewritten as:
ads
GFe
C (T, P, nCO) = G[nCO/Fe2 C(001)]-E[Fe2 C(001)]-nGCO (T, pCO )
2

(3)
From the phase diagram of CO adsorption on the Fe2 C(001) as
function of CO chemical potential (Fig. 5a), one can clearly see
that addition of more CO molecules up to a number of 8 is thermodynamically favorable, and that the incremental energy gained
by adding one more CO molecule is almost constant up to 4 CO
molecules, decreases up to 8 CO molecules, after which it becomes
thermodynamically unfavorable to add more CO molecules. In addition, another insightful form of the convex hulls of CO adsorption
on the Fe2 C(001) surface can be drawn in Fig. 5b, in which the phase
diagram is plotted as function of numbers of CO molecules. It can
be seen that for values of the oxygen chemical potential of less than
−1.98 eV, the clean Fe2 C(001) surface is the thermodynamically
most stable phase. For higher values of oxygen chemical potential from −1.98 to −0.10 eV, one can clearly see that the same CO
adsorption configurations are the most thermodynamically favorable. Then inserting Eq. (2) into (3), we can derive:
ads
GFe
C (T, P, nCO) = G[nCO/Fe2 C(001)]-E[Fe2 C(001)]
2

total
-nECO
− nCO (T, p0 ) − nkB T ln(p/p0 )

(4)

Now one can easily derive the phase diagram of CO molecules
adsorption on the Fe2 C(001) surface as function of given conditions
from Eq. (4). The phase diagram shows the effect of temperature and CO pressure on CO adsorption on the Fe2 C(001) surface
with different coverage (Fig. 6). In well agreement with former
two phase diagrams: addition of more CO molecules up to a num-

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X. Yu et al. / Applied Surface Science 434 (2018) 464–472
Table 2
Comparison of the largest adsorption energies for CO adsorbed on Fe5 C2 , Fe2 C, Fe3 C,
Fe4 C and Fe3 O4 at low coverage.

Fe5 C2

Fe3 C

Fe4 C

Fe2 C

Fe3 O4

a

surface

Method

Site

Eads (eV)

Ref.

(100)
(001)
(110)
(100)
(001)
(010)
(001)-TFe
(001)-TFe/C
(110)-TFe
(110)-TFe/C
(111)-TFe
(111)-TC
(001)
(111)-Fetet1
(111)-Feoct2
(110)-A layer
(110)-B layer
(001)-B layer
(001)-B layer

PBE
PBE
PBE
PW91
PW91
PW91
PBE(RPBE)
PBE(RPBE)
PBE(RPBE)
PBE(RPBE)
PBE(RPBE)
PBE(RPBE)
PBE
PBE + U(PBE)
PBE + U(PBE)
PBE + U
PBE + U
PBE + U
PBE + U

Three-fold
Three-fold
Three-fold
Three-fold
Four-fold
Two-fold
Four-fold
Fe-top
Three-fold
Fe-top
Three-fold
Three-fold
Fe-top
Fe-top
Fe-top
Fe-top
Two-fold
Fe-top
Fe-top

−2.21
−2.10
−2.34
−2.21
−2.19
−2.46
−2.53 (−1.98)
−1.36 (−1.04)
−2.74 (−2.22)
−1.81 (−1.52)
−2.54 (−2.16)
−2.32 (−1.87)
−1.99
−0.57 (−0.80)
−1.63 (−1.94)
−0.45
−0.67
−0.94
−0.24

[3]

[4]

[6]

a

[18]
[18]
[18]
[18]
[18]
[43]

This work.

lower CO concentration as temperature increases or CO pressure
decreases which is in well agreement with basic physical insights.
The reason of 1CO and 5 CO adsorptions on the Fe2 C(001) surface
not shown on the phase diagram is that the process is controlled
by kinetics rather than thermodynamics. The full desorption of
adsorbed CO molecules takes place 295 K and 10−40 atmosphere
of CO partial pressure.
3.5. Discussion

Fig. 5. Phase diagram of CO adsorption on the Fe2 C(001) surface as a function of (a)
number of CO molecules (b) CO chemical potential.

ber of 8 is thermodynamically favorable, and that the incremental
energy gained by adding one more CO molecule is almost constant up to 4 CO molecules, decreases up to 8 CO molecules, after
which it becomes thermodynamically unfavorable to add more
CO molecules. One can clearly see that equilibrium shift toward

It is interesting to compare the most stable CO adsorption on iron
carbide and iron oxide as listed in Table 2. It shows clearly that the
configuration with CO adsorbed on more iron termination surfaces
tend to have larger adsorption energies than those surfaces terminated with less iron atoms, indicating that the surface iron atoms
benefit CO adsorption. For example, more iron termination surfaces
for Fe5 C2 [3]: (110) (−2.34 eV) > (100) (−2.21 eV) > (001) (-2.10 eV);
for Fe3 C [4]: (010) (−2.46 eV) > (100) (−2.21 eV) > −2.19 eV); for
Fe4 C [6]: (110)-TFe (−2.74 eV) > (110)-TFe/C (−1.81 eV); (111)-TFe
(−2.54 eV) > (111)–TC (-2.32 eV); (001)-TFe (−2.53 eV) > (001)-TFe/C

Fig. 6. Phase diagram of different coverage CO adsorption on Fe2 C(001) surface at different temperatures and CO partial pressure.

X. Yu et al. / Applied Surface Science 434 (2018) 464–472

(−1.36 eV) agree well with larger CO adsorption energy as shown
Table 2. In this work CO adsorption on the Fe2 C(001) surface has
larger adsorption energy of −1.99 eV. There is same rule for different direction of Fe3 O4 surfaces: the termination with stronger
iron contribution has bigger CO adsorption energy than the termination with stronger oxygen contribution, for example, the Fe3 O4
(111) Feoct2 with stronger iron contribution has stronger CO adsorption energies (−1.63 eV [18]) than Fetet1 with stronger oxygen
contribution (−0.57 eV [18]), and Fe3 O4 (110) A layer with less
iron contribution has smaller CO adsorption energies (-0.45 eV[18])
than B layer with stronger iron contribution (−0.67 eV[18]). CO
adsorption on Fe3 O4 (001) surface has adsorpion energy of −0.94
eV[18] which is larger than other theoretical results (−0.24 eV) [43].
Obvious, there is no general rule for more stable surface has small
CO adsorption energy since structure complex of Fe3 O4 surfaces. In
addition, comparing the CO adsorption energy on both iron carbide
and iron oxide, one can clearly see that the formation of iron carbide is advantageous for the CO adsorption, while the formation of
iron oxide is not advantageous for the CO adsorption as shown in
Table 2.
It is found that CO dissociation is very difficult on the Fe2 C(001)
surface which agrees well with former theoretical results: CO is
difficult to dissociate on iron carbide surfaces [7,32]. In addition,
it is found that CO binds on surface iron atom very strongly on
the Fe2 C(001) surface. So the dissociated H atoms should adsorb
on the surface carbon atoms in FTs reaction. It agrees well with
recently our results that dissociated H atoms prefer to adsorb on
surface carbon atom and form CH2 species on the Fe2 C(001) surface (unpublished results). Dissociated H atoms adsorb on carbon
atom and will form carbon vacancies on the Fe2 C(001) surface
which is also in well agreement with former theoretical result
[7,32]. Carbide mechanism is deemed to play an important role
in the Fischer-Tropsch process over years [1,44]: carbon monoxide
and hydrogen are both adsorbed dissociatively on the surface of
active catalysts, subsequently hydrocarbon fragments (CHx ) would
be formed by hydrogenation of atomic carbon and these fragments
then polymerise to chain growth. But according to our data and
former theoretical results [7,32], one can easily know that CO is
difficult to dissociate on iron carbide surfaces. It shows that carbide mechanism may not be the main reaction in iron-based FTs
reaction. In addition, it is reported that direct reaction of adsorbed
CO with CHx species is kinetically and thermochemically preferred
over CO dissociation theoretically recently [45]. In particular, it is
reported that CH2 plays an important role as building block for
chain growth in Fischer-Tropsch synthesis reaction [46,47]. For
example, early experimentally work, which prepared surface with
adsorbed CH2 by dosing Ru(0001) with CH2 N2 , suggested CH2 was
the fundamental building block for chain growth [48]. In addition,
it is reported that the results of computational studies of barriers
for possible coupling reactions are consistent with this conclusion:
in general, reactions involving CH2 as the chain building moiety in
FTs reaction are kinetically favored over involving CH [47,49,50].
According to the above data, formation of CH2 from two hydrogen
atoms interacting with surface carbon atom is favorable thermodynamically, one can derive that CH2 may be the chain building
moiety in iron-based FTs reaction which agrees well with recently
theoretical predication. One can see that CO direct reaction with
CH2 maybe play an important role iron based in FTs reaction. We
hope that carefully designed experiments should be performed to
verify the phenomenon.

4. Conclusion
To contribute to the understanding of the mechanism of CO
adsorption, coupling, mixed and dissociation over iron carbide sur-

471

faces, we have considered the interaction of CO with the Fe2 C(001)
surface at different coverage using DFT calculations and atomic
thermodynamics. For one to eight CO molecules, tilted CO prefers
to adsorb on the top of surface iron atom of the Fe2 C(001) surface. While for nine to twelve CO molecules, CO prefers to adsorb
at bridge sites of surface Fe and C atoms. According to stepwise
adsorption energy, eight CO molecules binding on the Fe2 C(001)
surface is thermodynamically favored. CO coupling and dissociation is not favorable thermodynamically compared with CO
adsorption on surface iron atom of the Fe2 C(001) surface.
It shows clearly that CO prefers to adsorb on iron carbide surfaces than on magnetite surfaces, indicating that formation of iron
carbide is advantageous for the CO adsorption than iron oxide. In
addition, one can easily know that the surfaces terminated with
much more iron atoms tend to have larger CO adsorption energies
than those surfaces terminated with less iron atoms, indicating that
the surface iron atoms benefit CO adsorption for both iron carbide
and Fe3 O4 surfaces. It is found that different adsorption mechanisms of CO on different positions can be attributed to the difference
in surface electronic structures on the basis of PDOS.
A deeper understanding of the reaction mechanism of CO
adsorption, coupling, mixed and dissociation on Fe2 C-based catalysts has been obtained. CO molecule can react directly with the
lattice carbon atom and forms C CO which is the important stage
of Fischer-Tropsch synthesis reaction over iron carbide catalysts.
It has been found that CO direct reaction with CHx species maybe
play an important role in iron-based FTs reaction. The deep understanding of mechanism of CO adsorption, coupling, mixed and
dissociation on different iron carbide surfaces will benefit to design
iron-based Fischer-Tropsch synthesis reaction catalyst.
Acknowledgments
This work was supported by National Science Foundation of
Henan Province (grant No. 162300410001) and Natural Science
Foundation of Shaanxi University of Technology (No. SLGQD201713).
Supporting Information: The computed less stable adsorption,
dissociation and coulpling configurations of CO on Fe2 C(001) surface. This material is available free of charge via the Internet at
Appendix A. Supplementary data
Supplementary data associated with this article can be found,
in the online version, at https://doi.org/10.1016/j.apsusc.2017.10.
225.
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