Adsorption and Reaction of Surface Carbon Species on Fe5C2(001)

Aug 28, 2008 - dFe-C (Å). 1.809. 1.819. 1.801. 1.794. 1.897. 1.824. 1.806. 1.967. 1.957. 1.838. 1.836. 1.965. 1.969. 2.146. Figure 2. Surface C adsor...
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J. Phys. Chem. C 2008, 112, 14883–14890

14883

Adsorption and Reaction of Surface Carbon Species on Fe5C2(001) Dong-Bo Cao,† Yong-Wang Li,† Jianguo Wang,† and Haijun Jiao*,†,‡ State Key Laboratory of Coal ConVersion, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan, 030001, People’s Republic of China, and Leibniz-Institut fu¨r Katalyse e.V. an der UniVersita¨t Rostock, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany ReceiVed: April 17, 2008; ReVised Manuscript ReceiVed: July 10, 2008

The adsorption and reaction of carbon atoms on the Fe5C2(001) surface have been computed at four different levels of density functional theory. The formation of surface carbon clusters, carbon chains, and graphitic carbon is favored thermodynamically, and graphitic carbon is the final surface product. With hydrogen available on the surface, however, surface carbon hydrogenation (C + H) is more favored kinetically over its coupling reaction (C + C), and surface CH should be the most favorable species. 1. Introduction In Fischer-Tropsch synthesis (FTS), the key factors, which influence the catalyst activity, are the reactions of the highly reactive carbon species on the catalyst surface. At least three reaction channels are proposed:1 (i) Diffusion of carbon atoms into metal to form bulk carbides. On iron-based catalysts, formation of iron carbides is very important for a stable FTS operation, and transmission electron microscopy, X-ray analysis, and Mo¨ssbauer spectroscopy indicate that the highly dispersed Fe5C2 is responsible for the high FTS activity.2 (ii) Interaction of surface carbon with hydrogen to form C1 intermediates, which can form high hydrocarbons by polymerization or CH4 by hydrogenation.3 (iii) Formation of polymeric carbon or graphitic carbon.4 Temperature-programmed hydrogenation and Mo¨ssbauer spectroscopy studies on FePtK/SiO2 catalysts showed four carbonaceous species in FTS: (a) atomic carbon; (b) polymerized hydrocarbon or disordered polymeric carbon; (c) bulk carbides (Fe2.2C and Fe2.5C); and (d) graphitic carbon.5 Among these carbonaceous species, steady-state activity of iron catalysts is much correlated with iron carbides.5a Competition between hydrogenation of the reactive surface carbon and its conversion to surface polymeric carbon or graphite carbon over iron carbide surfaces determines the catalyst lifetime.1 Therefore it is of primary importance to understand the formation mechanism of these carbonaceous species on iron carbide surfaces. CHx species are key intermediates in FTS. Surface CH and CH2 were observed by high-resolution electron-energy-loss spectroscopy on Fe(110).6 Surface CH, CH2, and CH3 intermediates were observed by secondary-ion mass spectroscopy over a Ni(111) methanation catalyst.7 Among these surface species over nickel catalysts, surface CH is the most abundant intermediate by multiple isotope tracing.7 Although hydrogenation reaction of carbon atom has been investigated on various transition metal surfaces extensively, the scheme about the ratedetermining step is still controversial. Hayes et al.8 used computer enhanced multiple reflectance infrared method to investigate the mechanism of CO hydrogenation on Ni catalysts, and proposed the rate determining step to be probably the C + H f CH step. Agnelli et al.9 used steady state isotopic transient * To whom correspondence should be addressed. E-mail: haijun.jiao@ catalysis.de. † Chinese Academy of Sciences. ‡ Leibniz-Institut fu ¨ r Katalyse e.V. an der Universita¨t Rostock.

kinetic analysis techniques to study CO methanation and proposed the rate-determining step to be CH + H f CH2. Geerlings et al.10 studied FTS reaction on Co(0001) and proposed the last hydrogenation step (CH3 + H f CH4) to be rate-determining. Sorescu11 studied hydrogenation reaction of carbon atom on Fe(100) surface by using density functional theory (DFT) and found that the CH2 + H f CH3 step has the highest activation energy among the four hydrogenation reactions. Deactivation of catalysts by carbonaceous deposits is a serious problem in FTS and many other important catalytic processes. Studying deactivation mechanism is important for investigating catalyst activity. The coupling of surface carbon atoms can lead to the formation of graphitic carbon, which can deactivate the surfaces. On the other hand, hydrogenation of surface carbon atoms can result in formation of surface CHx species and hydrocarbons. However, it is rather difficult to characterize the structure and formation mechanism of small carbon clusters experimentally. Only a few studies focused this topic. Kalibaeva et al.12 calculated carbon deposition over the Ni(111) surface by using free energy DFT and found that the stable state of the nickel/carbon surface to be either a clean nickel surface or a fully carbon covered nickel surface with a graphitic configuration. The relative stability of the two states depends on the temperature and partial pressure of the carbon gas. At fixed nominal carbon coverage, the most stable configurations are those forming carbon clusters. Wang et al.13 calculated the structures of C2, C3, C4 clusters and graphitic carbon on Ni(111) by using DFT method and found the stability order as graphitic carbon monolayer > C in Ni bulk > carbon chain > small cluster > atomic carbon and the Ni(111) surface reconstructs at 0.75 and 1 monolayer. It is also found that carbon diffusion of surface into bulk needs high barriers. Xu and Saeys14 found that carbon diffusion from surface layer to bulk is thermodynamically favorable, but kinetically limited. The objective of this work was the understanding of the deactivation mechanism of Fe5C2(001) surface on the basis of the formation of surface carbonaceous species and surface CHx species. Section 2 describes the computational methodology. Section 3.1 shows the adsorption properties of carbon atoms, small carbon clusters, and graphitic carbon at various coverages by using CASTEP and VASP programs. The adsorption properties of CHx species on Fe5C2(001) were presented in Section 3.2. The reaction mechanism of carbon atom metha-

10.1021/jp803326k CCC: $40.75  2008 American Chemical Society Published on Web 08/28/2008

14884 J. Phys. Chem. C, Vol. 112, No. 38, 2008 nation and small carbon cluster formation were discussed in Section 3.3. Finally, Section 4 summarized the main conclusion.

Cao et al. TABLE 1: Cell Parameters and Average Magnetic Moment (µB, unit) of Fe5C2 with Different Methods (a, b, c) (Å)

β (°)

µB

(11.562, 4.574, 5.059) (11.522, 4.731, 5.042) (11.395, 4.408, 4.909) (11.586, 4.419, 4.981) (11.466, 4.450, 4.927) (11.451, 4.456, 4.941) (11.522, 4.499, 4.981)

97.74 97.98 99.56 99.00 97.49 97.56 97.68

1.72-1.75 1.98 1.61 1.74 1.69 1.76 1.87

Fe5C2 cell

2. Methods and Models Carbon atom hydrogenation and the respective coupling were computed at the levels of DFT by using Vienna ab initio simulation package (VASP)15 and Cambridge sequential total energy package (CASTEP).16 For both VASP and CASTEP, the Kohn-Sham one-electron states were expanded in a plane wave basis set up to 340 eV. Brillouin zone integration was approximated by a sum over special k-points chosen using the Monkhorst-Pack scheme,17 according to k-point spacing of ∼0.04 Å-1 in all lattice directions, except for the surface normal direction with a single k-point. The pseudopotential with partial core was used in spin-polarized calculations to include nonlinear core corrections.18 Spin polarization was used to calculate the energies and structures of isolated CHx. Without counting the adsorbate, the vacuum of the slabs was set to span a range of 10 Å to ensure no significant interaction between the slabs. For VASP, the convergence criteria for structure optimization and energy calculation were set to the following: (a) SCF tolerance of 1.0 × 10-4 eV; (b) energy tolerance of 1 × 10-3 eV; and (c) force tolerance of 0.03 eV/Å. For CASTEP, the convergence criteria for structure optimization and energy calculation were set to the following: (a) SCF tolerance of 2.0 × 10-6 eV/atom; (b) energy tolerance of 2.0 × 10-5 eV/atom; (c) displacement tolerance of 2.0 × 10-3 Å; (d) force tolerance of 0.03 eV/Å. The vibrational frequencies of adsorbed surface species and transition states were calculated by VASP. This was done with the frozen phonon mode approximation in which the metal atoms are fixed at the relaxed geometries. Due to the large mass difference between Fe and surface carbon species, the vibrations of Fe atoms can be neglected. The Hessian matrix was determined based on a finite difference approach with a step size of 0.024 Å for the displacements of the individual atoms of the adorbate along each Cartesian coordinate. By diagonallization of the mass-weighted Hessian matrix, the corresponding frequencies and normal modes have been determined. The activation energies for carbon hydrogenation and the respective coupling reactions were done by using the nudged elastic band method of VASP.19 In this approach, the reaction path is discretized with the discrete configurations or images between minima being connected by elastic springs to prevent the images from sliding to the minima in the optimization. For comparison, the activation energies for these reactions were also done by using the complete LST/QST20 method of CASTEP. It starts with linear synchronous transit (LST) maximization, followed by energy minimization in directions conjugate to the reaction pathway. These approximated TS are then used to perform quadratic synchronous transit (QST) maximization. From that point, another conjugate gradient minimization is performed. The cycle is repeated until a stationary point is located. The difference between VASP and CASTEP is that the optimized structures can be characterized by frequency calculations with VASP, while it is technically not possible with CASTEP. It is noteworthy that VASP and CASTEP can give the same results as discussed in a later section. The cell parameters of Ha¨gg iron carbide (Fe5C2), calculated with projector augmented wave (PAW)21 in VASP and ultrasoft pseudopotential (USPP)22 in VASP and CASTEP, are listed in Table 1. For the experimental data, lattice parameters are taken from X-ray diffraction,23 and the magnetic moment is the range of an average over all Fe atoms.24 It shows clearly that the calculated cell parameters and magnetic moment are very close

experimenta VASP-USPP-PW91 VASP-PAW-PW91 VASP-PAW-PBE CASTEP-USPP-PW91 CASTEP-USPP-PBE CASTEP-USPP-RPBE a

References 22 and 23.

Figure 1. Schematic top (T), front (F) and side (S) views of Fe5C2(001) in a p(1 × 1) unit cell (purple, Fe atom; black, C atom).

to each other and they are in reasonable agreement with the experimental values. On the basis of these agreements, VASP-PAW-PBE results are used for discussion, and the data by other methods were given for comparison. For characterizing the nature of the optimized structures, frequency analysis with VASP-PAW-PBE was performed, and this is presented the Supporting Information. If not otherwise mentioned, the optimized structures are true energy minimum states with only real frequencies and the optimized transition structures are authentic maximum states with only one imaginary frequency on the potential energy surface. As shown in the side view of Fe5C2(001) in Figure 1, we used a model system with five iron layers and three carbon layers (5Fe/3C), in which the bottom two iron layers and two carbon layers (2Fe/2C) are fixed in their bulk positions, while the three iron layers and one carbon layer on the top (3Fe/1C) can relax. The top layer of Fe5C2(001) has both Fe and C in 1 to 1 ratio, while the second and third layers contain only Fe atoms. A model system with seven iron layers and three carbon layers (7Fe/3C) under the relaxation of the top four iron layers and two layer carbon layers (4Fe/2C) was tested, and the difference in adsorption energy of the most stable carbon atom (1a) is 0.03 eV, validating the applicability of the thin model. Since there are carbon atoms on the top layer of Fe5C2(001), and Stockwell et al.25 verified with 13C traces that surface carbons of carbide catalysts are incorporated in the FTS products, surface carbon hydrogenation was studied in this work. For the adsorbed carbon atoms, clusters, and graphitic carbon at different coverage, the average adsorption energy is defined

Surface Carbon Species on Fe5C2(001)

J. Phys. Chem. C, Vol. 112, No. 38, 2008 14885

TABLE 2: Surface C Adsorption at 1/5 ML Coverage on Fe5C2(001) (VASP-PAW-PBE) species

1a

1b

1c

1d

Eads (eV) dFe-C (Å)

-7.83 1.809 1.897 1.957 1.969

-7.16 1.819 1.824 1.838

-6.96 1.801 1.806 1.836

-6.97 1.794 1.967 1.965 2.146

as ∆Eads ) (1/n)[E(n-absorbate/slab′) - E(slab′)] - E(absorbate), where E(absorbate/slab′) is the total energy for the slabs excluding surface carbon atom with adsorbate formed on the surface, E(slab′) is the total energy of the slab excluding surface carbon atom, E(absorbate) is the total energies of free absorbate, n is the number of adsorbate. The repulsive interaction between the coadsorbed species is defined as: Er ) (EA + EB) - (E(slab′) + E(A+B)). The energy barrier for activation between reactant and transition state is defined as: ∆E ) ETS - (EA + EB). 3. Results and Discussion 3.1. Carbon Adsorption. Surface carbonaceous species were calculated at different monolayer coverage (ML) on Fe5C2(001). At 1/5 ML, the computed adsorption energies and bond parameters are shown in Table 2 and the optimized structures are shown in Figure 2. Four adsorbed sites are found, where surface C atoms (Cs) are absorbed at 4-fold site (1a), 3-fold site (1b), 3-fold site (1c), and 4-fold site (1d). Surface C atom prefers binding at 4-fold sites (1a) with adsorption energy of -7.83 eV. Compared with C adsorption on Fe(100) and Fe(110) by Jiang et al.,26 the adsorption energies of the most stable 4-fold

Figure 2. Surface C adsorption at 1/5 ML coverage on Fe5C2(001) (purple, Fe atom; black, C atom; Cs for surface carbon atom).

TABLE 3: Average Adsorption Energies and Bond Parameters of Carbon Species at Different Coverage (ML) (VASP-PAW-PBE) ML

Eads (eV)

dC-C (Å)

C2(a) C2(b) C3

2/5 2/5 3/5

-7.77 -7.26 -7.74

C4(a)

4/5

-7.40

C4(b)

4/5

-7.17

chain

1

-7.34

graphitic

8/5

-7.39

dC1-C2 dC1-C2 dC1-C2 dC2-C3 dC1-C2 dC2-C3 dC3-C4 dC1-C2 dC1-C3 dC1-C4 dC1-C2 dC2-C3 dC2-C4 dC4-C5 dC5-C3 dC1-C2 dC2-C3 dC3-C4 dC3-C5 dC5-C6 dC6-C7 dC7-C1 dC7-C8

1.367 1.403 1.350 1.350 1.352 1.398 1.372 1.500 1.477 1.451 1.506 1.402 1.408 1.426 1.415 1.407 1.447 1.373 1.378 1.411 1.445 1.403 1.400

site and long-bridge sites at 1/4 ML are -8.24 and -7.77 eV, respectively. Sorescu11 calculated C adsorption on Fe(100), the adsorption energy of 4-fold site is -8.07 eV at 1/4 ML. With increased coverage, small carbon clusters are possible to form. Thus, we further discuss the formation and stability of these carbon clusters, carbon chain, and graphitic carbon on Fe5C2(001). The calculated adsorption energies of small carbon clusters, chain, and graphitic carbon are listed in Table 3, and the optimized structures are shown in Figure 3. For the adsorbed C2 cluster, two stable structures C2(a,b) are obtained at 2/5 ML, and the two carbon atoms are adsorbed at 3- and 4-fold sites. C2(a) is more stable than C2(b) by 0.51 eV. For C3 cluster adsorption at 3/5 ML, two carbon atoms are adsorbed at 3-fold sites, and one is adsorbed at 2-fold sites. The average adsorption energy of C3 is -7.74 eV. For C4 cluster adsorption at 4/5 ML, two absorbed forms are obtained C4(a,b). C4(a) has a linear structure, and C4(b) has a triangular structure. For C4(a), the four carbon atoms are absorbed at 3-fold sites. For C4(b), the middle carbon atom is adsorbed at 2-fold site, while the two terminal carbon atoms are adsorbed at 3-fold sites, and one terminal carbon atom is adsorbed at 2-fold sites. The adsorption energy of C4(a) is -7.40 eV, which is 0.23 eV higher than that of C4(b). For adsorbed carbon chain at 1 ML, five atoms are put into a p(1 × 1) unit cell. Two carbon atoms are adsorbed at top sites, and one carbon atom is adsorbed at 2-fold site, as well as two carbon atoms are adsorbed at 3-fold sites. The average adsorption energy of chain is -7.34 eV. For graphitic carbon adsorption at 8/5 ML, and eight atoms are put into a p(1 × 1) unit cell. Among the eight carbon atoms, four bind with the Fe atoms on the top sites, the other four do not. DFT calculations on graphitic carbon on the Ni(111) surface also result in similar geometries.12,13 The average adsorption energy of graphitic is -7.39 eV. The size effects of the unit cell (surface coverage) to the lateral relaxation of the adsorbed carbon clusters, chain, and graphitic have been tested by the p(1 × 2) and p(2 × 1) unit cell models, as listed in Table 4. The adsorption energies and

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Figure 3. Surface carbon clusters, chain, and graphitic adsorption on Fe5C2(001) (purple, Fe atom; black, C atom).

TABLE 4: Size Effect of Unit Cell on the Lateral Relaxation of the C2, C3, C4, Chain, and Graphitic Carbon at Different Coverage (ML) (VASP-PAW-PBE) p(1 × 2) ML Eads (eV) C2(a) C2(b) C3 C4(a)

1/5 1/5 3/10 2/5

-7.78 -7.33 -7.62 -7.38

C4(b)

2/5

-7.33

chain

dC-C (Å)

TABLE 5: Comparison of Average Adsorption Energy of Carbon Cluster, Chain, Graphitic with That of Dispersed Carbon Atoms (VASP-PAW-PBE)

p(2 × 1) ML Eads (eV) -7.67 -7.18 -7.55 -7.24

1/2

1.370 1/5 1.429 1/5 1.345, 1.353 3/10 1.371, 1.389 2/5 1.366 1.459, 1.495 2/5 1.479 1/2

graphitic 4/5

4/5

-7.31

-7.22 -7.26

dC-C (Å) 1.369 1.406 1.339, 1.352 1.346, 1.408 1.382 1.465, 1.470 1.456 1.484, 1.394 1.395, 1.421 1.413 1.397, 1.455 1.379, 1.380 1.397, 1.476 1.397, 1.399

C-C bond length with p(1 × 2) and p(2 × 1) unit cell models are similar with those of p(1 × 1) unit cell models. Since carbon clusters, chains, and graphitic carbon are formed by dispersed carbon atoms coupling, the comparison of average adsorption energies of carbon clusters, chain, and graphitic carbon with those of the same number carbon atoms coadsorption are listed in Table 5. The C2 cluster is formed by the coupling reaction of two separately adsorbed carbon atoms (1a and 1b). Without considering the lateral interaction between the coadsorbed 1a and 1b, the average adsorption energy of C2 is 0.27 eV higher than that of the two separately adsorbed carbon atoms (1a and 1b), indicating that the reaction of C2 formation by C-C coupling is exothermal. Similarly, the average adsorption energies of C3, C4, chain, and graphitic carbon are all higher than those of the same number separately adsorbed carbon atoms. As a result, the reactions of C3, C4, chain, and graphitic carbon formation by coadsorbed carbon atoms are all exothermal. It is to conclude that graphitic carbon formation is favored thermodynamically. It also agrees with the experiments, in which

species

Eads (eV)

C2(a) C3 C4(a) chain graphitic

-7.77 -7.74 -7.40 -7.34 -7.39

1/n (ΣCi) 1/2 (1a + 1b) 1/3 (1a + 1b + 1/4 (1a + 1b + 1/5 (1a + 1b + 1/8 (1a + 1b + 1d + 1b + 1c

∆E (eV)

Eads (eV)

-7.50 1c) -7.32 1c + 1b) -7.28 1c + 1b + 1d) -7.22 1c + 1b + -7.17 + 1b)

-0.27 -0.42 -0.12 -0.12 -0.22

TABLE 6: CH Adsorption on Fe5C2(001) at 1/5 ML Coverage (VASP-PAW-PBE). 2a 2b 2c 2d

Eads (eV)

dFe-C (Å)

dC-H (Å)

-7.29 -6.80 -6.59 -6.54

1.918, 1.994, 2.010, 2.084 1.852, 1.888, 2.017 1.963, 1.978, 2.043, 2.220 1.919, 1.921, 1.923

1.108 1.103 1.107 1.109

surface carbon atoms are converted to disordered polymeric carbon or graphitic multilayer-island in the absence of hydrogen on iron-based catalysts in FTS, which lead to the deactivation of catalysts.5a,27 3.2. CHx (x ) 1-4) Adsorption. Four adsorbed sites for CH are found at 1/5 ML, 2a-d. The adsorption energies and bond parameters are listed in Table 6, and the structures are shown in Figure 4. For 2a-d, CH is adsorbed at 4-fold, 3-fold, 4-fold, and 3-fold sites, respectively. The adsorption energy of 2a is the highest with -7.29 eV. The stretching frequency of the most stable 2a is 2940 cm-1. The vibrational frequencies of CH on Fe(100),28 Fe(111),29 and Fe(110)30 are 2840, 2850, and 2940 cm-1, respectively, by high-resolution electron-energyloss spectroscopy measurements. Five adsorbed structures for CH2 are obtained at 1/5 ML, 3a-e. The adsorption energies and bond parameters are listed in Table 7, and the structures are shown in Figure 5. For 3a-e, CH2 is adsorbed at 4-fold, 3-fold, 3-fold, 2-fold, and 3-fold,

Surface Carbon Species on Fe5C2(001)

J. Phys. Chem. C, Vol. 112, No. 38, 2008 14887

Figure 4. Surface CH adsorption on Fe5C2(001) at 1/5 coverage (purple, Fe atom; black, C atom; white, H atom; Cs for surface carbon atom).

TABLE 7: CH2 Adsorption on Fe5C2(001) at 1/5 ML Coverage (VASP-PAW-PBE) 3a 3b 3c 3d 3e

Eads (eV)

dFe-C (Å)

dC-H (Å)

-4.50 -4.28 -4.26 -4.05 -4.01

1.970, 2.041, 2.076, 2.162 1.981, 1.986, 2.039 1.989, 2.032, 2.180 1.926, 1.966 2.022, 2.114, 2.134

1.120, 1.200 1.105, 1.167 1.112, 1.127 1.107, 1.110 1.108, 1.110

respectively. The adsorption energy of 3a is the highest with -4.50 eV. The stretching frequencies of 3a, 3b, and 3c are 2771, 2935, and 2890 cm-1, corresponding to 2980 cm-1 of those of CH2 on Fe(111)29 and 2960 cm-1 on Fe(110).30 There are two adsorbed forms for CH3 at 1/5 ML, 4a-b. The adsorption energies and bond parameters are listed in Table 8, and the structures are shown in Figure 6. For 4a and 4b, CH3 are adsorbed at 2-fold sites, and the adsorption energy of 4a is -2.22 eV, which is 0.31 eV higher than that of 4b. For CH4 (5), the adsorption energy and bond parameters are also listed in Table 8, and the structure is shown in Figure 6. The adsorption energy is only -0.02 eV, indicating free CH4 on the surface. 3.3. Hydrogenation and C-C Coupling. Due to the competition between the hydrogenation of the reactive carbon and its conversion to surface polymeric carbon or graphite carbon, we investigate the thermodynamic and kinetic properties of C-C coupling and hydrogenation reactions on Fe5C2(001). The energy barrier and enthalpy change of C-C coupling and hydrogenation reactions are listed in Table 9. The structure of transition states

Figure 5. Surface CH2 adsorption on Fe5C2(001) at 1/5 coverage (purple, Fe atom; black, C atom; white, H atom; Cs for surface carbon atom).

TABLE 8: CH3 and CH4 Adsorption on Fe5C2(001) at 1/5 ML Coverage (VASP-PAW-PBE) 4a 4b 5

Eads (eV)

dFe-C (Å)

dC-H (Å)

-2.22 -1.91 -0.02

2.059, 2.224 2.022, 2.306 3.812

1.103, 1.113, 1.124 1.105, 1.108, 1.135 1.100, 1.100, 1.100, 1.105

are shown in Figure 7, and the bond parameters are listed in Table 10. The frequency analysis of the transition states is given in Supporting Information. It is interesting to note that the computed kinetic and thermodynamic parameters with VASP and CASTEP are very close and these indicate that computed energetic and geometric parameters of the transition states with the LST/QST method in CASTEP are reasonable and reliable, despite that fact that CASTEP can not perform frequency calculation to characterize nature of the optimized states.

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Figure 6. Surface CH3 and CH4 adsorption on Fe5C2(001) at 1/5 coverage (purple, Fe atom; black, C atom; white, H atom; Cs, surface carbon atom).

TABLE 9: The Energy Barriers of Forward Reactions (∆Ef) and Reversed Reactions (∆Er) and Reaction Enthalpies (∆H) for Carbon Hydrogenation and Coupling Reactions on Fe5C2(001) reactions C + C f C2

methods VASP CASTEP

C + H f CH

VASP CASTEP

CH + H f CH2

VASP CASTEP

CH2(3a) f CH2(3d) VASP CASTEP CH2 + H f CH3

VASP CASTEP

CH3 + H f CH4

VASP CASTEP

PAW-PBE USPP-PW91 USPP-PBE USPP-PW91 PAW-PBE USPP-PW91 USPP-PBE USPP-PW91 PAW-PBE USPP-PW91 USPP-PBE USPP-PW91 PAW-PBE USPP-PW91 USPP-PBE USPP-PW91 PAW-PBE USPP-PW91 USPP-PBE USPP-PW91 PAW-PBE USPP-PW91 USPP-PBE USPP-PW91

∆Ef ∆Er (eV) (eV) 1.34 1.27 1.31 1.28 0.79 0.76 0.54 0.53 0.87 0.89 0.88 0.92 0.49 0.44 0.62 0.55 0.45 0.44 0.54 0.54 1.09 1.05 1.24 1.30

1.88 1.89 2.00 1.97 1.01 1.07 0.78 0.76 0.13 0.12 0.11 0.14 0.04 0.09 0.08 0.06 0.84 1.04 0.83 0.84 0.79 0.91 0.85 0.86

∆H (eV) -0.54 -0.62 -0.69 -0.69 -0.22 -0.31 -0.22 -0.23 0.74 0.77 0.77 0.78 0.45 0.35 0.54 0.49 -0.39 -0.60 -0.29 -0.30 0.30 0.14 0.39 0.44

For C-C coupling reactions, the coadsorbed two carbon atoms are optimized at 2/5 ML in a p(1 × 1) unit cell. The lateral interaction of coadsorbed two carbon atoms is 0.17 eV.

Without considering the lateral interaction, the energy barrier for the most stable C2(a) formation is 1.34 eV, and this reaction is exothermic by 0.54 eV. In TS(C/C2(a)), one carbon atom diffuses from 3-fold (reactant) to 2-fold sites, the other carbon atom keeps in the 4-fold sites, and the C-C distance is 2.144 Å. TS(C/C2(a)) has an imaginary frequency at 331 cm-1. For the first hydrogenation step, the most stable configuration is the coadsorption of 3-fold H atom and 4-fold C (1a). There are two 3-fold sites for added H atom (H and H′), and their energy difference is only 0.06 eV based on CASTEP-USPPPBE.31 On the basis of their similar local structures, hydrogen migration from H to H′ is very easy.31 There is no lateral interaction for coadsorbed H and C atoms. In TS(1a/2a), H is adsorbed at top sites, and the Fe-H and C-H distances are 1.575 and 1.584 Å, respectively, and the imaginary frequency is at 964 cm-1. For CH (2a) formation, the energy barrier is 0.79 eV without considering the lateral interaction, and this step is exothermic by 0.22 eV. Compared with C-C coupling reaction, the energy barrier of hydrogenation is lower by 0.55 eV. Consequently, C2 cluster formation is rather difficult kinetically if there are H atoms on the Fe5C2(001) surface. This agrees with the experimental studies on silica-supported iron FTS catalysts, which indicate that surface carbon atoms are converted to disordered polymeric carbon in the absence of hydrogen, which lead to the deactivation of catalysts.5a This also implies that Fe5C2(001) has long catalyst lifetime if H atoms exist on surfaces. On this basis, the kinetic studies of C3, C4, chain, and graphitic carbon formation are not considered further. For the second hydrogenation step, the most stable configuration is the coadsorption of 3-fold H atom and 4-fold CH (2a). The repulsive interaction of coadsorbed H and CH atoms is 0.06 eV. For CH2 (3a) formation, the energy barrier is 0.87 eV without considering the lateral interaction, and this step is endothermic by 0.74 eV. In TS(2a/3a), H is adsorbed at both top sites, and the Fe-H and C-H distances are 1.620 and 1.249 Å, respectively; the imaginary frequency is at 129 cm-1. For the third hydrogenation step, CH2 diffuses from 4-fold site (3a) to 2-fold site (3d) and then is hydrogenated. The energy barrier of diffusion is 0.49 eV, and this step is endothermic by 0.45 eV. In TS(3a/3d), CH2 is adsorbed at 3-fold sites, and the imaginary frequency is at 299 cm-1. For 3d hydrogenation, the lateral interaction of coadsorbed 3-fold H′ and CH2 species is 0.02 eV. This reaction has an energy barrier of 0.45 eV and is exothermic by 0.39 eV. In TS(3d/4a), H is adsorbed at top sites, and the Fe-H and C-H distances are 1.545 and 1.906 Å, respectively; the imaginary frequency is at 532 cm-1. For the last hydrogenation step, the most stable configuration is the coadsorption of 3-fold H atom and 2-fold CH3 (4a). The lateral interaction of coadsorbed H and CH3 species is 0.26 eV. For CH4 (5) formation, the energy barrier is 1.09 eV without considering the lateral interaction, and this step is endothermic by 0.30 eV. In TS(4a/5), CH3 and H are also adsorbed at top site, and the Fe-C and Fe-H distances are 2.157 and 1.616 Å, respectively; the imaginary frequency is at 724 cm-1. Thus, the last hydrogenation step is the rate determining step on Fe5C2(001). This differs from carbon hydrogenation on Fe(100), where the third hydrogenation step (CH2 + H f CH3) has the highest energy barrier (0.82 eV), while the energy barriers of other three hydrogenation steps are 0.72 eV of the first step (C + H f CH), 0.71 eV of the second step (CH + H f CH2), and 0.50 eV of the last step (CH3 + H f CH4).11 Due to lower energy barrier of rate determining step on Fe(100) than that on Fe5C2(001), CH4 is easier formed on Fe(100), in line with the high yield of CH4 on iron surfaces in FTS.32

Surface Carbon Species on Fe5C2(001)

J. Phys. Chem. C, Vol. 112, No. 38, 2008 14889

Figure 7. The structures of transition states of carbon hydrogenation and coupling reactions on Fe5C2(001) (purple, Fe atom; black, C atom; white, H atom; Cs for surface carbon atom).

TABLE 10: The Bond Parameters (Å) of Transition States of Carbon Hydrogenation and Coupling Reactions on Fe5C2(001) (VASP-PAW-PBE) TS

dFe-C

TS(C/C2(a))

1.778, 1.781 1.849, 1.861 1.944, 2.033 1.842, 1.893 1.957, 1.983 1.955, 2.005 2.100, 2.212 1.916, 1.998 2.263 1.941, 1.976 2.157

TS(1a/2a) TS(2a/3a) TS(3a/3d) TS(3d/4a) TS(4a/5)

dFe-H

dC-H

dC-C 2.144

1.575

1.584

1.620

1.101, 1.249 1.106, 1.113

1.545 1.616

1.107, 1.110 1.906 1.095, 1.104 1.109, 1.692

Since C-C coupling has a higher energy barrier than C hydrogenation by 0.55 eV, formation of polymeric carbons is not possible under hydrogen atmosphere; suggesting that H2 partial pressure is important for catalyst activity during pretreatment and reaction in FTS. Both kinetic and thermodynamic parameters (Table 9) show that CH should be the dominant surface species. Since CHx hydrogenation to CH4 and chain growth from CHx + CHx coupling to high hydrocarbons are competitive, the selectivity of CHx + CHx coupling reaction over CH4 formation should provide the insights into FTS mechanism; this directs our next research work.

CH4 is not adsorbed. The hydrogenation steps of C and CH2 to form CH and CH3, respectively, are exothermic, while those of CH and CH3 to form CH2 and CH4, respectively, are endothermic. Both CH and CH3 are the most stable surface species. Hydrogenation and coupling reaction of surface carbon are competitive and their selectivity will determine the formation of the preferred intermediates, and the reaction mechanisms. The C-C coupling reaction of surface carbon is more favored thermodynamically on the competitive hydrogenation (-0.54 versus -0.22 eV, respectively); however, the hydrogenation step is more favored kinetically over the coupling step (0.79 versus 1.34 eV, respectively). The chemical consequence is that surface hydrogen will hinder C-C coupling reaction and prevent deactivation of Fe5C2(001). Acknowledgment. This work was supported by Chinese Academy of Sciences and the National Nature Foundation of China, the National Outstanding Young Scientists Foundation of China (20625620), National Key Basic Research Program of China (973 Program, 2007CB216401). This work is also supported by Synfuels CHINA. Co., Ltd. Supporting Information Available: The computed bond parameters and energetic data with VASP-PAW-PBE, VASPUSPP-PW91, CASTEP-USPP-PBE, and CASTEP-USPP-PW91 have been summarized. The frequency analysis of optimized structure and transition states is also given. This material is available free of charge via the Internet at http://pubs.acs.org.

4. Conclusion The hydrogenation and the respective C-C coupling reactions of carbon species on the Fe5C2(001) surface were investigated at the levels of density functional theory by using both CASTEP and VASP programs. It shows those four different functional methods, i.e., PAW-PBE and USPP-PW91 with VASP, and USPP-PBE and USPP-PW91 with CASTEP, can give very close structural as well as kinetic and thermodynamic parameters. It is therefore confident to use each of these methods for our computations. It is found that the most stable adsorbed site of surface carbon atom at 1/5 ML is 4-fold site. Stable structures of adsorbed carbon clusters (C2, C3, C4), carbon chain, and graphitic carbon at various coverage are obtained, and their formations are exothermal and favored thermodynamically. For surface CHx (x ) 1-4), the most stable adsorbed sites is 4-fold site for CH, 4-fold site for CH2, 2-fold site for CH3, while

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