Density Functional Theory Study of Iron and Cobalt ... - ACS Publications

J. Phys. Chem. C 2010, 114, 1085–1093

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Density Functional Theory Study of Iron and Cobalt Carbides for Fischer-Tropsch Synthesis Jun Cheng and P. Hu* School of Chemistry, The Queen’s UniVersity of Belfast, Belfast BT9 5AG, United Kingdom

Peter Ellis,† Sam French,† Gordon Kelly,‡ and C. Martin Lok‡ Johnson Matthey Technology Centre, Reading RG4 9NH, United Kingdom and Billingham CleVeland, TS23 1LB, United Kingdom ReceiVed: September 2, 2009; ReVised Manuscript ReceiVed: NoVember 23, 2009

Carbides are important phases in heterogeneous catalysis. However, the understanding of carbide phases is inadequate: Fe and Co are the two commercial catalysts for Fischer-Tropsch (FT) synthesis, and experimental work showed that Fe carbide is the active phase in FT synthesis, whereas the appearance of Co carbide is considered as a possible deactivation cause. To understand very different catalytic roles of carbides, all the key elementary steps in FT synthesis, that is, CO dissociation, C1 hydrogenation, and C1+C1 coupling, are extensively investigated on both carbide surfaces using first principles calculations. In particular, the most important issues in FT synthesis, the activity and methane selectivity, on the carbide surfaces are quantitatively determined and analyzed. They are also discussed together with metallic Fe and Co surfaces. It is found that (i) Fe carbide is more active than metallic Fe and has similar methane selectivity to Fe, being consistent with the experiments; and (ii) Co carbide is less active than Co and has higher methane selectivity, providing evidence on the molecular level to support the suggestion that the formation of Co carbide is a cause of relatively high methane selectivity and deactivation on Co catalysts. 1. Introduction The Fischer-Tropsch (FT) synthesis1-10 has recently received a renewed interest in both industry and academia because it produces hydrocarbons (i.e., fuels and chemicals) from noncrude oil supplies such as natural gas, coal, and biomass. Stringent environmental regulations and the rising price of crude oil are rendering FT synthesis more economically attractive for many applications. Only Fe, Co, Ru, and Ni have sufficient activity in FT synthesis for industrial applications. However, Ni is too hydrogenating, and the product is mainly methane. Ru is not currently used industrially because of its high price and low availability. These result in Fe and Co being the metals used as catalysts commercially. Fe is more than 200 times less expensive than Co, but Co is more active and more resistant to deactivation. An interesting phenomenon on Fe and Co catalysts is the different catalytic role of carbides. Under real FT reaction conditions, on Fe catalysts metallic Fe evolves to Fe carbides, such as Ha¨gg carbide (χ-Fe5C2), and many experimental results have shown that Fe carbides are the real active phase for FT synthesis.11-16 However, on Co catalysts Co mainly stays in the metallic state. The formation of Co carbide, such as Co2C, is often referred to as a sign of deactivation.17-21 It is clear that the carbide phases play very different roles in FT synthesis. Although the existence of carbide phases affects significantly FT synthesis, the following questions have long remained to be answered in the field: Why do carbides play opposite roles on Fe and Co catalysts? Is there a common physical origin * Corresponding author. † Reading. ‡ Billingham Cleveland.

behind their opposite catalytic roles? If the answer is yes, what is its implication to other catalytic reactions? It is worth mentioning that FT synthesis is one of the most complicated systems in heterogeneous catalysis mainly due to two reasons: (i) there are hundreds of elementary reactions on catalytic surfaces and they are all interconnected with each other; and (ii) both activity and selectivity are important in the catalytic system. Therefore, to obtain a comprehensive answer to the questions mentioned above, one needs to obtain a clear kinetic description of the complicated system to address both the activity and the selectivity. In this work, we extensively investigate Fe and Co carbides in the two most important aspects of FT synthesis, namely, activity and methane selectivity, and further compare them with metallic Fe and Co catalysts, aiming to answer the questions. Although some density functional theory (DFT) studies have been performed on metallic surfaces in the literature,22-28 the theoretical work focused on carbides is very rare. Some work was carried out to study surface stability of Ha¨gg29 and cementite carbide.30 A few investigations were performed for CO and H adsorption/coadsorption on Ha¨gg carbide.31-33 To the best of our knowledge, no DFT work on catalytic reactions on Fe and Co carbides has been reported in the literature despite their importance. In this work, we investigate all the key elementary reactions including CO dissociation, C1 hydrogenation, and C1+C1 coupling on Fe and Co carbides (χ-Fe5C2 and Co2C) using DFT calculations to understand their catalytic roles in FT synthesis. The paper is arranged as follows. In the next section, calculation methods will be described and the carbide surface structures will be given in detail. Following this, the calculation results of CO dissociation, C1 hydrogenation, and C1+C1

10.1021/jp908482q  2010 American Chemical Society Published on Web 12/18/2009

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Figure 1. Geometric structures of the conventional unit cell (a) and (100) plane ((b) top view and (c) side view) of Ha¨gg iron carbide. The blue box in (a) shows the cleavage position and depth to obtain the (100) plane. The purple balls are Fe atoms and the gray ones are C atoms. In (b) and (c), the Fe atoms constituting the B5 site are highlighted in red.

coupling on Fe and Co carbides will be presented in section 3. In section 4, the reactivity and CH4 selectivity of Fe and Co carbides will be analyzed and their catalytic role will also be discussed. In the last section, some conclusions will be summarized. 2. Computational Details In this work, the SIESTA code was used with TroullierMartins norm-conserving scalar relativistic pseudopotentials.34-36 A double-ζ plus polarization (DZP) basis set was utilized. The localization radii of the basis functions were determined from an energy shift of 0.01 eV. A standard DFT supercell approach with the Perdew-Burke-Ernzerhof form of the generalized gradient approximation (GGA) functional was implemented and the Kohn-Sham orbitals were expanded in a localized basis (double-ζ) set with a mesh cutoff of 180 Ry. Spin polarization was included in the calculations. Ha¨gg Fe carbide (χ-Fe5C2) has a monoclinic bulk structure (space group C2/c) with the experimental lattice constant:37 a ) 11.5620 Å, b ) 4.5727 Å, c ) 5.0595 Å, and β ) 97.74°. Our calculated lattice constant is a ) 11.7413 Å, b ) 4.6165 Å, c ) 5.0868 Å, and β ) 97.82°. The conventional unit cell, as shown in Figure 1a, was used, which contains 20 Fe atoms and 8 C atoms. It is well-known that monatomic steps containing B5 sites are the active sites for many dissociation reactions, such as CO, NO, and N2 dissociation.38-45 Our recent work also showed that step sites are preferred for C-C coupling reactions.46-48 Therefore, we employed stepped Fe5C2(100) and Co2C(001) surfaces, both of which contain B5 sites, as the models to simulate reactive sites for FT synthesis. In theory, there are 26 low Miller index planes, the index numbers of which only consist of -1, 0, and 1. Nine unique planes are enough to describe all the possibilities, and the others are equivalent to these nine planes (see ref 29 for detail). To obtain B5 sites of χ-Fe5C2, we examined all the nine types of low Miller index planes with different cleavage positions, and found that many planes with appropriate cleavage positions, such as (100), (110), (011), and (111), can achieve B5 sites. Furthermore, Steynberg

et al.29 found that the surface energies of different planes fall in a very narrow range. This suggests that many different planes of χ-Fe5C2 can coexist under reaction conditions. In this work, the (100) plane cleaved at 0.287 fractional distance from the bulk origin was chosen to investigate elementary surface reactions in FT synthesis on Ha¨gg Fe carbide. The cleavage position is illustrated in Figure 1a. Surface reactions were calculated in p(2 × 1) unit cells, and the surface was modeled by a slab with thickness of ∼5.8 Å, consisting of five layers of Fe atoms and two layers of C atoms (20 Fe atoms and 8 C atoms in total). The vacuum region between slabs was around 15 Å. The surface structure of Fe5C2(100) is shown in Figure 1b,c, and the B5 site constituted by five surface Fe atoms is highlighted in red. During the calculations, surface Monkhorst Pack meshes of 2 × 4 × 1 k-point sampling in the surface Brillouin zone were used, and the bottom two layers of Fe atoms and one layer of C atoms were fixed and the top three layers of Fe atoms, one layer of C atoms and the adsorbates were relaxed. The effect of the slab thickness was checked by comparing the C chemisorption energy on the slab with the thickness of ∼5.8 and ∼11.6 Å (see the Results for the structure). The difference is only 0.04 eV (-7.58 eV on the thin slab and -7.62 eV on the thick slab, respectively). Co carbide (Co2C) has an orthorhombic bulk structure (space group Pnnm) with the experimental lattice constant:49 a ) 2.8969 Å, b ) 4.4465 Å, and c ) 4.3707 Å. Our optimized lattice constant is a ) 2.9209 Å, b ) 4.4787 Å, and c ) 4.4107 Å. As shown in Figure 2a, one C atom is in the center of the unit cell, and eight C atoms are on the corners of the unit cell, with each C atom shared by the neighboring eight unit cells; there are two Co atoms in the unit cell and four Co atoms on the planes shared by the neighboring two unit cells. As a result, each unit cell contains two C atoms and four Co atoms. It can be seen from Figure 2b that, in bulk Co2C, each C atom binds with six Co atoms and each Co atoms binds with three C atoms. The Co-C bond length is about 1.93 Å. Interestingly, it is found that the (001) plane cleaved at 0.258 fractional distance from the bulk origin has a very similar geometry to Co(0001). In contrast to Co(0001), C atoms are embedded in between Co

DFT Study of Iron and Cobalt Carbides

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Figure 2. Geometric structures of the conventional unit cell (a), bulk structure (b), and (001) plane ((c) top view and (d) side view) of stepped cobalt carbide. The blue balls are Co atoms and the gray ones are C atoms. The Co atoms constituting the B5 site are highlighted in red.

layers. Thus, we used a similar method to the stepped Co(0001) surface46 to create monatomic steps on Co2C(001): p(2 × 2) unit cells were employed, and then two neighboring rows of Co atoms on the top layer and one row of C atoms underneath were removed. The structure of the stepped Co2C(001) is shown in Figure 2c,d. As we can see, the surface was modeled by a slab consisting of four layers of Co atoms and four layers of C atoms (28 Co atoms and 14 C atoms in total). The vacuum region between slabs was around 15 Å. The B5 site consisted of five surface Co atoms at the monatomic step is highlighted in red. During the calculations, surface Monkhorst Pack meshes of 4 × 2 × 1 k-point sampling in the surface Brillouin zone were used, the bottom two layers of Co atoms and two layers of C atoms were fixed, and the top two layers of Co atoms, two layers of C atoms, and the adsorbates were relaxed. The transition states (TSs) were searched using a constrained optimization scheme.50-52 The distance between the reactants is constrained at an estimated value and the total energy of the system is minimized with respect to all the other degrees of freedom. The TSs can be located via changing the fixed distance, and must be confirmed by the following two rules: (i) all forces on atoms vanish; (ii) the total energy is a maximum along the reaction coordinate, but a minimum with respect to the rest of the degrees of freedom. 3. Results 3.1. Reactions on Fe5C2(100). 3.1.1. CO Dissociation and H Adsorption. CO dissociation was calculated on Fe5C2(100), and the TS is shown in Figure 3a. Similar to these at other B5 sites, the C atom is on the 3-fold hollow site on the lower terrace and the O atom is on the 2-fold edge-bridge site at the TS (the detailed description of the adsorption sites around monatomic steps can be found in our previous work46). The C-O distance stretches to 2.170 Å at the TS, and the dissociation barrier is -0.76 eV with CO in the gas phase as the initial state (IS). This barrier is higher than that on corrugated Fe(210) surface (-1.16 eV53).

Figure 3. Top views and side views (inserted) of the TS of CO dissociation (a) and the H adsorption (b) on Fe5C2(100). The purple balls are Fe atoms, the gray ones are C atoms, the red ones are O atoms, and the white ones are H atoms. The Fe atoms are represented in CPK style, while the others are in ball and stick style.

H2 can readily dissociate on many transition metal surfaces, often without a dissociation barrier except on late transition metals such as Cu.54 Thus, only the adsorption of H atom on Fe5C2(100) was calculated, and the structure is shown in Figure 3b. The preferred adsorption site is a near-edge-hollow site on the upper terrace, and the adsorption energy is -2.86 eV. The adsorption energy is very similar to that on Fe(210) (-2.85 eV53). 3.1.2. Hydrogenation of C1 Species. After CO dissociation, carbon species are hydrogenated in FT synthesis. The adsorption of C1 species on Fe5C2(100) was calculated, and the structures are shown in Figure 4a-d. The most stable adsorption site for C, CH, and CH2 is the corner site, while the edge-bridge site is favored by CH3. The preferred sites of C, CH, and CH3 on Fe5C2(100) are the same as those on stepped Co(0001),55 while for CH2 it differs; CH2 prefers the edge-bridge site on stepped Co(0001). After obtaining the adsorption structures of the C1 species, the TSs of C1 hydrogenation were located, and the structures are illustrated in Figure 4e-h. As we can see, at the TSs, C atom and CH adsorb at the corner site, CH2 is on the edgebridge site, and CH3 is on the edge-top site. The geometries are similar to those on stepped Co(0001).55 The calculated

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Figure 4. Top views and side views (inserted) of the adsorption of C1 species and the TSs of C1 hydrogenation on Fe5C2(100): (a-d) show the adsorption of C, CH, CH2, and CH3. (e-h) show the TSs of the hydrogenation of C, CH, CH2, and CH3. The purple balls are Fe atoms, the gray ones are C atoms, and the white ones are H atoms. The Fe atoms are represented in CPK style, while the others are in ball and stick style.

TABLE 1: Reaction Barriers of C1 Hydrogenation and Structural Parameters at the TSs on Fe5C2(100)a reactions

dC-H (Å)

Eafor (eV)

Earev (eV)

C+HfCH CH+HfCH2 CH2+HfCH3 CH3+HfCH4

1.590 1.555 1.740 1.600

0.80 0.68 0.81 0.96

0.59 0.09 0.69 0.57

a dC-H is the distance between the reacting C and H atoms at the TS. Eafor and Earev are the barriers of the forward and reverse reactions, respectively.

forward and reverse reaction barriers (Eafor and Earev, respectively) and the distances between the reacting C and H atoms at TSs (dC-H) are given in Table 1. 3.1.3. C1+C1 Coupling Reactions. In our previous work, C1+C1 coupling reactions were extensively studied on stepped Co, Ru, Rh, Re, and Fe surfaces.47 Similar to our previous work, nine possible coupling pathways, C+C, C+CH, C+CH2, C+CH3, CH+CH, CH+CH2, CH+CH3, CH2+CH2, and CH2+CH3, were investigated. The calculated TS structures of these coupling reactions on Fe5C2(100) are illustrated in Figure 5a-i. Generally, these TS structures are very similar to those on the stepped metal surfaces,47 which are consistent with the rule proposed by Michaelides and Hu:56 The higher the valency of the adsorbate, the greater its tendency to access a TS close to a high coordination site. As can be seen from Figure 5a-i, at the TSs, C and CH are usually on the high coordination sites (the 4-fold corner site and 3-fold hollow site on the lower terrace), and CH2 and CH3 are on the edge-bridge site, except that CH3 is on the off-top site at the TS of the CH2+CH3 coupling. The calculated coupling barriers (Ea) and the C-C distances at the TSs (dC-C) are listed in Table 2. In line with our previous finding47 that dC-C is similar on different surfaces for each coupling reaction, dC-C on Fe5C2(100) is also similar to those on the stepped metal surfaces. The dC-C is usually about 2 Å, except for C+C and C+CH coupling in which it is longer. Regarding the coupling barriers, there is no such similarity. Compared to the barriers on Fe(210), the coupling reactions of C+C, C+CH3, CH+CH, and CH+CH3 have very similar barriers, while the rest are different. 3.2. Reactions on Stepped Co2C(001). 3.2.1. CO Dissociation and H Adsorption. On stepped Co2C(001), CO dissociation was calculated, and the TS is shown in Figure 6a. It can be seen that the structure is very similar to that on the stepped Co

surface.45 At the TS, the C-O bond length is 2.200 Å, compared to 2.170 Å on the stepped Co surface. The dissociation barrier is -0.52 eV with respective to CO in the gas phase and slightly higher than that on stepped Co surface (-0.56 eV53). The adsorption of the H atom was also calculated, and the structure is shown in Figure 6b. The preferred adsorption site is a near-edge-hollow site on the upper terrace, and the adsorption energy is -2.86 eV. The adsorption energy is slightly stronger than that on the stepped Co surface (-2.78 eV46). 3.2.2. Hydrogenation of the C1 Species. The adsorption of the C1 species on stepped Co2C(001) was calculated, and the structures are shown in Figure 7a-d. The most stable sites of C1 species are the same as those on the stepped Co surface.55 In contrast to the preferred corner site of CH2 on Fe5C2(100) (see Figure 4c), CH2 prefers the edge-bridge site. The TSs of C1 hydrogenation were further searched on stepped Co2C(001). As illustrated in Figure 7e-h, the TS structures are also similar to those on the stepped Co surface.55 The calculated barriers and the bond distances between the reacting H and C (dC-H) at the TSs are listed in Table 3. It is interesting to note that both hydrogenation barriers and dC-H on Co2C(001) are very close to those on the stepped Co surface. This can be understood from the fact that both surfaces have very similar geometries, as mentioned in section 2, and the ISs and TSs of C1 hydrogenation on both surfaces are also very similar. 3.2.3. C1+C1 Coupling Reactions. We also calculated the TSs of C1+C1 coupling reactions on stepped Co2C(001). However, we cannot find the TSs of the coupling of C+C, CH+C, and CH+CH. The other TSs located are shown in Figure 8a-f. Generally speaking, these TS structures are very similar to those on the stepped Co surface.46 The calculated coupling barriers (Ea) and the C-C distances at the TSs (dC-C) are listed in Table 4. Because of the structural similarity, dC-Cs on stepped Co2C(001) are also similar to those on stepped metal surfaces.47 In comparison to the barriers on the stepped Co surface,46 the coupling of C+CH3, CH+CH3, and CH2+CH3 is very similar on these two surfaces, while for the coupling of C+CH2, CH+CH2, and CH2+CH2, the barriers are different. 4. Discussions 4.1. C1 Hydrogenation on Fe5C2(100) and Stepped Co2C(001). Our calculated energy profiles of C1 hydrogenation on Fe5C2(100) and stepped Co2C(001) are illustrated in Figure 9. It can be seen from the energy profiles that on both



Figure 5. Top views and side views (inserted) of the TSs of C1+C1 coupling reactions on Fe5C2(100): (a) C+C; (b) C+CH; (c) C+CH2; (d) C+CH3; (e) CH+CH; (f) CH+CH2; (g) CH+CH3; (h) CH2+CH2; (i) CH2+CH3. The purple balls are Fe atoms, the gray ones are C atoms, and the white ones are H atoms.

TABLE 2: Reaction Barriers of C1+C1 Coupling and Structural Parameters at the TSs on Fe5C2(100)a Pathway

C+C

C+CH

C+CH2

dC-C (Å) Ea (eV)

2.365 3.00

2.453 2.41

2.180 1.55

Pathway dC-C (Å) Ea (eV)

C+CH3 1.973 1.02

CH+CH 2.260 1.99

CH+CH2 2.282 1.57


CH+CH3 2.000 1.39

CH2+CH2 2.190 0.95

CH2+CH3 2.115 1.35

a dC-C is the C-C distance at the TS. Ea is the coupling reaction barrier.

Figure 6. Top views and side views (inserted) of the TS of CO dissociation (a) and the H adsorption (b) on stepped Co2C(001). The blue balls are Co atoms, the gray ones are C atoms, the red ones are O atoms, and the white ones are H atoms.

surfaces the energy levels of the TSs increase along the reaction coordinate. This means that the last hydrogenation step (CH3+H) has the highest TS energy. This would suggest, according to our previous work,46 that the last steps are the slowest, that is, rate-determining, in C1 hydrogenation on both

surfaces. Thus, the preceding hydrogenation steps may reach quasi-equilibrium, and the coverages of surface species CHi (i ) 1∼3) can be referenced to the C coverage as follows:46

θCHi ) e-Ei/RTθC

θHi i

θ *

) e-Ei/RTθCti, i ) 1 ∼ 3

(1)

where θCHi, θH, and θ* are the coverage of CHi, H, and free surface site, respectively, t is equal to θH/θ* and Ei is the relative stability of CHi with respect to a C atom (the energy difference between adsorbed CHi and C+iH). It should be mentioned that the ratio of H to free surface site coverage, t, is related to H2 partial pressure and H chemisorption energy. Our previous work46 showed that it is about 1 on the Co surface under typical reaction conditions. The H chemisorption energies on Fe5C2(100) and stepped Co2C(001) (see sections 3.1.1 and 3.2.1) are very close to that on the Co surface, and hence, t should also be around 1 on the carbide surfaces. 4.2. C1+C1 Coupling on Fe5C2(100) and Stepped Co2C(001). According to transition state theory, the C1+C1 coupling reaction rate can be expressed as

rCHi+CHj ) Ae-Ei,j/RTθCHiθCHj, i, j ) 0 ∼ 3

(2)

where Ei,j is the barrier of CHi+CHj coupling reaction and A is the pre-exponential factor. Substituting eq 1 into eq 2, we can obtain the following equation:

rCHi+CHj ) Ae-(Ei,j+Ei+Ej)/RTti+jθC2, i, j ) 0 ∼ 3 57

(3)

For surface chemical reactions, the pre-exponential factor A is usually about 1013. Parameter t is about one and can be neglected. On the same surface, C coverage is the same for different coupling pathways and, hence, can also be ignored.

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Figure 7. Top views and side views (inserted) of the adsorption of C1 species and the TSs of C1 hydrogenation on stepped Co2C(001): (a-d) show the adsorption of C, CH, CH2, and CH3; (e-h) show the TSs of the hydrogenation of C, CH, CH2, and CH3. The blue balls are Co atoms, the gray ones are C atoms, and the white ones are H atoms.

TABLE 3: Reaction Barriers of C1 Hydrogenation and Structural Parameters at the TSs on Stepped Co2C(001)a reactions

dC-H (Å)

Eafor (eV)

Earev (eV)

C+HfCH CH+HfCH2 CH2+HfCH3 CH3+HfCH4

1.510 1.450 1.900 1.600

0.78 0.78 0.43 0.88

0.75 0.14 0.70 0.31

a

dC-H is the distance between the reacting C and H atoms at the TS. Eafor and Earev are the barriers of the forward and reverse reaction, respectively.

Therefore, it can be seen from eq 3 that the reaction rate of each C1+C1 coupling pathway is mainly determined by Ei,j+Ei+Ej, the barrier of the coupling reaction and the stabilities of reactants. The values of Ei,j+Ei+Ej of C1+C1 coupling reactions on Fe5C2(100) and stepped Co2C(001) were calculated and listed in Table 5. It can be seen from the table that the coupling of C+CH3 is the fastest coupling pathway on both carbide surfaces. 4.3. CH4 Selectivity. The CH4 selectivity is one of the most important issues in FT synthesis. To understand the catalytic roles of Fe and Co carbides in FT synthesis, we investigated the CH4 selectivity on the carbide surfaces as we studied on metal surfaces recently58 and further compared the results between metals and the corresponding carbides. In our previous work,58 it was shown that the CH4 selectivity, determined by the competition between CH4 formation and chain growth processes, can be described by one energy term (∆Eeff), which is the difference between the effective barriers of CH4 formation (Eeff,CH4) and chain growth (Eeff,C-C). For the benefit of readers, it is worth summarizing the derivation as follows. Under typical FT reaction conditions, the readsorption of CH4 on the surface is negligible, and thus, the CH4 formation rate (rCH4) can be expressed as58

rCH4 ) Ae-Ea /RTθCH3θH ) Ae-(Ea +E3)/RT(θH /θ*)3θCθH ) hy

hy

Ae-Eeff,CH4/RTt3θCθH (4) where eq 1 is used, Eahy is the reaction barrier of CH3 hydrogenation, and Eeff,CH4 (Eahy+E3) is the effective barrier of CH4 formation. It is worth mentioning that Eeff,CH4 is the energy difference between the TS of CH3 hydrogenation and the C+4H atoms (Figure 9). Theoretically, the total chain growth rate should be equal to the sum of all the coupling channels. Because the reaction rates of the other coupling channels are usually several orders of

magnitude smaller than the major one, we only consider the fastest channel to describe the total chain growth rate. Thus,58

rC-C ≈ max(Ae-(Ei,j+Ei+Ej)/RTti+jθC2) ) Ae-min(Ei,j+Ei+Ej)/RTti+jθC2 ) Ae-Eeff,C-C/RTti+jθC2

(5)

where Eeff,C-C stands for the effective barrier of the chain growth process, which is identical to the minimum of Ei,j+Ei+Ej on each surface. Combining eqs 4 and 5, we can quantify CH4 selectivity by using the ratio of CH4 formation rate to chain growth rate as58

rCH4 /rC-C ) t3-i-j(θH /θC) × e-∆Eeff/RT

(6)

where ∆Eeff is the difference between the effective barrier of CH4 formation (Eeff,CH4) and chain growth (Eeff,C-C). As addressed in previous work,58 the term t and θH/θC in eq 6 have little effect on the CH4 selectivity (rCH4/rC-C), as compared to ∆Eeff, which affects the CH4 selectivity exponentially. If ∆Eeff changes by 0.1 eV, rCH4/rC-C will change 10 times at 500 K. Therefore, ∆Eeff is more important than t and θH/θC and can be considered as an energy descriptor to measure the CH4 selectivity on different surfaces. A surface with a small ∆Eeff will have a high CH4 selectivity, and the surface with a large ∆Eeff should be good for production of long chain hydrocarbons. Eeff,CH4, Eeff,C-C, and ∆Eeff on Fe5C2(100) and stepped Co2C(001) were calculated and given in Table 6. The results on stepped Fe and Co surfaces from our previous work58 are also included for comparison. From Table 6, we can see that Eeff,CH4 and Eeff,C-C on Fe5C2(100) are smaller than those on Fe(210), and ∆Eeff on Fe and Fe carbide surfaces are very similar. Thus, the CH4 selectivity on Fe5C2(100) may be very similar to that on Fe(210). With respect to Co and Co carbide, ∆Eeff on stepped Co2C(001) is 0.08 eV smaller than that on stepped Co(0001). This suggests that the CH4 selectivity on stepped Co2C(001) should be about 1 order of magnitude higher than that on stepped Co(0001) at 500 K if assuming the other effects are minimal. 4.4. General Discussion. In sections 3.1.1 and 3.2.1, we showed the results of CO dissociation on Fe5C2(100) and stepped Co2C(001). Our results revealed that the CO dissociation barriers on both carbide surfaces are higher than those on metal surfaces, reflecting that the carbide formation reduces the binding strength of C and O atoms on the surfaces. It is well-known that the activity of CO hydrogenation versus the binding strength of C and O atoms generally shows a volcano curve.53,59 We may use this notion to provide a further understanding of the results presented above: On the Fe catalyst, the binding strength of C



Figure 8. Top views and side views (inserted) of the TSs of C1+C1 coupling reactions on Co2C(001): (a) C+CH2; (b) C+CH3; (c) CH+CH2; (d) CH+CH3; (e) CH2+CH2; (f) CH2+CH3. The blue balls are Co atoms, the gray ones are C atoms, and the white ones are H atoms.

TABLE 4: Reaction Barriers of C1+C1 Coupling and Structural Parameters at the TSs on Co2C(001)a Pathway

C+CH2

C+CH3

CH+CH2

TABLE 5: Values of Ei,j+Ei+Ej of the C1+C1 Coupling Reactions on Fe5C2(100) and Stepped Co2C(001)a Ei,j+Ei+Ej (eV)

C+C

C+CH

C+CH2

dC-C (Å) Ea (eV)

2.110 1.02

1.950 1.19

2.060 1.08

Fe5C2(100) stepped Co2C(001)

3.00 -

2.62 -

2.35 1.69


CH+CH3 1.864 1.65

CH2+CH2 2.060 0.52

CH2+CH3 2.140 0.78

Ei,j+Ei+Ej (eV) Fe5C2(100) stepped Co2C(001)

C+CH3 1.94 1.59

CH+CH 2.41 -

CH+CH2 2.59 1.78

Ei,j+Ei+Ej (eV) Fe5C2(100) stepped Co2C(001)

CH+CH3 2.53 2.08

CH2+CH2 2.55 1.85

CH2+CH3 3.08 1.85

a dC-C is the C-C distance at the TS. Ea is the coupling reaction barrier.

a The value of the fastest coupling pathway on each surface is highlighted in bold.

TABLE 6: Effective Barriers on Stepped Fe and Co and their Carbide Surfacesa Fe5C2(100) Fe(210) stepped Co2C(001) stepped Co(0001)

Eeff,CH4

Eeff,C-C

∆Eeff

1.89 2.13 1.27 1.31

1.94 2.19 1.59 1.55

-0.05 -0.06 -0.32 -0.24

a Eeff,CH4, Eeff,C-C, and ∆Eeff are the effective barrier of CH4 formation and chain growth and their difference, respectively. The unit is eV.

Figure 9. Energy profiles of C1 hydrogenation on Fe5C2(100) (in black) and stepped Co2C(001) (in red). The energy levels of adsorbed C+4H on both surfaces are chosen as a reference in both energy profiles.

and O atoms is too strong. To improve the activity of CO hydrogenation, the binding strength should be decreased in order to increase the rate of the hydrogenation of C and O atoms. Although CO dissociation is more difficult on Fe carbide, the removal of C and O atoms from the surface is easier. This is consistent with the fact that Eeff,CH4 is smaller on Fe carbide surface than on Fe surface (in Table 6). In fact, the removal of C and O atoms by hydrogenation is more important for the surfaces on the left side of the volcano curve. Hence, Fe carbide should be more active in CO hydrogenation than Fe. In contrast, Co is on the right side of volcano curve. To increase the activity, the binding strength of C and O atoms must be increased to facilitate CO dissociation. However, Co carbide has a higher CO dissociation barrier, suggesting that Co carbide is less active than Co. The effects of the carbide formation are illustrated in

Figure 10. It can be seen from the figure that the reduction of binding strength of C and O with the surfaces due to carbide formation is the physical origin underlying the paradoxical behaviors of carbides on Fe and Co catalysts in FT synthesis. As mentioned in the Introduction, experimental work11 suggested that on Fe-based catalysts Fe carbides are the dominant phase rather than metallic Fe under FT reaction conditions, and Fe carbides (mainly Fe5C2) are the true active phase for FT synthesis. In contrast, Co carbide was considered as the cause of the deactivation of Co-based catalysts.17 It is clear from the above discussions that our results are consistent with these experimental findings. However, the current work provides a further understanding of carbide phases in FT synthesis. Our results suggest that Fe carbide is more active to FT synthesis than Fe, and the CH4 selectivity on Fe carbide is similar to that on Fe surface. On the other hand, Co carbide is less active, and also produces more CH4 than Co. Furthermore, these results may also provide an explanation for the increasing CH4 selectivity on Co-based catalysts at higher temperature; it may be due to the formation of carbide phases: as the reaction temperature increases, CO conversion will increase, accompa-

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Cheng et al. It is clear that Fe carbide is superior to metallic Fe due to its higher activity and similar CH4 selectivity, while catalytic performance of Co carbide is worse than metallic Co. Therefore, Fe carbide and metallic Co are the preferred active phases, and the formation of Co carbide may be the cause of deactivation and relatively high methane selectivity. Acknowledgment. We gratefully thank The Queen’s University of Belfast for computing time. J.C. acknowledges Johnson Matthey for financial support. References and Notes

Figure 10. Schematic illustration how the formation of carbides influences the activity.

nied by the accumulation of more carbon species on the Co surface. This may speed up the phase transition from metallic Co to Co carbides (Co2C or Co3C), which are less active and increase methanation, leading to the catalyst deactivation and the higher CH4 selectivity. It should be pointed out that some differences in our calculated results between Fe/Fe carbide and Co/Co carbide (see Table 6) are very small, and some of them are close to the standard error of DFT calculations. For example, the difference of ∆Eeff between Fe and Fe carbide is only 0.01 eV, and the CO dissociation barrier on Co surface differs by 0.04 eV from that on Co carbide surface (see section 3.2.1). Thus, it may be difficult to obtain a quantitative estimation for the activity and methane selectivity. However, we believe that the trends obtained from our DFT calculations are reasonable to give a qualitative understanding on the activity and methane selectivity on the metals and carbides. 5. Conclusions This work represents one of the first attempts to obtain a comprehensive understanding of carbide phases in FT synthesis. Extensive DFT calculations are carried out to investigate CO dissociation, C1 hydrogenation, and C1+C1 coupling, the key reactions in FT synthesis, on Fe and Co carbide surfaces. Both the activity and CH4 selectivity are studied and compared to those on metallic surfaces. An understanding of catalytic effects of carbides is obtained. The main findings are summarized as follows: (i) The CO dissociation barriers on Fe and Co carbide surfaces are higher than those on the corresponding metal surfaces. According to the volcano curve plot of CO hydrogenation, in which Fe lies on the left side of the top, while Co lies on the right side, this suggests that Fe carbide is more active for CO hydrogenation than Fe, while Co carbide is less active than Co. (ii) In C1 hydrogenation, the IS and TS structures on Fe and Co carbide surfaces are very similar to those on stepped Co surface except for the adsorption of CH2; it is on the corner site on the Fe carbide surface, as opposed to the edge-bridge site on Co carbide surface. Along the hydrogenation reaction coordinate, the TS energy increases, and the last steps are ratedetermining. (iii) The TS structures of C1+C1 coupling on both carbide surfaces are very similar to those on metal surfaces. The fastest coupling pathways on both carbide surfaces are the coupling of C+CH3. (iv) The CH4 selectivity on both surfaces of Fe and Co carbides is quantitatively analyzed. It is found that Fe carbide possesses similar CH4 selectivity to that on Fe surface, while it is higher on Co carbide surface than on the Co surface.

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