Insight into the Fischer–Tropsch mechanism on hcp-Fe₇C₃ (211) by density functional theory: the roles of surface carbon and vacancies

Abstract

Iron carbide phases discovered in the spent iron catalysts have proved to be active in the Fischer–Tropsch process. The surface carbon of the iron carbide played a key role in the Fischer–Tropsch mechanism. Since there are two surface carbons, C1 and C2, on the hcp-Fe₇C₃ (211), which are close to each other, their reaction mechanisms would be significant. Hence, the DFT calculations were performed to investigate the Fischer–Tropsch mechanism involving the surface carbon. It was found that the HC¹ + C² pathway was the major C–C coupling reaction pathway with an effective energy barrier of 0.97 eV. Ethane would be the major C₂ product from the HC¹C2 species through the stepwise hydrogenation pathway due to the high adsorption energy of ethylene (1.67 eV). After the desorption process of ethane, the carbon vacancy would form. The carbon vacancy was found to be the CO activation site through the CO direct dissociation pathway and the carbon vacancy would recover. It was concluded that the defect-hcp-Fe₇C₃ (211) is the high active facet of the Fischer–Tropsch synthesis, the carbon vacancy sites are the CO activation sites and the surface carbon sites are the C–C coupling sites. The surface carbons not only act as the chain initiation sites but also act as the chain growth sites in the Fischer–Tropsch mechanism on hcp-Fe₇C₃ (211).

---

Introduction

Fischer–Tropsch synthesis (FTS) is a promising process since it can convert syngas into liquid fuels and chemicals so that other carbon-based energy such as coal and biomass can be utilized.^1,2 The FTS process has been studied for a long time for the production of long-chain fuels.^3,4 In a recent study, the Fischer–Tropsch synthesis was proved to produce light olefins with acceptable selectivity.^5,6 Iron-based catalysts are usually selected as fundamental catalysts for the production of light olefins.^7–10 The promoter addition is one of the major modifications,^11–14 while the design of specific catalyst structures is another optimization method for improving the catalyst performance.^15,16 However, the selectivity of light olefins in the hydrocarbon species over the iron catalysts cannot meet the economic demand in the industry.¹⁷ As a result, the performance of the iron catalysts requires urgent improvement.

Nowadays, there are different kinds of iron-containing phases in the spent iron catalysts.^18–23 The major iron carbide phases are ε-Fe₂C, ε-Fe_2.2C, Fe₇C₃, χ-Fe₅C₂, θ-Fe₃C, and so on.^24,25 χ-Fe₅C₂ and ε-Fe₂C have been proved to be the active phases in the iron catalysts.^26,27 θ-Fe₃C is always considered as the inactive phase as it mainly appears in deactivated iron-based catalysts.^28,29 Fe₇C₃ would be present after a long run and high-temperature Fischer–Tropsch synthesis,^30,31 which has been proved to be the active phase by Brent Williams et al. and Yongwang Li et al.^32,33

A comprehensive understanding of the Fischer–Tropsch mechanism on the iron catalysts would assist the researcher to improve the catalysis performance. Since the iron catalysts are composed of different iron carbide phases, the Fischer–Tropsch mechanism on the iron catalysts is also composed of the Fischer–Tropsch mechanism on different iron carbide phases. Thus, it is necessary to investigate the Fischer–Tropsch mechanism on each iron carbide phase, especially the one that was proved to be active in the Fischer–Tropsch synthesis. However, the preparation, characterization, and exploration of the single iron carbide phase under the reaction conditions are difficult. As a result, the theoretical method is used for investigating the Fischer–Tropsch mechanism on the single iron carbide phase and is applied in this research.

To date, the Fischer–Tropsch mechanism is clear for some iron carbide phases. Thanh Hai Pham et al. pointed out that the direct CO dissociation reaction and the coupling reaction of C + HC or HC + HC are the major CO activation pathway and chain-growth pathway, respectively, on the χ-Fe₅C₂ (510).^34,35 After that, the influence of the H coverage effect on the Fischer–Tropsch mechanism was introduced by Minhua Zhang et al. Due to the existence of the H coverage effect, the CO insertion mechanism rather than the carbide mechanism is the Fischer–Tropsch mechanism on the χ-Fe₅C₂ (510).³⁶ The CO activation mechanism on the χ-Fe₅C₂ (001), χ-Fe₅C₂ (221), χ-Fe₅C₂ (010), χ-Fe₅C₂ (110), χ-Fe₅C₂ (111) has been discussed thoroughly by Yurong He et al.^37,38 On θ-Fe₃C (100)³⁹ and θ-Fe₃C (010),⁴⁰ the CO insertion dissociation pathway is the major CO activation mechanism and the C–C coupling mechanism. On θ-Fe₃C (031), the coupling reaction of HC + HC and H₂C + H₂C is the major chain-growth pathway.⁴¹ However, the Fischer–Tropsch mechanism on other iron carbide phases has not yet been discussed thoroughly.

As mentioned before, the hcp-Fe₇C₃ phase has been proved to be active in Fischer–Tropsch synthesis by experimental research.^32,33 In previous research, DFT calculations were applied to investigate the CO activation pathway on hcp-Fe₇C₃ (211).⁴² The results showed that CO would undergo the H-assisted dissociation pathway on the top site rather than the CO insertion dissociation pathway with the surface carbon. However, the C–C coupling pathway and the product formation pathway on hcp-Fe₇C₃ (211) are not clear. Thus, this article aims to investigate the Fischer–Tropsch mechanism on the hcp-Fe₇C₃ phase so that the understanding of the iron catalyst's mechanism could be improved.

According to the known mechanism on other iron carbide phases, the surface carbon that belongs to the catalyst would participate in the Fischer–Tropsch synthesis. On the Fe₂C (011), Fe₅C₂ (010), Fe₃C (001), and Fe₄C (100), the surface carbon was found to be the carbon source of the product methane.⁴³ On the χ-Fe₅C₂ (510), the surface carbon would undergo a stepwise hydrogenation reaction to give the H_xC species. Then the H_xC species can participate in the subsequent C–C coupling reaction.^34–36 On θ-Fe₃C (100) and θ-Fe₃C (010),^39,40 the surface carbon would act as the chain initiation site so that the reactant CO could be coupled with it to accomplish the CO activation pathway and chain-growth pathway. Other than theoretical work, Khodakov et al. proved that the initiation of chain growth involves the surface carbon through isotope C13 research.⁴⁴ As a result, the surface carbon would always play a key role in the Fischer–Tropsch mechanism.

The previously researched model of hcp-Fe₇C₃ (211) showed that two surface carbons are close to each other, leading to the problem of what role they play in the Fischer–Tropsch mechanism. Hence, when the DFT calculations were performed to accomplish the full map of the Fischer–Tropsch mechanism on hcp-Fe₇C₃ (211), the surface carbon was considered to be the significant reactant and was thoroughly discussed in the designed reaction pathway.

In short, as the iron catalysts are combined with different kinds of iron carbide phases, including the hcp-Fe₇C₃ phase, the research on the Fischer–Tropsch mechanism on the hcp-Fe₇C₃ phase would be valuable in the iron catalysts and deserves to be researched. The experimental research on the reaction mechanism in the pure hcp-Fe₇C₃ phase would be difficult since the specific iron carbide would be transferred to another kind of iron carbide under the Fischer–Tropsch synthesis. Hence, DFT calculations are applied in this article to investigate the Fischer–Tropsch mechanism on the hcp-Fe₇C₃ (211) facet, because it possesses the largest percentage among the exposed crystal facets.

We expect that this research will provide a better comprehension of the Fischer–Tropsch mechanism on the hcp-Fe₇C₃ phase so that the iron-based catalysts can be understood clearly and be modified efficiently.

Computational details

Surface model

In this study, the bulk hcp-Fe₇C₃ was selected as the bulk catalyst according to the experimental results.³³ The hcp-Fe₇C₃ belongs to the hexagonal system with the P6₃mc space group. The lattice constants of hcp-Fe₇C₃ are a = 6.826 Å; b = 6.826 Å; c = 4.495 Å; γ = 120°. The bulk structure of hcp-Fe₇C₃ was optimized with a 3 × 3 × 5 Monkhorst–Pack k-point mesh. The optimized lattice constants are a = 6.748 Å; b = 6.748 Å; c = 4.434 Å; γ = 120°, which are in agreement with the experimental values. The hcp-Fe₇C₃ (211) facet possesses the largest percentage among the exposed crystal facets based on the surface energy calculation³⁶ and the XRD results (PDF #89-7273).⁴⁵ The surface reactions were calculated on a p (1 × 1) hcp-Fe₇C₃ (211) slab with a stable terminal surface. The size of the p (1 × 1) hcp-Fe₇C₃ (211) slab is a = 11.14 Å; b = 8.074 Å, which could avoid the interactions between the adsorbate with itself in the neighbouring repeated images. In all calculations, the bottom two Fe layers were fixed in their bulk position, while the top two Fe layers and the adsorbents were allowed to relax. The top view and side view of the hcp-Fe₇C₃ (211) slab model are shown in Fig. 1.

Fig. 1 Top (left) and side (right) views of hcp-Fe₇C₃ (211) surface (blue: Fe atoms; gray: C atoms).

First-principles calculations

The spin-polarized DFT calculations were performed via the projector augmented wave (PAW) method^46–48 using the Vienna ab initio simulation package (VASP). In this article, the Perdew–Burke–Ernzerhof (PBE) functional⁴⁹ with the plane wave cutoff energy of 400 eV was applied. The Brillouin zone sampling of the bulk calculation and the surface calculation were set as 3 × 3 × 5 and 2 × 2 × 1 Monkhorst–Pack grids,⁵⁰ respectively. The electron smearing was employed via the Methfessel–Paxton technique with a smearing width consistent with 0.2 eV.⁵¹ The effects of van der Waals corrections were taken into account by the DFT-D3 method with Becke–Jonson (BJ) damping.^52,53

The convergence standard of the SCF calculation and the geometry optimization were set as 1 × 10⁻⁵ eV and 0.03 eV Å⁻¹, respectively. The climbing-image nudged elastic band method (CI-NEB)^54,55 was selected to search the transition state and to evaluate the intrinsic energy barrier. The convergence standard of the CI-NEB calculation was set as 0.05 eV Å⁻¹. The frequency calculation was performed to confirm the TS structure after the CI-NEB calculation. Only if the TS structure of the researched elementary reaction has only one imaginary frequency can the TS structure be confirmed.

The adsorption energy of surface species is defined and calculated by E_ads = E(adsorbate/slab) − [E(slab) + E(adsorbate)], in which E(adsorbate/slab) is the energy of the slab with surface adsorbate, E(slab) is the energy of the slab, and E(adsorbate) is the energy of the free adsorbate. The reaction energy and the intrinsic energy barrier are calculated by ΔE_r = E(FS) − E(IS) and E_a = E(TS) − E(IS), respectively, where E(IS), E(FS), and E(TS) are the energies of the corresponding initial state (IS), final state (FS), and transition state (TS), respectively.

The reaction pathways researched in the article are combined with a series of consecutive reactions. For an elementary reaction, if the coverage of the reactant is extremely low, the reaction rate would be slow due to the mass law, even though the intrinsic energy barrier of this elementary reaction is not high. As a result, the determination of the major reaction pathway based only on the intrinsic energy barrier would be doubtful. In order to solve such a problem, the effective energy barrier^56–58 was applied to evaluate the major reaction pathway. The effective energy barrier of the k^th elementary reaction in the consecutive reactions is represented by E_eff,k and is calculated by In the equation, E_a,k is the intrinsic energy barrier of the k^th step elementary reaction, is the sum of the reaction energy from the i^th step elementary reaction to the (k − 1)^th step elementary reaction and the i^th step elementary reaction is the elementary reaction whose initial state shows the lowest electronic energy among all the states of the studied consecutive reactions.

In the consecutive reactions, there are some elementary reactions, which are the transfer reaction of the surface species from one adsorption site to another, or the structure transformation reaction; these two types of reactions are named migration reactions in this article. Most of the migration reactions show relatively low intrinsic energy barrier in this article, the computational intrinsic energy barrier of each migration reaction can be found in the ESI.† To avoid the energy profile diagram being tedious and unreadable, only the reaction energies of migration reactions are taken into account in the energy profile diagram, which is named as migration energy and denoted as ΔE_m.

In short, when the migration energy is applied in the energy profile diagram, the effective energy barrier of the k^th elementary reaction in the consecutive reactions is calculated by where the is the sum of the migration energy from the i^th elementary reaction in the consecutive reactions to the (k − 1)^th elementary reaction in the consecutive reactions.

Results and discussion

The C–C coupling reactions of the surface carbon

Fig. 2 shows the sites of the major carbon-containing species (in the red box) on hcp-Fe₇C₃ (211), which are the C1 site, C2 site, and HC site, based on the previous research.⁴³ The C¹ site and C² site are the surface carbons that belong to the catalysts. The C¹ species and C² species are the hydrogenation products of the surface carbon. The HC site is the CO activation site of the H-assisted CO activation pathway and the HC species is the product of the known CO activation pathway.

Fig. 2 The site of major carbon-containing species on hcp-Fe₇C₃ (211).

Since the H-assisted CO activation pathway is the known CO activation mechanism, the carbide mechanism seems to be the major Fischer–Tropsch mechanism on the Fe₇C₃ (211). The detailed possible designed reaction pathway is shown below: (1) the CO adsorption process (2) the CO activation process on the HC site. (3) The C–C coupling process of H_xC species with the C¹ species or C² species to be the C₂ species (4) The hydrogenation process, the product desorption process, or chain-growth process of the C₂ species. (5) The recovery process of C¹ or C².

All the surface carbon-containing species are the possible reactants of the C–C coupling reaction. Before starting to calculate and research the C–C coupling process of H_xC species with C¹ species or C² species, it should be noted that the distance from the C¹ site to the C² site is close to the distance from the HC site to the C¹ site, and the distance from the HC site to the C² site as shown in Fig. 2.

The distances between the C¹ site, C² site, and HC site were calculated and shown in Table 1. The results show that the distance from the C¹ site to the C² site, the distance from the HC site to the C¹ site, and the distance from the HC site to C² site are 3.212 Å, 3.205 Å, and 3.460 Å, respectively, and are close.

Table 1 The distance of the C atom between the C¹ site, C² site and HC site on hcp-Fe₇C₃ (211)

Distance between C atom(Å)	C^1	C^2	HC
C^1	—	3.212	3.205
C^2	—	—	3.460
CH	—	—	—

---

As a result, if the H_xC species can be coupled with the C¹ species or C² species, the C¹ species and C² species could also possibly couple with each other.

Hence, another possible C–C coupling pathway was presented, which is denoted as the C¹–C² coupling pathway. In the C¹–C² coupling pathway, the C¹ species and C² species can be coupled with each other to be C₂ species. Based on the new idea of the C¹–C² coupling pathway, the designed reaction pathway is shown in Scheme 1 and the calculated results are shown in Table 2. It was found that some of the coupling reactions showed relatively low energy barriers, which proved that the C¹–C² coupling pathway is likely to be the major C–C coupling pathway on the hcp-Fe₇C₃ (211).

Scheme 1 The designed C¹–C² coupling pathways on hcp-Fe₇C₃ (211).

Table 2 The intrinsic energy barriers (E_a, eV), reaction energies (E_r, eV) and migration energies (E_m, eV) of the C¹–C² coupling pathway

No	Reaction	Em	Ea	Er
1	C^1 + H = HC^1	0	0.73	−0.26
2	HC^1 + H = H2C^1	0	0.73	0.71
3	H2C^1 + H = H3C^1	0.09	0.91	0.48
4	H3C^1 + H = H4C^1	0	0.60	0.03
5	C^2 + H = HC^2	0	0.99	0.23
6	HC^2 + H = H2C^2	0	0.67	0.60
7	H2C^2 + H = H3C^2	−0.09	1.14	0.43
8	H3C^2 + H = H4C^2	0	0.83	0.04
9	C^1 + C^2 = C^1C^2	0	1.25	0.44
10	C^1+ HC^2 = C^1HC^2	0	0.95	0.05
11	C^1+ H2C^2 = C^1H2C^2	−0.09	1.05	0.26
12	C^1+ H3C^2 = C^1H3C^2	−0.45	0.97	0.10
13	HC^1 + C^2 = HC^1C^2	0	0.97	0.44
14	HC^1+ HC^2 = HC^1HC^2	0	0.76	0.46
15	HC^1+ H2C^2 = HC^1H2C^2	0.39	0.87	0.28
16	HC^1+ H3C^2 = HC^1H3C^2	−0.46	1.43	0.38
17	H2C^1 + C^2 = H2C^1C^2	0	0.73	−0.23
18	H2C^1 + HC^2 = H2C^1HC^2	0	0.74	0.20
19	H2C^1 + H2C^2 = H2C^1H2C^2	−0.09	0.83	−0.27
20	H2C^1 + H3C^2 = H2C^1H3C^2	−0.46	1.00	0.31
21	H3C^1 + C^2 = H3C^1C^2	−0.13	1.01	−0.24
22	H3C^1 + HC^2 = H3C^1HC^2	−0.17	1.41	0.77
23	H3C^1+ H2C^2 = H3C^1H2C^2	−0.34	1.45	0.31
24	H3C^1+ H3C^2 = H3C^1H3C^2	−0.62	2.92	0.10

---

The energy profile diagrams of the C¹–C² coupling pathway are shown in Fig. 3. The C¹–C² coupling reaction pathway involving C¹, HC¹, H₂C¹, and H₃C¹ species are present in Fig. 3(a–d) and were denoted as the C¹ coupling pathway, HC¹ coupling pathway, H₂C¹ coupling pathway, and H₃C¹ coupling pathway, respectively. The black line represents the C–C coupling reaction pathway involving the C¹ species and C² species. The blue line represents the stepwise hydrogenation pathway of the C² hydrocarbon species.

Fig. 3 Energy profile diagrams for the C¹–C² coupling pathways on the hcp-Fe₇C₃ (211) surface: (a) the C¹–C²coupling reaction pathway involving C¹ species; (b) the C¹–C² coupling reaction pathway involving HC¹ species; (c) the C¹–C² coupling reaction pathway involving H₂C¹ species; (d) the C¹–C² coupling reaction pathway involving H₃C¹ species. Black lines: the C–C coupling reaction pathways of different kinds of C¹ hydrocarbon species. Blue lines: the stepwise hydrogenation pathways of C² hydrocarbon species.

Comparing the effective energy barriers of the coupling pathways involving different C¹ species and C² species, the major C¹–C² coupling pathway would be achieved. The HC¹ + C² pathway showed the lowest effective energy barrier of 0.97 eV, while the effective energy barrier of the HC¹ + HC² pathway is close to that of the HC¹ + C² pathway (0.99 eV). The effective energy barriers of the C¹ + C² pathway and the C¹ + HC² pathway are a bit higher than that of the HC¹ + C² pathway, which are 1.25 eV and 1.18 eV, respectively. The effective energy barriers of the C¹–C² coupling reactions involving H₂C species and H₃C species are much higher, making them impossible.

There are two major reasons why the C–C coupling reaction involving H₂C species and H₃C species would show high effective energy barriers. Firstly, Table 2 shows that in the C¹ coupling pathway, HC¹ coupling pathway, and H₂C¹ coupling pathway, the intrinsic energy barrier of the C–C coupling reaction is not extremely high. However, the hydrogenation reactions of HC species are endothermic with high reaction energies, which are 0.71 eV and 0.60 eV for HC¹ and HC2, respectively. The high reaction energy of the HC hydrogenation reaction represents the instability of the H₂C species so that the dehydrogenation reaction of the H₂C species would take place easily. Hence, the degree of coverage of the H₂C species would be small on the hcp-Fe₇C₃ (211). The small coverage of the reactant species would result in the slow reaction rate of the specific C–C coupling reaction involving H₂C species according to the mass law. Hence, the high effective energy barrier of the C¹–C² coupling pathways involving H₂C could be attributed to the high instability of the H₂C species. This situation was also found in other iron carbides from theoretical and experimental research.^35,36

Secondly, Table 2 shows that the C–C coupling reactions involving H₃C species have high intrinsic energy barriers, which could be attributed to the weak interactions between the surface and H₃C species. To confirm the inference, Table 3 presents the Bader charge analysis on the C₁ species. The “C”, “H¹”, “H²”, and “H³” represent the number of “Bader charges” in specific atoms in the C₁ species. The “charge transfer” represents the Bader charge transfer between the C₁ species and hcp-Fe₇C₃ (211), in which “+” represents the charge obtained by the C₁ species from the hcp-Fe₇C₃ (211).

Table 3 The results of the Bader charge analysis on the C₁ species on hcp-Fe₇C₃ (211)

Species	C	H^1	H^2	H^3	Total	Charge transfer
C^1	4.91	—	—	—	4.91	+0.91
HC^1	4.86	0.87	—	—	5.73	+0.73
H2C^1	4.79	0.87	0.97	—	6.63	+0.63
H3C^1	4.59	0.83	0.98	0.90	7.30	+0.30
C^2	4.92	—	—	—	4.92	+0.92
HC^2	4.88	0.88	—	—	5.76	+0.76
H2C^2	4.78	0.90	0.97	—	6.65	+0.65
H3C^2	4.48	0.94	0.98	0.95	7.35	+0.35

---

Table 3 shows that the charge obtained by the C₁ species from the hcp-Fe₇C₃ (211) would decrease with the increase in H atoms in the C₁ species. The decrease in the charge transfer indicates the decrease in the interactions between the C₁ species and hcp-Fe₇C₃ (211). The charge transfers of the H₃C¹ species with the hcp-Fe₇C₃ (211) and the H₃C² species with the hcp-Fe₇C₃ (211) were +0.30 and +0.35, respectively, which are much lower as compared to the other C₁ species with the hcp-Fe₇C₃ (211). Hence, the hcp-Fe₇C₃ (211) could hardly activate the C–C coupling reaction involving the H₃C species so that the intrinsic energy barrier would be high as shown in Table 2. This phenomenon has also been found and reported on other iron carbides.³⁶

The major C¹–C² coupling pathways were achieved and are shown in Scheme 2, including the C¹ + C² pathway, HC¹ + C² pathway, C¹ + HC² pathway, and HC¹ + HC² pathway. Among the major C¹–C² coupling pathways, the HC¹ + C² pathway is the preferred C¹–C² coupling pathway with an effective energy barrier of 0.97 eV.

Scheme 2 The major C¹–C² coupling pathways (black lines) and preferred C¹–C² coupling pathways (blue lines) on hcp-Fe₇C₃ (211).

According to the results, a new possible C–C coupling pathway with a relatively low energy barrier was discovered and it could be the major C–C coupling mechanism. However, the preferred C¹–C² coupling pathway needs to be compared with other possible C–C coupling pathways to decide whether or not it could be the major C–C coupling mechanism.

The major possible C–C coupling mechanisms in the Fischer–Tropsch synthesis are the carbide mechanism and CO insertion mechanism.

On hcp-Fe₇C₃ (211), the C–C coupling pathway through the CO insertion mechanism has been discussed thoroughly.⁴³ The effective energy barrier of the preferred C–C coupling pathway through the CO insertion mechanism is 1.48 eV, which is much higher than that of the preferred C¹–C² coupling pathway. Thus, the C¹ species and the C² species prefer to be coupled with each other rather than with adsorbed CO.

Another possible C–C coupling pathway is the coupling reaction between surface carbon and H_xC species through the carbide mechanism, in which the H_xC species are the products through the H-assisted CO activation pathway. The effective energy barrier of the H_xC species formation pathway is 1.30 eV, which is also higher than that of the preferred C¹–C² coupling pathway. As a result, the effective energy barrier of the preferred C¹–C² coupling pathway is much lower than those of the other two possible C–C coupling pathways. It can be concluded that on the hcp-Fe₇C₃ (211), the C¹–C² coupling pathway is the major C–C coupling mechanism of the C₂ species and the major coupling products are HC¹C² and HC¹HC² species.

The stepwise hydrogenation pathway of the C₂ species

After the C–C coupling reaction pathway, the subsequent reaction pathways of the major C₂ species are the parts of the Fischer–Tropsch mechanism on the hcp-Fe₇C₃ (211). The possible ensuing reaction pathways are the stepwise hydrogenation pathway and the subsequent C–C coupling pathway.

The discussion of the subsequent C–C coupling pathway would be almost the same as the C–C coupling pathway discussed before, except that the chain initiation site is the C₂ species rather than the C₁ species. Although the influence of the carbon chain length on the C–C coupling mechanism is important, it will not be discussed here.

The stepwise hydrogenation pathway of the C₂ species is another possible subsequent reaction pathway. The discussion of the stepwise hydrogenation pathway is necessary, as it could determine whether the major C₂ product on the hcp-Fe₇C₃ (211) is acetylene, ethylene, or ethane.

The designed stepwise hydrogenation pathway is shown in Scheme 3. The idea of the designed stepwise hydrogenation pathway is the hydrogenation elementary reaction on C¹ and C² of each possible C₂ species from the initial C₂ species, C₁C₂. In each hydrogenation elementary reaction, the 3-fold H sites are thought of as the reactants. The adsorption sites and adsorption energy of possible 3-fold sites H have been discussed in the previous study.⁴³ The calculation results of the stepwise hydrogenation pathways are shown in Table 4.

Scheme 3 The designed stepwise hydrogenation pathway of C₂ species on hcp-Fe₇C₃ (211).

Table 4 The intrinsic energy barrier (E_a, eV), reaction energy (E_r, eV) and migration energy (E_m, eV) of the C² stepwise hydrogenation pathway

No	Reaction	Em	Ea	Er
1	H + C^1C^2 = HC^1C^2	0	0.78	−0.20
2	C^1C^2 + H = C^1HC^2	0	0.96	−0.15
3	HC^1C^2 + H = HC^1HC^2	0	0.65	0.27
4	C^1HC^2 + H = C^1H2C^2	0.11	0.68	0.28
5	H + HC^1C^2 = H2C^1C^2	0	0.79	0.38
6	H + C^1HC^2 = HC^1HC^2	0.29	0.73	0.08
7	H + H2C^1C^2 = H3C^1C^2	0	0.59	0.39
8	H2C^1C^2 + H = H2C^1HC^2	−0.10	0.27	0.19
9	H + C^1H2C^2 = HC^1H2C^2	0.42	0.62	0.15
10	HC^1HC^2 + H = HC^1H2C^2	0	1.04	0.62
11	C^1H2C^2 + H = C^1H3C^2	0	1.13	0.41
12	H + HC^1HC^2 = H2C^1HC^2	0	1.21	0.81
13	H3C^1C^2 + H = H3C^1HC^2	0.02	0.69	0.66
14	H + HC^1H2C^2 = H2C^1H2C^2	0	0.66	0.33
15	HC^1H2C^2 + H = HC^1H3C^2	0.10	0.67	0.20
16	H2C^1HC^2 + H = H2C^1H2C^2	0	0.60	0.11
17	H + H2C^1HC^2 = H3C^1HC^2	0	0.74	0.44
18	H + C^1H3C^2 = HC^1H3C^2	0	1.22	1.17
19	H2C^1H2C^2 + H = H2C^1H3C^2	0.10	0.47	0.25
20	H + H2C^1H2C^2 = H3C^1H2C^2	0	0.95	0.89
21	H + HC^1H3C^2 = H2C^1H3C^2	0	0.99	0.51
22	H3C^1HC^2 + H = H3C^1H2C^2	0	0.76	0.46
23	H + H2C^1H3C^2 = H3C^1H3C^2	0	0.87	0.16
24	H3C^1H2C^2 + H = H3C^1H3C^2	0	0.99	−0.05

---

Table 4 shows that the intrinsic energy barrier and reaction energy of the hydrogenation reaction are not high, which indicates that both the hydrogenation reaction and the dehydrogenation reaction could take place.

The energy profile diagram of the stepwise hydrogenation pathway based on the hydrogenation elementary reactions in Table 4 is shown in Fig. 4. The diagram can be divided into two parts: the hydrogenation reactions on C¹ (black lines) and the hydrogenation reactions on C² (blue lines). The green lines represent products that could be formed from both kinds of hydrogenation reactions.

Fig. 4 Energy profile diagram for the stepwise hydrogenation pathway of C₂ species on the hcp-Fe₇C₃ (211) surface. Black lines: hydrogenation reactions occurring on C¹. Blue lines: hydrogenation reactions occurring on C². Green lines: products from both kinds of hydrogenation reactions.

According to Fig. 4, the HC¹C² species is the most stable species among the C₂ species on hcp-Fe₇C₃ (211). Since most hydrogenation reactions of the HC¹C² species and their hydrogenation products are endothermic, the effective energy barrier of the hydrogenation reactions would increase gradually along with the increase of H atoms in the reactant.

Ethylene and ethane are two major C₂ products in the Fischer–Tropsch synthesis. The effective energy barriers of the ethylene formation pathway and the ethane formation pathway are 1.56 eV and 2.41 eV, respectively. It seems that ethylene would be the major C₂ product since the effective energy barrier of the ethylene formation pathway is much lower than that of the ethane formation pathway. However, the ethylene adsorption energy is 1.67 eV, which is much higher than the intrinsic energy barrier of the ethylene hydrogenation reaction (0.47 eV). As a result, the hydrogenation reaction of the ethylene adsorption would take place more easily than the ethane adsorption. The adsorption energy of ethane (0.53 eV) is lower than the intrinsic energy barrier of the ethane dehydrogenation reaction (0.70 eV). Hence, the adsorbed ethane could escape from the hcp-Fe₇C₃ (211) easily to form the ethane product. As a result, the ethane formation pathway is thought to be the major C₂ stepwise hydrogenation pathway. The detailed ethane formation pathway is shown in Scheme 4. The effective energy barrier of the ethane formation pathway is 2.41 eV, which is much higher than that of the preferred C–C coupling pathway and the CO activation pathway. The stepwise hydrogenation pathway would be the rate-determining step.

Scheme 4 The preferred stepwise hydrogenation pathway of the C₂ coupling product on hcp-Fe₇C₃ (211).

The over-hydrogenation of the C₂ species resulted in the ethane being be the major C₂ product on hcp-Fe₇C₃ (211) in the Fischer–Tropsch synthesis. This could mainly be attributed to the strong interactions between the hcp-Fe₇C₃ (211) and the adsorbed ethylene, which is characterized by the high adsorption energy of the adsorbed ethylene. Hence, if the target product in the Fischer–Tropsch synthesis is the olefin, the over-hydrogenation phenomenon should be suppressed.

The surface recovery pathway for the defect-hcp-Fe₇C₃ (211)

From the previous section, C¹ and C² are the surface carbons of the hcp-Fe₇C₃ (211) and they could be a part of the product through the C¹–C² coupling pathway, as well as the stepwise hydrogenation pathway. Regardless of the type of hydrocarbon, once the products are desorbed from the surface, the two carbon vacancy sites would form, which are denoted as the Cv1 site and Cv2 site, and the surface is denoted as the defect-hcp-Fe₇C₃ (211).

The structure of the defect-hcp-Fe₇C₃ (211) is different from that of the hcp-Fe₇C₃ (211). To allow the discovered Fischer–Tropsch reaction pathway to be repeatable and the discussed Fischer–Tropsch mechanism to make sense, the defect-hcp-Fe₇C₃ (211) should be able to recover to the hcp-Fe₇C₃ (211). Due to the CO being the major feedstock in the Fischer–Tropsch synthesis, the adsorption and activation pathways of CO on the Cv1 site and Cv2 site are thought to be the possible surface recovery pathway, which is denoted as the carbon vacancy recovery pathway.

The designed carbon vacancy recovery pathway contained three kinds of elementary reactions after the CO adsorption on the Cv1 site or the Cv2 site, which are the hydrogenation reactions on the carbon site, the hydrogenation reactions on the oxygen site, and the dissociation reactions of C–O bonds.

The computation results are shown in Table 5. The intrinsic energy barrier of the elementary reaction in the carbon vacancy recovery pathway is a bit high, which indicates that the carbon vacancy recovery pathway may occur with difficulty.

Table 5 The intrinsic energy barrier (E_a, eV), the reaction energy (E_r, eV), and migration energy (E_m, eV) of the reactions in the carbon vacancy recovery pathway

No	Reaction	Em	Ea	Er
1	H + C^1O = HC^1O	0	1.04	1.03
2	C^2O = C^2 + O	0	1.18	−0.75
3	H + C^2O = HC^2O	0	1.27	1.13
4	C^1O = C^1 + O	0	1.37	0.17
5	C^1O + H = C^1OH	0	1.58	0.81
6	C^2O + H = C^2OH	0	1.66	1.04
7	HC^1O = HC^1 + O	0	0.46	−0.90
8	H + HC^1O = H2C^1O	0	0.89	0.65
9	HC^1O + H = HC^1OH	0	1.64	1.15

---

The energy profile diagram of the carbon vacancy recovery pathway is shown in Fig. 5. The blue line represents the carbon vacancy recovery pathway in the Cv1 site and the black line represents the carbon vacancy recovery pathway in the Cv2 site.

Fig. 5 Energy profile diagram for the carbon vacancy recovery pathway on defect-hcp-Fe₇C₃ (211). Blue lines: the carbon vacancy recovery pathway in the Cv1 site. Black lines: the carbon vacancy recovery pathway in the Cv2 site.

On the Cv1 site, in the first step, the HCO formation reaction showed a relatively low intrinsic energy barrier of 1.04 eV. However, in the subsequent reactions, the effective energy barrier of the HCO dissociation reaction would be high (1.49 eV) because of the high instability of HCO species. At the same time, the intrinsic energy barriers of the CO dissociation reaction and COH formation reaction were 1.37 eV and 1.58 eV, respectively. As a result, the dissociation reaction of the adsorbed CO is the preferred carbon vacancy recovery pathway in the Cv1 site.

On the Cv2 site, among the three kinds of elementary reactions in the carbon vacancy recovery pathway, the CO dissociation reaction shows the lowest intrinsic energy barrier (1.18 eV). The intrinsic energy barriers of the HCO formation pathway and COH formation pathway are 1.27 eV and 1.66 eV, respectively. Thus, the dissociation reaction of adsorbed CO is also the preferred carbon vacancy recovery pathway in the Cv2 site and the subsequent reactions of HCO species and COH species need not be taken into account.

From another perspective, the carbon vacancy recovery pathway is the CO activation pathway on carbon vacancy. Thus, the effective energy barriers of the CO activation pathway on the Cv1 site and the Cv2 site are 1.37 eV and 1.18 eV, respectively, which are close to the effective energy barrier of the H-assisted CO activation pathway on the top site (1.30 eV).

The results above indicate that the carbon vacancy is the possible CO activation site. Since the C¹–C² coupling pathway is the major C–C coupling mechanism, the surface carbon would be consumed rapidly so that the carbon vacancy would form frequently. Hence, it could be inferred that the C vacancy, especially the Cv2 site, is the major CO activation site.

After completing the carbon vacancy recovery pathway, the dissociation oxygen would be left on the hcp-Fe₇C₃ (211). The accumulation of surface oxygen would result in the changing of the iron carbide phase. As a result, whether the surface oxygen could be removed from the surface efficiently is the last piece of the puzzle to confirm the Fischer–Tropsch mechanism achieved in this article.

CO₂ or H₂O are the major products of the surface oxygen on the iron catalysts. Therefore, the H₂O formation pathway and CO₂ formation pathway are set as the designed oxygen removal pathways, shown in Scheme 5. The computation results are shown in Table 6.

Scheme 5 The designed oxygen removal pathways on hcp-Fe₇C₃ (211).

Table 6 The intrinsic energy barrier (E_a, eV), the reaction energy (E_r, eV), and migration energy (E_m, eV) of the reactions in the oxygen removal pathway

No	Reaction	Em	Ea	Er
1	O + H = OH	0	1.30	0.53
2	O + CO = CO2	0	1.40	0.87
3	OH + CO = COOH	−0.01	1.24	0.89
4	OH + H = H2O	−0.01	1.49	0.87
5	COOH = CO2 + H	−0.02	0.70	−0.30

---

The energy profile diagram of the oxygen removal pathway is shown in Fig. 6. In the first step, the intrinsic energy barriers of the O + H pathway and O + CO pathway are 1.30 eV and 1.40 eV, respectively, which are close. In the subsequent reaction, the desorption energy of CO₂ is 0.53 eV, which is much lower than the intrinsic energy barrier of the OH + H pathway and OH + CO pathway. As a result, the CO₂ formation pathway is the preferred oxygen removal pathway with a relatively low effective energy barrier (1.50 eV), while the H₂O formation pathway is suppressed due to the high effective energy barrier of 2.01 eV.

Fig. 6 Energy profile diagram for oxygen removal pathways on hcp-Fe₇C₃ (211). Blue lines: the H₂O formation pathways. Black lines: the CO₂ formation pathways.

In brief, the surface recovery pathway contains the C recovery vacancy pathway and the oxygen removal pathway is clear. The effective energy barrier of the preferred C recovery vacancy pathway in the Cv1 site, the preferred C recover vacancy pathway in the Cv2 site, and the oxygen removal pathway are 1.37 eV, 1.18 eV, and 1.50 eV, respectively. The effective energy barrier of the preferred surface recovery pathway is higher than that of the major C–C coupling mechanism but lower than the preferred C₂ stepwise hydrogenation pathway. Hence, it could be proved that if the C₂ product could be properly produced through the preferred C₂ stepwise hydrogenation pathway, the defect-hcp-Fe₇C₃ (211) could also possibly recover to the hcp-Fe₇C₃ (211). The presence of the surface recovery pathway could confirm that the studied surface is stable under the Fischer–Tropsch synthesis reaction conditions and the Fischer–Tropsch mechanism achieved above is universal on hcp-Fe₇C₃ (211).

The full map of the Fischer–Tropsch mechanism and the role of the surface carbon on hcp-Fe₇C₃ (211)

According to the discussion in this article, the full map of the Fischer–Tropsch mechanism on hcp-Fe₇C₃ (211) can be achieved. The achieved Fischer–Tropsch mechanism would begin with the adsorption of CO and the dissociation H, which are from the reactant syngas, and end with the C₂ product. The full map of the Fischer–Tropsch mechanism is shown in Scheme 6.

Scheme 6 The full map of the Fischer–Tropsch mechanism on hcp-Fe₇C₃ (211).

On hcp-Fe₇C₃ (211), the Fischer–Tropsch mechanism can be divided into several parts. First, the C¹ would undergo the hydrogenation reaction to form the HC species. Second, the HC¹ species would be able to couple with the C² so that the HC¹C² species would come into being. Third, the HC¹C² species would form the ethane product through a stepwise hydrogenation pathway. Fourth, two carbon vacancy sites would form after the desorption of the ethane product, resulting in the changing of the hcp-Fe₇C₃ (211) to the defect-hcp-Fe₇C₃ (211). Fifth, the CO would adsorb and dissociate directly on the C vacancy so that the C¹ and C² would recover. Sixth, the surface oxygen from the CO would be removed in the form of CO₂ and the Fischer–Tropsch synthesis would restart in the first step.

In the achieved Fischer–Tropsch mechanism, the effective energy barriers of the six steps are 0.73 eV, 0.97 eV, 2.41 eV, 0.53 eV, 1.37 eV and 1.50 eV, respectively. As a result, on the hcp-Fe₇C₃ (211), the stepwise hydrogenation pathway is thought to be the rate-determining step of the Fischer–Tropsch mechanism. Hence, it could be inferred that the C₂ species and the C vacancy would accumulate on the hcp-Fe₇C₃ (211) surface. Since the effective energy barrier of the C vacancy recovery pathway is not high, the Cv1 site and Cv2 site could act as the CO activation site to produce the C₁ species with the co-adsorption C₂ species. After that, the C–C coupling reaction could take place, possibly involving the C₂ species and C₁ species so that the length of the carbon chain would increase.

The adsorption energy of ethylene is high (1.67 eV). It could also be inferred that after the chain growth process, if the adsorption site of the long-chain olefins is on the same site, the adsorption energy of long-chain olefin would be close to that of ethylene, which would result in the alkane rather than the olefin being the major product on the hcp-Fe₇C₃ (211).

During the Fischer–Tropsch mechanism, it was found that carbon vacancy sites are the CO activation pathway sites and the surface carbon sites are the C–C coupling pathway sites; the surface carbon and its vacancy play a key role in the Fischer–Tropsch mechanism on the hcp-Fe₇C₃ (211).

As mentioned before, the surface carbon is always thought to be able to participate in the Fischer–Tropsch synthesis in iron carbide. On the other iron carbide, such as χ-Fe₅C₂ (510), θ-Fe₃C (100), and θ-Fe₃C (010), the surface carbon just acts as the chain initiation site, the C₁ species participating in the chain growth process are the CO-activated products from the surface sites.^39,40 On the hcp-Fe₇C₃ (211), the surface carbon not only acts as the chain initiation site but also acts as the chain growth site. Hence, it could be concluded that on the hcp-Fe₇C₃ (211), the total Fischer–Tropsch synthesis takes place on the vacancy site while on the other iron carbide, only a part of the Fischer–Tropsch synthesis takes place on the vacancy site. This property may result in the high reactant conversion and reaction rate of the Fischer–Tropsch synthesis.³³

From another perspective, it is the defect-hcp-Fe₇C₃ (211) rather than the hcp-Fe₇C₃ (211) that is the high active facet of the Fischer–Tropsch synthesis. However, at first, the defect-hcp-Fe₇C₃ (211) is not thought of as the stable surface to be researched. Based on this article, it could be found that under the Fischer–Tropsch synthesis conditions, the exposed surface would change and update with the influence of CO and H₂. As a result, when researching the Fischer–Tropsch mechanism on the iron carbide phase through the theoretical method, the change in the selected surface structure should be taken into account, especially the change in the surface carbon.

According to the mechanism achieved in this article, the hcp-Fe₇C₃ (211) shows high conversion of syngas, which is the advantage of the Fischer–Tropsch synthesis. However, the major products in the hcp-Fe₇C₃ (211) would be the long-chain products or the alkane products, which is the disadvantage of the Fischer–Tropsch synthesis, especially when the target products are the light olefins. As a result, promoting or suppressing the formation of the hcp-Fe₇C₃ phase is dependent on the purpose of the iron catalyst.

Conclusions

The Fischer–Tropsch mechanism along with the role of surface carbon and vacancies have been studied on the hcp-Fe₇C₃ (211). The major conclusion is shown below:

First, the C¹–C² coupling pathway was presented as a possible C–C coupling pathway. In the C¹–C² coupling pathway, it was found that the HC¹ + C² pathway is the preferred C¹–C² coupling pathway with the effective energy barrier of 0.97 eV, which is much lower than that of the other possible C–C coupling pathway found before. Hence, the HC¹ + C² pathway is thought to be the major C–C coupling pathway and the HC¹C² species are the major C₂ species from the C–C coupling pathway on the hcp-Fe₇C₃ (211).

Second, the stepwise hydrogenation pathway was discussed. Ethylene and ethane are the two major possible C₂ products. Since the adsorption energy of ethylene (1.67 eV) is higher than the intrinsic energy barrier of the ethylene hydrogenation reaction (0.47 eV), the desorption process of the ethylene hardly takes place. As a result, the ethane formation pathway is the preferred stepwise hydrogenation pathway on hcp-Fe₇C₃ (211).

Third, the surface recovery pathway was discussed to allow the Fischer–Tropsch mechanism to make sense. The direct dissociation reaction of adsorption CO on the Cv1 site and Cv2 site is thought to be the preferred carbon vacancy recovery pathway with the effective energy barriers of 1.37 eV and 1.18 eV, respectively. The dissociated oxygen from the carbon vacancy recovery pathway would be removed from the surface in the form of CO₂ with the effective energy barrier of 1.50 eV. Since the effective energy barrier of the surface recovery pathway is lower than that of the stepwise hydrogenation pathway of C₂ species, the hcp-Fe₇C₃ (211) would likely recover from the defect-hcp-Fe₇C₃ (211).

Fourth, the full map of the Fischer–Tropsch mechanism on the hcp-Fe₇C₃ (211) was presented. In the achieved Fischer–Tropsch mechanism, the stepwise hydrogenation pathway is the rate-determining step for the high effective energy barrier (2.41 eV), which would also cause the increase in the carbon chain length. Moreover, due to the adsorption energy of ethylene, it could be inferred that the alkanes would be the major hydrocarbon products on the hcp-Fe₇C₃ (211).

Fifth, the roles of the surface carbon and vacancies were concluded according to the Fischer–Tropsch mechanism. It was found that the carbon vacancy sites were the CO activation pathway sites and the surface carbon sites were the C–C coupling pathway sites. The surface carbon not only acted as the chain initiation site but also acted as the chain growth site on the hcp-Fe₇C₃ (211). From another point of view, the circulation of the surface carbon indicated that the defect-hcp-Fe₇C₃ (211) was the high active facet of the Fischer–Tropsch synthesis in which the carbon vacancy was the active site.

Finally, we hope that all these findings from DFT calculations could provide a detailed and comprehensive understanding of the Fischer–Tropsch mechanism on the hcp-Fe₇C₃ phase and the role played by surface carbon in the Fischer–Tropsch synthesis. We hope that other researchers can utilize the information produced in this article to decide whether to promote, suppress, or modify the hcp-Fe₇C₃ phase in the iron catalysts. Also, we hope that the changes in the surface structure would be taken into account when researching the Fischer–Tropsch mechanism on the iron carbide phase through the theoretical method.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors gratefully acknowledge the College of Biological, Chemical Sciences and Engineering of Jiaxing University and the R&D Center for Petrochemical Technology of Tianjin University for providing high performance computing service.

References

1. M. E. Dry, Appl. Catal., A, 2004, 276, 1–3.
2. M. Stcker, Angew. Chem., Int. Ed., 2008, 47, 9200–9211.
3. M. E. Dry, Catal. Today, 2002, 71, 227–241.
4. H. Schulz, Appl. Catal., A, 1999, 186, 3–12.
5. J. Bao, G. Yang, Y. Yoneyama and N. Tsubaki, ACS Catal., 2019, 9, 3026–3053.
6. H. M. T. Galvis and K. P. de Jong, ACS Catal., 2013, 3, 2130–2149.
7. H. M. T. Galvis, A. C. J. Koeken, J. H. Bitter, T. Davidian, M. Ruitenbeek, A. I. Dugulan and K. P. de Jong, J. Catal., 2013, 303, 22–30.
8. G. B. Yu, B. Sun, Y. Pei, S. H. Xie, S. R. Yan, M. H. Qiao, K. N. Fan, X. X. Zhang and B. N. Zong, J. Am. Chem. Soc., 2010, 132, 935–937.
9. B. Gu, V. V. Ordomsky, M. Bahri, O. Ersen, P. A. Chemayskii, D. Filimonov and A. Y. Khodakov, Appl. Catal., B, 2018, 234, 153–166.
10. V. V. Ordomsky, Y. Luo, B. Gu, A. Carvalho, P. A. Chernavskii, K. Cheng and A. Y. Khodakov, ACS Catal., 2017, 7, 6445–6452.
11. Z. P. Tian, C. G. Wang, J. Yue, X. H. Zhang and L. L. Ma, Catal. Sci. Technol., 2019, 9, 2728–2741.
12. P. C. Psarras, J. Wilcox and D. W. Ball, Phys. Chem. Chem. Phys., 2017, 19, 5495–5503.
13. Y. R. He, P. Zhao, J. J. Liu, W. P. Guo, Y. Yang, Y. W. Li, C. F. Huo and X. D. Wen, Phys. Chem. Chem. Phys., 2018, 20, 25246–25255.
14. E. de Smit, F. M. F. de Groot, R. Blume, M. Havecker, A. Knop-Gericke and B. M. Weckhuysen, Phys. Chem. Chem. Phys., 2010, 12, 667–680.
15. L. Oar-Arteta, M. J. Valero-Romero, T. Wezendonk, F. Kapteijn and J. Gascon, Catal. Sci. Technol., 2018, 8, 210–220.
16. F. Jiang, B. Liu, W. P. Li, M. Zhang, Z. J. Li and X. H. Liu, Catal. Sci. Technol., 2017, 7, 4609–4621.
17. J. Mulpuri, Ind. Eng. Chem. Res., 1990, 29, 1735–1753.
18. T. A. Wezendonk, X. H. Sun, A. I. Dugulan, A. J. F. van Hoof, E. J. M. Hensen, F. Kapteijn and J. Gascon, J. Catal., 2018, 362, 106–117.
19. S. Janbroers, J. N. Louwen, H. W. Zandbergen and P. J. Kooyman, J. Catal., 2009, 268, 235–242.
20. O. Zhuo, L. J. Yang, F. J. Gao, B. L. Xu, Q. Wu, Y. N. Fan, Y. Zhang, Y. F. Jiang, R. S. Huang, X. Z. Wang and Z. Hu, Chem. Sci., 2019, 10, 6083–6090.
21. L. W. Niu, X. W. Liu, J. J. Liu, X. Liu, X. D. Wen, Y. Yang, J. Xu and Y. W. Li, J. Catal., 2019, 371, 333–345.
22. Y. J. Li, Z. S. Li, A. Ahsen, L. Lammich, G. J. A. Mannie, J. W. H. Niemantsverdriet and J. V. Lauritsen, ACS Catal., 2019, 9, 1264–1273.
23. J. Zhang, M. Abbas and J. G. Chen, Catal. Sci. Technol., 2017, 7, 3626–3636.
24. C. S. Kuivila, P. C. Stair and J. B. Butt, J. Catal., 1989, 118, 299–311.
25. C. S. Huang, L. Xu and B. H. Davis, Fuel Sci. Technol. Int., 1993, 11, 639–664.
26. R. Christoffersen and P. R. Buseck, Science, 1983, 222, 1327–1329.
27. C. Yang, H. B. Zhao, Y. L. Hou and D. Ma, J. Am. Chem. Soc., 2012, 134, 15814–15821.
28. E. de Smit, A. M. Beale, S. Nikitenko and B. M. Weckhuysen, J. Catal., 2009, 262, 244–256.
29. T. Herranz, S. Rojas, F. J. Perez-Alonso, M. Ojeda, P. Terreros and J. L. G. Fierro, J. Catal., 2006, 243, 199–211.
30. J. D. Louw, J. P. Vandenberg, L. C. Ferreira and J. J. Pienaar, J. Am. Chem. Soc., 1957, 79, 5899–5902.
31. A. K. Datye, L. Mansker and Y. M. Jin, Stud. Surf. Sci. Catal., 2000, 130, 1139–1144.
32. B. Williams, D. Clifford, A. A. El-Gendy and E. E. Carpenter, J. Appl. Phys., 2016, 120, 6.
33. Q. Chang, C. H. Zhang, C. W. Liu, Y. X. Wei, A. V. Cheruvathur, A. I. Dugulan, J. W. Niemantsverdriet, X. W. Liu, Y. R. He, M. Qing, L. R. Zheng, Y. F. Yun, Y. Yang and Y. W. Li, ACS Catal., 2018, 8, 3304–3316.
34. T. H. Pham, X. Z. Duan, G. Qian, X. G. Zhou and D. Chen, J. Phys. Chem. C, 2014, 118, 10170–10176.
35. T. H. Pham, Y. Y. Qi, J. Yang, X. Z. Duan, G. Qian, X. G. Zhou, D. Chen and W. K. Yuan, ACS Catal., 2015, 5, 2203–2208.
36. M. H. Zhang, J. Ren and Y. Z. Yu, ACS Catal., 2020, 10, 689–701.
37. Y. R. He, P. Zhao, J. Q. Yin, W. P. Guo, Y. Yang, Y. W. Li, C. F. Huo and X. D. Wen, J. Phys. Chem. C, 2018, 122, 20907–20917.
38. B. X. Chen, D. Wang, X. Z. Duan, W. Liu, Y. F. Li, G. Qian, W. K. Yuan, A. Holmen, X. G. Zhou and D. Chen, ACS Catal., 2018, 8, 2709–2714.
39. L. J. Deng, C. F. Huo, X. W. Liu, X. H. Zhao, Y. W. Li, J. G. Wang and H. J. Jiao, J. Phys. Chem. C, 2010, 114, 21585–21592.
40. T. Li, X. D. Wen, Y. Yang, Y. W. Li and H. J. Jiao, ACS Catal., 2020, 10, 877–890.
41. Y. F. Wang, Y. Li, S. Y. Huang, J. Wang, H. Y. Wang, J. Lv and X. B. Ma, Chem. Phys. Lett., 2017, 682, 115–121.
42. C. F. Huo, Y. W. Li, J. G. Wang and H. J. Jiao, J. Am. Chem. Soc., 2009, 131, 14713–14721.
43. M. Zhang, J. Ren and Y. Yu, Mol. Catal., 2021, 505, 111506.
44. V. V. Ordomsky, B. Legras, K. Cheng, S. Paul and A. Y. Khodakov, Catal. Sci. Technol., 2015, 5, 1433–1437.
45. F. H. Herbstein and J. A. Snyman, Inorg. Chem., 1964, 3, 894–896.
46. P. E. Blochl, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 50, 17953–17979.
47. G. Kresse and J. Furthmüller, Comput. Mater. Sci., 1996, 6, 15–50.
48. F. Kresse, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169–11186.
49. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
50. P. Methfessel, Phys. Rev. B: Condens. Matter Mater. Phys., 1989, 40, 3616–3621.
51. H. J. Monkhorst and J. D. Pack, Phys. Rev. B: Condens. Matter Mater. Phys., 1976, 13, 5188–5192.
52. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem. Phys., 2010, 132, 19.
53. S. Grimme, S. Ehrlich and L. Goerigk, J. Comput. Chem., 2011, 32, 1456–1465.
54. D. Sheppard, R. Terrell and G. Henkelman, J. Chem. Phys., 2008, 128, 10.
55. D. Sheppard, P. H. Xiao, W. Chemelewski, D. D. Johnson and G. Henkelman, J. Chem. Phys., 2012, 136, 8.
56. J. Cheng, P. Hu, P. Ellis, S. French, G. Kelly and C. M. Lok, J. Phys. Chem. C, 2010, 114, 1085–1093.
57. J. Cheng, P. Hu, P. Ellis, S. French, G. Kelly and C. M. Lok, J. Phys. Chem. C, 2009, 113, 8858–8863.
58. J. Cheng, X. Q. Gong, P. Hu, C. M. Lok, P. Ellis and S. French, J. Catal., 2008, 254, 285–295.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1ra06396k

---