Iron Carbides in Fischer-Tropsch Synthesis: Theoretical and

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Iron Carbides in Fischer-Tropsch Synthesis: Theoretical and Experimental Understanding in Epsilon-Iron Carbide Phase Assignment Xing-Wu Liu, Zhi Cao, Shu Zhao, Rui Gao, Yu Meng, Jianxin Zhu, Cameron Rogers, Chun-Fang Huo, Yong Yang, Yongwang Li, and Xiaodong Wen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06104 • Publication Date (Web): 11 Sep 2017 Downloaded from http://pubs.acs.org on September 13, 2017

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The Journal of Physical Chemistry

Iron Carbides in Fischer-Tropsch Synthesis: Theoretical and Experimental Understanding in Epsilon-Iron Carbide Phase Assignment Xing-Wu Liu,1,2+ Zhi Cao,3+ Shu Zhao,4+ Rui Gao,1,2 Yu Meng,

1,2

Jian-Xin Zhu,5 Cameron

Rogers,3 Chun-Fang Huo,2* Yong Yang,1,2 Yong-Wang Li,1,2* Xiao-Dong Wen,1,2*

1

State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of

Sciences, Taiyuan, 030001, P.R. China 2

National Energy Center for Coal to Clean Fuels, Synfuels China Co., Ltd, Huairou District,

Beijing, 101400, P.R. China 3

Department of Chemistry, University of California, Berkeley, California 94720, USA

4

Beijing Guyue New Materials Research Institute, Beijing University of Technology, Beijing

100124, PR China 5

Theoretical Division and Center for Integrated Nanotechnologies, Los Alamos National

Laboratory, Los Alamos, NM 87544, USA

ACS Paragon Plus Environment

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ABSTRACT: As active phases in low-temperature Fischer–Tropsch synthesis for liquid fuel production, epsilon iron carbides are critically important industrial materials. However, the precise atomic structure of epsilon iron carbides remains unclear, leading to a half-century of debate on the phase assignment of the ε-Fe2C and ε’-Fe2.2C. Here, we resolve this decades-long question by a combining theoretical and experimental investigation to assign the phases unambiguously. First, we have investigated the equilibrium structures and thermal stabilities of ε-FexC, (x = 1, 2, 2.2, 3, 4, 6, 8) by first-principles calculations. We have also acquired X-ray diffraction patterns and Mössbauer spectra for these epsilon iron carbides, and compared them with the simulated results. These analyses indicate that the unit cell of ε-Fe2C contains only one type of chemical environment for Fe atoms, while ε’-Fe2.2C has six sets of chemically distinct Fe atoms.


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1. Introduction As one of the most powerful technologies in heterogeneous catalysis, Fischer–Tropsch synthesis (FTS) has significantly advanced the production of value-added liquid fuels from coal and renewable biomass.1-3 Among existing FTS catalysts, transition metal-based catalysts are the most prevalent, for instance, iron, cobalt, nickel and ruthenium. Iron catalysts are especially desirable, since iron features low cost, very high abundance, and high water-gas-shift activity.5 During FTS, iron carbides form by the reaction of syngas with various iron facets, which typically consist of many active phases. The Hägg (χ-Fe5C2), cementite (θ-Fe3C), and Hexagonal (epsilon or ε-) iron carbides are believed to be the active phases of FTS.2,6,7 While the χ-Fe5C2 and θ-Fe3C phases are structurally and chemically well defined,8 ε-carbides remain insufficiently understood.9,10 The study of various ε-carbides dates to the 1950s, with the report of iron carbides featuring a crystallographically hexagonal structure by Hofer11 and Jack12. Much effort since then has been devoted to identifying the possible hexagonal phases and evaluating their structural role in the promotion of the FTS. Barton discussed the possible structures on the basis of the formula Fe2C.13 The most acceptable structure is space group P63/mmc with cell dimensions of a = b = 2.794 Å, c = 4.360 Å (from PDF data card (36-1249)). The structure of ε-Fe3C with lattice constants of a = 4.767 Å and c = 4.354 Å, and the space group P6322 was reported by Nagakura. 14 To date, ε-Fe2C, ε’-Fe2.2C, and ε-Fe3C are the only three phases identified experimentally in the literature; in each case, carbon atoms are situated in the octahedral interstices of the hexagonal close-packed (hcp) Fe lattice.6 Among these three phases, rich crystalographic structure information (such as space group, lattice parameters, etc.) is known only for ε-Fe2C and ε-Fe3C.11,13 In contrast, the precise structure of the ε’-Fe2.2C phase remains a


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mystery. Following literature precedent, the ε’-Fe2.2C phase is frequently conflated with the εFe2C phase, as the ε’-Fe2.2C is isostructural to the ε-Fe2C, and the carbon placement in the hcp Fe matrix is disordered for the ε-Fe2C and ε’-Fe2.2C phases. As such, the site occupancy of C in εFe2C and ε’-Fe2.2C is 0.50 and 0.45, respectively. Much effort has been devoted to distinguishing and identifying these two ε-carbides experimentally and theoretically. Maksimov and co-workers reported the first Mössbauer spectroscopic study of the ε-carbide, and the chemical environment of iron atoms can be assigned, according to their different hyperfine fields. Particularly, the spectrum of ε-Fe2C features three different sextets with room-temperature hyperfine fields of 170 ± 3, 237 ± 3 and 130 ± 6 kGauss,15,16 indicative of three distinct chemical environments for Fe atoms in the εFe2C. The ε’-Fe2.2C was speculated to have hyperfine field of about 170 kGauss, which was further demonstrated in a carburized Fe/SiO2 catalyst, 17 revealing the singular chemical environment of iron in ε’-Fe2.2C. Since then, most researchers have differentiated the ε-Fe2C and ε’-Fe2.2C phases according to the aforementioned Mössbauer assignments.6,18-20 However, these assignments have been the subject of suspicion by both Niemantsverdriet et al.21 and Gridnev et al.22 due to the unsatisfied criterion of invariance of nuclear constants. In this contribution, for the first time, we report the precise atomic arrangement of the εFe2C and ε’-Fe2.2C phase of the iron-based FTS catalysts. Using first-principle calculations, the possible equilibrium structures and thermodynamic stabilities of various epsilon iron carbides have been fully explored. Further, we exhibit a unified approach to this phase assignment problem by combining both experimentally observed and theoretically simulated XRD and MES results to distinguish the atomic arrangement of these two phases. Importantly, we have fully considered the magnetism induced by the incorporation of carbon atoms into the framework of


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hcp iron. We hope the precisely defined atomic arrangement verified by this unified approach can end the decades-long confusion of the phase assignments for ε-Fe2C and ε’-Fe2.2C. 2. Experimental and theoretical details 2.1 ε-carbide synthesis and Mössbauer spectra α-Fe2O3 used in present study was prepared by a combination of precipitation and spraydrying technologies. In brief, a solution containing Fe(NO3)3•9H2O was used in precipitation with NH4OH solution as precipitator at pH = 8.5 ~ 9.0 and T = 70 oC. The precipitate was washed, and then filtered. The mixture was reslurried and spray-dried. Finally, the sample with diameters of 20 ~ 26 µm was calcined at 450 oC for 5 h in a muffle furnace. Samples of ε-carbide was prepared by gas carburization method. α-Fe2O3 (about 1 g) was loaded in the quart tube and reduced to α-Fe by H2 (80 ml/min) at 300 oC for 24 h. And then, ε-carbide would be prepared by carburizing α-Fe under 1:4 CO/H2 (80 ml/min) at 180 oC for 48 h. The Mössbauer spectra of ε-carbide was acquired in an MR-351 constant-acceleration Mössbauer spectrometer (FAST, Germany) drive with a triangular reference signal at the temperature of 11 K. The radioactive source was 57Co source in an Rh matrix. Data analysis was performed using a nonlinear least-squares fitting routine that modeled the spectra as a combination of singlets, quadruple doublets, and magnetic sextets based on a Lorentzian line shape profile. Isomer shifts values reported in this work are relative to that of α-Fe foil at 11 K. 2.2 The structure searching for ε-carbides In this work, the ε-carbide phases were represented by a symmetry-adapted ensemble of configurations in a supercell, using the methodology implemented in the SOD (Site Occupancy


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Disorder) program23. The SOD program generates the complete configurational space for each composition in a supercell of the structure before extracting the subspace of symmetrically inequivalent configurations, for which energies are evaluated by Vienna ab initio simulation package (VASP). 24,25 Take ε-Fe2C for example, we obtained all the different substitutions of C and vacancy in the octahedral sites of different supercells of the ε-Fe2C structure (Table S1). It is clearly that Number of independent configurations increases sharply from 2×2×1 to 2×2×2 to 2×2×3. For ε’Fe2.2C, the supercell 2×2×3 was used and there were 9551 independent configurations. Figure S1 exhibits the total energies of the independent configurations for ε-Fe2C (2×2×3) and ε’-Fe2.2C (2×2×3), respectively. The configurations with the lowest total energy are marked with a red cycle. For ε-Fe2C, we also searched the most stable structure within the supercells 2×2×1 and 2×2×2. Moreover, we found that the most stable structures from these three supercells are consistent with each other. The most stable structure of ε-Fe2C (2×2×3) is the supercell of that of ε-Fe2C (2×2×1). 2.3 Iron carbides optimizations and Mössbauer modeling All structural relaxations were performed at the level of density functional theory (DFT) with VASP. Electron-ion interaction was described by the projector augmented wave (PAW) method.24,25 Electron exchange and correlation energy was treated within the generalized gradient approximation and the Perdew-Burke-Ernzerhof scheme (GGA-PBE).

26

Spin

polarization was included in all calculations on the ferromagnetic iron carbide systems and this is essential for an accurate description of the magnetic properties. Iterative solutions of the KohnSham equations were done using a plane-wave basis with energy cutoff of 400 eV, and the


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samplings of the Brillouin zone were generated from the Monkhorst-Pack scheme. A secondorder Methfessel-Paxton 27 electron smearing with σ = 0.2 eV was used to ensure accurate energies with errors due to smearing of less than 1 meV per unit cell. The convergence criteria for the force and electronic self-consistent iteration were set to 0.03 eV/Å and 10–4 eV, respectively. The formation energy (∆fH) per atom of an iron carbide is found using the following formula: ∆fH = {E(FexCy) – [xE(α-Fe) + yE(C)]}/(x + y). We use the WIEN2k code28,29 to calculate theoretical Mössbauer parameters. The APW+lo basis for l = 0, 1, 2 and the standard LAPW expansion for higher angular momenta l were used. States lying more than 7 Ry below Fermi level were treated as the core states. The radii RMT used in the calculations fall in the range of 1.89 − 2.2 a.u. for Fe, and 1.54 – 1.6 a.u. for C. The wave functions in the interstitial regions were expanded in plane waves with a cutoff of Rmt Kmax = 7.0, while the magnitude of the largest vector in the Fourier expansion of the charge density Gmax was set to 16 Ry . The number of k points in the whole Brillouin zone was set to 10000, and spinorbit coupling was taken into account in the iron carbides. The convergence criterion for all calculations is the charge convergence, which was set to (0.0001 e). From the Mössbauer calculations, the following results were obtained: the magnetic moment, the magnetic hyperfine field (Hhf), the electronic concentration presented at nucleus position (ρ0) and the electric field gradient tensor (EFG) expressed by its main component (Vzz) and the asymmetry parameter (η). Details of Mössbauer parameters calculation are described in our previous work.30 3. Results and discussion


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Notably, hcp iron is only observed at high pressure,31,32 since at lower pressures Fe-hcp rapidly reforms α-Fe.33 Therefore, the ε-carbides that exist under FTS conditions imply that the hcp iron matrix might be stabilized by the interstitial octahedral carbon atoms. To gain deeper insight into the influence of carbon incorporation on the thermodynamic stability of ε-carbides, the equilibrium structures (Figure 1) of ε-Fe2C, ε’-Fe2.2C, ε-Fe3C, ε-Fe4C, ε-Fe6C, and ε-Fe8C were searched by code Site Occupancy Disorder (SOD) interfaced with VASP.

Figure 1. Structures (left) and Formation energies (right) of various epsilon iron carbides, referenced to α-Fe and graphite. (Large yellow spheres indicate Fe atoms; smaller black spheres indicate C atoms). To evaluate the thermodynamic stability as a function of the change in interstitial carbon atom concentration, the formation energies of various ε-carbides ε-FexC, [(x = 1, 2, 2.2, 3, 4, 6, 8)] have been calculated, and the results are shown in Figure 1. The formation energies of εFe3C (33.3 meV/atom) and ε-Fe2C (36.4 meV/atom) are among the lowest. Another relatively


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stable carbide is ε’-Fe2.2C (44.1 meV/atom), which has a formation energy close to that of ηFe2C (41.5 meV/atom). As might be expected, these four stoichiometrically similar compositions feature comparable thermodynamic stability. The ε-Fe4C (57.4 meV/atom) and ε-Fe6C (55.8 meV/atom) are less stable than ε’-Fe2.2C, but are more stable than Fe-hcp (80.2 meV/atom). εFe8C (165 meV/atom) and ε-FeC (486 meV/atom) are less stable than Fe-hcp. Therefore, the trend in stability is ε-Fe3C > ε-Fe2C > ε’-Fe2.2C > ε-Fe6C > ε-Fe4C > Fe-hcp >> ε-Fe8C > ε-FeC, which agrees well with the fact that ε-Fe3C, ε-Fe2C, and ε’-Fe2.2C are the only experimentally verified epsilon iron carbide phases. Phonon calculations further confirm that the models of εFe2C and ε’-Fe2.2C are dynamically stable (see Figure S2). Recently, Lv et al.9 and Fang et al.35 proposed another models for ε-Fe2C, respectively. These models for ε-Fe2C are very different from the structure parameters of ε-Fe2C in our calculations. As shown in Table S2, Lv’s model is that the Fe atoms are at 4f (1/3, 2/3, 0) and the C atoms at 2a (0, 0, 0) with the space group P63/mmc. The calculated formation energy is 1101.2 meV/atom. Fang’s model employs a supercell with ah = 2√3a0, ch=c0, (a0 = 2.7727, c0 = 4.2951) which contains 24 Fe atoms, and has the formation energy of 52.6 meV/atom. Our model was screened from a (2×2×2) supercell with 122 independent configurations, which has the lowest formation energy (37.9 meV/atom) among them. Furthermore, the calculations show that only our model for ε-Fe2C is more stable than η-Fe2C (∆fH = 36.4 vs 41.5 meV/atom, respectively). Following optimization of the equilibrium structures, we can further scrutinize the calculated structural features of the ε-Fe2C and ε’-Fe2.2C phases, and the calculated lattice constants are provided in Table S3. For a given atom in both ε-Fe2C and ε’-Fe2.2C, the number


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of structurally adjacent atoms as a function of the distance to this atom is summarized in Figure 2. From the histogram, it is clear that ε-Fe2C and ε’-Fe2.2C possess similar coordination environments, with each iron atom participating in three Fe−C bonds (ca. 1.90 Å) and twelve Fe−Fe bonds (ca. 2.60 ~2.80 Å). The shortest Fe-C bond is around 1.90 Å in both carbides, and falls into the range of expected Fe-C bond distance for many structures in the Inorganic Crystal Structure Database (see Figure S3 and Figure S4). The shortest distance between adjacent carbon atoms is 2.80 Å, much longer than that of the C-C bond (1.54 Å) in ethane, indicating no C-C bond formation in both ε-carbides. Likewise, the 3.5 Å distance between adjacent iron atoms is sufficiently far as to preclude Fe-Fe bond formation. Consequently, only the twelve Fe−Fe bonds (ca. 2.60 ~2.80 Å) are counted in both ε-carbides.

Figure 2. The number of structurally adjacent atoms as a function of the distance to a central atom: (a) ε-Fe2C and (b) ε’-Fe2.2C. Among crystalline materials, XRD is quite evidently an efficient tool for phase identification, and provides rich information regarding unit cell dimensions. It is therefore the


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ideal tool to scrutinize the subtle differences between various experimentally prepared ε-carbide phases during the FTS process. Therefore, we prepared an iron-based sample containing εcarbides. Briefly, the sample of ε-carbide was prepared by heating iron in an atmosphere of 1:4 CO/H2 at 180 °C for 48 h. The resulting sample gives the MES and XRD pattern shown in Figure S5 and Figure 3 (a), indicating that the sample is pure ε-carbide without any impurity phases (χ-Fe5C2, θ-Fe3C or Fe3O4, see Figure S5). As shown in Figure 3 (a), X-ray diffraction peaks with 2θ of 44.08, 48.5, 50.66, 67.6, and 81.08 were indexed to the (100), (002), (101), (102), and (110), reflections of either ε-Fe2C (JCPDS 36-1249), ε’-Fe2.2C (JCPDS 36-1249), or ε-Fe3C (JCPDS 89-3689), respectively. This result confirmed unambiguously that we had successfully synthesized a sample containing ε-carbide phases.

Figure 3. (a) Experimental XRD of ε-carbide and simulated XRD of ε-Fe2C, η-Fe2C, ε’-Fe2.2C, and ε-Fe3C with peak broadening by particle size effects (15 nm). (b) Experimental and simulated Mossbauer spectra of ε-Fe2C, η-Fe2C, ε’-Fe2.2C, and ε-Fe3C.


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Simulated XRD patterns of the ε-Fe2C, ε’-Fe2.2C, ε-Fe3C and even η-Fe2C phases were then compared with that acquired from the experimentally prepared ε-carbide, as shown in Figure 3 (a). The peak broadening effect associated with particle size (average 15 nm) has been fully addressed. The η-Fe2C was included in this discussion, since η-Fe2C has a crystalline structure similar to that of the ε-carbide.34,35 Upon comparison of the experimental and theoretical XRD patterns, it is very clear that the simulated data for ε-Fe2C and ε’-Fe2.2C fit extremely well with the experimentally acquired pattern for ε-carbide. However, given that the ε-Fe2C and ε’-Fe2.2C phases feature identical lattice parameters and vary only in the site occupancy of carbon atoms, additional XRD investigations were unable to further distinguish between these structures.

Table 1. Theoretical Mössbauer Parameters of ε-Fe2C, ε'-Fe2.2C, η-Fe2C, and ε-Fe3C predicted in this work and Experimental Mössbauer Parameters of these carbides reported in literature at room temperature.

this work IS Hhf (mm/s) (kGauss) 0.2 180

Name

Sites

ε-Fe2C

Fe1 Fe2 Fe3

ε'- Fe2.2C

Fe1 Fe2 Fe3 Fe4 Fe5 Fe6

0.3 0.3 0.3 0.3 0.3 0.2

259 232 186 181 177 170

η-Fe2C

Fe1

0.29

ε-Fe3C

Fe1

0.23

Ratio

1 2 2 5 1 1

lit data (Room temperature) IS Hhf Refs (mm/s) (kGauss) 170±3 4 237±3 1.6 15,16 130±6 1 0.51±0.01

173±1

15,16

179

0.28±0.08

178±0.4

36,37

250

0.38

247

38


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To differentiate between the ε-Fe2C and ε’-Fe2.2C phases, and thereby identify the composition of the ε-carbide in the iron-based FTS catalysts, a Mössbauer study was carried out at 11 K to characterize as-synthesized ε-carbide, and the resulting spectrum is shown in Figure 3 (b). MES spectra of all the ε-Fe2C, ε’-Fe2.2C, ε-Fe3C and η-Fe2C have been simulated at 0 K under 0 atm. They can be obtained from wave function calculations by using a full-potential linear-augmented plane wave (FLAPW) or Gaussian basis sets methods. 39,40 In our previous work,30 the MES of iron carbides (α-Fe, γ'-FeC, η-Fe2C, ζ-Fe2C, χ-Fe5C2, h-Fe7C3, θ-Fe3C, oFe7C3, γ'-Fe4C, γ''-Fe4C, and α'-Fe16C2) was predicted utilizing the FLAPW approach with various functionals from LDA to GGA (PBE, PBEsol, and GGA+U) to meta-GGA to hybrid functionals. By comparison to experimental data, we find that the GGA functional (especially, the PBEsol) is remarkably successful for the prediction of MES spectra for α-Fe, χ-Fe5C2, and θFe3C with delocalized Fe 3d-electrons. In the work, the simulated Mössbauer parameters were calculated at 0 K and 0 atm under the framework of full-potential linear-augmented plane wave (FLAPW). It is hard to calculate the Mössbauer parameters under various temperature using the current methodology. Indeed, there was a gap between the theoretical Mössbauer parameters and experimental parameters in room temperature. As we have studied in our previous work,30 the Mössbauer parameters especially hyperfine fields at experimental conditions can be extrapolated from the theoretical parameters 0 K and 0 atm by using the formula Hhf(T) = Hhf(0 K)(1 − T/Tc)β, where Tc is the curie temperature and β is called a critical exponent (for mean field theory β = 0.5). However, we don’t have the reliable curie temperature of ε-Fe2C and ε’-Fe2.2C to calculate the Mössbauer parameters at liquid helium (4.2 K), liquid nitrogen (77 K) and room temperature (298 K).


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According to our previous work,30 the experimental Mössbauer parameters at low temperature (11 K) are very close to the theoretical values. Therefore, in this work, the Mössbauer spectra of ε-carbide was acquired at the temperature of 11 K. The calculated MES were then compared with the experimentally acquired spectrum, as shown in Figure 3 (b) and Table 1. In each of the simulated MES spectra for ε-Fe2C, η-Fe2C, and ε-Fe3C, there is only one sextet (Figure 3 (b)) with hyperfine fields of 180, 179, and 250 kGauss (Table 1), respectively, indicating uniform chemical environments for Fe atoms in the unit cells of ε-Fe2C, η-Fe2C and ε-Fe3C. In stark contrast, the predicted MES spectrum of ε’Fe2.2C consists of six subspectra with hyperfine fields of 259, 232, 186, 182, 179, and 171 kGauss, respectively, and the stoichiometric ratio of Fe1 : Fe2 : Fe3 : Fe4 : Fe5 : Fe6 is 1 : 2 : 2 : 5 : 1: 1. It should be noted that the simulated hyperfine fields (0 K) of ε’-Fe2.2C at 232, 186, 182, 179, and 171 kGauss are comparable to experimentally determined (room temperature) hyperfine fields at 170 ± 3 and 237 ± 3 kGauss of the ε-Fe2C. We conclude that ε-Fe2C has only one chemical environment for the Fe atoms in the unit cell, with hyperfine field of 180 kGauss, while the ε’-Fe2.2C features 6 distinct types of Fe atoms in the unit cell. As shown in Figure S5 (b) and Table 2, the experimental MES spectrum of the sample also was fitted by using Mössbauer parameters of ε’-Fe2.2C predicted in this work and Mössbauer parameters of ε-Fe2C reported by Maksimov.15,16 It is clearly that the value of R-squared for ε’-Fe2.2C is better than that for Maksimov’s parameters. Most importantly, the theoretical MES spectrum of ε’-Fe2.2C is in excellent agreement with that obtained experimentally for ε-carbide, indicating that the assynthesized ε-carbide is principally the ε’-Fe2.2C.


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Table 2. Fitting results of the ε-carbide sample based on Mössbauer Parameters of ε’-Fe2.2C predicted in this work and Mössbauer parameters of ε-Fe2C reported by Maksimov, respectively.

Fe1 Fe2 Fe3 Fe4 Fe5 Fe6

IS (mm/s) 0.40 0.40 0.35 0.40 0.37 0.00

QS (mm/s) -0.04 0.06 -0.15 0.23 0.20 -0.76

Hhf (kGauss) 266 243 193 190 170 165

LWa (mm/s) 0.58 0.419 0.519 0.488 0.34 0.5

RAb (%) 19.5 7.57 25.5 35.1 6.13 6.23

Fe1 Fe2 Fe3

0.36 0.40 0.19

0.07 -0.04 -0.23

191 258 147

0.5 0.582 0.582

61.42 27.49 11.09

Sites

This work

Maksimov

1.59

2.6

Line Width; b Relative area. (a) 350 300

Hhf (kGauss)

250 200 150 100 50 0

C Fe ε- C 2 Fe η- C 2 Fe ε- 2C 2. Fe ε- C-2 3 Fe ε- C-1 3 Fe ε- C 4 Fe ε- C 6 Fe ε- C 8 Fe cp

-h Fe

(b) 0.3 0.2

0 −0.1 −0.2 −0.3 −0.4

Average valence charge (e/Fe)

0.1 IS (mm/s)

a

15,16

R-squared

ε-

14.0 13.8 13.6 13.4 13.2 0

0.1 0.2 0.3 0.4 0.5 C Concentration (%)

C Fe ε- C 2 Fe η- C 2 Fe ε- .2C 2 Fe ε- C-2 3 Fe ε- C-1 3 Fe ε- C 4 Fe ε- C 6 Fe ε- C 8 Fe ε- p c -h Fe

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



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Figure 4. (a) The hyperfine fields (kGauss) of Fe atom in various ε-carbides. The triangledashed line highlights the trend in average Hhf as a function of the C/Fe ratio. (b) The IS (mm/s) of an Fe atom in various ε-carbides. The triangle-dashed line highlights the trend in average IS as a function of the C/Fe ratio. The insert shows the linear relationship between average valence electrons (AVE) of Fe atoms and the C/Fe ratio. In addition to thermodynamically stabilizing the parent hcp iron structure, carbon atom incorporation will also impact the magnetic properties of the resulting iron carbide. We sought to quantify this influence by performing hyperfine field calculations for many other ε-carbides (εFe8C, ε-Fe6C, ε-Fe4C and ε-Fe3C), as well as for the Fe-hcp, and obtained values consistent with literature results32 as shown in Figure 4 (a). By directly comparing Fe-hcp and the ε-carbides in this manner, we find tentative correlation between magnetism and thermodynamic stability in these systems. Importantly, Fe-hcp exhibits Hhf of 0 kGauss, in keeping with the fact that Fe-hcp is experimentally nonmagnetic. Further, ε-FeC also exhibits Hhf of 0 kGauss; it has the highest formation energy among the ε-carbides, due to having the largest lattice distortion energy and no contribution of magnetic exchange interaction. In contrast, all other ε-carbides with lower formation energies possess some degree of magnetism. Importantly, the contribution from magnetism is known to be an important determinant of thermodynamic stability in iron carbides. 41 Induced magnetism in the ε-carbides further stabilizes the ferromagnetic state in comparison to the nonmagnetic state; we calculated this change in the energetic gap between the two states, as well as the distortion energy of all the ε-carbides, and the results are summarized in Figure S7. The isomer shift (IS) is a crucial metric for MES analysis, and it provides useful information about the nuclear structure and chemical environment of the relevant atoms. Our


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calculations of this parameter in various ε-carbides clearly indicate that as carbon atom dissolution increases in the Fe-hcp matrix, the IS of ε-carbides relative to that of Fe-hcp increases monotonically as a consequence of electron density transfer from Fe to C (see Figure 4 (b) insertion). 4. Concluding remarks In conclusion, we have resolved the precise atomic arrangement of the ε-Fe2C and ε’-Fe2.2C phases for iron-based FTS catalysts, and have thereby resolved a long-standing controversy over the phase assignments of ε-Fe2C and ε’-Fe2.2C. We made use of a unified approach to this phase assignment challenge, combining experimentally observed and theoretically simulated XRD and MES results to distinguish the atomic arrangement of the two phases. We anticipate that this generalizable strategy can be brought to bear across a wide range of catalytic applications for which experimental and theoretical results can be effectively correlated and analyzed. In particular, we seek to expand this unified approach to examine novel materials applications, where design and performance can be greatly enhanced through an improved understanding of atomic arrangement and interfacial structure.


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ASSOCIATED CONTENT Supporting Information. Structure information and the phonon band structure of ε-Fe2C and ε’-Fe2.2C, experimental XRD and MES of ε-Fe2C, χ-Fe5C2, θ-Fe3C, and Fe3O4 are provided in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Author Contributions Xing-Wu Liu, Zhi. Cao, Shu. Zhao contributed equally to this work. Xing-Wu Liu, Xiao-Dong Wen, Yong-Wang Li, and Chun-Fang Huo designed the study. Xing-Wu Liu performed the experiments and DFT calculations. Xing-Wu Liu, Shu Zhao and Xiao-Dong Wen wrote the paper. Xiao-Dong Wen, Shu Zhao, Chun-Fang Huo, Jian-Xin Zhu, Cameron Rogers, and Zhi Cao revised the paper. Shu Zhao and Yu Meng analyzed data. All authors contributed the idea and participated in the scientific discussions, manuscript comments and corrections. The authors declare no conflict of interest. Corresponding Author * E-mail: [email protected], [email protected], [email protected] Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT


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The authors are grateful for the financial support from the National Natural Science Foundation of China (No. 21473229, No. 91545121, and No. 21273261, No. 21603252), No. 201601D021048 from the Shanxi Province Science Foundation for Youth, and Synfuels China, Co. Ltd. We also acknowledge National Thousand Young Talents Program of China, HundredTalent Program of Chinese Academy of Sciences and Shanxi Hundred-Talent Program. This work was supported, in part, by the Center for Integrated Nanotechnologies, a U.S. DOE Office of Basic Energy Sciences user facility. We are grateful to Prof. Roald Hoffmann in Cornell University for critical comments and suggestions. Finally, the authors would like to dedicate the work to Professor Roald Hoffmann on the occasion of his 80th birthday.

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Iron Carbides in Fischer-Tropsch Synthesis: Theoretical and

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