Role of Step Sites and Surface Vacancies in the Adsorption and

J. Phys. Chem. C 2010, 114, 7863–7879

7863

Role of Step Sites and Surface Vacancies in the Adsorption and Activation of CO on χ-Fe5C2 Surfaces Melissa A. Petersen,* Jan-Albert van den Berg, and Werner Janse van Rensburg Sasol Technology (Pty) Ltd., R&D DiVision, 1 Klasie HaVenga Road, Sasolburg 1947, South Africa ReceiVed: December 11, 2009; ReVised Manuscript ReceiVed: March 9, 2010

Density functional theory calculations have been used to investigate CO adsorption on three surface terminations of χ-Fe5C2 in the presence of carbon vacancy sites. CO did not show a strong energetic preference for a particular adsorption site on each surface, since similar adsorption energies were obtained for structurally distinct adsorption configurations. In addition, it was found that the adsorption of CO in a vacancy site is not necessarily more favorable energetically, compared with adsorption in alternative Fe sites. The presence of a subsurface carbon atom directly below a 4-fold site was found to inhibit or significantly destabilize adsorption of CO in that site. The role of step sites in activating CO has been investigated by comparing the calculated adsorption energies, structural properties, and vibrational stretching frequencies of CO adsorbed in equivalent sites in the presence or absence of steps. Coordination of CO to the surface through both ends of the molecule was associated with a lengthening of the C-O bond and a red-shift of the C-O stretching frequency, and such geometries were readily obtained for adsorption at the bottom of a step. Activation energies were calculated for the dissociation of CO initially adsorbed in a vacancy site in the presence and absence of steps. The step sites were found to lower the activation energy by at least 0.3 to 0.6 eV, without destabilizing the initial state. 1. Introduction The Fischer-Tropsch synthesis (FTS) reaction converts synthesis gas (a mixture of H2 and CO) derived from coal, natural gas, or biomass into chemicals and hydrocarbon fuels.1,2 Commercially, catalysts based mainly on Fe or Co are used, the choice of which is dependent on factors such as the source from which the synthesis gas is derived, the cost of the catalyst material, and the desired product distribution. In particular, ironbased catalysts are suited to coal-to-liquid (CTL) technologies due to their ability to catalyze the water-gas shift reaction, which can increase the low H2/CO ratio typical of synthesis gas derived from coal gasification.3 This, coupled with the abundance and low cost of iron, has led to the use of ironbased catalysts in commercial CTL operations, such as at the Sasol facilities based in Secunda, South Africa.1 Iron-based Fischer-Tropsch (FT) catalysts undergo complex phase transformations both during catalyst pretreatment and during FTS.4–6 Typically, the catalyst precursor phase (such as R-Fe2O3) is treated in H2, CO, or synthesis gas, followed by FTS, during which a mixture of carbide, oxide, and metallic iron phases may coexist.5 In particular, the formation of iron carbide phases has been associated with FT activity,7–9 and in some instances a correlation between the extent of bulk carburization of the catalyst and the FT activity has been reported.7,8 At least five different carbide phases have been identified as forming under FTS conditions, including the ε′Fe2.2C, ε-Fe2C, χ-Fe5C2, θ-Fe3C, and Fe7C3 phases.10–13 The extent of carburization of the catalyst and identity of the carbide phases present both prior to and during FTS have been observed to be sensitively dependent on the preparation, pretreatment, and process conditions.9,11–14 Although the formation of iron carbide phases has been cited to be a necessary prerequisite for FTS activity,9,15 a correlation between the bulk carbide phase * E-mail: [email protected].

composition and catalyst activity has not been consistently observed,3,16,17 and the role of bulk carbide phases in FTS remains under debate.4 Nevertheless, FT activity has in a number of cases been related to the amount of χ-Fe5C2 phase present in the catalyst,5,14,18,19 suggesting that the Ha¨gg iron carbide phase (χ-Fe5C2) may play an important role in FT activity. Although it should be acknowledged that the working catalyst is likely to be a mixture of phases4,20 that may exhibit amorphous regions,5 and in which the surface composition may differ from the bulk,17,21 an understanding of the intrinsic reactivity of an iron carbide phase that has been associated with FT activity, such as χ-Fe5C2, is likely to yield fundamental insight into the underlying catalytic role of carbide phases during iron-based FTS. One way to obtain such insight is through the use of first principles calculations based on density functional theory (DFT), which have been successfully applied in the elucidation of fundamental aspects of catalytic processes of industrial relevance.22,23 With respect to iron carbides, a number of studies based on DFT calculations have emerged in recent years, focusing on the bulk and surface properties of Fe3C,24,25 Fe4C,26 and Fe5C2,24,27 or on the chemisorption of CO and/or H2 on Fe3C,28 Fe4C,29 and Fe5C2 surfaces.30–33 Two further studies on ketene hydrogenation34 and carbon species35 adsorbed on Fe5C2(001) have also been reported, and very recently the role of vacancy sites on iron carbides, formed through surface carbon hydrogenation, has been highlighted.36,37 A common feature of all of these studies is that they have focused on the low Miller index iron carbide surfaces, without placing any particular emphasis on the relationship between similar adsorption sites in different surface environments. FTS necessarily starts with the adsorption and activation of CO on the catalyst surface. Recent DFT studies that have focused on the structure sensitivity of elementary catalytic reactions such as CO dissociation, have revealed that steps sites can significantly lower the activation energy for CO dissociation on a range of transition metals, including Fe,38 Co,39–41 Ni,42 Ru,43 Rh,44,45 and Pd.44 Specifically

10.1021/jp911725u  2010 American Chemical Society Published on Web 04/01/2010

7864

J. Phys. Chem. C, Vol. 114, No. 17, 2010

in the context of FT catalysis, Huo et al.41 concluded that on cobalt surfaces, step sites are favored for CO dissociation through both a direct and a hydrogen-assisted route, and steps have also been suggested to be the preferred sites for surface coupling reactions between C1 species.46 Such studies highlight the importance of considering a variety of surface environments in a study of the catalytic reactivity of a chosen system. In this work we investigate the adsorption of CO on three χ-Fe5C2 surfaces, placing particular emphasis on the role of the local surface environment in influencing the adsorption properties of related adsorption sites on the surfaces. The calculation methodology is described in section 2. A description of the surfaces and the relationship between them is given in section 3, together with the results and discussion of CO adsorption and activation on the surfaces. We conclude with a summary of the main findings in section 4. 2. Calculation Methodology Spin-polarized density functional theory calculations were performed using the Vienna ab initio simulation package (VASP).47,48 The exchange-correlation energy was calculated using the RPBE functional,49 together with the projector augmented wave (PAW) method to describe the electron-ion interactions.48,50 This methodology is denoted by RPBE-PAW in the current work and refers to fully self-consistent calculations. For comparison, a second set of calculations was also performed using the PW91 functional51 with the spin interpolation of Vosko-Wilk-Nusair,52 in combination with ultrasoft pseudopotentials53 (USPP) to describe the electron-ion interactions, which we denote PW91-USPP. Throughout this work, results obtained with the PW91 functional are reported in parentheses. VASP employs a plane wave basis set, for which a cutoff energy of 400 eV was used, unless stated otherwise. Brillouin zone integration was achieved by summation over a MonkhorstPack mesh54 of k-points, with a sampling density of ∼0.04 Å-1. Specific details of the k-point meshes used for the bulk and surface calculations are given in the corresponding sections below. In all bulk and surface calculations, Methfessel-Paxton55 smearing to first order was employed, with σ ) 0.1 eV. For the calculation of CO adsorption energies and geometries, a periodic slab representation of the surfaces was used, with a vacuum spacing of ∼10 Å between neighboring slabs. Test calculations indicate that, by increasing the vacuum spacing to 14 Å, the calculated CO adsorption energies change by only 0.02 eV/ CO. CO was adsorbed on only one side of the slab, and the atom positions of the adsorbate and approximately the upper half of the slab were optimized based on the calculated forces, while the bottom half of the slab was constrained in the bulkoptimized configuration. Specific parameters describing the slab geometry and constraints for each iron carbide surface investigated in this work are given in the corresponding sections below. In all cases, the structural optimization was continued until the forces on the unconstrained atoms fell below 0.03 eV/ Å. Dipole corrections to the total energy have been included following the prescription implemented in the VASP code.56 The nudged elastic band (NEB) method of Jońsson et al.,57 implemented in the VASP code, was used to locate transition states for CO dissociation, which were further refined using a quasi-Newton algorithm to minimize the forces. All stationary points identified on the respective potential energy surfaces have been characterized based on a normal-mode analysis within the frozen phonon approximation: the Hessian matrix is constructed using finite differences, by perturbing the adsorbate atoms by

Petersen et al. 0.02 Å in the direction of each of the Cartesian coordinates, while keeping the substrate atoms fixed at their optimized positions. Diagonalization of the mass-weighted Hessian matrix yields the vibrational frequencies of adsorbed CO, within the harmonic approximation, from which zero-point energy (ZPE) contributions have been calculated. Atom-resolved magnetic moments were calculated by projecting the eigenstates onto spherical harmonics within spheres centered on each atom, and integrating the site- and spin-resolved density of states up to the Fermi level. For the PW91-USPP method, Wigner-Seitz radii of 1.302 Å (Fe) and 0.863 Å (C) were used, while for the RPBEPAW method the projection scheme based on the radial cutoffs of the PAW potentials was used.56 For the isolated CO molecule, the calculated equilibrium C-O bond length, ZPE-corrected bond dissociation energy, and harmonic vibrational frequency of 1.14 Å (1.15 Å), 1067 kJ/ mol (1074 kJ/mol) and 2118 cm-1 (2104 cm-1) obtained with the RPBE-PAW (PW91-USPP) methodology are in satisfactory agreement with the experimental values58 of 1.13 Å, 1076 kJ/ mol and 2170 cm-1, respectively. 3. Results and Discussion 3.1. Bulk Properties of Fe5C2. The crystal structure of χ-Fe5C2 has been determined to be monoclinic (space group C2/c) using X-ray diffraction techniques, with conventional lattice parameters a ) 11.588 Å, b ) 4.579 Å, c ) 5.059 Å, and β ) 97.746°.59 The conventional unit cell has a stoichiometry of Fe20C8 and contains three unique Fe atoms (with Wyckoff positions of Fe-I (x1, y1, z1) (8f), Fe-II (x2, y2, z2) (8f), Fe-III (0, y3, 0.25) (4e)), and one unique carbon atom (C (x4, y4, z4) (8f)), for which the experimentally determined parameters for the Wyckoff positions are given in Table 1. A full optimization of the primitive unit cell parameters (stoichiometry Fe10C4) and atomic positions has been performed60 using both the RPBE-PAW and PW91-USPP methodologies with a k-point mesh of 6 × 6 × 5 (sampling density ∼0.04 Å-1). Increasing the k-point mesh to 12 × 12 × 10 (sampling density ∼0.02 Å-1) leads to a change in the total energy of less than 0.1 meV, indicating that the total energy is well converged with respect to the k-point sampling density already at 0.04 Å-1. The calculated lattice parameters of a ) 11.622 Å, b ) 4.549 Å, c ) 5.032 Å, and β ) 97.81° obtained with the RPBE-PAW methodology deviate by less than 1% from the experimental values (see Table 1). This satisfactory agreement with experiment is also obtained with the PW91-USPP approach, for which calculated lattice parameters of a ) 11.612 Å, b ) 4.560 Å, c ) 5.037 Å, and β ) 97.87° were obtained. Comparison with the results of Sorescu,33 who used the PBE functional61 and the PAW method as implemented in the VASP code to calculate the bulk structure of χ-Fe5C2, demonstrates that both the RPBEPAW and PW91-USPP protocols provide marginally improved agreement with experiment in terms of reproducing the unit cell parameters (Table 1). A similar improved agreement with experiment as compared to results obtained in our previous work27 using a different software package is noted. The calculated parameters describing the Wyckoff positions of the three unique Fe atoms and the unique C atom in the unit cell are also reported in Table 1. The most significant deviation from the experimentally determined parameters is obtained for the carbon atom. We note, however, that some variation in the experimental crystal structure has been reported, particularly with respect to the distribution of carbon atoms in the unit cell.62 The local magnetic moments on each unique atom in the unit cell calculated with the RPBE-PAW (PW91-USPP) method are

Adsorption and Activation of CO on χ-Fe5C2 Surfaces

J. Phys. Chem. C, Vol. 114, No. 17, 2010 7865

TABLE 1: Calculated and Experimentally Determined Lattice Parameters and Wyckoff Positions Defining the Conventional Bulk Unit Cell of χ-Fe5C2 lattice parametersa method b

PW91-USPP RPBE-PAWb PBE-PAWc expt.d

a (Å)

b (Å)

c (Å)

β (deg)

11.612 (0.21) 11.622 (0.29) 11.580 (-0.07) 11.588

4.560 (-0.41) 4.549 (-0.66) 4.508 (-1.55) 4.579

5.037 (-0.43) 5.032 (-0.53) 4.994 (-1.28) 5.059

97.87 (0.13) 97.81 (0.07) 96.64 (-1.13) 97.746

Wyckoff positions method b

PW91-USPP RPBE-PAWb expt.d d

Fe-I (8f)

Fe-II (8f)

Fe-III (4e)

C (8f)

(0.097, 0.082, 0.415) (0.098, 0.082, 0.416) (0.097, 0.078, 0.423)

(0.215, 0.581, 0.312) (0.215, 0.580, 0.312) (0.215, 0.581, 0.306)

(0, 0.570, 0.25) (0, 0.570, 0.25) (0, 0.561, 0.25)

(0.113, 0.312, 0.080) (0.113, 0.313, 0.079) (0.107, 0.285, 0.149)

a Percentage deviations from the experimental parameters are given in parentheses. Experimental parameters from ref 59.

2.21 µB (2.31 µB) for Fe-I, 1.83 µB (1.98 µB) for Fe-II, and 1.24 µB (1.38 µB) for Fe-III, whereas the carbon atom is polarized in the opposite sense with a local magnetic moment of -0.11 µB (-0.12 µB). This opposite spin-polarization of the carbon atom appears to be a common feature of iron carbides,24,25,27,33 with similar results being obtained for Fe3C24,25 and Fe2C.24 The calculated average magnetic moment on the Fe atoms of 1.86 µB (1.99 µB) is higher than the experimental estimate of 1.72-1.75 µB based on saturation magnetization measurements.63 A similar overestimation of the average magnetic moment was obtained by Chiou and Carter25 in their calculations of cementite (Fe3C) using a similar calculation methodology. Sorescu33 obtained a calculated average magnetic moment in agreement with experiment using the PBE-PAW approach. Nevertheless, we note that the calculated local magnetic moments are sensitive to the projection scheme used, particularly with regard to the choice of radii used to partition the spindensity, and therefore should be regarded as qualitative. 3.2. Surfaces of χ-Fe5C2. The nature of the active surface phase in iron-based FTS remains under debate,4 particularly with regard to the role of Fe and C atoms in the FT mechanism. Niemantsverdriet and van der Kraan64 put forward three interpretations of the role of iron in the FTS reaction. In the “competition model” iron sites are considered to be active for FTS and the formation of the bulk carbide phase competes with hydrocarbon and inactive carbon formation, which all have a common surface carbide precursor. In the “slow activation” model, a unique surface arrangement of carbon, iron and hydrogen is necessary for hydrocarbon formation (and the carbide phase can be regarded as a spectator phase), whereas in the “carbide model”, the active sites are attributed to the bulk iron carbide phase. In their isotope-labeling experiments of FTS using a Fe/Al2O3 catalyst, Stockwell et al.65 noted that the exchange of carbon between the surface and bulk was slow, and they suggested that bulk carbide does not participate appreciably in the hydrocarbon synthesis. They further concluded that the active sites for hydrocarbon formation may be highly localized on the catalyst surface. Sirimanothan et al.17 have stressed that catalyst activity is determined by the nature of the surface phase rather that the bulk phase composition. Xu and Bartholomew66 have characterized different types of carbonaceous species that form during iron-based FTS, identifying atomic, “lightly polymerized” and bulk carbide species using temperature programmed hydrogenation. Despite these research efforts, however, a consensus on the nature of the active surface phase, as well as the nature and role of surface, subsurface and bulk carbon in FTS has not yet emerged. In this work we focus

b

This work.

c

Theoretical values reported in ref 33.

on three surface terminations of χ-Fe5C2 that have closely related adsorption sites, but which differ in terms of the presence or absence of step sites, as described below. As a first step toward characterizing the reactivity of the iron carbide surfaces as a function of surface carbon coverage, we investigate CO adsorption on the surfaces in the regime where the surface coverage of atomic carbon is zero, an approach that is distinct from that of earlier studies.30,33 We note that this approach effectively introduces carbon vacancy sites at the surface, the role of which has only very recently been highlighted for iron carbides using DFT methods.36,37 3.2.1. Fe5C2(010)0.25 Surface. As illustrated in Figure 1, the bulk structure of χ-Fe5C2 can be viewed as an alternating series of (010) Fe layers (indicated in orange or green in Figure 1) stacked in the [010] direction with carbon atoms positioned inbetween. Each such Fe5C2(010) layer has an identical arrangement of atoms within the plane, but every alternate plane is displaced laterally in the [100] direction by a distance equivalent to half the length of the unit cell, giving rise to a stacking sequence that repeats in the [010] direction only every second layer. The calculated average distance between successive Fe5C2(010) planes in the bulk is 2.27 Å (2.28 Å), while the calculated buckling amplitude of Fe atoms within each (010) plane is 0.75 Å (0.75 Å). We have previously adopted a notation to label distinct surface terminations corresponding to a particular Miller plane (ref 27). Extending this notation, the surface termination that exposes the repeating (010) plane as defined above, is the Fe5C2(010)0.25 surface, which is obtained by cleaving the conventional monoclinic unit cell of Ha¨gg iron carbide parallel to the (010) Miller plane at a fractional displacement of 0.25 along the unit cell axes. (In this work, all surface terminations are referenced to the origin of the conventional unit cell, as defined by Retief.59) In recent DFT studies of Ha¨gg iron carbide surfaces,27,33 the Fe5C2(010)0.25 surface was found to have the lowest surface energy of a set of low Miller index surfaces that could be represented by symmetric slabs that maintain the stoichiometry of the bulk. However, it was also demonstrated27 that structurally distinct surface orientations can have similar surface energies, suggesting that other equally stable surface orientations not explicitly considered in these studies may also exist. Therefore, an a priori identification of dominant surface planes on the catalyst particle based on the calculated surface energies alone is unlikely to be definitive in the absence of experimental observation, which is currently lacking. The Fe5C2(010)0.25 surface is shown in Figure 1a in which the p(1 × 1) surface unit cell is indicated. Based on the RPBE-

7866


Petersen et al.

Figure 1. Schematic depiction of the bulk structure of Ha¨gg iron carbide and the structural relationship between three surface terminations: (a) Fe5C2(010)0.25, (b) Fe5C2(110)0.00, and (c) Fe5C2(110)0.80. Identical (010) layers are highlighted in green and orange, and the surface unit cell is indicated in red for each surface. Fe atoms are shown in purple and carbon atoms in yellow.

PAW (PW91-USPP) calculated bulk parameters, the surface unit cell of Fe5C2(010)0.25 has optimized dimensions of 5.032 Å × 11.622 Å (5.037 Å × 11.612 Å) with γ ) 97.81° (97.87°), and has C2-1 symmetry, which reduces the number of unique adsorption sites on the surface. The surface is characterized by two structural regions in which the local arrangement of Fe atoms within the surface atomic plane is either “square” or “hexagonal” (cf. Figure 2). For the study of CO adsorption on Fe5C2(010)0.25, we consider adsorption in the absence of surface atomic carbon, as shown in Figure 2a. The “square” 4-fold sites thus exposed may be thought of as carbon vacancy sites, by virtue of the fact that the readsorption of carbon in such sites represents a continuation of the bulk χ-Fe5C2 structure. We note too that this surface is equivalent to the Fe5C2(010)0.10 termination, in which only Fe atoms are present at the surface. 3.2.2. Stepped Fe5C2(110)0.00 and Fe5C2(110)0.80 Surfaces. Due to the stacking sequence inherent in the bulk structure of Ha¨gg iron carbide, it is also possible to generate stepped surfaces with Fe5C2(010)0.25 terraces. Two such surfaces, corresponding to the Fe5C2(110)0.00 and Fe5C2(110)0.80 terminations, are schematically illustrated in Figure 1, panels b and c, respectively. These two terminations differ in terms of the portion of the Fe5C2(010)0.25 plane that is exposed at the terraces, as is evident in Figure 2, panels b and c, in which the view normal to the terrace plane of each surface is shown, without surface atomic carbon present. On the Fe5C2(110)0.00 surface a portion of the

“square” and ‘hexagonal’ adsorption sites are exposed on the terraces, while on the Fe5C2(110)0.80 termination, only “square sites” are exposed. The p(1 × 1) surface unit cell is indicated for both terminations, and has dimensions of 5.032 Å × 6.240 Å (5.037 Å × 6.238 Å) and γ ) 97.27° (97.32°), consistent with the optimized bulk lattice parameters. Of particular interest is the geometry of the step planes of the two surfaces, which bear a close similarity in terms of the Fe atom arrangement but which differ in terms of the position of subsurface carbide atoms. We note that removal of atomic carbon from each surface introduces a carbon vacancy at the bottom of the step. The surface energies of the Fe5C2(010)0.25 and Fe5C2(110)0.00 terminations, as cleaved from the bulk (i.e., in the absence of surface vacancies), were calculated using the RPBE-PAW and PW91-USPP methods, following the prescription outlined in ref 27 based on the approach of Boettger.67 The Fe5C2(010)0.25 surface energy is 1.90 J/m2 (2.06 J/m2) calculated with the RPBE-PAW (PW91-USPP) method, and the surface energy of Fe5C2(110)0.00 is 2.07 J/m2 (2.28 J/m2). For comparison we have also calculated the surface energy of the Fe3C(001) surface investigated by Chiou and Carter,25 which has surface structural features closely resembling that of Fe5C2(010)0.25. The calculated surface energy is 1.94 J/m2 (2.10 J/m2) using the RPBE-PAW (PW91-USPP) method and is in agreement with the results of Chiou et al.,25 who used the PW91-USPP method and the VASP code. The calculated surface energies for the two Fe5C2 surfaces



Figure 2. Structural representations of the three Ha¨gg iron carbide surfaces containing carbon vacancy sites: (a) Fe5C2(010)0.25, (b) Fe5C2(110)0.00, and (c) Fe5C2(110)0.80. The surface regions containing “square” and “hexagonal” sites are indicated for each surface, together with the p(1 × 1) surface unit cell. The stepped nature of the two Fe5C2(110) terminations is highlighted by the side views, together with the structural features of the step plane for each surface. Fe atoms are shown in purple and carbon atoms in yellow.

are also consistent with those of Sorescu,33 who used the same code and the PBE-PAW method, but are significantly lower than those obtained previously27 with a different software package. However, direct comparisons cannot readily be made as we have used different exchange-correlation functionals in the present work. 3.3. CO Adsorption on χ-Fe5C2 Surfaces. CO adsorption was investigated on the three χ-Fe5C2 surfaces shown in Figure 2. Adsorption energies (Eads) of CO for each site on each surface are calculated using the equation Eads ) E(slab+CO) - Eslab - ECO, where E(slab+CO) is the total energy of the slab with CO adsorbed in the applicable site, Eslab is the total energy of the optimized clean surface slab (without surface atomic C) and ECO is the energy of an isolated CO molecule in its calculated equilibrium geometry. ZPE contributions are given by EZPE ) (Σhνi)/2 where νi are the calculated vibrational frequencies of the adsorbed CO molecule, and h is Planck’s constant. In this section, we use the RPBE-PAW results for discussion and include the PW91USPP results in the respective tables for comparison. 3.3.1. CO Adsorption on Fe5C2(010)0.25. CO adsorption was investigated on a slab consisting of 25 Fe atoms and 8 C atoms in the unit cell, for which the lower 10 Fe and 4 C atoms were constrained at their bulk optimized positions. Test calculations indicate that by increasing the slab thickness to 40 Fe and 14 C atoms in the unit cell, the adsorption energies change by only 0.03 eV/CO. A (5 × 2 × 1) k-point mesh was used to sample the surface Brillouin zone, with the single k-point corresponding to the surface normal direction. The low symmetry of the adsorption sites on the Fe5C2(010)0.25 surface makes the possible adsorption modes for CO diverse. Inspection of the surface in Figure 2a reveals the presence of six unique one-fold (1F), fourteen unique 2-fold (2F), six unique 3-fold (3F), two unique “square” 4-fold (4F) and three unique “hexagonal” 4-fold (4F) sites. The variety of the CO adsorption modes is further realized from the distinctive ways in which CO can adsorb in a single site, e.g., different possible tilting directions for CO in 4-fold sites. In the current study all possible adsorption modes for all possible sites were explicitly considered. In most optimization attempts, however, CO migrated to an adjacent adsorption site, essentially resulting in the successful determination of fifteen unique structures illustrated in Figure 3. Associated structural

parameters, adsorption energies and CO stretching frequencies are summarized in Table 2 for both the RPBE and PW91 functionals. We note that the designation of an adsorption configuration as 1F, 2F, 3F, or 4F in Figure 3 and Table 2 is somewhat arbitrary, due to the low symmetry of both the adsorption sites and CO adsorption geometries on the surface. The nomenclature is therefore only intended to give an indication of the number of close Fe-C interactions between CO and the surface, for which the precise distances are summarized in the respective tables. It is immediately apparent from Table 2 that a number of equally stable CO adsorption geometries exist on the Fe5C2(010)0.25 surface, encompassing both low- and highcoordination modes. In particular, CO adsorption in one-fold sites (1F-1, 1F-2, 1F-5), in the “square” 4-fold site (4F-1) and in “hexagonal” 4-fold sites (4F-4, 4F-6) is energetically degenerate to within 0.04 eV/CO, and these are also the most stable adsorption geometries for CO on this surface. In contrast, adsorption of CO in the “square” 4-fold site in which a subsurface carbide atom resides below the site is not observed, suggesting that subsurface carbon inhibits the adsorption of CO in such sites. This observation is consistent with the results obtained by Sorescu33 for CO adsorption on Fe5C2(010)0.25 (in the presence of surface atomic carbon) and by both Sorescu33 and Cao et al.,30 for CO adsorption on Fe5C2(100)0.00 which has similar “square” Fe sites with subsurface carbide present. For the “square” 4-fold site for which stable adsorption configurations do exist, both an upright (4F-1) and a tilted (4F2) adsorption geometry were obtained. The upright configuration is more stable, and has an adsorption energy of -1.62 eV/CO calculated with the RPBE functional. The CO molecule is tilted by 10.4° relative to the normal of the least-squares-fitted plane through the four Fe atoms of the 4-fold site, and interacts with the surface Fe atoms only through the carbon of the CO molecule. Although the tilted adsorption mode (4F-2) is less stable by 0.18 eV, the C-O distance of 1.29 Å is elongated relative to that of the upright mode (1.23 Å), and the C-O stretching frequency of 1303 cm-1 is lower than that of the upright mode (1547 cm-1). Both of these observations indicate that the CO molecule is more activated in the tilted geometry in which the O-atom interacts with the surface Fe atoms (dFe-O

7868


Petersen et al.

Figure 3. Schematic representations of CO adsorbed in different sites on the Fe5C2(010)0.25 surface. Fe and C atoms of the iron carbide substrate are shown in purple and yellow, respectively. The C and O atoms of adsorbed CO are shown in green and red, respectively. Labels correspond to data summarized in Table 2.

) 2.15 Å and 2.23 Å), suggesting that the tilted mode may be a precursor to dissociation in the “square” 4-fold site. In fact, 4F-2 is the most activated adsorption mode for CO identified with the RPBE functional on the Fe5C2(010)0.25 surface in terms of both the elongation of the C-O bond, and the red-shift of the stretching frequency relative to those calculated for the gasphase molecule. The observation that the higher degree of coordination of the CO molecule to the surface in the tilted geometry is associated with a greater degree of activation of the molecule is consistent with the conclusions of Sorescu.33 It is of interest to note that CO preferentially adsorbs in a tilted configuration in the 4-fold hollow site at 0.25 ML on the Fe(100) surface of R-Fe, which has been observed both experimentally68–71 and theoretically.72–77 The Fe(100) surface is characterized by square 4-fold sites that resemble the Fe atom arrangement of the “square” sites on Fe5C2(010)0.25; however

we note that on the carbide surface the in-plane Fe-Fe nearestneighbor distances are contracted relative those of ideal Fe(100) [i.e., ∼2.56 to ∼2.65 Å for Fe5C2(010)0.25 relative to ∼2.86 Å on Fe(100)]. This preference for the tilted configuration of CO on Fe(100) is not borne out on the Fe5C2(010)0.25 surface, for which the upright mode is more stable. We calculate78 an adsorption energy of -1.50 eV/CO for CO adsorbed in the tilted hollow site on Fe(100) using the RPBE-PAW method. This result is in agreement with the prediction of Jiang and Carter,73 and indicates that the CO adsorption energy on Fe(100) is comparable to that obtained for the tilted state (4F-2) on Fe5C2(010)0.25, for which the calculated adsorption energy is -1.44 eV/CO. Eight stable CO adsorption structures at three “hexagonal” 4-fold sites were identified on the Fe5C2(010)0.25 surface, which are labeled 4F-3 to 4F-10 in Figure 3. The three unique



TABLE 2: Calculated Adsorption Energies (Eads), Zero-Point Energies (ZPE), C-O Stretching Frequencies (ν(C-O)), and Structural Parameters for CO Adsorbed on Fe5C2(010)0.25 structure RPBE-PAW 1F-1 1F-2 1F-3 1F-4 1F-5 4F-1 4F-2 4F-3 4F-4 4F-5 4F-6 4F-7 4F-8 4F-9 4F-10c PW91-USPP 1F-1 1F-2 1F-3 1F-4 1F-5 4F-1 4F-2 4F-3d 4F-4 4F-5 4F-6 4F-7 4F-8 4F-9 4F-10 a

Eads (eV/CO)a

ZPE (eV/CO)

ν(C-O) (cm-1)

dFe-C, Å

-1.65 -1.63 -1.58 -1.27 -1.66 -1.62 -1.44 -1.63 -1.65 -1.49 -1.66 -1.38 -1.49 -1.45

0.20 0.20 0.20 0.21 0.20 0.16 0.16 0.17 0.16 0.16 0.17 0.16 0.17 0.17

1904 1848 1906 1874 1897 1547 1303 1595 1477 1442 1664 1329 1319 1616

1.78 1.77; 2.39 1.77 1.77 1.79 2.01; 2.10; 2.10; 2.18 1.93; 1.95; 2.11; 2.14 1.99; 2.06; 2.10; 2.28 2.01; 2.02; 2.07; 2.17 1.98; 2.00; 2.09; 2.14 1.90; 2.08; 2.31; 2.41 1.90; 1.99; 2.02; 2.42 1.91; 1.95; 2.02; 2.46 1.99; 2.00; 2.24; 2.27

-1.94 -1.87 -1.80 -1.49 -1.90 -1.97 -1.86

0.21 0.20 0.21 0.20 0.20 0.17 0.17

1909 1827 1904 1870 1897 1549 1293

1.79 1.78; 2.26 1.78 1.77 1.79 2.02; 2.08; 2.09; 2.16 1.92; 1.94; 2.11; 2.15

-1.98 -1.88 -1.97 -1.77 -1.86 -1.78 -1.75

0.16 0.17 0.17 0.16 0.17 0.16 0.16

1427 1381 1650 1300 1280 1615 1447

1.99; 2.02; 2.07; 2.15 2.00; 2.01; 2.07; 2.10 1.97; 1.99; 2.32; 2.32 1.90; 1.99; 2.00; 2.42 1.91; 1.95; 1.99; 2.46 2.00; 2.00; 2.24; 2.24 1.98; 2.03; 2.08; 2.19

dFe-O, Å

2.15; 2.23 2.30 2.22 2.16; 2.32 2.16; 2.30

2.13; 2.16 2.17 2.07 2.10; 2.28 2.10; 2.24 2.22

dC-O, Å

CO tiltb

1.18 1.19 1.18 1.18 1.18 1.23 1.29 1.22 1.25 1.25 1.21 1.28 1.28 1.22

10.4 52.1 15.5 32.2 30.0 8.4 56.3 58.0 0.3

1.17 1.19 1.17 1.18 1.19 1.23 1.30

9.7 54.4

1.26 1.27 1.21 1.29 1.29 1.22 1.26

37.1 36.5 3.2 58.6 60.7 0.8 34.1

b

Eads excludes ZPE contributions. The tilt angle (in degrees) of CO adsorbed in a 4-fold site is defined relative to the surface normal of the least-squares-fitted plane through the four Fe atoms defining the 4-fold site. c No stable structure corresponding to 4F-10 identified using the PW91-USPP method was obtained with the RPBE-PAW approach. d No stable structure corresponding to 4F-3 obtained with the RPBE-PAW method was found using the PW91-USPP approach.

“hexagonal” 4F sites can be distinguished by the upright adsorption modes for CO in each of the sites, labeled 4F-3, 4F-6, and 4F-9 in Figure 3, respectively. Two structurally distinct, but energetically similar adsorption modes in the first “hexagonal” site, 4F-3 and 4F-4, were obtained with the RPBE functional, which differ in terms of the C-O bond distance (4F3: 1.22 Å; 4F-4: 1.25 Å), stretching frequency (4F-3: 1595 cm-1; 4F-4: 1477 cm-1) and tilt angle relative to the surface normal of the local least-squares-fitted plane (4F-3: 15.5°; 4F-4: 32.2°). However, we note that an equivalent configuration for 4F-3 was not obtained with the PW91 functional: all optimization attempts resulted in the spontaneous reorientation to the tilted structure 4F-4, suggesting that the potential energy surface (PES) is relatively flat in the region of the upright adsorption mode (4F3), and that the PESs obtained with the two functionals are not entirely equivalent. It is worth re-emphasizing that all structures reported in this work have been verified as minima on the PES based on a normal-mode analysis within the harmonic approximation and assuming frozen phonons. The oxygen of tilted CO in 4F-4 interacts with a single surface iron with a Fe-O distance of 2.30 Å, while a similar marginally less stable configuration, 4F-5, with CO tilted in the opposite direction, has a slightly shorter Fe-O distance of 2.22 Å. Sorescu33 reported an upright configuration similar to 4F-3 for CO adsorbed in the same site on Fe5C2(010)0.25 in the presence of surface carbon; however, no tilted modes were reported. Whether this is due to the presence of coadsorbed surface carbon or due to the different choice of exchange-correlation functional

used in that work cannot be conclusively determined. We note that similar CO adsorption geometries in which the molecule interacts through both the C-end and O-end, with formation of a single Fe-O bond to the surface, have also been calculated on the more corrugated Fe{111}38,79,80 and Fe{211}38,81 surfaces. Adsorption in the second “hexagonal” site is characterized by both upright (4F-6) and two tilted (4F-7 and 4F-8) modes, for which the upright configuration is again energetically more favorable. The upright adsorption geometry of CO has two close (1.90 and 2.08 Å) and two more distant (2.31 and 2.41 Å) Fe-C interactions and has a calculated adsorption energy of -1.66 eV/CO. The two tilted modes (4F-7 and 4F-8) are characterized by an asymmetrical bridged interaction of oxygen with two neighboring surface iron atoms. This is accompanied by a lengthening of the C-O bond and a lowering of the C-O stretching frequency, comparable to that of the tilted CO mode on the “square” 4F site, 4F-2 (refer to Table 2). Sorescu33 similarly identified both an upright and a tilted adsorption mode for CO in the equivalent site on Fe5C2(010)0.25 in the presence of neighboring surface carbon, analogous to 4F-6 and 4F-8 in the present work. Interestingly, no tilted mode corresponding to 4F-7 was reported however, which may either be due to the presence of surface atomic carbon in the neighboring “square” 4-fold site on the termination investigated in that work or to differences in the calculated features of the PES obtained with the PBE functional.33 Nevertheless, 4F-6 is the most stable adsorption geometry both in the current work and in the work of Sorescu.33 Sorescu further calculated a minimum energy

7870


pathway for the dissociation of CO in the hexagonal site (i.e., 4F-6), for which an activation energy of 1.73 eV was obtained using the PBE-PAW method implemented in VASP. A vertical (4F-9) and a tilted (4F-10) configuration were obtained for CO adsorbed in the third “hexagonal” 4-fold site, both of which are comparatively less favorable energetically relative to adsorption in the other “hexagonal” 4-fold sites. Interestingly, the tilted mode was only obtained using the PW91 functional, and neither geometry was reported in the investigations of Sorescu,33 once again demonstrating the subtle differences in the PES calculated with different exchange-correlation functionals. The “hexagonal” sites described here for the Fe5C2(010)0.25 surface partially resemble the hexagonal surface iron atom arrangements on the Fe(110) surface of R-Fe. The adsorption of CO on the close-packed Fe(110) surface has been investigated both experimentally82 and theoretically.38,83–85 At low coverage (0.25 ML) on Fe(110), Jiang et al.84 describe a vertical adsorption of CO in the long-bridge site (similar to vertical adsorption of CO on a “hexagonal” 4F site on the carbide surface), with a calculated adsorption energy of -1.43 eV/CO using the RPBE functional, and a CO stretching frequency of 1690 cm-1 (calculated with the PBE functional). In comparison, the vertical adsorption of CO on the “hexagonal” 4F sites of Fe5C2(010)0.25 proceeds with lower RPBE adsorption energies of -1.66 to -1.45 eV/CO (i.e., more exothermic), and slightly lower CO stretching frequencies in the range of 1595 to 1664 cm-1. Of the six unique on-top adsorption sites on Fe5C2(010)0.25, only five one-fold adsorption structures are stable, labeled 1F-1 to 1F-5 in Figure 3. The CO adsorption energies for 1F-1, 1F2, 1F-3, and 1F-5 are almost degenerate at -1.66 to -1.58 eV/CO, which is noteworthy since the environments of the surface iron atoms differ in terms of their positioning in “square” and/or “hexagonal” regions, and in “pseudoedge” (1F-1, 1F-3, and 1F-5) or “pseudovalley” (1F-2) sites arising from the corrugation of the Fe5C2(010)0.25 surface. In contrast, 1F-4 is the least stable adsorption configuration on Fe5C2(010)0.25, with an adsorption energy of only -1.27 eV/CO. The on-top adsorption modes are structurally similar, with calculated Fe-C distances of 1.77 to 1.79 Å, C-O distances of ∼1.18 Å and C-O stretching frequencies of 1848 to 1906 cm-1, and are therefore the least activated adsorption modes on this surface. In comparison, on the close-packed pure Fe(110) surface the on-top adsorption of CO has been calculated to be the most stable at low coverage (0.25 ML) using DFT,83–85 with a calculated adsorption energy of -1.58 eV/CO84 using the RPBEPAW approach in VASP. The adsorption energy, together with the calculated CO stretching frequency for the one-fold coordination on Fe(110) of 1928 cm-1 (experimentally determined82 as 1956 cm-1), are similar to the results obtained for on-top CO coordination on the Fe5C2(010)0.25 surface. For the more open Fe(100) surface, it was demonstrated by Bromfield et al.74 that on-top adsorption of CO only becomes stable at a higher coverage (0.50 ML), but remains the least stable CO adsorption mode on Fe(100). For the less stable and relatively more open Fe(111) surface of R-Fe, this trend is further enhanced: it was shown that the 1F coordination of CO at all coverages e1.00 ML is the least stable adsorption mode,79 in contrast to adsorption on the Fe5C2(010)0.25 surface for which the atop sites are of the most stable adsorption sites. Finally, it is of interest to note that both 1-fold and 4-fold coordinated adsorption configurations of CO on Fe5C2(010)0.25 are nearly degenerate in energy, given that DFT has been known

Petersen et al. to incorrectly predict the most favorable adsorption site for CO on some transition metal surfaces, notably on Fe(110).83,84 The possibility that the near-degeneracy of the low- and highcoordination modes on Fe5C2(010)0.25 is an artifact of the choice of exchange-correlation functionals used in this work cannot be ruled out. Unfortunately, in the absence of the experimental characterization of CO adsorbed on iron carbide surfaces, it is not possible to quantify the degree of error, if any. We note that where inconsistencies occur in the results obtained with the RPBE and PW91 functionals on this surface, such as in the case of 4F-3 and 4F-10, the PW91 functional favors a highercoordinated mode. A similar observation was made by Huo et al.41 in their study of CO adsorption on a double-stepped Co(0001) surface, in which a tendency of the PW91 functional to stabilize higher-coordinated adsorption modes relative to the RPBE functional was also noted. 3.3.2. CO Adsorption on Fe5C2(110)0.00. The PES for CO adsorption on Fe5C2(110)0.00 was investigated by considering adsorption in all 1-, 2-, 3-, and 4-fold sites within the p(1 × 1) surface unit cell shown in Figure 2b. There are two possible “square” 4-fold sites on the (010) terrace with a subsurface carbon atom either present or absent below the site. Since it has been shown both experimentally68–71 and theoretically72–77 that CO adsorbs in a tilted configuration in the hollow site on the Fe(100) surface at 0.25 ML, analogous tilted configurations were again considered for CO adsorbed in the “square” sites of Fe5C2(110)0.00 for each of the symmetry-inequivalent directions, in addition to a vertical adsorption mode. Similar stable tilted adsorption modes have been identified for CO adsorbed on the stepped Fe(310)38,86 and Fe(710)38 surfaces using calculations based on DFT. For the “hexagonal” sites on Fe5C2(110)0.00 both vertical and tilted adsorption modes were also investigated, allowing for the possibility of the interaction of the O-atom with a surface Fe. On optimization of the adsorbate and upper 11 Fe layers and 3 C layers of a slab consisting of 20 Fe atoms and 7 C atoms per unit cell, only a limited set of adsorption sites were found to give rise to stable adsorption configurations, while in the remaining cases the CO molecule migrated to a neighboring adsorption site. The stable adsorption configurations are shown in Figure 4 and the structural parameters, adsorption energies and C-O stretching frequencies are summarized in Table 3. All structures have been verified as local minima on the PES by performing a normal-mode analysis within the harmonic approximation and assuming frozen phonons. Test calculations indicate that by increasing the slab thickness to 26 Fe and 9 C atoms in the unit cell, the adsorption energies change by only 0.02 eV/CO. For all calculations a k-point mesh of (5 × 4 × 1) was used, consistent with the shorter dimensions of the surface unit cell of Fe5C2(110)0.00. Focusing on the results obtained with the RPBE functional, it is apparent that the PES for CO adsorbed on Fe5C2(110)0.00 is relatively flat. For example, the calculated adsorption energy for CO adsorbed in the “square” 4-fold site at the bottom of the step (4F-12); in the “hexagonal” 4-fold site at the top of the step (4F-13); in the 3-fold site on the side of the step (3F3); or in a 3-fold site at the top of the step (3F-1) differs by 0.08 eV/CO at most. These adsorption configurations are also the most stable adsorption modes identified on the Fe5C2(110)0.00 surface, for which the calculated adsorption energies vary between -1.71 and -1.63 eV/CO (Table 3). Despite the flatness of the PES, however, it is once again apparent that the presence of a subsurface carbon atom below the “square” 4-fold site inhibits adsorption of CO in that site. Therefore, no stable CO adsorption configurations were obtained in the 4-fold hollow



Figure 4. Schematic representations of CO adsorbed in different sites on the stepped Fe5C2(110)0.00 surface. Atom coloring is the same as in Figure 3. Structure labels correspond to the data summarized in Table 3.

site at the bottom of the step, or in the 4-fold site on the side of the step (i.e., on the step plane), where a subsurface carbide atom is present. This tendency of subsurface carbide to inhibit CO adsorption is consistent with the results obtained on the Fe5C2(010)0.25 surface. Given that the stepped Fe5C2(110)0.00 surface is characterized by Fe5C2(010)0.25 terraces, it is instructive to compare the stable adsorption modes obtained in the presence of steps with those identified on the Fe5C2(010)0.25 surface, as discussed in the previous section. On Fe5C2(110)0.00 the “square” 4-fold site is located at the bottom of the step. Although a stable tilted structure for adsorbed CO is found in the equivalent site on Fe5C2(010)0.25 (4F-2 in Figure 3), the tilted configuration is not stable on Fe5C2(110)0.00. Instead, an upright adsorption geometry is obtained at the bottom of the step (4F-12), which is equivalent to 4F-1 on Fe5C2(010)0.25. The adsorption energy calculated with the RPBE functional for this geometry is the same for both surfaces (4F-1: -1.62 eV/CO; 4F-12: -1.63 eV/CO). However, on the stepped surface, the O atom of CO interacts with a surface Fe atom at the edge of the step, resulting in an increase in the C-O distance from 1.23 Å on Fe5C2(010)0.25 to 1.29 Å on Fe5C2(110)0.00, and a concomitant decrease in the C-O stretching frequency from 1547 cm-1 on Fe5C2(010)0.25 to 1255 cm-1 on Fe5C2(110)0.00. It can further be concluded that adsorption in the “square” 4-fold site at the bottom of the step (4F-12) results in one of the most activated states of CO on Fe5C2(110)0.00, as defined in terms of the red-shift of the C-O stretching frequency, and the elongation of the C-O bond. A similar observation was made in a recent DFT study of CO

adsorption on Fe(710) and Fe(310),38 in which it was concluded that the most activated state of adsorbed CO corresponds to adsorption at the bottom of the step on both Fe(710) and Fe(310). For these two stepped surfaces, the CO molecule is adsorbed in the 4-fold hollow site on the Fe(001) terrace, but with the O atom of CO interacting with three Fe atoms at the side of the step. On the Fe(710) (Fe(310)) surface, Sorescu38 calculated an even longer C-O distance of 1.335 Å (1.329 Å) than is found on Fe5C2(110)0.00, and a lower C-O stretching frequency of 1092 cm-1 (1114 cm-1) using the PBE functional. Finally, we note that some structural variation is observed for adsorption in the “square” 4-fold site on Fe5C2(110)0.00, as can be seen by comparing structures 4F-12 and 2F-3. In the latter case (2F-3), the molecule has a 2-fold coordination to the surface through the C atom of CO, and a slight energetic destabilization is observed (Table 3). More significantly, however, the Fe-O distance in 2F-3 is lengthened relative to 4F-12, with a concomitant contraction of the C-O bond and an increase in the C-O vibrational frequency, indicative of a reduction in the degree of activation of the molecule. It is likely that 4F-12 is a precursor state for CO dissociation at the bottom of the step. For adsorption in the “hexagonal” 4-fold site at the top of the step, two stable structures are obtained, with the O atom of CO interacting either with an Fe atom at the edge of the step (4F-13) or an Fe atom on the terrace (4F-14). Two equivalent adsorption configurations are found on Fe5C2(010)0.25 (4F-4 and 4F-5, respectively), together with an upright adsorption mode (4F-3) which is not stable on the stepped Fe5C2(110)0.00 surface. The interaction of the O atom of CO with a step-edge Fe atom

7872


Petersen et al.

TABLE 3: Calculated Adsorption Energies (Eads), Zero-Point Energies (ZPE), C-O Stretching Frequencies (ν(C-O)), and Structural Parameters for CO Adsorbed on Fe5C2(110)0.00 structure RPBE-PAW 1F-6 1F-7 1F-8 2F-1 2F-2 2F-3 3F-1 3F-2 3F-3 4F-11c 4F-12 4F-13 4F-14 4F-15 PW91-USPP 1F-6d 1F-7 1F-8 2F-1d 2F-2 2F-3 3F-1 3F-2d 3F-3 4F-11 4F-12 4F-13 4F-14 4F-15d

Eads (eV/CO)a

ZPE (eV/CO)

ν(C-O) (cm-1)

-1.47 -1.54 -1.51 -1.71 -1.60 -1.57 -1.71 -1.28 -1.68

0.20 0.20 0.19 0.19 0.18 0.16 0.18 0.17 0.17

1825 1900 1865 1801 1612 1447 1726 1667 1374

1.78; 1.79 1.81; 1.80; 1.83; 1.93; 1.86; 1.96; 1.95;

2.40 2.18 2.00; 1.93 2.05; 1.99; 1.98;

2.31 2.15 2.02

-1.63 -1.69 -1.48 -0.77

0.16 0.17 0.16 0.17

1255 1411 1417 1246

2.00; 1.99; 1.99; 1.91;

2.06; 1.99; 2.02; 1.97;

2.17; 2.11; 2.11; 2.13;

-1.80 -1.82

0.21 0.19

1903 1844

1.79 1.82; 2.26

-1.96 -1.95 -2.04

0.18 0.18 0.17

1593 1350 1702

1.83; 1.97; 2.31 1.88; 1.94 1.90; 2.01; 2.20

-2.13 -1.86 -2.08 -2.09 -1.85

0.18 0.18 0.18 0.18 0.17

1378 1261 1250 1409 1416

1.94; 1.91; 1.99; 1.98; 1.99;

dFe-C, Å

dC-O, Å

CO tiltb

2.09

1.19 1.18 1.18 1.19 1.23 1.25 1.20 1.21 1.27

13.3 13.3 11.7

2.10 2.11 2.15 2.13; 2.13

1.29 1.26 1.26 1.31

7.5 39.4 35.1 54.6

dFe-O, Å

2.31

1.98; 1.94; 2.05; 1.99; 2.02;

2.35

2.22 2.23; 2.98

2.18 2.14 2.11 2.15

1.18 1.18

2.02 2.12; 2.16; 2.11; 2.08;

2.16 2.21; 2.31

2.13 2.17 2.14 2.11

2.05 2.04; 2.30 2.06 2.07 2.10

1.23 1.28 1.21 1.27 1.30 1.29 1.27 1.26

13.1 11.8 8.5 40.9 37.2

a

Eads excludes ZPE contributions. b The tilt angle (in degrees) of CO adsorbed in a 4-fold site is defined relative to the surface normal of the least-squares-fitted plane through the four Fe atoms defining the 4-fold site. c No equivalent structure found with the PW91-USPP approach was obtained using the RPBE-PAW method. d No equivalent structure obtained with the RPBE-PAW method was found using the PW91-USPP approach.

(4F-13) results in a slightly increased stabilization of the system relative to adsorption on the extended Fe5C2(010)0.25 surface (4F4): the CO adsorption energy is -1.65 eV/CO on Fe5C2(010)0.25 (4F-4) and -1.69 eV/CO on stepped Fe5C2(110)0.00 (4F-13). In contrast, no change in the adsorption energy is observed for the alternative tilted geometry, in which the O-atom interacts with a surface Fe on the terrace, when adsorption on Fe5C2(010)0.25 (4F-5) is compared with adsorption in the presence of steps (4F-14). We note that although the tilted geometry with the O-atom interacting with the step-edge is energetically more stable by 0.21 eV/CO, this effect appears to be only marginally influenced by the proximity of the stepedge, since a similar relative stability trend is observed on the extended Fe5C2(010)0.25 surface for the two equivalent tilted geometries (cf. Table 2). Structurally, however, the Fe-O distance is shorter for adsorption on the stepped surface for these tilted configurations, with a marginal increase in the C-O distance and a concomitant lowering of the C-O vibrational frequency. Finally, we note that adsorption at the top of the step in the “hexagonal” 4-fold site (4F-13) is only marginally more stable than adsorption at the bottom of the step in the “square” 4-fold site (4F-12) by 0.06 eV/CO. Thus, no significant preference for CO adsorption at the top or bottom of the step is observed on the Fe5C2(110)0.00 surface. There are three stable 3-fold coordinated adsorption configurations on Fe5C2(110)0.00, two corresponding to adsorption at the top of the step (3F-1, 3F-2), and one on the step plane (3F3). The PES is relatively flat in the vicinity of the first 3-fold site (3F-1), so that the adjacent bridging geometry (2F-1) at the step-edge is energetically degenerate with adsorption in the

3-fold site (refer to Figure 4). The C-O distance is shortened slightly by 0.01 Å and the calculated C-O stretching frequency is increased from 1726 cm-1 to 1801 cm-1 as the adsorbed molecule is displaced toward the step-edge. We note, however, that the stable bridging geometry along the step-edge was only obtained using the RPBE functional; no equivalent configuration was identified using the PW91 functional with the current search methodology. This is consistent with the observation on Fe5C2(010)0.25 that the PW91 functional appears to favor adsorption configurations in which CO is more highly coordinated to the surface. Adsorption in the 3-fold site (3F-1) is the most stable adsorption configuration on Fe5C2(110)0.00 obtained with the RPBE functional, with an adsorption energy of -1.71 eV/CO. We note that both configurations (2F-1 and 3F-1) are related to adsorption in the “hexagonal” 4-fold site (4F-6 in Figure 3) on the extended Fe5C2(010)0.25 plane. Adsorption in the 3-fold site on the step plane (3F-3) also results in one of the most stable configurations for adsorbed CO on Fe5C2(110)0.00. The orientation of the step plane relative to the (010) terrace enables the molecule to interact with the (010) terrace through the O-atom, while maintaining a nearideal 3-fold coordination to the step-plane. In fact, the CO molecule tilts by only 11.7° relative to the normal of the local plane defined by the 3-fold site, in order to interact with the terrace Fe atom. Interestingly, an analogous configuration is obtained for CO adsorption on the step-plane of Fe(310)38,86 and Fe(710),38 in which CO adsorbs in the 3-fold site involving two Fe atoms along the step-edge and one Fe at the bottom of the step, similar to 3F-3. However, no interaction of the O-end of the molecule with the terrace takes place on either Fe(310)

Adsorption and Activation of CO on χ-Fe5C2 Surfaces or Fe(710), and the C-O distance is both shorter (∼1.21 Å) and the C-O stretching frequency higher (Fe(310): 1659 cm-1; Fe(710): 1651 cm-1) than for the analogous configuration on the carbide surface (cf. Table 3). In contrast, in the tilted state of adsorbed CO on Fe{211}, the molecule does interact with one surface Fe through the O-end of the molecule, and has a similar calculated C-O stretch frequency of 1634 cm-1,81 but with a longer C-O bond distance of 1.28 Å.38,81 Interaction of the CO molecule with the Fe5C2(110)0.00 surface through both the C and O atoms once again is associated with a lengthening of the C-O bond (1.27 Å) and a lowering of the C-O stretching frequency (RPBE: 1374 cm-1), indicative of an enhanced activation of the CO adsorbate in this site. The remaining one-fold structures (1F-6, 1F-7, and 1F-8) are relatively less stable on Fe5C2(110)0.00. No stable on-top structures are found at the bottom of the step (cf. 1F-1 and 1F-4 on Fe5C2(010)0.25). The one-fold-coordinated configurations are all characterized by a short C-O bond distance of ∼1.18 Å and a C-O stretching frequency greater than 1800 cm-1. A similar observation is made for the related on-top configurations on Fe5C2(010)0.25 (cf. Figure 3 and Table 2). Sorescu33 and Cao et al.30 studied the adsorption of CO on the bulk-terminated Fe5C2(110)0.00 surface, in which surface carbon atoms are present in the “square” 4-fold sites at the bottom of the steps (cf. Figure 1b). In contrast, the Fe5C2(110)0.00 surface investigated in the present study is characterized by carbon vacancies at these sites (Figure 2b). In their work, Cao et al.30 reported only two stable adsorption modes at the equivalent coverage in which CO interacts with Fe atoms at the surface, analogous to configurations 3F-1 and 4F-13 in the present work. In addition, two adsorption configurations were reported in which CO interacts with the surface carbon in the “square” 4-fold site to form a C-C bond, but each with a significantly reduced (i.e., less favorable) adsorption energy relative to adsorption in the Fe sites. Sorescu33 similarly found that CO preferentially adsorbs on Fe sites; however, the most activated configuration was attributed to an adsorption geometry in which CO bonds directly to surface atomic C but which is significantly less favorable energetically. In contrast in the current work, adsorption of CO in the vacancy site at the bottom of the step (4F-12) not only leads to a more activated state than found by Sorescu33 in terms of the calculated red-shift of the C-O stretching frequency, but is also of comparable stability to the most stable adsorption configurations on this surface termination. In conclusion, the lowest energy configurations for CO adsorption on Fe5C2(110)0.00 occur for adsorption in the 4-fold sites at the bottom (4F-12) and the top of the step (4F-13), respectively, or in the 3-fold sites at the top of the step (3F-1) and on the step plane (3F-3). These configurations are energetically degenerate to within 0.08 eV/CO. Of the low-energy configurations, adsorbed CO is most activated in the 4-fold (vacancy) site at the bottom of the step (4F-12), with a calculated C-O distance of 1.29 Å and a C-O stretching frequency of 1255 cm-1. The presence of a subsurface carbon atom below the “square” 4-fold site is found to inhibit CO adsorption, such that no stable adsorption configurations were identified in such sites on Fe5C2(110)0.00. 3.3.3. CO Adsorption on Fe5C2(110)0.80. The ideal (010) terrace of the Fe5C2(110)0.80 surface is characterized by four possible “square” 4-fold sites, two situated at the bottom of the step and two at the top of the step (Figure 1c). In both cases on the Fe-terminated surface, one site has a subsurface carbide atom located below the site, while the other is characterized by a


Figure 5. Surface representations of the optimized metastable and lower-energy reconstructed Fe5C2(110)0.80 surface structures. Equivalent p(1 × 1) surface unit cell meshes are indicated in red for both surfaces.

carbon vacancy (Figure 2c). Depending on how the two carbon vacancies are introduced into the p(1 × 1) unit cell, the surface can be ‘trapped’ into a metastable state which is 0.06 eV (0.07 eV) per unit cell higher in energy than the most stable reconstruction identified for this particular surface termination. We note that the lower energy (more stable) surface is obtained when a carbon vacancy is first introduced at the top of the step, followed by optimization of the surface layers, after which a second vacancy is introduced at the bottom of the step and the surface optimized further. The resulting lower energy surface has a greater degree of reconstruction in the surface layers, compared to the metastable state, as shown in Figure 5. We note that alternative terminations can be generated in which carbon vacancies are introduced at subsurface sites, and it is conceivable that such terminations could have lower surface energies; however in the present study we focus specifically on Fe terminations of the Ha¨gg iron carbide phase in which carbon vacancies are only present at surface sites. This approach represents a first step to characterizing the role of the carbide phase in the mechanism of FT synthesis. CO adsorption was investigated on the stepped Fe5C2(110)0.80 termination using a slab consisting of 21 Fe atoms and 7 C atoms per unit cell. Adsorption was confined to one side of the slab, and the CO adsorbate and upper 11 Fe atoms and 3 C atoms of the slab were optimized. Test calculations indicate that the calculated adsorption energy varies by only 0.04 eV/CO on increasing the slab thickness to 26 Fe atoms and 9 C atoms per unit cell. CO adsorption was considered in all possible one-, two-, three- and 4-fold sites on the terrace and the step-plane of the surface. In addition to the 4-fold sites on the terrace, there is a “square” 4-fold site on the step plane which has no carbon atom below the site, in contrast to the analogous site on the Fe5C2(110)0.00 surface. For all 4-fold sites, both upright and tilted adsorption modes were investigated, as before. Adsorption on both the metastable surface and the lowest energy recon-

7874


Petersen et al.

Figure 6. Schematic representations of CO adsorbed in different sites on the Fe5C2(110)0.80 surface. Atom coloring is the same as in Figure 3, and structure labels correspond to data summarized in Table 4.

structed surface was considered, in order to facilitate the identification of the lowest energy adsorption configuration at each site, taking account of substrate relaxations. Since the “square” 4-fold site adjacent to the step-edge on the low-energy reconstructed surface is distorted, the possibility of CO adsorption in an upright 3-fold configuration was also considered for this site. Of the adsorption modes considered, only a limited set was found to correspond to stable structures, which are shown in Figure 6 with corresponding adsorption energies, structural parameters, and C-O stretching frequencies summarized in Table 4. All adsorption configurations were verified as corresponding to local minima on the PES based on a normalmode analysis. Adsorption configurations that are unique to the metastable surface are explicitly noted in the following discussion. For adsorption of CO on the Fe5C2(110)0.80 termination, the most stable adsorption configuration is obtained at the bottom of the step (3F-4 in Figure 6). In this low-symmetry geometry, the molecule is coordinated to the surface through both the O atom and the C atom. The corresponding adsorption energy of -1.77 eV/CO calculated with the RPBE functional is more exothermic than for adsorption in the most stable sites on the

alternative Fe5C2(110)0.00 termination (cf. -1.71 eV/CO) and on the Fe5C2(010)0.25 surface (cf. -1.66 eV/CO). A second lowenergy adsorption configuration (1F-9) is also obtained on Fe5C2(110)0.80, which is less stable than 3F-4 by only 0.03 eV/ CO, and in which CO is again coordinated to the surface through both the O-end and the C-end of the molecule. For both configurations, 1F-9 and 3F-4, the location of CO at the bottom of the step enables the molecule to interact with an Fe atom at the edge of the step through the O-end, while the C-end is primarily coordinated to the terrace atoms. This “double-ended” coordination of CO to Fe5C2(110)0.80 is correlated with an increase in the C-O bond distance and a red-shift of the C-O stretching frequency. The nature of the (010) terrace exposed on the Fe5C2(110)0.80 surface makes it possible to compare the features of CO adsorption in the same type of ‘square’ 4-fold site, both at the bottom and at the top of the step, and in the presence or absence of a subsurface carbon atom in each case. Considering adsorption first at the bottom of the step where there is no carbon below the site, two possible configurations are identified, in which CO either interacts with the step-edge (4F-16) or with a



TABLE 4: Calculated Adsorption Energies (Eads), Zero-Point Energies (ZPE), C-O Stretching Frequencies (ν(C-O)), and Structural Parameters for CO Adsorbed on Fe5C2(110)0.80 structure RPBE-PAW 1F-9 1F-10 1F-11c 1F-12 2F-4 2F-5 3F-4 3F-5 3F-6 3F-7 4F-16 4F-17 4F-18 4F-19 4F-20 4F-21 4F-22 PW91-USPP 1F-9 1F-10 1F-11 1F-12 2F-4 2F-5 3F-4 3F-5 3F-6 3F-7 4F-16 4F-17 4F-18 4F-19 4F-20 4F-21 4F-22

Eads (eV/CO)a

ZPE (eV/CO)

ν (CO) (cm-1)

-1.74 -1.66

0.19 0.20

1585 1862

1.76 1.78

-1.15 -1.60 -1.62 -1.77 -1.43 -1.47 -1.47 -1.62 -1.32 -1.44 -1.45 -1.12 -1.04 -0.95

0.20 0.19 0.19 0.18 0.17 0.18 0.17 0.17 0.16 0.16 0.17 0.16 0.16 0.17

1846 1881 1847 1450 1482 1515 1430 1161 1259 1569 1293 1118 1044 1252

1.77 1.83; 2.31 1.81; 2.24 1.86; 2.01; 2.19 1.91; 2.02; 2.05 1.87; 2.03; 2.30 1.91; 1.97; 2.20 1.96; 2.12; 2.12; 2.18; 2.21 1.92; 2.00; 2.04; 2.19; 2.46 2.02; 2.07; 2.09; 2.26 1.90; 2.00; 2.08; 2.09 1.99; 2.04; 2.08; 2.09 2.05; 2.08; 2.14; 2.15 1.94; 1.99; 2.00; 2.05

-2.10 -1.96 -1.54 -1.41 -1.91 -1.89 -2.16 -1.81 -1.87 -1.91 -2.04 -1.73 -1.78 -1.84 -1.63 -1.49 -1.35

0.19 0.20 0.21 0.20 0.20 0.20 0.18 0.17 0.17 0.18 0.17 0.16 0.17 0.17 0.17 0.16 0.18

1559 1869 1895 1849 1874 1833 1450 1476 1483 1376 1172 1255 1574 1280 1120 1036 1239

1.76 1.78 1.78 1.77 1.82; 2.29 1.83; 2.16 1.85; 2.02; 2.18 1.90; 2.02; 2.04 1.86; 2.00; 2.33 1.95; 1.98; 2.02 1.95; 2.12; 2.12; 2.19; 2.22 1.91; 2.00; 2.03; 2.22; 2.44 2.02; 2.06; 2.10; 2.23 1.90; 2.01; 2.07; 2.08 1.99; 2.03; 2.07; 2.13 2.05; 2.12; 2.13; 2.13 1.95; 2.00; 2.00; 2.04

dFe-C, Å

dFe-O, Å 2.10

2.10 2.17 2.11 2.09 1.98 2.09; 2.32 2.17; 2.24 2.15; 2.20 2.04; 2.09 2.10; 2.17 2.05

2.07 2.15 2.05 2.01 1.97 2.08; 2.23 2.13; 2.20 2.12; 2.17 2.01; 2.07 2.08; 2.13

dC-O, Å

CO tiltb (degrees)

1.23 1.18 1.18 1.18 1.18 1.25 1.25 1.24 1.26 1.31 1.30 1.23 1.29 1.32 1.35 1.31 1.23 1.18 1.18 1.18 1.18 1.18 1.26 1.25 1.25 1.27 1.31 1.30 1.23 1.30 1.33 1.35 1.31

9.6 7.4 1.5 1.1 51.6 15.7 15.8

13.8 8.2 3.7 0.2 53.3 17.9 16.3

a Eads excludes ZPE contributions. b The tilt angle of CO adsorbed in a 4-fold site is defined relative to the surface normal of the least-squares-fitted plane through the four Fe atoms defining the 4-fold site. c No equivalent structure corresponding to 1F-11 obtained with the PW91-USPP method was found using the RPBE-PAW approach.

terrace Fe atom (4F-17). Adsorption in an upright configuration enabling coordination of CO to an edge-Fe atom through the O-end of the molecule (4F-16) is energetically preferred by 0.30 eV/CO over interaction with a terrace Fe atom (4F-17). However, we note that these two configurations are only obtained on the metastable surface. Comparing 4F-16 with 3F4, and 4F-17 with 3F-5, it is seen (Table 4) that it is energetically favorable for the surface to undergo reconstruction such that the adsorption geometry is distorted. However, this energylowering structural relaxation is accompanied by an decrease in the C-O bond distance, and an increase in the stretching frequency of the adsorbate in both cases, indicative of a reduction in the degree of activation of the CO adsorbate. For example, comparing 4F-16 and 3F-4, the C-O bond distance decreases from 1.31 Å on the metastable surface (4F-16) to 1.25 Å on the more reconstructed surface (3F-4), and the C-O stretch frequency increases from 1161 cm-1 for 4F-16 to 1450 cm-1 for 3F-4. Although 3F-4 is more stable than 4F-16 by 0.15 eV, the latter structure can be considered to be an intermediate for dissociation of CO on the surface, due to its more activated nature both in terms of the longer C-O bond length and lower stretching frequency. Interestingly, adsorption in the analogous “square” 4-fold site at the bottom of the step on the alternative Fe5C2(110)0.00 surface is characterized by the same adsorption energy as on the metastable Fe5C2(110)0.80 termination (for

which the adsorption geometry is similar), i.e., for 4F-12 on Fe5C2(110)0.00 an adsorption energy of -1.63 eV/CO is calculated, while on Fe5C2(110)0.80 the adsorption energy is -1.62 eV/CO for 4F-16. Thus, although the structural features of the (010) terrace exposed on Fe5C2(110)0.00 and Fe5C2(110)0.80 differ, the adsorption characteristics are localized on the surface, such that the presence of “hexagonal” sites at the top of the step on Fe5C2(110)0.00 does not appreciably alter the structural and energetic features for adsorption in a similar site at the bottom of the step, when compared with adsorption on Fe5C2(110)0.80. Two stable configurations (4F-18, 4F-19) were identified for CO adsorption in the “square” 4-fold site at the top of the step without a subsurface carbon.87 Adsorption at the top of the step is found to be less stable than at the bottom of the step (4F-16) by ∼0.2 eV/CO for both the upright (4F-18) and tilted (4F-19) modes. This is in contrast to the result obtained by Sorescu38 for CO adsorption on Fe(710), for which it was found that the most stable adsorption site is the 4-fold hollow site at the top of the step, with the CO molecule tilted toward the step-edge, analogous to 4F-19. Although adsorption of CO in the hollow site on Fe(100) shows a strong energetic preference for the tilted state,74,75 this preference is not borne out on the carbide surfaces. For adsorption in the “square” 4-fold hollow site on Fe5C2(010)0.25, the upright adsorption mode (4F-1) is more stable than a tilted mode (4F-2) by 0.18 eV/CO. However, at the top

7876


of the step, a tilted state (4F-19) is stabilized relative to the vertical adsorption mode (4F-18) through interaction with the edge Fe atoms through the O-end of the adsorbate, such that the tilted configuration is now degenerate with the vertical mode. Coordination of CO to the surface through both ends of the molecule is once again associated with an increase in the C-O bond distance and a decrease in the stretch frequency, relative to the vertical adsorption mode (Table 4). We note that the calculated adsorption energy of -1.44 eV/CO for CO in the upright configuration at the top of the step (4F-18) is less exothermic than for adsorption in the analogous site on the extended Fe5C2(010)0.25 surface (4F-1), for which an adsorption energy of -1.62 eV/CO was calculated using the RPBE functional. The general observation that the presence of a subsurface carbon below the “square” hollow site inhibits CO adsorption in that site is borne out on the Fe5C2(110)0.80 surface for sites at the top of the step. However, at the bottom of the step, two stable adsorption configurations are identified, labeled 4F-20 and 4F-21 in Figure 6. This is in contrast to the Fe5C2(110)0.00 surface, for which no stable adsorption modes were identified in the analogous site (cf. Figure 4). However, on Fe5C2(110)0.80 the side of the step differs in that the 4-fold site on the step plane does not have a carbon atom beneath it. Consequently, adsorption at the bottom of the step is stabilized through either the C-end (4F-20) or the O-end (4F-21) of CO interacting with the Fe atoms of the step 4-fold site. Although these two configurations are the least stable adsorption modes on Fe5C2(110)0.80, they are of the most activated species identified on this surface. In fact, 4F-21 has the longest C-O distance of 1.35 Å and lowest C-O stretching frequency of 1044 cm-1 calculated on Fe5C2(110)0.80 using the RPBE functional and is furthermore the most activated species identified on all three carbide surfaces investigated in the present study. A similar influence of the nature of the sites on the stepplane is noted for adsorption in the 3-fold site on the side of the step on Fe5C2(110)0.80 and Fe5C2(110)0.00. Adsorption in the step 3-fold site results in one of the most stable adsorption configurations (refer to Table 3) on Fe5C2(110)0.00, 3F-3, with a calculated adsorption energy of -1.68 eV/CO. However, for the analogous configuration on Fe5C2(110)0.80, 3F-7, the adsorption energy is reduced to -1.47 eV/CO. On the Fe5C2(110)0.80 surface, however, a subsurface carbon resides below the site, while on Fe5C2(110)0.00 no such carbide atom is present (see Figure 2). Once again, the destabilizing influence of subsurface carbon on the adsorption properties of CO is noted. Finally, we note that for adsorption in a bridge site along the step-edge (2F-4, 2F-5), the molecule adopts a tilted configuration characterized by one short (∼1.8 Å) and one longer (∼2.0 to ∼2.3 Å) Fe-C distance. This tilted pseudobridging geometry appears to be a general feature of adsorption on Fe and other Fe carbide surfaces, as similar stable asymmetric bridging geometries have been reported on Fe(100),75 Fe(310),38,86 and Fe(710),38 as well as on Fe3C,28 Fe4C,29 and other Fe5C233 surfaces using calculations based on DFT. 3.4. General Features of CO Adsorption and Activation on Fe5C2(010)0.25, Fe5C2(110)0.00, and Fe5C2(110)0.80. Based on the results summarized in Tables 2-4 in the previous three sections, some common features of CO adsorption on the three surfaces may be identified. First, CO does not show a clear energetic preference for a particular adsorption site on each surface, since similar adsorption energies are obtained for quite diverse stable adsorption modes. For example, adsorption in an atop site (1F-5) and in a hexagonal 4-fold site (4F-6) on the

Petersen et al. Fe5C2(010)0.25 surface is energetically degenerate, and analogous observations may also be made for the most stable adsorption geometries on the two stepped surfaces. This observation is in agreement with the conclusions of Sorescu33 for CO adsorbed in Fe sites with up to 4-fold coordination to the surface, based on his investigation of CO adsorption on seven bulk-terminated low Miller index planes of χ-Fe5C2. Second, and related to the above result, is the observation that the adsorption of CO in a vacancy site (i.e., a “square” 4-fold site) is not necessarily more favorable energetically compared to adsorption in other Fe-sites on the surface terminations studied here. In particular, for the Fe5C2(010)0.25 surface, the calculated adsorption energy (using the RPBE functional) of CO adsorbed in the vacancy site in the more stable upright orientation, 4F-1, is -1.62 eV/CO, whereas adsorption in the hexagonal 4-fold site, 4F-6, has a slightly more favorable adsorption energy of -1.66 eV/CO. We note that this is in contrast to the conclusions of Huo et al.,36 who report that adsorption of CO in a single vacancy site on Fe5C2(010)0.25 has a more favorable adsorption energy compared to adsorption on the bulk-terminated surface. However, the (010) termination studied here has two vacancies per p(1 × 1) surface unit cell, whereas only one vacancy site is present in the work of Huo et al. A third, important, observation is that the presence of a subsurface carbon atom below a “square” 4-fold site inhibits adsorption of CO in that site on all three surfaces. Only when the CO molecule interacts with the step edge, as is the case for 4F-21 on Fe5C2(110)0.80, is a stable adsorption geometry obtained in such a site. Nevertheless, the corresponding adsorption energy is reduced by ∼0.7 eV/CO relative to the most stable adsorption geometry on the Fe5C2(110)0.80 surface, to just -1.04 eV/CO. The inhibition of CO adsorption in 4-fold sites in which subsurface carbon is present is consistent with the results of Sorescu33 for CO adsorption on bulk-terminated Fe5C2(010)0.25, and by both Cao et al.30 and Sorescu33 for adsorption on Fe5C2(100)0.00 which has similar such “square” 4-fold sites. It is of interest to note that the tilted modes of CO on Fe5C2(010)0.25 are in general less stable energetically than the upright orientation for adsorption in the 4-fold sites, in contrast to the energetic preference for the tilted adsorption mode of CO in the hollow site on Fe(100).68–77 This is particularly evident for 4F-1 and 4F-2, as well as 4F-6 and 4F-7 or 4F-8. Nevertheless, as Sorescu similarly noted,33 the increased coordination of the molecule to the surface, with the formation of Fe-O bonds, is associated with a lowering of the C-O stretching frequency and an elongation of the C-O bond, and in this sense is associated with a greater degree of activation of the ad-molecule. We note, therefore, that the presence of step sites can facilitate the formation of multiple bonds to the surface and help activate the C-O bond, as demonstrated for example for 1F-9 and 1F-10, where the interaction of CO with the stepedge in 1F-9 is accompanied by a red-shift of the C-O stretching frequency and a lengthening of the C-O bond compared to 1F-10. However, what is of greater importance is that the increased coordination of CO to the surface at step sites is apparently not accompanied by an energetic destabilization of the molecule. This is elegantly demonstrated for adsorption in the equivalent 4-fold sites on the three surfaces, 4F-1, 4F12 and 4F-16, which have similar (RPBE) calculated adsorption energies of -1.62, -1.63, and -1.62 eV/CO, but substantially different C-O bond distances of 1.23, 1.29, and 1.31 Å and stretching frequencies of 1547, 1255, and 1161 cm-1, respectively. In addition, for the surfaces investigated here, the



Figure 7. Initial, transition and direct product state structures for the dissociation of CO initially adsorbed in the vacancy site on Fe5C2(010)0.25 (a), and in the vacancy site at the bottom of the step on Fe5C2(110)0.00 (b) and Fe5C2(110)0.80 (c). Transition state (TS) structures are shown in the center, and the direct product state consisting of coadsorbed C and O is shown on the right for each surface. Atom coloring is the same as in Figure 3.

introduction of carbon vacancies frees up the “square” 4-fold site for CO adsorption, for which the calculated adsorption energies are comparable to the most stable adsorption modes on each surface (to within 0.15 eV/CO). It is worth bearing in mind that the rate of CO dissociation on the surface is determined not only by the activation energy for dissociation, which is anticipated to be lower for a more activated state, but also by the concentration of such activated CO species (as well as empty sites) on the surface, and the latter is in part governed by the relative thermodynamic stability of CO adsorbed in different available sites. Therefore, the increased activation of the adsorbate at a step site without an appreciable loss of stability, together with the availability of a vacancy site at the bottom of the step which enables CO to adsorb in a stable, low energy configuration, may be expected to give rise to an overall low-energy dissociation pathway for CO on the surface. To illustrate the role of the vacancy and step sites in activating CO on these surfaces, transition states were located for dissociation of CO adsorbed in the vacancy site on Fe5C2(010)0.25, and at the bottom of the step on the two (110) terminations, using the nudged elastic band (NEB) method.57 The transition states are shown in Figure 7, together with the direct dissociated product state consisting of coadsorbed surface C and O, while additional energetic and structural parameters characterizing the dissociation paths are provided in the Supporting Information. Relative to the more activated, but less stable tilted precursor state, 4F-2, on Fe5C2(010)0.25, the calculated activation energy for dissociation is 1.24 eV (1.20 eV) using the RPBE (PW91) functional, excluding ZPE

contributions (Figure 7a). In the presence of the step, however, the activation energy is reduced to 0.92 eV (0.84 eV) for dissociation of 4F-12 on Fe5C2(110)0.00 (Figure 7b), and is lowered even further to just 0.56 eV (0.51 eV) for dissociation of 4F-16 on the alternative (110) termination, Fe5C2(110)0.80 (Figure 7c). The energy barriers calculated with the RPBE (PW91) functional are reduced slightly on inclusion of ZPE corrections, to 1.21 eV (1.17 eV), 0.88 eV (0.79 eV), and 0.51 eV (0.46 eV) for dissociation of 4F-2, 4F-12, and 4F-16, respectively. These results demonstrate the substantial lowering of the dissociation barrier at the step site, which together with the favorable adsorption energy of CO in these vacancy sites, gives rise to an overall low energy dissociation pathway on the stepped surfaces. The results suggest that carbon vacancy sites on stepped surfaces may play an important role in the dissociation of CO on iron carbides. Sorescu33 and Cao et al.30 have noted that CO preferentially adsorbs in Fe sites on χ-Fe5C2 surfaces; therefore, it may reasonably be anticipated that the presence of surface carbon vacancies that expose Fe sites for CO adsorption may give rise to energetically stable CO adsorption configurations. In addition, corrugated surfaces that enable CO to adsorb with high coordination to the surface and through both ends of the molecule, while minimizing the extent to which the C- and O-atoms bond to the same surface Fe atoms, can help activate the C-O bond. We note, however, that the availability of vacancy sites in a stepped or corrugated environment will be dependent on both the rate of carbon addition to and removal from the surface. The formation of vacancy sites on iron carbide surfaces through hydrogenation of surface

7878


carbon, as well as the role of vacancy sites in iron-catalyzed FTS, have very recently begun to receive attention in studies using DFT calculations.36,37 4. Conclusions Density functional theory was used to investigate the adsorption of CO on three surface terminations of χ-Fe5C2 in the presence of carbon vacancies. CO does not show a strong energetic preference for a particular adsorption site on all three surfaces, with similar adsorption energies being calculated for structurally distinct adsorption configurations. On Fe5C2(010)0.25, the energetically most favorable adsorption geometries are obtained for on-top configurations (1F-1, 1F-2, and 1F-5) as well as adsorption in 4-fold sites (4F-1, 4F-3, 4F-4, and 4F-6). The calculated adsorption energies for these configurations are in the range of -1.66 to -1.62 eV/CO using the RPBE-PAW method, and -1.97 to -1.87 eV/CO with the PW91-USPP approach. On the stepped Fe5C2(110)0.00 surface, adsorption in 3-fold sites (3F-1, 3F-3) and 4-fold sites (4F-12, 4F-13) is energetically most stable, with calculated adsorption energies in the range of -1.71 to -1.63 eV/CO (-2.13 to -2.04 eV/ CO) using the RPBE-PAW (PW91-USPP) method. On the alternative Fe5C2(110)0.80 termination, the lowest energy adsorption configurations 1F-9 and 3F-4 have adsorption energies of -1.74 eV/CO (-2.10 eV/CO) and -1.77 eV/CO (-2.16 eV/ CO), respectively, as calculated with the RPBE (PW91) functional. Adsorption is more favorable on the stepped terminations than on Fe5C2(010)0.25; calculated adsorption energies for the lowest energy adsorption geometries on Fe5C2(010)0.25, Fe5C2(110)0.00, and Fe5C2(110)0.80 are -1.66 eV/ CO (-1.97 eV/CO), -1.71 eV/CO (-2.13 eV/CO), and -1.77 eV/CO (-2.16 eV/CO), respectively. No energetic preference, to within the accuracy of the DFT calculations, is obtained for adsorption in the vacancy sites relative to adsorption in alternative sites on each surface. Nevertheless, these sites remain energetically favorable to within 0.15 eV/CO, relative to the most stable adsorption modes on each surface. In contrast, the presence of subsurface carbon below a “square” 4-fold site inhibits adsorption in that site, except on Fe5C2(110)0.80 where CO adsorbed at the bottom of the step interacts with the step edge resulting in a stable, though energetically less favorable, geometry. The coordination of CO to the surface through both the C atom and O atom is correlated with a lengthening of the C-O bond, and a lowering of the C-O stretching frequency. The step sites are found to facilitate such multiply coordinated adsorption modes, in particular when CO is adsorbed at the bottom of the step. The adsorption energy of CO adsorbed in equivalent vacancy sites on Fe5C2(010)0.25 (4F-1) and at the bottom of the steps on Fe5C2(110)0.00 (4F-12) and Fe5C2(110)0.80 (4F-16) is the same to within the accuracy of the DFT calculations using the RPBE functional, and is even slightly more favorable on the stepped surfaces using the PW91 functional. However, the RPBE (PW91) calculated activation energy for dissociation of CO in the vacancy site on Fe5C2(010)0.25 is 1.24 eV (1.20 eV) relative to the tilted precursor state, decreasing on the stepped surfaces to 0.92 eV (0.84 eV) on Fe5C2(110)0.00 and 0.56 eV (0.51 eV) on Fe5C2(110)0.80. The lowering of the activation energy for CO dissociation at the steps, together with the favorable thermodynamic stability of CO adsorbed in the vacancy sites on the three surface terminations of χ-Fe5C2, suggest that vacancy sites on stepped and corrugated surfaces may play an important role in the adsorption and activation of CO on χ-Fe5C2 surfaces.

Petersen et al. Acknowledgment. We thank the members of the Sasol Fischer-Tropsch Molecular Modeling study team for useful discussions. We acknowledge Mr Ivan Bester (Information Management, Sasol) for infrastructure support to the Sasol Molecular Modeling Group. Supporting Information Available: Activation and reaction energies for the CO dissociation paths on the three χ-Fe5C2 surfaces and key structural parameters for the transition and dissociated product states. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Steynberg, A. P.; Dry, M. E., Eds. Studies in Surface Science and Catalysis: Fischer-Tropsch Technology; Elsevier: Amsterdam, 2004; Vol. 152. (2) van Steen, E.; Claeys, M. Chem. Eng. Technol. 2008, 31, 655. (3) Luo, M.; Hamdeh, H.; Davis, B. H. Catal. Today 2009, 140, 127. (4) de Smit, E.; Weckhuysen, B. M. Chem. Soc. ReV. 2008, 37, 2758. (5) de Smit, E.; Beale, A. M.; Nikitenko, S.; Weckhuysen, B. M. J. Catal. 2009, 262, 244. (6) de Smit, E.; Swart, I.; Creemer, J. F.; Hoveling, G. H.; Gilles, M. K.; Tyliszczak, T.; Kooyman, P. J.; Zandbergen, H. W.; Morin, C.; Weckhuysen, B. M.; de Groot, F. M. F. Nature 2008, 456, 222. (7) Raupp, G. B.; Delgass, W. N. J. Catal. 1979, 58, 361. (8) Amelse, J. A.; Butt, J. B.; Schwartz, L. H. J. Phys. Chem. 1978, 82, 558. (9) Shroff, M. D.; Kalakkad, D. S.; Coulter, K. E.; Ko¨hler., S. D.; Harrington, M. S.; Jackson, N. B.; Sault, A. G.; Datye, A. K. J. Catal. 1995, 156, 185. (10) Datye, A. K.; Jin, Y.; Mansker, L.; Motjope, T.; Dlamini, T. H.; Coville, N. J. Stud. Surf. Sci. Catal. 2000, 130, 1139. (11) Niemantsverdriet, J. W.; van der Kraan, A. M.; van Dijk, W. L.; van der Baan, H. S. J. Phys. Chem. 1980, 84, 3363. (12) Raupp, G. B.; Delgass, W. N. J. Catal. 1979, 58, 348. (13) Bukur, D. B.; Okabe, K.; Rosynek, M. P.; Li, C.; Wang, D.; Rao, K. R. P. M.; Huffman, G. P. J. Catal. 1995, 155, 353. (14) Herranz, T.; Rojas, S.; Pe´rez-Alonso, F. J.; Ojeda, M.; Terreros, P.; Fierro, J. L. G. J. Catal. 2006, 243, 199. (15) O’Brien, R. J.; Xu, L.; Spicer, R. L.; Davis, B. H. Energy Fuels 1996, 10, 921. (16) Davis, B. H. Catal. Today 2003, 84, 83. (17) Sirimanothan, N.; Hamdeh, H. H.; Zhang, Y.; Davis, B. H. Catal. Lett. 2002, 82, 181. (18) Riedel, T.; Schulz, H.; Schaub, G.; Jun, K.-W.; Hwang, J.-S.; Lee, K.-W. Top. Catal. 2003, 26, 41. (19) Rao, K. R. P. M.; Huggins, F. E.; Mahajan, V.; Huffman, G. P.; Bukur, D. B.; Rao, V. U. S. Hyperfine Interact. 1994, 93, 1751. (20) Shashkin, D. P.; Shiryaev, P. A.; Chichagov, A. V.; Morozova, O. S.; Krylov, O. V. Kinet. Catal. 1992, 33, 744. (21) Matsumoto, H. J. Catal. 1984, 86, 201. (22) Honkala, K.; Hellman, A.; Remediakis, I. N.; Logadottir, A.; Carlsson, A.; Dahl, S.; Christensen, C. H.; Nørskov, J. K. Science 2005, 307, 555. (23) Studt, F.; Abild-Pedersen, F.; Bligaard, T.; Sørensen, R. Z.; Christensen, C. H.; Nørskov, J. K. Science 2008, 320, 1320. (24) Faraoun, H. I.; Zhang, Y. D.; Esling, C.; Aourag, H. J. Appl. Phys. 2006, 99, 093508. (25) Chiou, W. C.; Carter, E. A. Surf. Sci. 2003, 530, 87. (26) Deng, C.-M.; Huo, C.-F.; Bao, L.-L.; Shi, X.-R.; Li, Y.-W.; Wang, J.; Jiao, H. Chem. Phys. Lett. 2007, 448, 83. (27) Steynberg, P. J.; van den Berg, J. A.; Janse van Rensburg, W. J. Phys.: Condens. Matter 2008, 20, 064238. (28) Liao, X.-Y.; Cao, D.-B.; Wang, S.-G.; Ma, Z.-Y.; Li, Y.-W.; Wang, J.; Jiao, H. J. Mol. Catal. A: Chem. 2007, 269, 169. (29) Deng, C.-M.; Huo, C.-F.; Bao, L.-L.; Feng, G.; Li, Y.-W.; Wang, J.; Jiao, H. J. Phys. Chem. C 2008, 112, 19018. (30) Cao, D.-B.; Zhang, F.-Q.; Li, Y.-W.; Jiao, H. J. Phys. Chem. B 2004, 108, 9094. (31) Cao, D.-B.; Zhang, F.-Q.; Li, Y.-W.; Wang, J.; Jiao, H. J. Phys. Chem. B 2005, 109, 833. (32) Cao, D.-B.; Zhang, F.-Q.; Li, Y.-W.; Wang, J.; Jiao, H. J. Phys. Chem. B 2005, 109, 10922. (33) Sorescu, D. C. J. Phys. Chem. C 2009, 113, 9256. (34) Cao, D.-B.; Wang, S. G.; Li, Y.-W.; Wang, J.; Jiao, H. J. Mol. Catal. A: Chem. 2007, 272, 275. (35) Cao, D.-B.; Li, Y.-W.; Wang, J.; Jiao, H. J. Phys. Chem. C 2008, 112, 14883.

Adsorption and Activation of CO on χ-Fe5C2 Surfaces (36) Huo, C.-F.; Li, Y.-W.; Wang, J.; Jiao, H. J. Am. Chem. Soc. 2009, 131, 14713. (37) Gracia, J. M.; Prinsloo, F. F.; Niemantsverdriet, J. W. Catal. Lett. 2009, 133, 257. (38) Sorescu, D. C. J. Phys. Chem. C 2008, 112, 10472. (39) Gong, X.-Q.; Raval, R.; Hu, P. Surf. Sci. 2004, 562, 247. (40) Ge, Q.; Neurock, M. J. Phys. Chem. B 2006, 110, 15368. (41) Huo, C.-F.; Li, Y.-W.; Wang, J.; Jiao, H. J. Phys. Chem. C 2008, 112, 14108. (42) Andersson, M. P.; Abild-Pedersen, F.; Remediakis, I. N.; Bligaard, T.; Jones, G.; Engbæk, J.; Lytken, O.; Horch, S.; Nielsen, J. H.; Sehested, J.; Rostrup-Nielsen, J. R.; Nørskov, J. K.; Chorkendorff, I. J. Catal. 2008, 255, 6. (43) Ciobıˆca˜, I. M.; van Santen, R. A. J. Phys. Chem. B 2003, 107, 3808. (44) Liu, Z.-P.; Hu, P. J. Am. Chem. Soc. 2003, 125, 1958. (45) Mavrikakis, M.; Baümer, M.; Freund, H. J.; Nørskov, J. K. Catal. Lett. 2002, 81, 153. (46) Cheng, J.; Gong, X.-Q.; Hu, P.; Lok, C. M.; Ellis, P.; French, S. J. Catal. 2008, 254, 285. (47) (a) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, 558. (b) Kresse, G.; Hafner, J. Phys. ReV. B 1994, 49, 14251. (c) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169. (d) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (48) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (49) Hammer, B.; Hansen, L. B.; Nørskov, J. K. Phys. ReV. B 1999, 59, 7413. (50) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953. (51) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (52) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (53) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892. (54) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (55) Methfessel, M.; Paxton, A. T. Phys. ReV. B 1989, 40, 3616. (56) Kresse, G.; Marsman, M.; Furthmu¨ller, J. VASP the Guide, 2009. http://cms.mpi.univie.ac.at/vasp/vasp/vasp.html (accessed Sept 03, 2009). (57) Jońsson, H.; Mills, G.; Jacobsen, K. W. Nudged Elastic Band Method for finding Minimum Energy Paths of Transitions. In Classical and Quantum Dynamics in Condensed Phase Simulations; Berne, B. J., Ciccotti, G., Coker, D. F., Eds.; World Scientific: Singapore, 1998; pp 385404. (58) Lide, D. R. CRC Handbook of Chemistry and Physics, 89th ed.; CRC Press: Boca Raton, FL, 2008. (59) Retief, J. J. Powder Diff. 1999, 14, 130. (60) The cell shape, cell volume and ionic positions were fully relaxed to determine the unit cell parameters, following the protocol outlined in ref 56. A larger basis set was used for the bulk calculations, in order to avoid errors due to inaccuracies in the calculated stress tensor. For the RPBEPAW method, an energy cutoff of 520 eV was used. For the PW91-USPP calculations, a cutoff energy of 400 eV was used. (61) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865.

J. Phys. Chem. C, Vol. 114, No. 17, 2010 7879 (62) du Plessis, E. H.; de Villiers, J. P. R.; Kruger, G. J. Z. Kristallogr. 2007, 222, 211. (63) Hofer, L. J. E.; Cohn, E. M. J. Am. Chem. Soc. 1959, 81, 1576. (64) Niemantsverdriet, J. W.; van der Kraan, A. M. J. Catal. 1981, 72, 385. (65) Stockwell, D. M.; Bianchi, D.; Bennett, C. O. J. Catal. 1988, 113, 13. (66) Xu, J.; Bartholomew, C. H. J. Phys. Chem. B 2005, 109, 2392. (67) Boettger, J. C. Phys. ReV. B 1994, 49, 16798. (68) Moon, D. W.; Cameron, S.; Zaera, F.; Eberhardt, W.; Carr, R.; Bernasek, S. L.; Gland, J. L.; Dwyer, D. J. Surf. Sci. 1987, 180, L123. (69) Cameron, S. D.; Dwyer, D. J. Langmuir 1988, 4, 282. (70) Dwyer, D. J.; Rausenberger, B.; Lu, J. P.; Bernasek, S. L.; Fischer, D. A.; Cameron, S. D.; Parker, D. H.; Gland, J. L. Surf. Sci. 1989, 224, 375. (71) Saiki, R. S.; Herman, G. S.; Yamada, M.; Osterwalder, J.; Fadley, C. S. Phys. ReV. Lett. 1989, 63, 283. (72) Nayak, S. K.; Nooijen, M.; Bernasek, S. L. J. Phys. Chem. B 2001, 105, 164. (73) Jiang, D. E.; Carter, E. A. J. Phys. Chem. B 2006, 110, 22213. (74) Bromfield, T. C.; Curulla Ferre´, D.; Niemantsverdriet, J. W. ChemPhysChem 2005, 6, 254. (75) Sorescu, D. C.; Thompson, D. L.; Hurley, M. M.; Chabalowski, C. F. Phys. ReV. B 2002, 66, 035416. (76) Lo, J. M. H.; Ziegler, T. J. Phys. Chem. C 2007, 111, 11012. (77) van Helden, P.; van Steen, E. J. Phys. Chem. C 2008, 112, 16505. (78) Calculations were performed with the RPBE-PAW method using the VASP code and a 5 layer slab of Fe. CO was adsorbed on one side of the slab, and the top two Fe layers and the adsorbate were fully optimized. A cut-off energy of 400 eV and a 5 × 5×1 Monkhorst-Pack mesh of special k-points were used in the calculations. (79) Chen, Y.-H.; Cao, D.-B.; Jun, Y.; Li, Y.-W.; Wang, J.; Jiao, H. Chem. Phys. Lett. 2004, 400, 35. (80) Huo, C.-F.; Ren, J.; Li, Y.-W.; Wang, J.; Jiao, H. J. Catal. 2007, 249, 174. (81) Borthwick, D.; Fiorin, V.; Jenkins, S. J.; King, D. A. Surf. Sci. 2008, 602, 2325. (82) Erley, W. J. Vac. Sci. Technol. 1981, 18, 472. (83) Stibor, A.; Kresse, G.; Eichler, A.; Hafner, J. Surf. Sci. 2002, 507510, 99. (84) Jiang, D. E.; Carter, E. A. Surf. Sci. 2004, 570, 167. (85) Gokhale, A. A.; Mavrikakis, M. Prepr. Pap.-Am. Chem. Soc., DiV. Fuel Chem. 2005, 50, 149. (86) Lo, J. M. H.; Ziegler, T. J. Phys. Chem. C 2008, 112, 3692. (87) For the initial tilted and upright CO adsorption configurations investigated on the lower energy reconstructed surface, the (partial) lifting of the reconstruction observed for 4F-18 and 4F-19 shown in Figure 6 was only obtained in calculations using the PW91 functional. The configurations 4F-18 and 4F-19 reported using the RPBE functional therefore correspond to adsorption on the metastable surface. For adsorption on the lower energy reconstructed surface, the CO molecule migrated to a neighbouring atop configuration.

JP911725U

Role of Step Sites and Surface Vacancies in the Adsorption and

Recommend Documents