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Steam reforming on transition-metal carbides from density-functional theory

A screening study of the steam reforming reaction (CH_4 + H_2O ->CO + 3H_2) on early transition-metal carbides (TMC's) is performed by means of density-functional theory calculations. The set of considered surfaces includes the alpha-Mo_2C(100) surfaces, the low-index (111) and (100) surfaces of TiC, VC, and delta-MoC, and the oxygenated alpha-Mo_2C(100) and TMC(111) surfaces. It is found that carbides provide a wide spectrum of reactivities towards the steam reforming reaction, from too reactive via suitable to too inert. The reactivity is discussed in terms of the electronic structure of the clean surfaces. Two surfaces, the delta-MoC(100) and the oxygen passivated alpha-Mo_2C(100) surfaces, are identified as promising steam reforming catalysts. These findings suggest that carbides provide a playground for reactivity tuning, comparable to the one for pure metals.


I. INTRODUCTION
Steam reforming is an important industrial process, where natural gas (CH 4 ) is converted into synthesis gas (CO and H 2 ) according to the overall reaction (1) The synthesis gas is subsequently transformed into more valuable chemicals, such as ammonia, methanol, and diesel. Since steam reforming acts as a source of hydrogen, it is also potentially important for any emerging hydrogen economy. For a detailed review of the steam reforming process and its applications the reader can consult Ref. 1. Commercially the steam reforming reaction is conducted over a Ni-based catalyst due to the relatively low cost and good activity of nickel. This reaction has been studied in detail on the close-packed Ni(111) surface and on the stepped Ni(211) surface by means of density-functional theory. 2 The major technological challenge for Ni catalysts is the formation of carbonaceous deposits, termed coke, that lead to catalyst deactivation. In Refs. 2,3 it was established that the step edges on Ni surfaces act as growth centers for graphite. Other transition metals (TM), such as Ru, Rh, Pd, Ir, and Pt also show high activity and selectivity towards steam reforming 4 and have a high resistance against carbon formation. However, these materials are scarce in nature and expensive. Therefore new materials that are resistant to carbon formation are needed.
Transition-metal carbides (TMC's) have gained quite some attention since Levy and Boudart reported that they have "platinum-like behavior" for certain reactions. 5 The starting material for the production of carbides is cheap and abundant and therefore it has been suggested that they can replace the noble metals in catalysis. The main problem with the carbides has been to produce materials with sufficiently high surface area for them to be interesting for catalytic applications. This problem has been overcome and several studies report on carbides with surface areas as high as 200 m 2 /g. 6,7,8,9 In Refs. 10 and 11, it was shown that carbides of molybdenum and tungsten are stable and extremely ac-tive catalysts for not only the steam reforming but also the dry reforming and the partial oxidation of methane at elevated pressure. Moreover, no macroscopic carbon was deposition on the catalysts during the catalytic reactions. The relative activity of a number of steam reforming catalysts was established as: Several density-functional theory studies concerning adsorption on TMC's have been conducted, for example, atomic adsorption, 12,13,14,15,16,17,18,19,20 O 2 adsorption, 21 CO adsorption, 22,23,24 19,20 methanol adsorption, 25 CH x (x = 0 − 3) and C 2 H 4 adsorption. 26 In addition, the water-gas-shift reaction has been studied in Refs. 27,28,29. To our knowledge, a theoretical understanding of the steam reforming reaction on TMC's is missing in the literature. The aim of this paper is to investigate how the TMC's are suited for the steam reforming reaction by performing a set of density-functional theory (DFT) calculations on different surfaces of α-Mo 2 C, TiC, VC, and δ-MoC in order to catch the trends between TMC's composed of different TM atoms and of different structures. The influence of the surfaces being covered with oxygen is also investigated.
The outline of this paper is as follows. To begin with the systems to be investigated are defined in Sec. II. This is followed by Sec. III, which describes the calculation details. Our results are presented in Sec. IV and discussed in Section V. The paper ends with a conclusion in Section VI.

II. INVESTIGATED TMC SYSTEMS
The Mo-C system can occur in several crystalline forms, see for example the phase diagrams in Refs. 30 and 31. There are two types of Mo 2 C phases, one orthorhombic (α) and one hexagonal (β), which is a high temperature phase. In this study, we focus on the α phase. For this phase the Mo atoms are only slightly distorted from an hcp arrangement and the carbon atoms occupy one half of the octahedral interstitial sites. In the present molybdenum carbide literature there seems to be a confusion when it comes to the attribution of the symbols to the different phases, especially regarding the α and β phases. This is probably because the α-Mo 2 C phase was originally assigned a hexagonal structure but refined experiments identified the structure to be of orthorhombic type 32 , with lattice parameters a = 4.729Å, b = 6.028Å and c = 5.197Å. 33 The close-packed surface of α-Mo 2 C is the (100) surface. It consists of alternating Mo and C layers and can be either Mo-or C-terminated. Experimental studies of α-Mo 2 C(100) show that the surface termination and structure depend strongly on the cleaning procedure. Both the Mo-and the C-terminated surfaces have been observed. 34,35 Therefore we consider both the TM-and the C-terminated carbide surfaces.
The TiC, VC and δ-MoC adopt the NaCl structure. The (100) surface of these carbides consists of layers of equal amounts of TM and C atoms. The (111) surface, however, is polar and consists of alternating TM and C layers, similar to the α-Mo 2 C(100) surfaces. One important difference is that the C-terminated α-Mo 2 C(100) surface has half the amount of C atoms as compared to a C-terminated TMC(111) surface.

III. THEORETICAL DETAILS
All the DFT calculations in this paper are performed with the computer code DACAPO 36 , which uses planewaves and ultra-soft pseudopotentials. For the optimization of the bulk lattice parameters of the considered TMC's a plane-wave cutoff of 400 eV, a 8 × 8 × 8 kpoint sampling, and the RPBE exchange-correlation (xc) functional 37 are used. The bulk structure of α-Mo 2 C was obtained by minimizing the total energy of the unit cell with respect to the length of the lattice vectors using a Newton-Raphson scheme and allowing for complete internal relaxation at each step. The calculated lattice parameters a = 4.825Å, b = 6.162Å, and c = 5.304Å differ by ∼ 2% from the experimental values. 33 For TiC, VC and δ-MoC, the equilibrium bulk structure was obtained utilizing the Murnaghan equation of state. 38 The calculated lattice constants are 4.336Å, 4.171Å, and 4.444Å for TiC, VC, and δ-MoC, respectively. A quantitative agreement is found between the theoretical and experimental lattice constants. 39,40 The surfaces are modeled using the supercell approach, with the DFT lattice parameters given above. A 400 eV energy cutoff for the plane-wave expansion of the oneelectron orbitals, a 4 × 4 × 1 k-point grid, and the RPBE xc functional are used. Each TMC(111) and TMC(100) surface is represented by a slab with the geometry defined in Fig. 1 and a thickness of four atomic layers. Repeated slabs are separated by at least a 10.8Å thick vacuum region. The Mo-and C-terminated α-Mo 2 C(100) slabs have a surface geometry as defined in Fig. 1 and consist of four layers Mo and four layers C separated by 10.6Å vacuum. During structural relaxations, the two bottom atomic layers are constrained to the corresponding bulk geometry. Figure 1 shows the relaxed structures of the Mo-and C-terminated δ-MoC(111) surfaces, the δ-MoC(100) surface, and the Mo-and C-terminated α-Mo 2 C(100) surfaces. These relaxed surfaces and the corresponding VC and TiC surfaces are used as starting points for the modeling of the steam reforming reaction.
The investigated steam reforming reaction is assumed to have the following nine elementary steps: where * (2 * ) denotes one (two) empty surface site and X * denotes the adsorbate X bonded to this site. Adsorption

IV. RESULTS
This Section focuses on the results obtained from the screening calculations study. We provide the calculated potential energy diagrams for the steam reforming reaction on all the considered TMC surfaces. These are compared with existing results on Ni(111) and Ni(211) 2 .
A. TMC(111) and α-Mo2C(100) surfaces The calculated potential energy diagram for the steam reforming reaction on the TM-and C-terminated TMC's is shown in Fig. 2. First of all we notice that the span of the potential energies of the investigated surfaces is huge. Compared to the Ni surfaces 2 , all the TMC surfaces are much more reactive because they bind the intermediates too strongly. Therefore none of these surfaces is suitable for the steam reforming reaction.
In the following we present the trends in reactivity that are found when changing the TM atom in the TMC compound. For each of the considered TMC's, the Cterminated surface is found to be more reactive than the TM-terminated one. This is to be expected since the TMC(111) surfaces are found to be TM terminated under UHV conditions. 41,42 All the TM-terminated TMC(111) surfaces have similar potential energy shape as a function of the reaction intermediates. The same is found for the C-terminated group of TMC surfaces. For the TMterminated TMC surfaces, the reactivity can be ordered as TiC(111) > VC(111) > α-Mo 2 C(100) > δ-MoC(111), while for the C-terminated TMC surfaces we find that the reactivity order is TiC(111) > VC(111) > δ-MoC(111) > α-Mo 2 C(100). Hence different trends are observed for the different terminations.
The considered α-Mo 2 C(100) surfaces are less reactive than the C-terminated δ-MoC(111) surface but more reactive than the Mo-terminated δ-MoC(111). For a given carbide, the smallest difference in reactivity between the TM-and the C-terminated surfaces is found for α-Mo 2 C(100). This can be due to the fact that the C-terminated α-Mo 2 C(100) surface has 50% less C than the C-terminated TMC(111) surfaces.
The largest minimum in the potential energy surface is found upon adsorption of O-carrying intermediates, that is, a strong O-surface bond is formed. This implies that the TMC(111) surfaces are easily oxidized. Experimental studies show that the O 2 adsorption on TiC(111) 43 and α-Mo 2 C(100) 35 are dissociative. Therefore we investigate how the steam reforming reaction is influenced when the TMC(111) and the α-Mo 2 C(100) surfaces are oxygenated. TM-and C-terminated TMC surfaces. We find that the O-covered C-terminated α-Mo 2 C(100) has a potential energy profile similar to that reported for the Ni(111) surface, which is the preferred Ni facet for the steam reforming reaction according to the DFT calculations in Ref. 2. The other O-covered surfaces are unsuitable as catalysts for the steam reforming either because several of the reaction steps are significantly uphill energetically, or because the surface gets poisoned by some of the intermediates.
Some of the trends that are found for this class of surfaces are here described. Each of the O-covered TMC surfaces is less reactive than its corresponding non-oxidized surface. For a given O-covered TMC surface the TMterminated surface has higher reactivity than the Cterminated one, in contrast to the finding on the nonoxidized surfaces. For the O-covered TM-terminated TMC surfaces, the reactivity can be ordered as follows α-Mo 2 C(100) > δ-MoC(111) > VC(111) > TiC(111), while for the O-covered C-terminated TMC surfaces we find that α-Mo 2 C(100) > TiC(111) > VC(111) > δ-MoC(111). The order in reactivity between the different surfaces is thus different for the TM-and for the C-terminated O-covered surfaces.

C. TMC(100) surfaces
The calculated potential energy diagram for the steam reforming reaction on the TMC(100) surfaces is shown in Fig. 4. The δ-MoC(100) surface is found to have a potential energy curve similar to the one of the Ni(111) surface. We find the same shape of the potential energy curves for all the TMC(100) surfaces. A local minimum is found for all the TMC(100) surfaces upon adsorption of CO. The reactivity of the surfaces follows the order δ-MoC(100) > TiC(100) > VC(100), that is, a non linear variation when moving from right to left in the periodic table. Compared to the TMC(111) surface the TMC(100) surfaces are far less reactive. In Ref. 29 it was suggested that the TiC(100) surface is a suitable catalyst for the water-gasshift reaction. However, according to our calculation it is not the surface of choice for the steam reforming reaction since it is inert (see Fig. 4).

V. DISCUSSION
The conducted computational screening study clearly shows that only two surfaces, the O-covered Cterminated α-Mo 2 C(100) and the δ-MoC(100), are suitable for the steam reforming reaction. These two surfaces are found to have potential energy profiles similar to the one of Ni(111), which is the preferred Ni surface for steam reforming according to Ref. 2.
The obtained potential energy diagrams show that there is a large variety in the reactivities of the different carbides (see Figs. 2, 3 and 4). However, besides the two candidate surfaces none of the other considered TMC surfaces are suitable for the steam reforming reaction since they either get self-poisoned by the intermediates or they show a significant energetical uphill for some of the elementary steps in Eqs. (2)- (10).
An understanding of the reactivity can be achieved by studying the electronic structure of the surface. In Refs. 15,16,17,18,19,20 a thorough analysis of the electronic structure established that the TM-terminated TMC(111) surfaces possess surface resonances (SR's). These were identified to be responsible for strong adsorbate-surface bonds. Therefore the high reactivities of the TM-terminated TMC(111) surfaces (see Fig. 2) are attributed to the presence of these SR's. Preliminary electronic structure calculations show that similar resonances are present also on the layered polar α-Mo 2 C(100) surfaces, which would explain their high reactivities.
The NaCl TMC(100) surfaces, on the other hand, do not posses any SR's 17,44 and show a much lower reactivity (see Fig. 4) compared to the TMC(111) surfaces. Since a suitable candidate, the δ-MoC(100) surface, is found among these surfaces we have tried to change the reactivity of the TMC(111) surfaces by weakening their SR's.
The lower reactivities of the O-covered TMC(111) and α-Mo 2 C(100) surfaces (see Fig. 3), compared to the corresponding clean surfaces can be understood as follows. Adsorption of oxygen on the TMC(111) results in a quenching of the SR's. Thus, the surfaces are passivated, that is, their ability to form strong bonds with other adsorbates decreases due to the strong O-surface bond. This result shows that the reactivity of carbides surfaces can be tuned.
An important question for catalytic applications is the stability of the candidate materials. Steam reforming operates over a large range of working conditions with temperatures 700 − 1100 • C and pressures 1 − 25 bar. The most recent phase diagram for Mo-C systems is the one by Velikanova et al. 31 It shows that the bulk α-Mo 2 C phase exists for temperatures < 1440 • C, while the δ-MoC is a high temperature phase which exists above 1956 • C. Based only on bulk data, α-Mo 2 C is preferred over δ-MoC.
When it comes to the stability of a surface the situation can of course differ from the bulk. According to York and coworkers 10,11 , Mo 2 C was active and selective for the stoichiometric steam reforming of methane to synthesis gas. The catalyst deactivated at atmospheric pressure, but was very stable when elevated pressures were employed, and no carbon deposition was observed on the catalysts. In those studies the surface characteristics was, however, not addressed.
A surface characterization of α-Mo 2 C(100) has been performed in Ref. 34. The surface preparation consisted of Ar ion bombardment followed by annealing at successively higher temperatures. The surface was found to change from being Mo terminated to C terminated at annealing temperatures above 1300 K. Despite that these surfaces are stable at temperatures relevant for the steam reforming, our study shows that they are too reactive. Adsorption of O 2 on both the Mo-and the C-terminated α-Mo 2 C(100) surfaces were found to be dissociative and the surfaces were covered with oxygen at 800 K. 35 This supports the stability of the O-covered α-Mo 2 C(100) surface.
In addition, stable crystalline molybdenum carbide films prepared by chemical vapor deposition (CVD) and physical vapor deposition (PVD) have been found to contain either Mo 2 C and/or the δ-MoC 1−x phase. 45,46,47,48 Hence it seems plausible that both the O-covered Cterminated α-Mo 2 C(100) and the δ-MoC(100) surfaces may be stable at relevant steam reforming conditions, however, further studies are needed.

VI. CONCLUSION
In this paper, a computational screening study of the steam reforming reaction on transition-mental carbides has been presented. By using a screening approach we are able to map out the huge reactivity space, which ranges from very reactive to inert, provided by the carbides. A small set of surfaces, consisting of the δ-MoC(100) and the O-covered C-terminated α-Mo 2 C(100), is identified as promising candidate for the steam reforming reaction. With this thermochemical data at hand we lay a basis for a thermodynamic and micro-kinetic treatment of the carbides. This study illustrates the versatility and tunabilty of the TMC systems for the steam reforming reaction. The results can be understood in terms of the previously proposed model of chemisorption on TMC surfaces, in which surface resonances play crucial roles. However, further studies of the surface electronic structure are needed to establish what surface characteristics that are required of a carbide to make is a suitable catalyst for steam reforming.