Carbon-induced Ru nanorod formation

Abstract

Using DFT calculations we study morphology of C-covered Ru nanostructures. We find that the equilibrium shape of clean Ru nanoparticles is a polyhedron consisting mainly of {0001}, {101̄0}, and {101̄1} faces. At low and intermediate coverages of C the shape does not deviate much from that of clean nanoparticles. However, at higher coverages the particle's morphology transforms from the polyhedron to a rod-like shape, which mainly consists of {101̄0} faces. The formation of nanorods is due to a high stability of Ru(101̄0), which is induced by the formation of chains of C atoms on this surface. We find that under conditions of Fischer–Tropsch synthesis, in which C forms from the hydrogenation of CO, the rod-like Ru nanoparticle is the most favorable shape.

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Industrial catalysts are often in nanoparticle (NP) form. Reactivity and selectivity of the catalysts depend strongly on size and shape of the NPs. The shape of freshly prepared and operating NPs are expected to be different. This is because the interaction between dissociated reactants and fresh NPs under high temperatures and reactant pressures (i.e. industrial reaction conditions) can destabilize the surfaces of NPs in favor of formation of other surfaces.^1,2 This leads to a dramatic change in the shape of NPs. Consequently the activity of the operating NPs depends on the structure of stabilized surfaces.

Ruthenium is the most active metal catalyst for Fischer–Tropsch (FT) reactions,³ which are part of gas-to-liquid technology. In FT process, hydrogen and carbon monoxide react over a catalyst to form hydrocarbons. This is used to convert traditional fuel sources such as natural gas and coal into synthetic fuels such as methanol and gasoline.^3–5 Among the proposed FT synthesis mechanisms, the carbide mechanism is the most accepted one. In this mechanism, FT synthesis begins with the dissociation of CO followed by hydrogenation of the chemisorbed C. It is therefore of interest to study the interaction of C with the Ru surfaces as a key step in understanding the FT synthesis.

There are only a few studies on adsorption of C over Ru surfaces. To our knowledge, only C/Ru(0001)⁶ and C/Ru(112̄1)⁷ have been investigated. In these studies, the preferred adsorption site and binding energy of C have been determined using density functional theory (DFT) calculations.

In the aforementioned studies only a low coverage of C on the Ru(0001) and Ru(112̄1) surfaces have been considered. In this work, by combining DFT and thermodynamic considerations we study the adsorption of different coverages of C on Ru(0001), (101̄0), (101̄1), (112̄1), and (134̄2) surfaces and determine the shape of C/Ru NPs. We find that at low and intermediate coverages C adsorption has a minor influence on the particle shape, which is polyhedron consisting mainly of (0001), (101̄0), and (101̄1) faces. At very high coverages of C, particles are nonorods consisting mainly of (101̄0) faces.

The equilibrium shape of C/Ru NPs can be determined by Wulff's theorem.⁸ This theorem states that large particles (usually >3–5 nm) of a given volume in which the overall formation energy is dominated by surface contributions are bound with surfaces resulting in minimum total free energy:

where γ_i and A_i are the surface free energy and the area of the ith face, respectively, T is the temperature and p_gas the partial pressure of the surrounding gas.

To calculate the surface free energies we use an ab initio atomistic thermodynamics approach,^9–12 which allows for the calculation of the stability of surfaces in contact with surrounding gas atmospheres (reservoirs) using ab initio methods. The most stable structure of Ru surfaces in thermodynamic equilibrium with gas atmospheres is the one that has the lowest surface free energy:

Here, A and G_surf are the surface area and Gibbs free energy of the slab, respectively. T is the temperature. μ_i and p_i are the chemical potential and partial pressure of the ith species in the reservoir, respectively. N_i is the number of atoms of the ith species in the system.

To study the structure of Ru NPs in temperature and pressure conditions under which FT processes occur, we assume that each adsorbed C on Ru comes from the reaction between carbon monoxide and hydrogen:¹³

CO + H₂ ⇔ H₂O + C. (3)

We consider the constrained equilibrium approach^14,15 in which a surface is assumed to be in thermodynamic equilibrium with non-interacting gas phase reservoirs. The chemical potential of CO, H₂, and H₂O can then be described by the ideal gas law, which then enables us to relate μ_C to specific temperatures and pressures:

Here, [small mu, Greek, macron]_CO, [small mu, Greek, macron]_H2, and [small mu, Greek, macron]_H2O are the standard chemical potentials at temperature T, which includes all the contributions from vibrations and rotations of the molecules, and the ideal gas entropy at 1 atm. E^tot_CO, , and are the calculated total energies of the isolated molecules. The standard chemical potentials were obtained from the JANAF thermodynamic tables.¹⁶ The total energies required for eqn (2) and (4) were calculated using DFT.¹⁷

To construct Ru NPs we consider low-index Ru(0001), (101̄0), (101̄1), and (112̄1) as well as high-index Ru(134̄2) surface that was found to be a stable surface in contact with an nitrogen atmosphere.¹⁸

The calculated surface free energies for the clean surfaces (see Fig. 1) are listed in Table 1. Our calculations suggest the following order of stability from the most to least stable: γ₀₀₀₁ < γ_101̄0 < γ_101̄1 < γ_134̄2 < γ_112̄1. Although (134̄2) is the most open surface among the considered surfaces and is expected to be the least stable (i.e. highest surface free energy), its stability is comparable to that of (112̄1). This is because (134̄2) can be viewed as a vicinal (011̄1) surface with kinked steps and (011̄1) terraces that are more close-packed than (112̄1).¹⁹

Fig. 1 Top views of Ru surfaces, showing binding sites at which C adsorption has been studied. The (1 × 1) surface unit cells are presented in red.

Table 1 Surface free energies (in meV Å⁻²) for Ru surfaces obtained using the PBE functional

Surface	(0001)	(101̄0)	(101̄1)	(112̄1)	(134̄2)
γ	167	186	187	208	202

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Afterwards, we studied the adsorption of atomic carbon on Ru surfaces by examining carbon adsorption at the surface sites presented in Fig. 1. Although formation of graphene and subsurface adsorption of carbon have been reported in experimental studies of ethylene adsorption on Ru(0001),²⁰ we have not studied these structures in this work because of the following reasons: (i) the C/R(0001) surfaces with high coverage of carbon are much less stable than other C/Ru surfaces and therefore they can not affect the structure of C/Ru nanoparticles. (ii) Previous DFT calculations on C/Ru(0001) show that the subsurface structures are less favorable than surface adsorption.¹³

The most stable structures for different surfaces and coverages are presented in Fig. 2. We used geometrical coverages Θ given in GML, which are defined as the number of C adsorbates per (1 × 1)-unit cell of the substrate. As can be seen in Fig. 2C prefers binding at highest possible coordinated sites. This result is in line with previous studies for C/Ni,²¹ C/Fe,²² and C/Ir²³ surfaces. For the lowest coverages considered for Ru surfaces, the threefold hollow hcp sites on (0001), the four-fold hollow sites on (101̄0), (112̄1), and Ru(134̄2), and the five-fold hollow sites on (101̄1) are the most stable adsorption sites.

Fig. 2 Top views of the most stable structures for different coverages of C on Ru surfaces.

For higher coverages, the further adatoms bind at unoccupied high-coordinated sites on the Ru surfaces. Fig. 2 indicates that at high coverages, C atoms tend to be close to each other. On the (101̄0) surface, we find a chain of C atoms. The formation of C chains is only possible on this surface. Similar behavior has been reported for C adsorption on Ni(111).²⁴

The calculated binding energies versus coverage (in the unit of atom per m²) are illustrated in Fig. 3. The bond strength of C on Ru(0001) is the weakest for most of the coverages. Although the binding energy of C on Ru(101̄1) is the highest at low coverages, it decreases significantly with coverage, showing strong repulsive C–C interactions. The weakest C–C interactions are for (101̄0) and (112̄1). The binding energy of C on the former surface does not change much even at the high coverage of 2 GML, where the chain of C atoms form on the surface (see Fig. 2).

Fig. 3 Binding energy (referenced to C atom) as a function of carbon coverage on Ru surfaces.

The total energies obtained for the most favorable structures of the clean as well as C-covered Ru surfaces have then been used to construct the surface free energy plot presented in Fig. 4. Here, using eqn (2) we plot the stabilities versus Δμ_C = μ_c − E^tot_C, where E^tot_C is the total energy of an isolated C atom. Only those phases (lines) are shown which are most stable (lowest lying) in their particular chemical potential range. We have not considered Ru-carbide in our study since there is experimental evidence that a stable Ru-carbide cannot be obtained directly from the Ru and C elements.²⁵

Fig. 4 C/Ru phase diagram showing the surface stability γ as function of the chemical potential of carbon Δμ_C = μ_c − E^tot_C (see eqn (2)). Equilibrium shapes of Ru particles as function of carbon chemical potential, Δμ_C (eV), are presented below the phase diagram.

Fig. 4 shows that for Δμ_C lower than −8.35 eV no C atom adsorbs on the Ru surface. Above Δμ_C = −8.35 eV, adsorption of C occurs first on (101̄1). This result is due to the stronger binding energy of C with this surface compared to other Ru surfaces (see Fig. 3).

By increasing Δμ_C, C starts to adsorb on other surfaces. Although the (0001) surface is the most stable before adsorption of C, it becomes much less stable than other Ru surfaces at high Δμ_C. This is because the C–Ru interactions on this surface are weaker compared to those on other surfaces, which can be clearly seen in Fig. 3. Finally, at very high values of Δμ_C ≥ −6.8 eV the (101̄0) surface becomes the most stable.

The equilibrium shape of Ru nanoparticles at selected values of Δμ_C are presented in Fig. 4. We find that at low values of Δμ_C, where no C adsorbs on the surface, shape of Ru NPs is a polyhedron in which the {0001}, {101̄0}, and {101̄1} faces have the highest contribution to the NPs. This is because that these surfaces are more stable than high-index (112̄1) and (134̄2) surfaces (see Table 1). By increasing Δμ_C above −8.35 eV adsorption of C occurs on Ru(101̄1). Thus contribution of (101̄1) faces is larger at Δμ_C = −8.0 eV than Δμ_C ≤ −8.35 eV. Above Δμ_C = −6.8 eV, where the (101̄0) surface covered with a chain of C atoms becomes the most stable surface among considered surfaces, the NP shape starts to change. By increasing Δμ_C, {0001} and {101̄1} faces shrink while {101̄0} faces enlarge, leading finally to the formation of rod-like shape above Δμ_C = −6.5 eV.

To find the structure of Ru NPs under industrial conditions for the FT processes we calculate Δμ_C (see eqn (4)) for T ∼ 500 K, p_CO + p_H2 + p_H2O = p_tot ∼ 20–30 atm, p_H2/p_CO ∼ 2, and p_H2O/p_H2 < 1.5.^26–28 The calculated range of the carbon chemical potential satisfying these conditions is −6.3 eV ≤ Δμ_C ≤ −6.5 eV for 0.1 < p_H2O/p_H2. Fig. 4 indicates that rod-like NPs become thermodynamically stable under these conditions.

In summary, we used DFT-based thermodynamics to study the equilibrium shape of C-covered Ru particles. We showed that a low coverage of C does not change much the shape of Ru NP, which is a polyhedron. However, at high coverages of C, the rod-like shape, which mainly consists of {101̄0} faces, is the most stable. This is due to the weak C–C interactions on (101̄0) surfaces, where a chain of C atoms form. Our study suggests that under industrial FT processes and/or with high concentration of C impurities the structure of Ru catalysts can be strongly influenced.

Acknowledgements

The author gratefully acknowledges Prof. Timo Jacob for his valuable comments and the bw-grid for computing resources.²⁹

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