How bulk and surface properties of Ti 4 SiC 3 , V 4 SiC 3 , Nb 4 SiC 3 and Zr 4 SiC 3 tune reactivity: a computational study †

We present several in silico insights into the MAX-phase of early transition metal silicon carbides and explore how these a ﬀ ect carbon dioxide hydrogenation. Periodic density functional methodology is applied to models of Ti 4 SiC 3 , V 4 SiC 3 , Nb 4 SiC 3 and Zr 4 SiC 3 . We ﬁ nd that silicon and carbon terminations are unstable, with sintering occurring in vacuum and signi ﬁ cant reconstruction taking place under an oxidising environment. In contrast, the metal terminated surfaces are highly stable and very active towards CO 2 reduction. However, we predict that under reaction conditions these surfaces are likely to be oxidised. These results are compared to studies on comparable materials and we predict optimal values for hydrogen evolution and CO 2 reduction.


Introduction
The H-(Hägg)phase of over 100 ternary carbides/nitrides was rst identied in the 1960s. 1,2][8][9][10] Owing to this set of novel properties these materials are also called "metallic ceramics". 11Interestingly, this same mixture of properties is also present in the closely related monocarbide materials which in recent years have received a lot of interest from the catalytic a School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, UK.E-mail: quesnem@ cardiff.ac.uk

Methodology
9][30] Benchmark studies, using formation energies for these materials with both RPBE 45 and PBEsol, 46 have produced consistent values for all methods which validates our choice of methodology.Such a protocol has been shown to be sufficient for replicating experimental trends for both surface properties and reactivities of closely related carbide 26 and MXene materials. 25lane-wave basis sets are applied to valence electrons with core potentials produced using projected augmented wave methodology (PAW) 31 to describe the core electrons of each element.Long-range dispersion interactions were introduced via the D3 method. 32,33Bulk structures for a-Ti 4 SiC 3 (ref.7) and a-Nb 4 SiC 3 (ref.34) were taken from the Inorganic Structure Database (ICSD), 35 whilst the MAX-phase of a-V 4 SiC 3 and a-Zr 4 SiC 3 were created by in silico modication of the former structures.The lattice parameters and the internal coordinates of each material were then fully optimized for all degrees of freedom and the (0001) basal plane was cut between the metal-carbon and metal-silicon layers using the METADISE code. 36Since the materials consist of alternating layers of metal and either carbon or silicon, only two possible slabs can be constructed in this plane: both express one metal layer, with one slab also terminated by carbon and the other slab terminated by the corresponding silicon surface.This sequence is due to the stoichiometry of these materials with a 1 : 1 ratio of metal to either carbon or silicon.The primitive cell of each silicon carbide was replicated into a 2 Â 2 Â 2 simulation cell to give slabs with nine atoms in each layer and 16 atomic layers along the z-axis to give a total of 144 atoms per slab.Above each termination was placed 15 Å of vacuum.A ne Monkhorst-Pack grid with a 5 Â 5 Â 5 k-point mesh was applied to all bulk calculations, with surface properties being determined using a 5 Â 5 Â 1 mesh.In all cases, energies were converged to within 520 eV and a threshold of 0.01 eV ÅÀ1 was used for geometry optimisations.Self-consistency cycles (SCF) were converged to within 10 À5 eV and the Blöchl smearing method was applied for higher accuracy. 37In all cases, half of each slab (the top 8 layers) was allowed to relax fully, whilst the bottom 8 layers were xed to maintain their bulk-optimised positions.Spin polarization was also enabled to account for the magnetic moments in the materials and electron transfer during catalysis.
Adsorption energies for H 2 O, H 2 , O 2 , OH and CO 2 are dened as: where the sum of the energies of the pristine slab and gas phase adsorbate(s) are subtracted from the total energy of the minimum energy structure of the slab with adsorbates.Vibrational frequencies, calculated with the nite difference method, conrmed the global minima for all absorbed species.

Bulk properties
MAX-phase silicon carbide crystal structures for a-Ti 4 SiC 3 (ref.7) and a-Nb 4 SiC 3 (ref.34) were taken from the Inorganic Structure Database (ICSD). 35Since no structures were available for a-V 4 SiC 3 and a-Zr 4 SiC 3 , they were created in silico by exchanging the transition metal component and running full optimisations of both the lattice parameters and atomic coordinates.For a meaningful comparison, the same bulk references for the individual elements were used as previously reported for the carbides, 26 with the addition of an elemental silicon reference. 38ur results show that the addition of interstitial silicon layers into the carbide lattice has a relatively small effect on formation energies (see Table 1) with no consistent trend observed, although silicon addition does appear to have a very large effect on the relative lattice constants (Fig. 1), which is unsurprising since at 210 pm silicon has the largest atomic radius of any of the elements in the materials under investigation.This effect is most apparent when examining the relative surface areas of the carbide (111

Density of states
Total density of states plots for each of the materials are shown in Fig. 2. Importantly, all four materials are clearly metallic in nature, with some bands crossing the Fermi level.Decomposition of these states indicates that there is a high level of hybridization between 3d or 4d orbitals of the metal with both the 2p states of the carbon and 3s orbitals of the silicon.All these materials, therefore, show considerable amounts of M-C and M-Si covalency.These same general properties were also reported previously for the related monocarbide materials, 26 and our results replicate previously reported electronic structure analysis for a-Nb 4 SiC 3 . 34There is also the same apparent increase in peak intensity in the group 5 over the group 6 metals that in carbides has been associated with a decrease in the strength of the M-C bond and an increase in ionic character. 40This shi is primarily due to an increase in the number of valence d-electrons and also causes a negative shi in the position of the d-band centre in relation to the Fermi level.Finally, the density of states in the conduction band is much higher in the silicon-containing carbides with d 2 metals (i.e. the metals in group 4 with the valence electrons d 2 , s 2 ) than for the d 3 which could indicate greater redox potential in the former.To a large extent, catalytic activity as well as other surface properties, such as the stability of different facets, can be linked to surface energies (s), and work functions (F). 41We have calculated these properties for each silicon carbide by cleaving along the (0001) plane and allowing the uppermost half of the slab to relax; depictions of the morphology of each relaxed surface can be found in Fig. S1 (see ESI †).Interestingly, major reconstruction (leading to surface-mediated formation of elemental silicon) is observed when the silicon-terminated surfaces of the 3d silicon carbides are relaxed, which indicates that the M-Si bond broken is far weaker than the new Si-Si bonds formed.Relaxed surface energies (s) were calculated using eqn (2) and (3).A denotes the area of each surface, where E slab signies the total surface energy and n denotes the number of unit cells used for each slab.When calculating the energy to create two unrelaxed surfaces (eqn (2)) 2 is added to the denominators.
When only half the slab is relaxed, the relaxation component of the surface energy (s) must be determined, as shown in eqn (3); here the area of only one surface is included in the denominator and this energy is subtracted from that of the unrelaxed surfaces.The computed s for various facets of both the siliconcontaining carbides reported here and their corresponding monocarbide equivalents are shown in Table 2. Previous work by our group showed that relaxing only the surface layers of the (111) facets of the corresponding monocarbides was critically important in both explaining the energetic differences between the two very different facets and to maintain the constraints provided by the bulk properties. 26From the values in Table 2, it is clear that surface energies for the carbonterminated slabs in both the monocarbide and silicon carbide materials are very high.
The silicon carbide (0001) slabs with both silicon and metal terminations have much lower surface energies, closer to the dominant (001) surface of the monocarbides than to the (111) facets.This result is perhaps unsurprising since in the presence of absorbates the carbon terminated (111) facet of early transition metal carbides has been shown to be extremely unstable and therefore would only be expected as a meta-stable phase under vacuum conditions. 22,42Fig. S1 † shows that there is a major reconstruction of both the silicon and carbon terminated surfaces upon relaxation.To attempt to see if this major surface reconstruction also occurs in an oxygen-rich environment, we have also added a monolayer of eight oxygen atoms to each pristine termination; however, upon optimisation, various partially oxidised silicon and carbon species were formed in all cases (see Fig. S2, ESI †).Owing to their potential instability and relatively high surface energies, it is clear Table 2 Relaxed surface energies (s) and surface areas (a 2 ) for each possible termination of the four silicon containing carbides compared to values for the (001) and metal terminated (111) surfaces of the corresponding monocarbides. 26All surface energies are given in J m À2 with the corresponding areas shown in Å2  that the carbon and silicon terminated (0001) facets of these silicon carbides will be unstable under reaction conditions and that the surface morphology of the catalysts will be either dominated by pristine metal surfaces or by sintered coke/ elemental silicon on top of a metal surface support.Therefore, unless otherwise stated, the remainder of this study will focus on the activity of the metal terminated (0001) facets.

Reactivity on the pristine surfaces
Hydrogen adsorption.We attempted to identify barriers for hydrogen adsorption by performing geometry scans that sequentially lower physically adsorbed hydrogen from the vacuum to the silicon carbide surfaces.To this end, each hydrogen molecule was xed in the z-direction and sequentially lowered towards the surface, but allowing full relaxation along all other degrees of freedom.The resulting energies of these scans are shown in Table S3 (see ESI †).However, whilst no local minima in such stepwise pathways to adsorption were found, the subsequent chemical adsorption step was shown to be a barrierless and extremely exothermic process.Since the same barrierless adsorption mechanism has been reported previously for the metal terminated (111) surfaces of the corresponding monocarbides, 42 we will continue our study by examining hydrogen loading effects on these facets.Fig. 3 shows the adsorption energies for the most exothermic adsorption modes of hydrogen under various coverages on the pristine metal terminated surfaces of the four silicon carbides considered in this study.The trends reported here are very similar to those reported previously for the metal terminated (111) facets of the corresponding monocarbides, 42 where it was demonstrated that the decrease in adsorption energies with higher loading of hydrogen is primarily due to electronic effects, whereby electron donation into the conduction band of the carbides increases the surface work function.The same phenomenon is observed here, with a steeper slope obtained for the silicon carbides with group 5 transition metals owing to their increased number of electrons in the d-bands exacerbating this effect.Unfortunately, whilst smaller than those observed for the metal terminated (111) surfaces of the monocarbides (almost certainly due in part to the higher surface energies of those facets) the hydrogen adsorption energies here may still be too large at even the highest loadings for the adsorbed hydrogen to be useful for efficient CO 2 reduction.This prediction is informed by our previous work, where very similar hydrogen adsorption energies on the (111) surfaces of the corresponding monocarbides makes those facets less than ideal for hydrogenation processes under reaction conditions. 42arbon dioxide adsorption.The adsorption energies for the lowest energy chemical adsorption modes for CO 2 on top of the metal terminated (0001) facets of the four MAX-phase catalysts are shown by the orange bars in Fig. 4 and are considerably more exothermic than the energies previously reported for the monocarbide surfaces 22 for all materials except for V 4 SiC 3 , which is calculated to lead to a very similar adsorption energy to that of the metal terminated (111) surface of VC.The values that we present here correlate more closely to values obtained for MAXenes with M 2 C stoichiometry, for which adsorption energies of À3.69 for Ti 2 C and À3.16 for Zr 2 C were calculated. 43Important geometric and electronic information about the lowest energy adsorption modes for carbon dioxide on top of each silicon carbide surface is given in Fig. S5, ESI.† These data show that whilst the average metal oxygen bond distance between the surface and adsorbate is modulated almost completely by the ideal M-C bond distance the amount of charge transfer (and corresponding elongation of the C-O bond length) varies depending on the periodic position of the parent transition metal.Importantly, group IV metals (Ti/V) see an increase of $0.6 in number of electrons transferred to the CO 2 upon adsorption from the values observed for their V metal equivalents (Zr/Nb), which corresponds to both greater activation of the adsorbate and a more exothermic adsorption energy.Additionally, modelling of MAXenes with a M 3 C 2 stoichiometry and d 3 transition metals predicted much smaller adsorption energies of À2.19 for V 3 C 2 and À2.35 for Nb 3 C 2 . 23Whilst high carbon dioxide capture on the pristine facets is more reminiscent of the MAXene-phase than the metal terminated (111) facets of the fcc-monocarbides, the adsorption energies are still slightly smaller than those on the MAXenes.Such high energies in the MAXenes are explained by the absence of a free (pristine) metal surface under either synthesis or reaction conditions.Indeed, all these materials are capped by a terminating layer of either OH, O, F or H monolayers. 44 Therefore, the remainder of this paper will focus on the effects of monolayer formation on the metal facet of MAX-phase silicon carbides.

Atomic monolayer formation and reactivity
First, we consider solvation of the surfaces in an aqueous environment.The energy per molecule of eight water molecules adsorbed on each surface is shown in Fig. 5 and there is little variation between the values for each material, which range between À1.03 for V 4 SiC 3 to À0.91 for Zr 4 SiC 3 .To create each layer, water molecules were initially placed in the most exothermic binding motifs (corresponding to the highly coordinated hollow sites) aer which other molecules were sequentially added to ll each surface, whilst every attempt was made to maximise hydrogen-bonding networks between molecules.The extent to which this was possible was largely determined by surface structure, as is also shown in Fig. 5, where the bottom panels show the hydrogen-bonding energy per molecule, obtained aer the surface was removed and a single point energy calculation was performed.These results show that for each silicon carbide surface, except for Zr 4 SiC 3 (where the network is much weaker), the surface-mediated hydrogenbonding networks maintain approximately half the energy of each hydrogenbond formed by water under atmospheric conditions.The anomalous value for Zr 4 SiC 3 is possibly due to the larger distances between binding sites caused by the larger surface area.
Finally, we examined surface modications under oxidising environments.Fig. 6 shows the morphology and energetics of a fully oxidised or hydroxylated metal terminated (0001) surface for each catalyst.The references for the surface View Article Online formation energies are triplet oxygen and singlet hydrogen molecules in the gas phase.Importantly, the oxide and hydroxide layers on this surface are formed without major modication to the rest of the slab which contrasts strongly with the results obtained using the carbon and silicon terminations (see ESI Fig. S2 †).
The addition of other adlayers has an extremely exothermically favourable stabilising effect that again is in excellent agreement with previous experimental results from the related MAXene-phases. 44More interestingly, by subtracting the energies for the formation of the oxide layers from those of the hydroxyl layers, we observe a large reduction in the hydrogen adsorption values: Ti ).These latter energies are interesting, because they are close to the values determined via modelling of chemical potentials to be optimal for the CO 2 hydrogenation reaction over the monocarbide materials. 22However, it is still unknown whether these hydroxylated surfaces will also maintain their other catalytic properties that make silicon carbide MAX-phases such exciting candidates for CCC and CCU processes.

Conclusions
The MAX-phases of early transition metal silicon carbides represent an interesting class of materials, owing to both their novel mix of metallic, covalent and ionic properties, as well as their structural similarities to related redox catalysts for carbon utilisation reactions.Our results demonstrate that the silicon and carbon terminations of these materials are unstable, with strong silicon-silicon and carbon-carbon bonds causing sintering and coking respectively, when undercoordinated atomic layers are exposed to the vacuum.In the presence of oxygen these terminations lead to the formation of partially oxidised silicon-and carbon-containing species as well as massive surface reconstruction.However, these materials can also terminate at an extremely stable metal (0001) facet that is very active towards CO 2 adsorption and activation.Unfortunately, these facets adsorb hydrogen far too strongly for them to be useful for the hydrogenation of carbon dioxide, although further calculations suggest that oxidised surfaces may have the ideal properties for this process.Finally, whilst these materials appear to show many promising characteristics as potential CCU catalysts, much more experimental and theoretical work is required to study their activity and selectivity towards the production of industrially useful chemicals.

Fig. 1
Fig.1Comparison of lattice constants (a 0 ) for both the monocarbides and their comparable silicon carbides.All results are calculated using the PBE functional.

Fig. 3
Fig. 3 Adsorption energies for different hydrogen loadings on top of pristine metal terminated surfaces of four MAX-phase silicon carbides.Values are shown for: Ti 4 SiC 3 blue diamonds (solid trend line), V 4 SiC 3 brown circles (dotted and dashed trend line), Zr 4 SiC 3 green squares (dotted trend line) and Nb 4 SiC 3 purple triangles (dashed trend line).Energies are given in eV per atom with reference to gas phase molecular hydrogen.Number of hydrogen atoms added is given along the x-axis in multiples of two (i.e.indicating increasing molecules of H 2 added).

Fig. 4
Fig. 4 Adsorption energies for chemically adsorbed carbon dioxide on the metal terminated (0001) basal plane of the four silicon carbides, shown by the orange bars.These values are compared to adsorption energies for the comparable (001) (blue bar) and metal terminated (111) (green bar) surfaces of the comparable monocarbide catalysts [ref.22].

Fig. 5
Fig. 5 Water monolayers on top of exposed metal terminated (0001) basal plane of silicon carbides.(top) Adsorption energy in eV per H 2 O for eight water molecules adsorbed on each surface.(bottom) Hydrogen-bonding energy in eV per H 2 O for the water layer without the surface interactions.

Fig. 6
Fig. 6 Models of oxidised surfaces of the four metal terminated silicon carbides.(top) Oxygen monolayer of nine oxygen atoms with energies given in eV per O atom .(bottom) Hydroxylated surfaces with nine -OH groups per surface with values given in eV per OH molecule .

Table 1
Energies of formation (O f E 0 ) for each silicon carbide compared to the corresponding monocarbide material (with the same metal component).All values are normalised to eV per atom and compared with the experimental heat of formation a PBE.b PBE sol .c RPBE. d Experimental values.