MXenes Atomic Layer Stacking Phase Transitions and their Chemical Activity Consequences

Two-dimensional (2D) transition-metal nitrides and carbides (MXenes), containing a few atomic layers only, are novel materials which have become a hub of research in many applied technological fields, ranging from catalysis, to environmental scrubber materials, up to batteries. MXenes are obtained by removing the A element from precursor MAX phases, and it is for this reason that it is often assumed that the resulting 2D material displays the MAX atomic layer stacking —an ABC sequence with trigonal (D3d) symmetry. By means of density functional theory calculations, including dispersion, this work thoroughly explores the stability of alternative ABA stacking, with D3h hexagonal symmetry, for a total of 54 MXene materials with M2X, M3X2, and M4X3 stoichiometries (M=Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, or W; and X=C or N), revealing that for clean MXenes, the ABA stacking is fostered i) by the number of d electrons in M, ii) when X=N rather than X=C, and iii) when the surface is terminated by oxygen adatoms. The results suggest that stacking phase transitions are likely to take place under working operando conditions, surmounting affordable layer sliding energy barriers, in accordance to the experimentally observed layer distortions in Mo2N. Finally, we tackled the adsorptive and catalytic capabilities implications of such layer phase transition by considering N2 adsorption, dissociation, and hydrogenation on selected ABC and ABA stacked MXenes. Results highlight changes in adsorption energies of up to ~1 eV, and in N2 dissociation energy barriers of up to ~0.3 eV, which can critically change the reaction step rate constant by three to four orders of magnitude for working temperatures in the 400-700 K range. Consequently, it is mandatory to carefully determine the atomic structure of MXenes and to use models with the most stable stacking when inspecting their chemical or physical properties.


Introduction
Recently, a new class of two-dimensional (2D) materials was discovered by Naguib et al. [1] These materials, called MXenes, exhibit high electrical conductivity, hydrophilicity, large surface area, tunable structure, and superior oxidation resistance, among many other properties [2]. Not surprisingly, applications based on MXenes are gaining momentum in areas such as ecofriendly energy [3], greenhouse gases scrubber materials [4,5], batteries [6], water purification [7][8][9], or heterogeneous catalysis [10], among many other fields of technological applicability. MXenes are usually obtained by selective etching -typically with hydrofluoric acid, HF-of the A element from a precursor MAX phase [11][12][13]; where M is usually an early transition metal -e.g. Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W-, the A element belongs to a subset of groups XII-XVI of the periodic table, and X is carbon and/or nitrogen [14]. In general, MXenes have n+1 layers of hexagonal close-packed transition metals intercalated by n layers of hexagonal close-packed C or N atoms, with a face-centered cubic (fcc) -i.e. ABC-stacking, and n = 1-3. As a result of the synthesis procedure [1], MXenes feature a surface termination, usually denoted as Tx, so that the general formula of MXenes is often expressed as Mn+1XnTx, where Tx is in most cases a mixture of -OH, -O, -H, or -F moieties. Nevertheless, the progress in this field evolves very rapidly and recent HF-free syntheses have been reported yielding MXenes terminated by H and OH only [15,16], or upon fine tuning the layer sequence, reaching thicker n = 5 MXenes, with a central metal layer different from the other ones [17]. Also, even post-synthesis annealing and hydrogenation protocols have been developed to successfully defunctionalize MXene surfaces [5], thus modifying their properties by increasing their electrical conductivity [18].
While MXene surfaces are highly reactive, their atomic structure remains virtually unchanged in the presence of an adsorbate, yet some oddities have been found to occur. For instance, in a computational study, Shao et al. [19] predicted that Mo2N and W2N MXenes become structurally distorted upon adsorbing a nitrogen molecule. In a recent synthesis and characterization study, V2N and Mo2N MXenes were produced by ammonia treatment of the parent carbides [20]. There, the hexagonal phase of V2N displayed the usual trigonal D3d symmetry of MXenes -in line with an fcc ABC stacking-, but the resulting Mo2N sample was described as having a distorted structure with hexagonal close-packed (hcp) D3h symmetrywhich would be in line with an ABA stacking. Given the above subtlety, one may wonder if MXene stacking structures other than fcc may exist. Another important question concerns whether the transformation from ABC to ABA is intrinsic or can be prompted by either the Tx termination, as suggested on M2X MXenes with ABA stacking when having O termination, aka BiXenes [21], or by the presence of an adsorbate. Both sources of restacking may indeed bestow a symmetry change, eventually translatable into a lowering of the stacking conversion energy barrier, and, ultimately, prompting a stacking phase transition. Clearly, a deeper analysis regarding the intrinsic stability of the ABC and ABA stacking is needed.
Structural stacking changes may well imply different chemical surface activity, a point than can be key in chemically enhanced few-layered materials. Therefore, information on the preferred stacking of MXenes under working conditions is mandatory to guide future research on the field. However, obtaining this information requires investigating these materials at an inherent atomic level, an aspect difficult to be realized experimentally. Here, motivated by the aforementioned evidence indicating structural distortions and the existence of alternative stackings [19,20], we employ complete and accurate Density Functional Theory (DFT) simulations on suited MXene models to systematically analyze the stability of the ABA stacking relative to the usual ABC one. Thus, we consider a wide, organized set of MXenes encompassing different widths, inspecting both thermodynamic and kinetic aspects of the structural conversion. Although the study is mainly focused on pristine MXenes, the possible effect of surface termination on the stability of ABA stacking and/or its conversion is also addressed by considering Tx = O termination, one of the most common ones, and building phase diagrams as a function of oxygen-coverage. Finally, the effect of the ABA stacking on the surface chemical activity of the MXenes is analyzed addressing the textbook N2 adsorption and dissociation steps, key in the technologically relevant Haber-Bosch process of ammonia synthesis [22].

Computational details
The present study relies on DFT-based first-principles calculations using the Vienna Ab initio Simulation Package (VASP) [23], carried out on suitable MXene periodic slab models. The calculations were performed within the generalized gradient approximation to the many-body exchange-correlation potential, namely, using the functional developed by Perdew, Burke, and Ernzerhof (PBE) [24], augmented with the Grimme D3 method to account for dispersive forces [25], of relevance in the adsorption of N2 and N species on the explored MXenes. The valence electron density was expanded in plane-wave basis sets and the Projector Augmented Wave (PAW) method [26] was used to describe the effect of the atomic cores on the valence electronic density. The cutoff for the kinetic energy of the plane waves was set to 415 eV although a higher value of 550 eV was used for the calculation of lattice constants. The convergence criteria for the self-consistent energies and forces on the relaxed structures were set to 10 -6 eV and 0.01 eV·Å -1 , respectively.
The MXenes studied in the present work were modeled by hexagonal p(3×3) periodic supercells containing 9 atoms per layer, see Figure 1. In order to avoid interaction between MXene replicas due to periodic boundary conditions in the direction perpendicular to the surface, a vacuum region of at least 10 Å was set between periodic copies, both when the surface is clean and when it is Tx-terminated. We considered Mn+1Xn MXenes, where M is in the Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W list, X is C or N, and n = 1-3. Only two limit regular stacking possibilities -ABC and ABA-were initially considered, regardless of the MXene width, and thus, neglecting other possible mixed situations, see Figure 1. The calculated lattice parameters, a, for the ABC-stacked lattices are in consonance with those reported in the literature [27,28], see Table 1, while the change in a for n ≥ 2 was found to be lower than 1%; thus, the same lattice constant was used regardless of the MXene thickness. The lattice constants of the ABAstacked surfaces, however, can vary up to 8% with respect to the ABC situation, the former being smaller than the latter, with the exception of Mo2N. For example, the calculated lattice parameters for ABC-and ABA-stacked Mo2C are 3.10 Å and 2.84 Å, respectively, in very good agreement with the corresponding values reported by Sun et al. of 3.06 and 2.88 Å, respectively [29]. The differences in lattice parameter for each stacking are crucial to obtain accurate, reliable and physically meaningful results, both quantitative and qualitative. Using the example of Mo2C as a test case, when one uses the same lattice parameter for both stackings, one finds that ABC is more stable, by 0.59 eV per formula unit, while the usage of the proper lattice parameters for each stacking phase yields instead a preference for ABA stacking, by 0.29 eV per formula unit, in very good agreement with previous estimates [29].
The reciprocal space Brillouin zone was sampled using a Monkhorst-Pack 5×5×1 grid of special k-points [30]. Convergence tests on k-point density and basis set size showed that calculations have a numerical accuracy of about 1 meV per atom. Preliminary tests also showed that spin polarization is required in order to obtain correct total energies for Ti2C, Zr2C, and Cr2C, regardless of their stacking. The saddle-point configurations of the minimum-energy pathways for layer realignments were located via the dimer method [31]. Minimum energy and transition state structures were characterized by frequency analysis, with vibrational frequencies obtained within the harmonic approximation upon diagonalization of the corresponding block of the Hessian matrix, whose elements were computed by finite differences of 0.015 Å of analytical gradients. Note that the calculated frequencies were also used to calculate the zeropoint energy (ZPE) contribution to the total energy.
where θ O 2 is the rotational temperature of the O2 molecule, calculated from the diagonalization of its inertia tensor, and the translational partition function is where O 2 is the mass of one O2 molecule.

Results and discussion
Let us first assess the stability of ABA stacking relative to the ABC one for the explored 54 MXenes. Table 2 reports the calculated values and Figure 2 provides the corresponding plots of   preference for the latter.
The above trends are very similar when the MXene surfaces are terminated by oxygen, but generally considerably strengthening the ABA stacking, as shown in Table 2 and Figure 2.
In fact, nearly all Estack values for the O-terminated MXenes in Table 2 are smaller than those of clean systems. As seen in Figure 2, the O-termination greatly stabilizes ABA stacking on group VI Mn+1XnO2 MXenes, with Estack becoming even more negative, by differences between  [20], and the previously reported ABA energetic preferences for Mo2C [29], or the distortions reported on Mo2N and W2N [19]. Note also that, although the present results corroborate the stability of ABA Mo2C or Mo2CO2 on the hydrogen evolution reaction, as posed by Lv and coworkers [21], their proposal of preferential ABA stacking for Ti2C, Nb2C, V2C, and  Table 3. For n = 1, the mechanism involves only a simple C→A sliding.
However, for n ≥ 2, the transition from ABC to ABA may occur in several steps, involving the lateral sliding of a single or a few layers, with many local minima with regions of coexistence of ABC and ABA stacking. A careful examination of the sliding mechanism was carried out, guided by the found trends that the slide of surface metal layers is easier than the inner ones.
The Eb values shown in Table 3 correspond to the highest energy barrier among all the considered steps of the given found mechanism, whose respective slide acts as the rate-limiting energy step. Figure 3 shows examples for n = 1-3; W2C, W3C2, and W4C3, showing a guide to all the contemplated sliding steps, given that other MXenes follow similar mechanisms.
Let us analyze the exemplary W2C, W3C2, and W4C3 cases in fine detail. On W2C, the transition from ABC to ABA stacking (top row of Fig. 3) implies a single exothermic step. On W3C2, the ABCAB transition to ABABA stacking (middle row of Fig. 3) implies three exothermic steps; the first two align the outer W layers with the inner one, while the last one aligns the remaining C layers with each other. Lastly, the W4C3 transition from ABCABCA to ABABABA stacking comprises five steps (bottom row of Fig. 3); the first two are exothermic and align an outer W layer and its adjacent C layer with the inner closer W and C layers, respectively. The third step is highly exothermic, E = -1.08 eV per W4C3 unit, and aligns the other outer W layer with its closest W layer. After this step, the stacking is CACABAB, which is none other than two ABA-stacked W2C surfaces glued by a layer of carbon. This stacking is very stable and, for this reason, the step that follows, that is, the sliding of the first outer W layer to become aligned with the two farthest W layers is endothermic, E = 0.48 eV per W4C3 unit, making this the highest-barrier step in the process, with  Ti .
The ads step value gives information on the energy released when an MXene containing encompassed in Table 4, for W2N in either an ABC or an ABA configuration. On the one hand, the values of Eads/NO in Table 5 are all negative, implying exothermicity, at least until full O coverage, with values ranging from -3.56 to -5.08 eV for ABC stacking, and varying much less, between -4.07 and -4.27 eV, for ABA stacking. On the other hand, the ads step values are always negative as well, but on ABC stacking largely oscillate between -1.67 eV and -7.09 eV. Such fringe situations can be understood when the system symmetry is accounted for as NO increases.
Indeed, the stepwise adsorption is stronger whenever the symmetry is reduced from C3v to C1h by adsorbing the extra O atom. This situation is not observed on the ABA stacking, with ads step values ranging between -3.69 and -4.30 eV, as the surface is kept intact during the O coverage.  The strongest ads step values are associated to a surface relaxing effect observed on the MXene surface. As shown in Figure 5 for the initial O adsorptions with NO = 0-2, when the symmetry is C1h, the lattice becomes largely distorted, and the apparent stronger ads step = -6.59 eV is not due solely to the O adsorption itself, but in part due to the surface relaxation it promotes. The symmetry reduction caused by the adsorption seems to already reduce the energy barrier required by the W2N surface to relax into a more stable configuration. This explains the oscillation between small and large ads step alongside the C3v and C1h symmetries. This conclusion was confirmed by repeating the calculations, but breaking the symmetry of the system, making it C1. Similar oscillations to the ones in Table 2 were obtained, yet for the last O adsorption, an    Once the relative stability of the ABC and ABA stackings has been clarified for the scrutinized MXenes, there is still the question regarding the possible effect of the stacking on the chemical reactivity of the MXene surfaces. To answer that question, we studied the atomic N adsorption and molecular N2 adsorption and dissociation, technologically relevant in the Haber-Bosch ammonia synthesis [22], on the eight clean M2X where ABA stacking is preferred, following the recent study which dealt with these processes on MXenes with ABC stacking [34]. Thus, it appears that the impact of stacking on a reaction profile can be significant, with adsorption strengths changes up to ca. 1 eV, and energy barrier changes of up to ~0.3 eV, which can signify changes in the reaction step rate constant of up to three or four orders of magnitude in the temperature range of 400-700 K. Consequently, and to avoid unduly model-biased artifacts in computed results, the use of the correct stacking conformation under working operando conditions is strongly advised.

Conclusions
A first-principles DFT study including dispersion was carried out for a total of 54 MXene 2D transition metal carbide and nitride materials. The analysis of the results reveals that the ABA type of layer stacking is competitive for a number of cases meaning that the MAX-derived ABC stacking cannot be taken as granted. Energetic data reveal that the ABA stacking appears to be more frequent than anticipated and is fostered by the number of the constituent metal d electrons, preferred by nitride instead of carbide MXenes, and favored by the O surface termination. The calculated sliding energy barriers for the conversion of ABC towards ABA reveal very small energy barriers as low as 0.12 eV per formula unit for some MXenes, and higher ones, up to 1.12 eV per formula unit, for thicker M3X2 and M4X3 MXenes, in any case, surmountable at high temperature operando conditions. On M2X systems, the adsorption of species or the formation of an O overlayer can be enough to prompt the conversion from ABC towards an ABA stacking. This ABA layer stacking was found to influence the adsorption energies and reaction energy barriers of surface on-going processes, with energetic changes that can vary between a few hundredths of eV to ~1 eV, which can definitely bias the reaction profile, even the reaction step rate constants, by up to three or four orders of magnitude in usual working condition temperatures. To summarize, the present study provides compelling evidence that the atomic layer stacking on MXenes can be different from that expected from the MAX phase precursor for nearly half of the studied MXenes, with several important consequences for the MXene surfaces chemistry and, likely, on physical properties as well which call for further analysis. A careful atomic structure determination is advised rather than assuming that corresponding to the parent MAX phase. Computational models should seriously also consider this issue.