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Predicted Surface Composition and Thermodynamic Stability of MXenes in Solution Michael Ashton, Kiran Mathew, Richard G Hennig, and Susan B. Sinnott J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11887 • Publication Date (Web): 25 Jan 2016 Downloaded from http://pubs.acs.org on February 1, 2016
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Predicted Surface Composition and Thermodynamic Stability of MXenes in Solution Michael Ashton†, Kiran Mathew‡, Richard G. Hennig†*, Susan B. Sinnott†** † Department of Materials Science & Engineering, University of Florida, Gainesville, FL, 32611-6400 ‡ Department of Materials science and Engineering, Cornell University, Ithaca, NY, 14850 Keywords: MXene, surface, 2D materials, thermodynamic stability, adsorption, first-principles Abstract First-principles calculations are used to compare the binding energies of O, OH, and F on twodimensional, metal carbide and nitride, or MXene, surfaces in order to predict the dependence of the thermodynamic stability of these compounds on their chemical composition. Solvation effects are implicitly included in the calculations to reproduce experimental conditions as closely as possible. The results indicate that all MXene surfaces are saturated with oxygen when exposed to H2O/HF solutions at low hydrogen chemical potential, µH , and that Sc-based MXenes can also be fluorinated in solutions of higher µH . After investigating the thermodynamic stability of all 54 MXene compounds Mn+1XnO2 (M = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta; X = C, N; n = 1, 2, 3), 38 are predicted to have formation energies below 200 meV/atom. Of these, six are predicted to have formation energies below 100 meV/atom, only one of which has been synthesized. Sc-
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based MXenes are found to be highly stable when their surfaces are terminated with F, which also results in the easiest exfoliation to produce freestanding single layers. Introduction Two-dimensional (2D) materials, or crystals with high aspect ratios and few-layer thicknesses, have been the focus of many recent studies. This is largely due to the unique electronic properties of many of the recently discovered 2D materials. Following the intense interest in graphene beginning in 20041, several new classes of 2D materials were discovered and synthesized over the following decade. A few notable examples include hexagonal boron nitride,2 transition metal dichalcogenides3, and metal oxides4. In 2011, two-dimensional transition metal carbides and nitrides, also known as MXenes, were synthesized by Gogotsi et al5. The large number of theoretically possible members of the MXene family, the diversity of properties among the synthesized MXene compounds, and their relatively simple synthesis make these compounds attractive for a number of 2D material-related applications6. For instance, MXenes are promising candidates for thermoelectrics7, electrode materials in high-power lithium ion batteries5, 8-14, larger and multivalent ion batteries15, electrochemical catalytic surfaces16, and hydrogen storage17. They are also being investigated as sensors18 and components in electronic heterojunctions19. In each of these applications, knowledge of the chemical termination of the MXene surface is critical to predicting the material’s properties and performance. Because of MXenes’ characteristically high surface to volume ratio, the atomic or molecular groups chemisorbed to its surface play a critical role in controlling the overall stoichiometry, stability, and properties of the MXene. For instance, the diffusion barrier for Li on a Ti2C(OH)2 surface (1.02 eV) is almost three times as large as it is on a Ti2CF2 surface (0.36 eV)8, and MXene band gaps have been
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shown to depend significantly on the nature of the terminating atoms and molecules5, 8. This implies that an ability to control which species bind on a MXene’s surface can be used to design a material with fine-tuned properties for technological applications. Despite their importance, it is not yet understood precisely which chemical species bind to the MXene surfaces during synthesis, the exact manner in which they contribute to the overall stoichiometry, or the effect they have on the MXene’s overall thermodynamic stability. This is due in large part to the novelty of the MXene family; almost no experimental data, including structural and electronic properties, have yet been published to which the large and growing body of theoretical work can be compared. MXenes are synthesized by selective etching of the relatively weakly bound20 A elements from bulk MAX phases by a solution of H2O and HF5. MAX phases are layered solids of composition Mn+1AXn, where M = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, or Ta; A is a group 13 or 14 element, X is either C or N, and n is 1, 2 or 321, as illustrated in Figure 1a. Solid solutions are also possible for each of the M, A, and X species. The Mn+1Xn layers are joined by layers of A atoms in such a way that the removal of A layers results in separated Mn+1Xn layers, or MXenes (Figure 1b).
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Figure 1. A V2AlC MAX phase (a) from which a V2C MXene (b) can be derived by etching. Surface species have been shown to prefer FCC sites (c) over HCP sites (d) for binding on most MXenes.
Following their synthesis, MXene layers are held together as multilayer structures by dispersion forces5, 9. This dispersion interaction is caused by polarizable, non-metallic groups bound to MXene surfaces once the surfaces are exposed to the acidic solution. Of the molecular and atomic species present in solution, O, OH, and F are the most likely to bind to the newly formed surface and cause the observed dispersion interaction. Multilayer MXene structures can be separated mechanically, typically by ultrasonication, to form single- or few-layer MXenes in solution5. Filtering these solutions results in the isolation of freestanding MXene flakes. Other species can be intercalated after synthesis, including methoxy groups22, or small ions (e.g. Li+, Na+, Mg2+)23 to expand the interlayer spacing and facilitate the isolation of single MXene sheets. Because they are derived from MAX phases, the same compositional rules for choice of M, X, and n apply to MXenes as to bulk MAX phases (9 M species × 2 X species × 3 choices of n), resulting in 54 possible Mn+1Xn combinations, six of which have been successfully synthesized to date24. The large theoretical size of the MXene family and the significant experimental effort required to successfully synthesize each bulk and 2D compound make predicting the thermodynamic stability of MXene compounds a worthwhile and as yet incomplete endeavor.
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Additionally, the important and related question of the role of the atoms and molecules that adsorb on the MXene surfaces remains unanswered25. In this work, density-functional theory (DFT) calculations are used to address these questions and to assess the thermodynamic stability of each MXene compound. The paper is arranged as follows: the predicted results for low energy surface structures and thermodynamic stability are presented, followed by technical details on the DFT calculations. The results are summarized in the form of general experimental guidelines for stabilizing as-yet un-synthesized MXenes, including those of particular interest for use as Li-ion battery electrodes.
Surface Compositions Binding energies for molecules and atoms on MXene surfaces are calculated according to m
Eb = EMn+1 Xn Tm – EMn+1 Xn – 2 ET2 – mµT (1) where EMn+1 Xn Tm is the energy of the MXene with the chemisorbed atoms or molecules, EMn+1 Xn is the energy of the bare MXene, ET2 is the energy of the chemisorbed atoms or molecules in their gaseous reference state (O2, O2+H2, or F2), and µT is the chemical potential of the chemisorbed atoms or molecules in the solution phase. In Equation 1, a negative Eb is indicative of exothermic binding. To determine the degree of saturation predicted for MXene surface binding sites, Eb is calculated as a function of coverage for O, OH, and F on a Ti2C surface using Equation 1 with µT = 0 eV, and the results are shown in Figure 2. For these calculations, we use a 2 × 2 × 1 supercell containing 8 formula units. This supercell allows resolution in our values of coverage as low as 0.125 T species per formula unit. Previous work8, 26-28 has shown that FCC sites (see Figure 1(c)) are the most favorable binding sites for most MXene compositions. Therefore, our
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coverage profile begins with occupying FCC sites, and includes HCP sites after all FCC sites are filled. During the incremental occupation of FCC sites (and later, HCP sites), the sites are filled in such a way as to maximize the distance between neighboring surface groups. This configuration minimizes the ionic repulsion between neighboring species and results in the lowest energy configurations in our calculations. Figure 2 shows for all three species a sharp increase in Eb after all FCC sites are saturated, indicating that the system’s surface energy is minimized when all FCC sites are occupied and the HCP sites are empty. This suggests a general Mn+1XnT2 stoichiometry for all MXenes, in agreement with previous investigations27.
Figure 2. Binding energy vs. coverage for O, OH, and F on a Ti2C surface. The DFT energies of O2, O2+H2, and F2 are used as reference energies in Equation 1, and µT = 0 eV. We find that all species exactly saturate the FCC sites, corresponding to an Mn+1XnT2 stoichiometry. The abrupt upturn in binding energy for HCP sites can be explained as the result of steric hindrance. In particular, the average O-O distance when all FCC and HCP sites are occupied on a Ti2C surface is 0.78 Å, compared to 3.1 Å when only FCC sites are occupied. Treated as point charges, the difference in repulsive force between neighboring O anions is more than an order of
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magnitude in these two cases, and explains why the energy vs. coverage curve in Figure 2 increases more rapidly for O than for the other anions of lesser charge. Binding energies have already been calculated for all M2X compounds using µT = 0 eV27, which physically corresponds to the binding energy if the T species came from a gaseous source, as considered in Figure 2. A gaseous reference state is an easy but arbitrary choice within the framework of DFT calculations, and it does not describe the experimental conditions. In fact, it is expected that all three surface groups (shown in bold) come from liquid sources, following the reactions5 Ti2C + 2H2O Ti2CO2 + 2H2 (2) Ti2C + 2H2O Ti2C(OH)2 + H2 (3) Ti2C + 2HF Ti2CF2 + H2 (4) and that the chemical potential of each species in solution is a variable that can be experimentally controlled. Reactions 2-4 suggest that the most suitable reference chemical potentials are those of O and OH in H2O, and F in HF. The three chemical potentials µO , µOH , and µF are not independent of one another and are a function of the value of µH in the solution. The chemical potentials of all three surface groups are inversely related to µH , according to the energy required to split the liquid source (H2O or HF) into its components: H2 O
µO = ∆Gf
- 2µH (5)
H2 O
µOH = ∆Gf
- µH (6)
µF = ∆GHF f - µH (7)
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The values of µO , µOH , and µF in Equations 5-7 are substituted for µT in Equation 1 for their respective species to calculate the binding energy of that species on MXene surfaces. Solvated H2 O
formation energies for the liquids from the gaseous molecules (∆Gf
= -2.71 eV, and
29 ∆GHF f = -2.83 eV) are calculated using the implicit VASPsol method , and are in good
H2 O
quantitative agreement with their experimental formation energies (∆Gf
= -2.51 eV, and
30-32 ∆GHF . Instead of assuming a single value for µH , it is more useful to assume that f = -2.81 eV)
it is a variable bound by its minima and maxima in the H2O/HF solution. The maximum value of µH in any solution is equal to its value in H2 gas, which is generally set to be the zero reference, H
µH2 = 0 eV, and the minimum value of µH is calculated as the value in Equations 5-7 when ∆µT is T
set to its own zero reference, µT2 = 0 eV. This gives a minimum value of µH = –1.35 eV for Equation 5 (H2O), µH = –2.71 eV for Equation 6 (H2O), and µH = –2.83 eV for Equation 7 (HF). The shared range for µH among Equations 5-7, then, is from –1.35 eV to 0 eV. We calculate Eb in Equation 1 for all three species on all surfaces across this range of µH , and the results for the Ti2C surface are shown in Figure 3.
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Figure 3. Binding energy per single species vs. µH for O, OH, and F on a Ti2C surface. The binding energies calculated using Equation 1 and the values of µT described above indicate that all MXene surfaces strongly prefer O binding toward the lower limit of µH , as shown for Ti2C in Figure 3. In fact, all MXenes, except those with M = Sc, are predicted to prefer O binding across the entire range of µH . For Sc2C, Sc3C2, and Sc4C3, O binding is preferred for µH < –1.0 eV, –1.25 eV, and –1.05 eV, respectively, and F binding becomes preferred at higher µH . For Sc2N, Sc3N2, and Sc4N3, O binding is preferred for µH < –0.7 eV, –0.65 eV, and –0.65 eV, respectively, with F binding again becoming preferred at higher µH . The preference for F– over O2– on Sc surfaces is likely the result of scandium’s 1d valence that is unique among the M elements. The maximum and minimum binding energy for O, F, and OH on all MXene surfaces is listed in the Supporting Material. It should be noted that when µH is decreased (increased) in solution, the chemical potential for electrons, µe , may also need to be suitably decreased (increased) to ensure that H2O remains stable against H+ and OH- formation. Using an applied electric potential, it has been shown that µe can be varied between the band edges of H2O to stabilize H2O across the range of possible µH 33. To characterize the chemical bonding between O, OH, F and the MXene surfaces and ensure that the bonds are covalent/ionic and not dispersion-dominated, we calculate the charge transfer using the Bader charge analysis34. We find that the adsorbed oxygen species ionize to a charge states between –1 and –1.4, while the F and OH species ionize to states between –0.7 and –1. These findings are consistent with the idea that these chemisorbed atoms and molecules form
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strong covalent/ionic bonds with MXene surfaces. The degree of ionization of O, OH, and F on different MXenes is largely independent of the number of layers, n, and the anion species, X, but increases with decreasing electronegativity of the metal element, M. The enthalpy change described by Equation 1 is not the only descriptor required to predict adsorption events. Species leaving a liquid to adsorb on a solid surface, as do the O, OH, and F atoms/molecules considered here, will also undergo entropic changes that will influence the overall change in Gibbs free energy, according to the well known equation: ∆G = ∆H - T∆S (8) where the enthalpy change, ∆H, is equivalent to the value of Eb in Equation 1, T is the temperature, and ∆S is the difference in entropy between initial and final states. We point out that the value of ∆S entering Equation 8 is not the absolute value of the species’ entropy in the liquid or on the MXene surface, but the difference between the two values, which can be estimated analytically. We expect that vibrational contributions to each atom/molecule’s entropy will be roughly the same in the liquid as on the surface at constant temperature, and that the changes in vibrational entropy between initial and final states will therefore be close to zero. The same assumption cannot be made for configurational entropy, which will be significantly higher in the liquid than on the surface (especially the pristine, saturated surfaces we consider in our calculations, which have no configurational entropy). However, the configurational entropy of each species (O, OH, and F) in the liquid will be close to that of each other, as the same large number of configurations are available to each. Therefore, the magnitude of the entropic contribution to Equation 8 will be quite similar for all three species. This assumption is further supported by the small and very similar experimental entropies of aqueous F- (0.02 eV at 298K) and OH- (0.03 eV at 298K) ions35. Because our primary interest is in comparing the binding
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energies of these species against one another, we proceed under the assumption that the enthalpy differences captured by Equation 1 will correctly order the overall binding probability of the three species. MXene synthesis is typically carried out at or near room temperature, so the nature of these adsorption events will most likely be enthalpy-dominated anyway, but it bears mentioning that the lines plotted in Figure 3 may be shifted upward slightly by these entropic effects.
Exfoliation Energies As mentioned before, MXenes exist as dispersion-bound multilayer structures before they are exfoliated into single sheets by ultrasonication and filtering. However, not all MXenes are equally easy to exfoliate. For example, the Nb2C and V2C MXenes have been synthesized as multilayer structures, but have not been successfully exfoliated12. In order to investigate the effect of the three surface terminating groups on MXene exfoliation, the energy required to separate a multilayer MXene into freestanding 2D layers is calculated as the difference in energy per unit area between the multilayer structure and the isolated sheet for all six Ti2XT2 MXenes. These calculations require the explicit inclusion of dispersion forces, which are not accounted for in standard DFT, to accurately describe the bonding in the multilayer structure. Therefore, vdWDF-optB88 dispersion-corrected functionals36 are used to calculate the energies of multilayer and single-layer Ti2XT2, and the resulting exfoliation energies are shown in Figure 4.
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Figure 4. Exfoliation energies of all six Ti2XT2 MXenes. The exfoliation energy is lowest for T = OH surfaces and highest for T = O surfaces, indicating that hydroxylating a MXene’s surface can facilitate its exfoliation.
The exfoliation energies follow the trend T = O > T = F > T = OH for both X = C and X = N. The energy differences between the three surface groups are not large (< 0.8 eV/nm2) in relation to the exfoliation energies themselves, but oxygenated surfaces appear to have the strongest interactions. This can be explained by oxygen’s larger ionic radius than the other two species, whose ionic radii are quite similar to one another. This leads to a higher polarizability, and in turn, a stronger dispersion interaction between layers. These exfoliation energies are high relative to that of graphite (~1 eV/nm2),37 which may help to explain why the processes required to isolate single layer MXenes, such as intercalation, ultrasonication and filtering, are more involved than those used to isolate graphene.
Formation Energies The formation energies of the freestanding Mn+1XnT2 nanosheets are then calculated as the difference of the energy per atom for the 2D MXene structure with that of the most stable configuration possible for the same elements with the same stoichiometry38. For example, the 2D Ti2CO2 MXene is metastable against the three-dimensional bulk phases of TiO2 and TiC, and the
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energy difference between the 2D MXene and the competing 3D phases is the formation energy of the MXene. The competing phases for each MXene are chosen from data in the Materials Project database39, and are listed in the Supporting Material. The formation energies calculated here could be underestimates of the real values if more stable competing phases exist than are present in the Materials Project database40. Because all MXenes, except those with M = Sc, are predicted to be oxygenated for all possible solution conditions, we report their formation energies only for T = O in Figure 5.
Figure 5. Formation energies for Mn+1XnO2, MXenes relative to the lowest energy mixture of competing bulk phases. The green region highlights the general 0.2 eV/atom threshold observed for 2D material stability, and the yellow region highlights the 0.285 eV/atom formation energy of the V2CO2 MXene, the highest of those that been synthesized.
We also calculate the formation energies of all six fluorinated M = Sc MXenes, and find them all to be less than 0.1 eV/atom, much lower than the formation energies of their oxygenated counterparts. Therefore, etching solutions with higher µH should be used during attempted
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synthesis of Sc-based MXenes, in order to saturate their surfaces with fluorine. Other experimental factors must be considered as well; for example, MAX phases have been observed to decompose to nanocrystalline ternary fluoride compounds in experiments carried out at low pH41, and care should be taken to avoid creating these when attempting to synthesize fluorinated M = Sc MXenes. It is interesting to note that several nitride MXenes are predicted to be stable, as shown in Figure 5, although none have yet been synthesized. There could be several reasons for this, but perhaps the most compelling is that aqueous ions and molecules have not been considered as competing species in the calculated formation energies. These aqueous species represent an alternative route for the decomposition of MXenes, which will be quite different for nitrides than for carbides. Other possible reasons are the poor description by DFT of the triple bond in N2, which is a competing species for several nitride MXenes, or the effect of entropy at elevated temperatures. In addition, some transition metals (Nb, Ta) are more stable with X = C, others (Ti, Zr, Hf) are more or less equally stable for both C and N, and still others (Sc, V, Cr, Mo) are more stable with X = N. These three groups roughly correspond to the most common oxidation states of the transition metals: 5+ for Nb and Ta, 4+ for Ti, Zr, and Hf, and 3+ for Sc and Cr. Vanadium has several common oxidation states, including 3+. This grouping is intuitive; C accepts more valence electrons than N, and therefore it is the preferred X element for metals of high oxidation, and vice versa. The MXene formation energies generally follow the trend M2XT2 > M3X2T2 > M4X3T2. This can be understood to be the result of a higher volume to surface area ratio in thicker MXenes. Unfortunately, the reverse trend holds for the bulk MAX phases from which MXenes are
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derived, and relatively few unique M and X combinations in M4AX3 and M3AX2 bulk phases exist from which to synthesize these MXenes42. Importantly, of the six MXene compounds that have already been synthesized (Nb2CT2, Ti2CT2, V2CT2, Ti3C2T2, Nb4C3T2, and Ta4C3T2), five have formation energies within the general 0.2 eV/atom threshold observed for freestanding 2D materials formation energies43. The exception, V2CO2, has a formation energy of 0.285 eV/atom, which defines a more generous threshold for the stability of other MXenes. It is proposed that this higher metastability could be accommodated by the more kinetically complex decomposition pathways for MXenes to their competing 3D phases than those for unary (e.g. graphene) or binary (e.g. MoS2) 2D materials. In addition to the six fluorinated M = Sc Mxenes, six oxygenated MXenes are predicted to have formation energies below 0.1 eV/atom. A total of 28 MXenes have formation energies below 0.2 eV/atom, and 38 have formation energies below 0.285 eV/atom. The synthesis of MXenes with formation energies below 0.285 eV/atom is predicted to be possible from a thermodynamic perspective, revealing that this family of 2D materials remains a rich frontier for materials discovery. The existence of unique M-X combinations in existing MAX phases, however, will dictate which of these compositions can be immediately investigated for synthesis. Conclusions The findings presented here suggest that the surfaces of all MXenes except M = Sc are saturated with oxygen during synthesis. Five MXenes that have not already been synthesized (Ti3N2O2, Ti4N3O2, V3N2O2, V4N3O2, and Cr4N3O2) have formation energies less than 0.1 eV/atom, and should be straightforward to synthesize. Cr4N3O2 is of particular interest for synthesis, as other Cr-based MXenes have been predicted to possess ferromagnetic ordering44, a unique trait among most 2D materials. Efforts should be made to fluorinate M = Sc MXene
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surfaces to produce structures with the highest possible degree of thermodynamic stability, as well as reasonably low exfoliation energies to produce single layers. Their increased stability and lightweight formula unit, along with the low diffusion barriers predicted for Li on fluorinated MXene surfaces8, make Scn+1XnF2 MXenes possible candidates for electrode materials in Li-ion batteries, although the high price of Sc would likely restrict their usage to select highperformance batteries. Computational Methods The DFT calculations are performed using the Vienna Ab initio Simulation Package (VASP)45 , which employs a plane-wave basis and the projector-augmented wave method. Starting geometries and bond lengths for each MXene compound are estimated based on the covalent radii of M and X atoms, and employ the characteristic hexagonal layered P3 m1 MXene space group. Unit cells of two formula units are used for all calculations unless otherwise indicated. The PBE functional46 and the conjugate-gradient algorithm are used to obtain accurate relaxed structures during structure optimization for each MXene. PBE functionals are chosen for their ability to accurately reproduce both structural parameters and structural energy differences47-51. For a numeric demonstration of the agreement between PBE-generated and experimental formation enthalpies of selected transition metal oxides, for example, the reader is directed to the Supporting Material. The use of higher-order methods, such as hybrid functionals, for describing correlation in MXenes has been shown to be unnecessary26. The geometry optimizations are performed with a 12 × 12 × 1 k-point mesh and a 15 Å vacuum to prevent interlayer interaction52, 53. At this spacing, the total energy of a single MXene layer is converged to within 1 meV/atom of its value with a 30 Å vacuum, and its treatment is computationally much cheaper. The energy is converged to below 1meV/atom for a cutoff energy of 520 eV, and geometric
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optimizations are stopped after Hellman-Feynman forces on all atoms are less than 1 meV/Å and the stresses on the unit cell are below 0.1 GPa in the x and y directions. To preserve the vacuum spacing, the z components of cell vectors are not optimized, but atomic positions are optimized in all directions. Spin-polarized calculations are performed for all systems to capture any magnetic contributions to the overall energy. All M elements are initialized with large magnetic moments (5.0 µB), and all other elements are initialized with small magnetic moments (0.6 µB). Lattice parameters of geometrically optimized MXene structures are found to be within 2% of the only experimental data available54, which is calculated for Ti3C2T2 using pair distribution function analysis, and within 5% of other calculated DFT values where available5, 55. To ensure internal consistency between calculated energies, the VASPsol method29, which effectively fills the vacuum space around a molecule or between slabs with a dielectric continuum, is used to calculate the energies of all compounds. The default dielectric constant (ε = 80.0), which corresponds to that of water, is used in all calculations. The dielectric constant of the experimental H2O/HF solution is expected to be quite close to this value, as the dielectric constant of HF is nearly the same (ε = 83.6) as that of water. Supporting Material This material is available free of charge via the Internet at http://cams.mse.ufl.edu. Corresponding Authors *[email protected] **[email protected] Author Contributions
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The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interests. M.A. and S.B.S. gratefully acknowledge the support of the National Science Foundation (DMR1307840). K.M. and R.G.H. gratefully acknowledge the support of the National Science Foundation (DMR-1056587 and ACI-1440547). The calculations were performed using the resources of the University of Florida’s High Performance Computing clusters. References (1) Eizenberg, M. and J. Blakely, Carbon Monolayer Phase Condensation on Ni (111). Surface Science, 1979. 82(1): p. 228-236. (2)
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(6) Lei, J. C, Zhang, X., and Zhou, Z., Recent Advances in MXene: Preparation, Properties, and Applications. Frontiers of Physics, 2015, 10: 107303 (7)
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Materials of the Mxene Family. Physical Chemistry Chemical Physics, 2014. 16(17): p. 78417849. (8)
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Carbonitrides. Nature communications, 2013. 4: p. 1716. (10) Come, J., et al., A Non-Aqueous Asymmetric Cell with a Ti2C-Based Two-Dimensional Negative Electrode. Journal of The Electrochemical Society, 2012. 159(8): p. A1368-A1373. (11) Naguib, M., et al., MXene: A Promising Transition Metal Carbide Anode for Lithium-Ion Batteries. Electrochemistry Communications, 2012. 16(1): p. 61-64. (12) Naguib, M., et al., New Two-Dimensional Niobium and Vanadium Carbides as Promising Materials for Li-Ion Batteries. Journal of the American Chemical Society, 2013. 135(43): p. 15966-15969. (13) Hu, J., Xu, B., Ouyang, C., Yang, S. A., and Yao, Y., Investigations on V2C and V2CX2 (X = F, OH) Monolayer as a Promising Anode Material for Li Ion Batteries from First-Principles Calculations. Journal of Physical Chemistry C, 2014, 118(42), p. 24274-24281.
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(14) Xie, Y. et al., Role of Surface Structure on Li-Ion Energy Storage Capacity of TwoDimensional Transition Metal Carbides. Journal of the American Chemical Society., 2014, 136 (17), p. 6385–6394. (15) Eames, C., Islam, M. S., Ion Intercalation into Two-Dimensional Transition-Metal Carbides: Global Screening for New High-Capacity Battery Materials. Journal of the American Chemical Society, 2014. 136: p. 16271. (16) Xie, X., et al., An Extraordinarily Stable Catalyst: Pt Nps Supported on TwoDimensional Ti3C2X2 (X= OH, F) Nanosheets for Oxygen Reduction Reaction. Chemical Communications, 2013. 49(86): p. 10112-10114. (17) Hu, Q. et al., MXene: A New Family of Promising Hydrogen Storage Medium. Journal of Physical Chemistry A, 2013. 117(51): p. 14253-14260. (18) Yu, X. et al., Monolayer Ti2CO2: A Promising Candidate for NH3 Sensor or Capturer with High Sensitivity and Selectivity. Applied Material Interfaces, 2015. 7(24). p. 13707-13713. (19) Lee, Y. et al., Achieving Type I, II, and III Heterojunctions Using Functionalized MXene. Applied Material Interfaces, 2015. 7(13). p. 7163-7169. (20) Sun, Z., et al., Bonding And Classification of Nanolayered Ternary Carbides. Physical Review B, 2004. 70(9): p. 092102. (21) Barsoum, M., G. Yaroschuk, and S. Tyagi, Fabrication and Characterization of M2SnC (M= Ti, Zr, Hf and Nb). Scripta materialia, 1997. 37(10): p. 1583-1591.
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(22) Enyashin, A. N. and Ivanovskii, A.L., Structural, Electronic Properties and Stability of MXenes Ti2C and Ti3C2 Functionalized by Methoxy Groups. Journal of Physical Chemistry C, 2013. 117: p. 13637. (23) Lukatskaya, M. R., et al., Cation Intercalation and High Volumetric Capacitance of TwoDimensional Titanium Carbide. Science, 2013. 341: p. 1502. (24) Naguib, M., et al., Two-Dimensional Transition Metal Carbides. ACS nano, 2012. 6(2): p. 1322-1331. (25) Naguib, M., et al., 25th Anniversary Article: MXenes: A New Family of Two Dimensional Materials. Advanced Materials, 2014. 26(7): p. 992-1005. (26) Xie, Y. and P. Kent, Hybrid Density Functional Study of Structural and Electronic Properties of Functionalized TiN+1XN (X= C, N) Monolayers. Physical Review B, 2013. 87(23): p. 235441. (27) Khazaei, M., et al., Novel Electronic and Magnetic Properties of Two-Dimensional Transition Metal Carbides and Nitrides. Adv. Funct. Mater., 2013. 23: 2185–2192. (28) Enyashin, A. N.; Ivanovskii, A. L., 2D Titanium Carbonitrides and Their Hydroxylated Derivatives: Structural, Electronic Properties and Stability of MXenes Ti3C2-xNx and Ti3C2xNx(OH)2 from SSC-DFTB Calculations. Journal of Solid State Chemistry, 2013. 207: p. 42-48. (29) Mathew, K., et al., Implicit solvation model for density-functional study of nanocrystal surfaces and reaction pathways. J. Chem. Phys., 2014. 140, 084106. (30) Vendeneyev, V., et al., Bond Energies, Ionization Potentials and Electron Affinities. St. Martin's Press, NY, 1962.
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(31) Herzberg, G. and Monfils, A., The Dissociation Energies of the H2, HD, and D2 Molecules. J. Mol. Spect, 1960. 5(482) (32) Johns, J. and Barrow, F., The Ultraviolet Spectra of HF and DF. Proc. Roy. Soc., 1959. A251(504). (33) Todorova, M. and Neugebauer, J., Extending the Concept of Defect Chemistry from Semiconductor Physics to Electrochemistry. Phys. Rev. Appl. 2014. 1, 014001. (34) Tang, W., et al., Bader Charge Analysis. 2014. (35) Barner, H.S., RV, Handbook of Thermochemical Data for Compounds and Aqueous Species. Chemie Ingenieur Technik, 1978. 50(12): p. 933-933. (36) Klimeš, J. , Bowler, D. R. , and Michaelides, A., Van der Waals density functionals applied to solids. Journal of Physics: Condensed Matter, 2010. 22, 022201. (37) Rydberg, H., Dion, M., Jacobson, N., Schröder, E., Hyldgaard, P, Simak, S. I., Langreth, D. C., and Lundqvist, B. I., Van der Waals Density Functional for Layered Structures. Physical Review Letters 91, p. 126402 (38) Zhuang, H.L. and Hennig, R.G., Electronic Structures of Single-Layer Boron Pnictides. Applied Physics Letters, 2012. 101(15): p. 153109. (39) Jain, A., et al., A High-Throughput Infrastructure for Density Functional Theory Calculations. Computational Materials Science, 2011. 50(8): p. 2295-2310. (40) Armiento R., et al., High-Throughput Screening of Perovskite Alloys for Piezoelectric Performance and Thermodynamic Stability. Physical Review B, 2014. 89: p. 134103.
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(41) Naguib, M., et al., Synthesis of a New Nanocrystalline Titanium Aluminum Fluoride Phase by Reaction of Ti2AlC with Hydrofluoric Acid. RSC Advances, 2011. 1(8): p. 1493-1499. (42) Eklund, P., et al., The MN+1AXN Phases: Materials Science And Thin-Film Processing. Thin Solid Films, 2010. 518(8): p. 1851-1878. (43) Singh, A., Mathew, K., Zhuang, H.L. and Hennig, R.G., Computational Screening of 2D Materials for Photocatalysis. J. Phys. Chem. Lett., 2015. 6, 1087. (44) Chen, S., Zhou, J., and Sun, Z., Half-Metallic Ferromagnetism and Surface Functionalization-Induced Metal-Insulator Transition in Graphene-like Two-Dimensional Cr2C Crystals. ACS Applied Materials and Interfaces, 2015, 7(31), p. 17510–17515. (45) Kresse, G. and J. Furthmüller, Software VASP, vienna (1999). Phys. Rev. B, 1996. 54(11): p. 169. (46) Perdew, J.P., K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple. Physical review letters, 1996. 77(18): p. 3865. (47) Sousa, S. F. et al., General Performance of Density Functionals. Journal of Physical Chemistry A, 2007. 111: p. 42. (48) Becke, A. D., Density-Functional Thermochemistry. II. The Effect of the Perdew-Wang Generalized Gradient Correlation Correction. Journal of Chemical Physics, 1992. 97: p. 9173. (49) Kurth, S. et al., Molecular and Solid-State Tests of Density Functional Approximations: LSD, GGAs, and meta-GGAs. International Journal of Quantum Chemistry, 1999. 75: p. 889.
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(50) Langreth, D. C. and Mehl, M. J., Beyond the Local-Density Approximation in Calculations of Ground-State Electronic Properties. Physical Review B, 1983. 28: p. 1809. (51) Fishman, M. et al., Accuracy of Exchange-Correlation Functionals and Effect of Solvation on the Surface Energy of Copper. Physical Review B, 2013. 87, 245402. (52) Hennig, R. G. et al., Phase Transformation in Si From Seimconducting Diamond to Metallic beta-Sn Phase in QMC and DFT Under Hydrostatic and Anisotropic Stress. Physical Review B, 2010. 82, 014101. (53) Zhuang, H. L. and Hennig, R. G., Computational Discovery of Single-Layer CdO for Electronic and Optical Applications. Applied Physics Letters, 2013. 103, 212102. (54) Shi, C. et al., Structure of Nanocrystalline Ti3C2 MXene Using Atomic Pair Distribution Function. Physical Review Letters, 2014. 112: p. 125501. (55) Kurtoglu et al., First Principles Study of Two-Dimensional Early Transition Metal Carbides. MRS Communications, 2012. 2: p. 133-137 TOC Graphic
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Article
Predicted Surface Composition and Thermodynamic Stability of MXenes in Solution Michael Ashton, Kiran Mathew, Richard G Hennig, and Susan B. Sinnott J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11887 • Publication Date (Web): 25 Jan 2016 Downloaded from http://pubs.acs.org on February 1, 2016
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Predicted Surface Composition and Thermodynamic Stability of MXenes in Solution Michael Ashton†, Kiran Mathew‡, Richard G. Hennig†*, Susan B. Sinnott†** † Department of Materials Science & Engineering, University of Florida, Gainesville, FL, 32611-6400 ‡ Department of Materials science and Engineering, Cornell University, Ithaca, NY, 14850 Keywords: MXene, surface, 2D materials, thermodynamic stability, adsorption, first-principles Abstract First-principles calculations are used to compare the binding energies of O, OH, and F on twodimensional, metal carbide and nitride, or MXene, surfaces in order to predict the dependence of the thermodynamic stability of these compounds on their chemical composition. Solvation effects are implicitly included in the calculations to reproduce experimental conditions as closely as possible. The results indicate that all MXene surfaces are saturated with oxygen when exposed to H2O/HF solutions at low hydrogen chemical potential, µH , and that Sc-based MXenes can also be fluorinated in solutions of higher µH . After investigating the thermodynamic stability of all 54 MXene compounds Mn+1XnO2 (M = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta; X = C, N; n = 1, 2, 3), 38 are predicted to have formation energies below 200 meV/atom. Of these, six are predicted to have formation energies below 100 meV/atom, only one of which has been synthesized. Sc-
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based MXenes are found to be highly stable when their surfaces are terminated with F, which also results in the easiest exfoliation to produce freestanding single layers. Introduction Two-dimensional (2D) materials, or crystals with high aspect ratios and few-layer thicknesses, have been the focus of many recent studies. This is largely due to the unique electronic properties of many of the recently discovered 2D materials. Following the intense interest in graphene beginning in 20041, several new classes of 2D materials were discovered and synthesized over the following decade. A few notable examples include hexagonal boron nitride,2 transition metal dichalcogenides3, and metal oxides4. In 2011, two-dimensional transition metal carbides and nitrides, also known as MXenes, were synthesized by Gogotsi et al5. The large number of theoretically possible members of the MXene family, the diversity of properties among the synthesized MXene compounds, and their relatively simple synthesis make these compounds attractive for a number of 2D material-related applications6. For instance, MXenes are promising candidates for thermoelectrics7, electrode materials in high-power lithium ion batteries5, 8-14, larger and multivalent ion batteries15, electrochemical catalytic surfaces16, and hydrogen storage17. They are also being investigated as sensors18 and components in electronic heterojunctions19. In each of these applications, knowledge of the chemical termination of the MXene surface is critical to predicting the material’s properties and performance. Because of MXenes’ characteristically high surface to volume ratio, the atomic or molecular groups chemisorbed to its surface play a critical role in controlling the overall stoichiometry, stability, and properties of the MXene. For instance, the diffusion barrier for Li on a Ti2C(OH)2 surface (1.02 eV) is almost three times as large as it is on a Ti2CF2 surface (0.36 eV)8, and MXene band gaps have been
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shown to depend significantly on the nature of the terminating atoms and molecules5, 8. This implies that an ability to control which species bind on a MXene’s surface can be used to design a material with fine-tuned properties for technological applications. Despite their importance, it is not yet understood precisely which chemical species bind to the MXene surfaces during synthesis, the exact manner in which they contribute to the overall stoichiometry, or the effect they have on the MXene’s overall thermodynamic stability. This is due in large part to the novelty of the MXene family; almost no experimental data, including structural and electronic properties, have yet been published to which the large and growing body of theoretical work can be compared. MXenes are synthesized by selective etching of the relatively weakly bound20 A elements from bulk MAX phases by a solution of H2O and HF5. MAX phases are layered solids of composition Mn+1AXn, where M = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, or Ta; A is a group 13 or 14 element, X is either C or N, and n is 1, 2 or 321, as illustrated in Figure 1a. Solid solutions are also possible for each of the M, A, and X species. The Mn+1Xn layers are joined by layers of A atoms in such a way that the removal of A layers results in separated Mn+1Xn layers, or MXenes (Figure 1b).
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Figure 1. A V2AlC MAX phase (a) from which a V2C MXene (b) can be derived by etching. Surface species have been shown to prefer FCC sites (c) over HCP sites (d) for binding on most MXenes.
Following their synthesis, MXene layers are held together as multilayer structures by dispersion forces5, 9. This dispersion interaction is caused by polarizable, non-metallic groups bound to MXene surfaces once the surfaces are exposed to the acidic solution. Of the molecular and atomic species present in solution, O, OH, and F are the most likely to bind to the newly formed surface and cause the observed dispersion interaction. Multilayer MXene structures can be separated mechanically, typically by ultrasonication, to form single- or few-layer MXenes in solution5. Filtering these solutions results in the isolation of freestanding MXene flakes. Other species can be intercalated after synthesis, including methoxy groups22, or small ions (e.g. Li+, Na+, Mg2+)23 to expand the interlayer spacing and facilitate the isolation of single MXene sheets. Because they are derived from MAX phases, the same compositional rules for choice of M, X, and n apply to MXenes as to bulk MAX phases (9 M species × 2 X species × 3 choices of n), resulting in 54 possible Mn+1Xn combinations, six of which have been successfully synthesized to date24. The large theoretical size of the MXene family and the significant experimental effort required to successfully synthesize each bulk and 2D compound make predicting the thermodynamic stability of MXene compounds a worthwhile and as yet incomplete endeavor.
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Additionally, the important and related question of the role of the atoms and molecules that adsorb on the MXene surfaces remains unanswered25. In this work, density-functional theory (DFT) calculations are used to address these questions and to assess the thermodynamic stability of each MXene compound. The paper is arranged as follows: the predicted results for low energy surface structures and thermodynamic stability are presented, followed by technical details on the DFT calculations. The results are summarized in the form of general experimental guidelines for stabilizing as-yet un-synthesized MXenes, including those of particular interest for use as Li-ion battery electrodes.
Surface Compositions Binding energies for molecules and atoms on MXene surfaces are calculated according to m
Eb = EMn+1 Xn Tm – EMn+1 Xn – 2 ET2 – mµT (1) where EMn+1 Xn Tm is the energy of the MXene with the chemisorbed atoms or molecules, EMn+1 Xn is the energy of the bare MXene, ET2 is the energy of the chemisorbed atoms or molecules in their gaseous reference state (O2, O2+H2, or F2), and µT is the chemical potential of the chemisorbed atoms or molecules in the solution phase. In Equation 1, a negative Eb is indicative of exothermic binding. To determine the degree of saturation predicted for MXene surface binding sites, Eb is calculated as a function of coverage for O, OH, and F on a Ti2C surface using Equation 1 with µT = 0 eV, and the results are shown in Figure 2. For these calculations, we use a 2 × 2 × 1 supercell containing 8 formula units. This supercell allows resolution in our values of coverage as low as 0.125 T species per formula unit. Previous work8, 26-28 has shown that FCC sites (see Figure 1(c)) are the most favorable binding sites for most MXene compositions. Therefore, our
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coverage profile begins with occupying FCC sites, and includes HCP sites after all FCC sites are filled. During the incremental occupation of FCC sites (and later, HCP sites), the sites are filled in such a way as to maximize the distance between neighboring surface groups. This configuration minimizes the ionic repulsion between neighboring species and results in the lowest energy configurations in our calculations. Figure 2 shows for all three species a sharp increase in Eb after all FCC sites are saturated, indicating that the system’s surface energy is minimized when all FCC sites are occupied and the HCP sites are empty. This suggests a general Mn+1XnT2 stoichiometry for all MXenes, in agreement with previous investigations27.
Figure 2. Binding energy vs. coverage for O, OH, and F on a Ti2C surface. The DFT energies of O2, O2+H2, and F2 are used as reference energies in Equation 1, and µT = 0 eV. We find that all species exactly saturate the FCC sites, corresponding to an Mn+1XnT2 stoichiometry. The abrupt upturn in binding energy for HCP sites can be explained as the result of steric hindrance. In particular, the average O-O distance when all FCC and HCP sites are occupied on a Ti2C surface is 0.78 Å, compared to 3.1 Å when only FCC sites are occupied. Treated as point charges, the difference in repulsive force between neighboring O anions is more than an order of
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magnitude in these two cases, and explains why the energy vs. coverage curve in Figure 2 increases more rapidly for O than for the other anions of lesser charge. Binding energies have already been calculated for all M2X compounds using µT = 0 eV27, which physically corresponds to the binding energy if the T species came from a gaseous source, as considered in Figure 2. A gaseous reference state is an easy but arbitrary choice within the framework of DFT calculations, and it does not describe the experimental conditions. In fact, it is expected that all three surface groups (shown in bold) come from liquid sources, following the reactions5 Ti2C + 2H2O Ti2CO2 + 2H2 (2) Ti2C + 2H2O Ti2C(OH)2 + H2 (3) Ti2C + 2HF Ti2CF2 + H2 (4) and that the chemical potential of each species in solution is a variable that can be experimentally controlled. Reactions 2-4 suggest that the most suitable reference chemical potentials are those of O and OH in H2O, and F in HF. The three chemical potentials µO , µOH , and µF are not independent of one another and are a function of the value of µH in the solution. The chemical potentials of all three surface groups are inversely related to µH , according to the energy required to split the liquid source (H2O or HF) into its components: H2 O
µO = ∆Gf
- 2µH (5)
H2 O
µOH = ∆Gf
- µH (6)
µF = ∆GHF f - µH (7)
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The values of µO , µOH , and µF in Equations 5-7 are substituted for µT in Equation 1 for their respective species to calculate the binding energy of that species on MXene surfaces. Solvated H2 O
formation energies for the liquids from the gaseous molecules (∆Gf
= -2.71 eV, and
29 ∆GHF f = -2.83 eV) are calculated using the implicit VASPsol method , and are in good
H2 O
quantitative agreement with their experimental formation energies (∆Gf
= -2.51 eV, and
30-32 ∆GHF . Instead of assuming a single value for µH , it is more useful to assume that f = -2.81 eV)
it is a variable bound by its minima and maxima in the H2O/HF solution. The maximum value of µH in any solution is equal to its value in H2 gas, which is generally set to be the zero reference, H
µH2 = 0 eV, and the minimum value of µH is calculated as the value in Equations 5-7 when ∆µT is T
set to its own zero reference, µT2 = 0 eV. This gives a minimum value of µH = –1.35 eV for Equation 5 (H2O), µH = –2.71 eV for Equation 6 (H2O), and µH = –2.83 eV for Equation 7 (HF). The shared range for µH among Equations 5-7, then, is from –1.35 eV to 0 eV. We calculate Eb in Equation 1 for all three species on all surfaces across this range of µH , and the results for the Ti2C surface are shown in Figure 3.
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Figure 3. Binding energy per single species vs. µH for O, OH, and F on a Ti2C surface. The binding energies calculated using Equation 1 and the values of µT described above indicate that all MXene surfaces strongly prefer O binding toward the lower limit of µH , as shown for Ti2C in Figure 3. In fact, all MXenes, except those with M = Sc, are predicted to prefer O binding across the entire range of µH . For Sc2C, Sc3C2, and Sc4C3, O binding is preferred for µH < –1.0 eV, –1.25 eV, and –1.05 eV, respectively, and F binding becomes preferred at higher µH . For Sc2N, Sc3N2, and Sc4N3, O binding is preferred for µH < –0.7 eV, –0.65 eV, and –0.65 eV, respectively, with F binding again becoming preferred at higher µH . The preference for F– over O2– on Sc surfaces is likely the result of scandium’s 1d valence that is unique among the M elements. The maximum and minimum binding energy for O, F, and OH on all MXene surfaces is listed in the Supporting Material. It should be noted that when µH is decreased (increased) in solution, the chemical potential for electrons, µe , may also need to be suitably decreased (increased) to ensure that H2O remains stable against H+ and OH- formation. Using an applied electric potential, it has been shown that µe can be varied between the band edges of H2O to stabilize H2O across the range of possible µH 33. To characterize the chemical bonding between O, OH, F and the MXene surfaces and ensure that the bonds are covalent/ionic and not dispersion-dominated, we calculate the charge transfer using the Bader charge analysis34. We find that the adsorbed oxygen species ionize to a charge states between –1 and –1.4, while the F and OH species ionize to states between –0.7 and –1. These findings are consistent with the idea that these chemisorbed atoms and molecules form
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strong covalent/ionic bonds with MXene surfaces. The degree of ionization of O, OH, and F on different MXenes is largely independent of the number of layers, n, and the anion species, X, but increases with decreasing electronegativity of the metal element, M. The enthalpy change described by Equation 1 is not the only descriptor required to predict adsorption events. Species leaving a liquid to adsorb on a solid surface, as do the O, OH, and F atoms/molecules considered here, will also undergo entropic changes that will influence the overall change in Gibbs free energy, according to the well known equation: ∆G = ∆H - T∆S (8) where the enthalpy change, ∆H, is equivalent to the value of Eb in Equation 1, T is the temperature, and ∆S is the difference in entropy between initial and final states. We point out that the value of ∆S entering Equation 8 is not the absolute value of the species’ entropy in the liquid or on the MXene surface, but the difference between the two values, which can be estimated analytically. We expect that vibrational contributions to each atom/molecule’s entropy will be roughly the same in the liquid as on the surface at constant temperature, and that the changes in vibrational entropy between initial and final states will therefore be close to zero. The same assumption cannot be made for configurational entropy, which will be significantly higher in the liquid than on the surface (especially the pristine, saturated surfaces we consider in our calculations, which have no configurational entropy). However, the configurational entropy of each species (O, OH, and F) in the liquid will be close to that of each other, as the same large number of configurations are available to each. Therefore, the magnitude of the entropic contribution to Equation 8 will be quite similar for all three species. This assumption is further supported by the small and very similar experimental entropies of aqueous F- (0.02 eV at 298K) and OH- (0.03 eV at 298K) ions35. Because our primary interest is in comparing the binding
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energies of these species against one another, we proceed under the assumption that the enthalpy differences captured by Equation 1 will correctly order the overall binding probability of the three species. MXene synthesis is typically carried out at or near room temperature, so the nature of these adsorption events will most likely be enthalpy-dominated anyway, but it bears mentioning that the lines plotted in Figure 3 may be shifted upward slightly by these entropic effects.
Exfoliation Energies As mentioned before, MXenes exist as dispersion-bound multilayer structures before they are exfoliated into single sheets by ultrasonication and filtering. However, not all MXenes are equally easy to exfoliate. For example, the Nb2C and V2C MXenes have been synthesized as multilayer structures, but have not been successfully exfoliated12. In order to investigate the effect of the three surface terminating groups on MXene exfoliation, the energy required to separate a multilayer MXene into freestanding 2D layers is calculated as the difference in energy per unit area between the multilayer structure and the isolated sheet for all six Ti2XT2 MXenes. These calculations require the explicit inclusion of dispersion forces, which are not accounted for in standard DFT, to accurately describe the bonding in the multilayer structure. Therefore, vdWDF-optB88 dispersion-corrected functionals36 are used to calculate the energies of multilayer and single-layer Ti2XT2, and the resulting exfoliation energies are shown in Figure 4.
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Figure 4. Exfoliation energies of all six Ti2XT2 MXenes. The exfoliation energy is lowest for T = OH surfaces and highest for T = O surfaces, indicating that hydroxylating a MXene’s surface can facilitate its exfoliation.
The exfoliation energies follow the trend T = O > T = F > T = OH for both X = C and X = N. The energy differences between the three surface groups are not large (< 0.8 eV/nm2) in relation to the exfoliation energies themselves, but oxygenated surfaces appear to have the strongest interactions. This can be explained by oxygen’s larger ionic radius than the other two species, whose ionic radii are quite similar to one another. This leads to a higher polarizability, and in turn, a stronger dispersion interaction between layers. These exfoliation energies are high relative to that of graphite (~1 eV/nm2),37 which may help to explain why the processes required to isolate single layer MXenes, such as intercalation, ultrasonication and filtering, are more involved than those used to isolate graphene.
Formation Energies The formation energies of the freestanding Mn+1XnT2 nanosheets are then calculated as the difference of the energy per atom for the 2D MXene structure with that of the most stable configuration possible for the same elements with the same stoichiometry38. For example, the 2D Ti2CO2 MXene is metastable against the three-dimensional bulk phases of TiO2 and TiC, and the
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energy difference between the 2D MXene and the competing 3D phases is the formation energy of the MXene. The competing phases for each MXene are chosen from data in the Materials Project database39, and are listed in the Supporting Material. The formation energies calculated here could be underestimates of the real values if more stable competing phases exist than are present in the Materials Project database40. Because all MXenes, except those with M = Sc, are predicted to be oxygenated for all possible solution conditions, we report their formation energies only for T = O in Figure 5.
Figure 5. Formation energies for Mn+1XnO2, MXenes relative to the lowest energy mixture of competing bulk phases. The green region highlights the general 0.2 eV/atom threshold observed for 2D material stability, and the yellow region highlights the 0.285 eV/atom formation energy of the V2CO2 MXene, the highest of those that been synthesized.
We also calculate the formation energies of all six fluorinated M = Sc MXenes, and find them all to be less than 0.1 eV/atom, much lower than the formation energies of their oxygenated counterparts. Therefore, etching solutions with higher µH should be used during attempted
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synthesis of Sc-based MXenes, in order to saturate their surfaces with fluorine. Other experimental factors must be considered as well; for example, MAX phases have been observed to decompose to nanocrystalline ternary fluoride compounds in experiments carried out at low pH41, and care should be taken to avoid creating these when attempting to synthesize fluorinated M = Sc MXenes. It is interesting to note that several nitride MXenes are predicted to be stable, as shown in Figure 5, although none have yet been synthesized. There could be several reasons for this, but perhaps the most compelling is that aqueous ions and molecules have not been considered as competing species in the calculated formation energies. These aqueous species represent an alternative route for the decomposition of MXenes, which will be quite different for nitrides than for carbides. Other possible reasons are the poor description by DFT of the triple bond in N2, which is a competing species for several nitride MXenes, or the effect of entropy at elevated temperatures. In addition, some transition metals (Nb, Ta) are more stable with X = C, others (Ti, Zr, Hf) are more or less equally stable for both C and N, and still others (Sc, V, Cr, Mo) are more stable with X = N. These three groups roughly correspond to the most common oxidation states of the transition metals: 5+ for Nb and Ta, 4+ for Ti, Zr, and Hf, and 3+ for Sc and Cr. Vanadium has several common oxidation states, including 3+. This grouping is intuitive; C accepts more valence electrons than N, and therefore it is the preferred X element for metals of high oxidation, and vice versa. The MXene formation energies generally follow the trend M2XT2 > M3X2T2 > M4X3T2. This can be understood to be the result of a higher volume to surface area ratio in thicker MXenes. Unfortunately, the reverse trend holds for the bulk MAX phases from which MXenes are
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derived, and relatively few unique M and X combinations in M4AX3 and M3AX2 bulk phases exist from which to synthesize these MXenes42. Importantly, of the six MXene compounds that have already been synthesized (Nb2CT2, Ti2CT2, V2CT2, Ti3C2T2, Nb4C3T2, and Ta4C3T2), five have formation energies within the general 0.2 eV/atom threshold observed for freestanding 2D materials formation energies43. The exception, V2CO2, has a formation energy of 0.285 eV/atom, which defines a more generous threshold for the stability of other MXenes. It is proposed that this higher metastability could be accommodated by the more kinetically complex decomposition pathways for MXenes to their competing 3D phases than those for unary (e.g. graphene) or binary (e.g. MoS2) 2D materials. In addition to the six fluorinated M = Sc Mxenes, six oxygenated MXenes are predicted to have formation energies below 0.1 eV/atom. A total of 28 MXenes have formation energies below 0.2 eV/atom, and 38 have formation energies below 0.285 eV/atom. The synthesis of MXenes with formation energies below 0.285 eV/atom is predicted to be possible from a thermodynamic perspective, revealing that this family of 2D materials remains a rich frontier for materials discovery. The existence of unique M-X combinations in existing MAX phases, however, will dictate which of these compositions can be immediately investigated for synthesis. Conclusions The findings presented here suggest that the surfaces of all MXenes except M = Sc are saturated with oxygen during synthesis. Five MXenes that have not already been synthesized (Ti3N2O2, Ti4N3O2, V3N2O2, V4N3O2, and Cr4N3O2) have formation energies less than 0.1 eV/atom, and should be straightforward to synthesize. Cr4N3O2 is of particular interest for synthesis, as other Cr-based MXenes have been predicted to possess ferromagnetic ordering44, a unique trait among most 2D materials. Efforts should be made to fluorinate M = Sc MXene
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surfaces to produce structures with the highest possible degree of thermodynamic stability, as well as reasonably low exfoliation energies to produce single layers. Their increased stability and lightweight formula unit, along with the low diffusion barriers predicted for Li on fluorinated MXene surfaces8, make Scn+1XnF2 MXenes possible candidates for electrode materials in Li-ion batteries, although the high price of Sc would likely restrict their usage to select highperformance batteries. Computational Methods The DFT calculations are performed using the Vienna Ab initio Simulation Package (VASP)45 , which employs a plane-wave basis and the projector-augmented wave method. Starting geometries and bond lengths for each MXene compound are estimated based on the covalent radii of M and X atoms, and employ the characteristic hexagonal layered P3 m1 MXene space group. Unit cells of two formula units are used for all calculations unless otherwise indicated. The PBE functional46 and the conjugate-gradient algorithm are used to obtain accurate relaxed structures during structure optimization for each MXene. PBE functionals are chosen for their ability to accurately reproduce both structural parameters and structural energy differences47-51. For a numeric demonstration of the agreement between PBE-generated and experimental formation enthalpies of selected transition metal oxides, for example, the reader is directed to the Supporting Material. The use of higher-order methods, such as hybrid functionals, for describing correlation in MXenes has been shown to be unnecessary26. The geometry optimizations are performed with a 12 × 12 × 1 k-point mesh and a 15 Å vacuum to prevent interlayer interaction52, 53. At this spacing, the total energy of a single MXene layer is converged to within 1 meV/atom of its value with a 30 Å vacuum, and its treatment is computationally much cheaper. The energy is converged to below 1meV/atom for a cutoff energy of 520 eV, and geometric
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optimizations are stopped after Hellman-Feynman forces on all atoms are less than 1 meV/Å and the stresses on the unit cell are below 0.1 GPa in the x and y directions. To preserve the vacuum spacing, the z components of cell vectors are not optimized, but atomic positions are optimized in all directions. Spin-polarized calculations are performed for all systems to capture any magnetic contributions to the overall energy. All M elements are initialized with large magnetic moments (5.0 µB), and all other elements are initialized with small magnetic moments (0.6 µB). Lattice parameters of geometrically optimized MXene structures are found to be within 2% of the only experimental data available54, which is calculated for Ti3C2T2 using pair distribution function analysis, and within 5% of other calculated DFT values where available5, 55. To ensure internal consistency between calculated energies, the VASPsol method29, which effectively fills the vacuum space around a molecule or between slabs with a dielectric continuum, is used to calculate the energies of all compounds. The default dielectric constant (ε = 80.0), which corresponds to that of water, is used in all calculations. The dielectric constant of the experimental H2O/HF solution is expected to be quite close to this value, as the dielectric constant of HF is nearly the same (ε = 83.6) as that of water. Supporting Material This material is available free of charge via the Internet at http://cams.mse.ufl.edu. Corresponding Authors *[email protected] **[email protected] Author Contributions
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The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interests. M.A. and S.B.S. gratefully acknowledge the support of the National Science Foundation (DMR1307840). K.M. and R.G.H. gratefully acknowledge the support of the National Science Foundation (DMR-1056587 and ACI-1440547). The calculations were performed using the resources of the University of Florida’s High Performance Computing clusters. References (1) Eizenberg, M. and J. Blakely, Carbon Monolayer Phase Condensation on Ni (111). Surface Science, 1979. 82(1): p. 228-236. (2)
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