Exfoliation of Ti 2 C and Ti 3 C 2 Mxenes from Bulk Phases of Titanium Carbide: A Theoretical Prediction
aa r X i v : . [ c ond - m a t . m t r l - s c i ] A p r Exfoliation of Ti C and Ti C Mxenes from BulkPhases of Titanium Carbide: A TheoreticalPrediction
Krishnakanta Mondal † , ¶ and Prasenjit Ghosh ∗ , ‡ † Department of Physics, Indian Institute of Science Education and Research, Dr. HomiBhabha Road, Pune-411008, India ‡ Department of Physics, Centre for Energy Sciences, Indian Institute of Science Educationand Research, Dr. Homi Bhabha Road, Pune-411008, India ¶ Current affiliation: Department of Physical Sciences, Central University of Punjab,Bathinda, Punjab-151001, India
E-mail: [email protected]
Abstract
MXenes, a new class of two dimensional materials with several novel properties,are usually prepared from their MAX phases by etching out the A element usingstrong chemical reagents. This results in passivation of the surfaces of MXene withdifferent functional groups like O, -OH, -F, etc., which in many cases tend to degradetheir properties. In this work, using first principle density functional theory basedcalculations, we propose a novel method to synthesize pristine Ti C and Ti C MXenesfrom the bulk titanium carbides with corresponding stoichiometry. Based on the valuesof cleavage energy obtained from our calculations, we envisage that pristine Ti C andTi C MXenes can be prepared, using mechanical or sonification-assisted liquid-phaseexfoliation techniques, from their bulk phases. eywords DFT, 2D Materials, Pristine MXene
Introduction
MXenes, with a general formula of M n +1 X n (M represents a transition metal element, whileX can be carbon or nitrogen), are the latest additions to the family of two-dimensional(2D) materials. These newly discovered materials are being extensively investigated dueto their novel structural, chemical, optical, and magnetic properties, which make thempromising candidates for various applications such as catalysis, anode materials for Li-ionbattery, hydrogen storage, supercapacitors, environmental pollutant decontaminators, etc. Till date 19 MXenes are experimentally realized and about 50 have been theoreticallypredicted to be stable. These MXenes are mainly synthesized from the MAX phase by chemical etching of A-metal, where A is a Group 13 or 14 element. Typically HF, HCl, LiF and NH HF are usedas etching reagents.
The surfaces of MXenes prepared from the MAX phases usingthis method are usually passivated with various chemical groups like -OH, -O, -F, -H etc.Often this surface passivation has degrading effects on the performance of the MXenes. Forexample, Tang et al., theoretically predicted that the Li ion storage capacity of Ti C MXeneis larger than that of the -OH or F passivated ones. Moreover, Junkaew et al. reported thatthe chemical activity of the pristine Ti C is higher than that of the O-terminated one. Further, the magnetism of Ti C is quenched due the termination of surfaces with O-atom or-OH group. Additionally, due to the unavailability of the pristine MXenes, the experimentalresearchers are not able to verify several of the theoretically predicted superior properties ofMXenes. Therefore, it is highly desirable to develop novel methods, that do not use etchingagents, for synthesis of high quality pristine MXenes.In view of preparing pristine MXene, in 2015, a bottom up approach, with chemical2apour deposition (CVD) method, was used to synthesize 2D layers of α -Mo C. Using thismethod a ultrathin (few nano meter) layer of α -Mo C was prepared. Similar method wasalso used to synthesize ultrathin layers of tungsten and tantalum carbides. However, thesynthesis of a monolayer of MXene is yet to be demonstrated. A method leading to therealizaton of pristine MXene will be a breakthrough in this field. To this end, in this work,using first principles density functional theory (DFT) based calculations, we have proposeda novel process that uses physical methods to synthesize Ti C and Ti C MXenes from theircorresponding titanium carbide bulk phases without using etching agents.
Computational details
All the calculations were performed with the Quantum ESPRESSO (QE) package whichis an implementation of DFT in a plane wave pseudopotential framework. The electron-electron exchange and correlation functional was described with the Perdew-Burke-Ernzerhof(PBE) parametrization of the generalized gradient approximation(GGA). To include thevan der Waals correction we have used Grimme’s dispersion method as implemented in QE. The calculations were performed employing kinetic energy cutoffs of 55 and 480 Ry for thewave function and augmentation charge density, respectively. To speed up the convergence,we have used the Marzari-Vanderbilt smearing with a smearing width of 0.007 Ry. Wehave modelled the surfaces of Ti C and Ti C using six and four layered slabs respectively.Further, to avoid the interactions between the periodic images we have used a vacuum ofmore than 16 ˚A along z-axis. We have ensured that this vacuum is maintained even for thecase where we have displaced the top most layer to a distance of 10 ˚A from the layer belowit to mimic the exfoliation process. The Brillouin zone has been sampled using 12 × × C and Ti C we have carriedout NCI (Non Covalent Interaction) analysis, as implemented in CRITIC2 code, on3hese systems. NCI analysis is based on the electron density, ρ and its reduced densitygradient, s, which is defied in the following, s = 12(3 π ) / |∇ ρ | ρ / (1)The isosurface of s in 3D have been visualised using VMD. The isosurface is colored (blue-green-red color scale) according to the value of sign( λ ) ρ . Blue indicates the weak attractiveinteraction and green represents the van der Waals interaction while red shows non-bondinginteraction.The formation energy ( E form ) of the bulk phases of Ti C has been calculated using thefollowing equation: E form = E ( T i m C n ) − m × µ ( T i hcp ) − n × µ ( C grap ) n + m (2)where E ( T i m C n ) is the energy of the bulk unitcell of Ti C and µ ( T i hcp ) and µ ( C grap ) are thechemical potentials of Ti and C atoms, respectively. µ ( T i hcp ) has been calculated from thebulk HCP phase of Ti and µ ( C grap ) is taken from the graphite phase of C. m and n indicatethe number of Ti and C atoms in the bulk phase of Ti C, respectively.
Results and Discussion
We begin by noting that amongst the many polytypes of bulk Ti C, the two most stable onesare the trigonal (Figure 1(a)) and the cubic (Figure S1(a)) phases.
Depending on theexperimental conditions, both these phases have been successfully synthesized.
Fromour calculations we find that, in agreement with previous literature report, the cubic phaseis about 0.02 eV/atom more stable than the trigonal phase (Table S1). While the cubic phaseof Ti C have a sodium chloride structure with the C atoms or vacancy surrounded by thedistorted octahedra of Ti atoms, the trigonal phase forms a layered structure of the form4i-C-Ti, where the Ti atoms in the two hexagonal planes are separated by a plane of Catoms. We note that each Ti-C-Ti layer of the bulk trigonal phase is similar to that of alayer of Ti C MXene (Figure 1(c)). Moreover, the in plane lattice parameter of 3.08 ˚A ofthe trigonal phase is also similar to that of the Ti C MXene lattice parameter of 3.01 ˚A . Analogous to the layered trigonal structure of bulk Ti C, bulk Ti C also have a layeredstructure with hexagonal symmetry, the layers being stacked along the (0001) direction(Figure 1(b)). Each layer in the bulk hexagonal phase of Ti C is constructed with theatomic arrangement of Ti-C-Ti-C-Ti, where the C atoms are sandwiched between Ti layers.It is observed that the in plane lattice parameters (3.07 ˚A) of the hexagonal phase of Ti C is similar to those of the corresponding MXene (3.10 ˚A). Therefore, each layer of Ti-C-Ti-C-Ti in the bulk hexagonal phase of Ti C can be identified as the well known Ti C MXene.The above observations of the exceptional similarity between the layered structures of thetrigonal (hexagonal) phase of bulk Ti C (Ti C ) with that of Ti C (Ti C ) MXene stimulatedus to ask the question: Is it possible to mechanically exfoliate a single layer of Ti C (Ti C )from the bulk trigonal (hexagonal) phase? If this can be achieved, then it will provide anovel route to synthesize highly desirable pristine Ti C and Ti C MXenes. (a) (b)(c) (d)
Figure 1: Side view of the structure of bulk phase and MXene of Ti C (a, c) and Ti C (b, d). In this and the subsequent figures in this manuscript the Ti and C atoms are representedby large blue spheres and small brown spheres, respectively.5o provide an answer to the above mentioned question it is imperative to understandthe nature and strength of the interaction between two MXene layers in the bulk phases ofTi C and Ti C . The charge density distribution between two such layers in the bulk trig-onal (hexagonal) phase will provide an indication of the nature and strength of interactionsbetween them. A strong covalent interaction between two layers will result in significantaccumulation of charge density between them while weak metallic/van der Waals interactionwill result in negligible charge density between two such layers. Figure 2(a) (Figure 2(c))shows the charge density isosurface plot for the layered bulk phase of Ti C (Ti C ). Toquantify the interlayer charge density further, we have also plotted in Figure 2(b) (Figure2(d)) the planar average (averaged over the xy -plane) of the charge density as a function of z along the (0001) direction in bulk Ti C (Ti C ). From Figure 2 we find that for both Ti Cand Ti C the charge is localized within the layer with negligible charge density in betweenthe two layers. Further for comparison with Ti C (Ti C ) MXene, we have also plotted theplanar average of the charge density of MXene in Figure 2(b) (Figure 2(d)). We find thatthe two charge density profiles are almost identical.Furthermore, to get more insight into the bonding be- tween the layers we have carried outNCI (Non Covalent Interaction) analysis on the bulk phase of Ti C (Ti C ). Figure 3(a)and (b) show the s vs. sign( λ ) ρ for Ti C and Ti C respectively. We find that there are tailsof s at very low negative values of sign( λ ) ρ ) suggesting that there might be weak attractiveinteractions between the layers. Further we plotted the isosurface of s for s =0.1 (denotedby the blue horizontal line in Figure 3(a) and (b)) for sign( λ ) ρ between -0.05 and 0.05 a.u.These isosurfaces are shown in Figure 3(c) and (d). The plots show greenish isosurfaces atthe interlayer positions thereby further supporting our claim that the interaction betweentwo such layers are indeed weak and of non-covalent origin.From the above discussion it is clear that the interlayer interaction in bulk Ti C (Ti C )is significantly weak which suggest that a single layer can be exfoliated from a slab of Ti C(Ti C ). 6 a) (b)(c) (d) Figure 2: Charge density isosurfaces of the bulk (a) Ti C, and (c) Ti C . Planar average ofcharge density of MXene (b) Ti C, and (d) Ti C .7 a) (b)(c)(c) Figure 3: NCI plots for the bulk phases of (a,c) Ti C and (b,d) Ti C . NCI plots havebeen shown for s=0.1 a.u. (dotted line in (a) and (b)). The color scale shows the range ofsign( λ ) ρ between -0.05 and 0.05 a.u.Since we have ascertained that the interlayer interactions in bulk trigonal Ti C andhexagonal Ti C is weak, we proceed to compute the energy cost of exfoliating a single layerof Ti-C-Ti or Ti-C-Ti-C-Ti from their corresponding bulk phases. First, we have investigatedthe exfoliation of Ti-C-Ti layer from the trigonal phase of Ti C. For this purpose we havechosen the (0001) surface of the bulk phase, which is represented by a slab with a thicknessof six layers (Slab6) (see Figure S3). From this slab, we gradually exfoliate the surface Ti-C-Ti layer by slowly increasing interlayer distance between the surface Ti-C-Ti layer and thatbelow it. At each step we have performed a constrained relaxation keeping the z-coordinateof the C-atom of the exfoliated surface layer and the middle C-atom of the slab fixed. Thisstep-wise detachment of the surface layer is done till the exfoliated layer does not interactwith the rest of the slab. The cleavage energy ( E cl ) has been calculated using the followingequation: E cl = 12 A [ E ( slab − E d ( slab E ( slab
6) is the energy of the Slab6 and E d ( slab
6) indicates the energy corresponding8o the Slab6 when the topmost layer is shifted to a distance d away from the Slab6. E cl asa function of d is plotted in Figure 4. A denotes the area of the surface unit cell. We findthat the cleavage energy for the single layer is 1.82 J/m . Moreover, to check whether itis easier to cleave a single Ti-C-Ti layer or two such layers during exfoliation, we have alsocomputed the cleavage energy for the exfoliation of bilayer of Ti C MXene. For the bilayer,we determine E cl to be 1.78 J/m which is slightly less than that of the single layer. Thissuggests that during the exfoliation process both bilayers and monolayers will be present.We note that from two such bilayers, single layers can also be exfoliated.Figure 4: Cleavage energy of the MXenes as a function of the distance ( d ) of the cleavedlayer from the surface.Following similar exfoliation process described above we have calculated the cleavageenergy for the exfoliation of Ti C layer from its bulk hexagonal phase. In Figure 4 wehave plotted E cl vs d for the case of Ti C . The details of the exfoliation process used inthe calculations have been described in the Supporting Information. We found the cleavageenergy for the exfoliation of Ti C to be 1.51 J/m , which is 0.31 J/m lower than thecorresponding value for the case of Ti C. This indicates that the exfoliation of Ti C MXene9rom its bulk phase is easier than that for the case of Ti C MXene.In order to provide a perspective as to how easy or difficult to exfoliate a single layer ofTi C or Ti C , we compare our computed cleavage energy with those reported for other lay-ered materials in literature. For example for exfoliating a single atomic layer thick graphenesheet from bulk graphite the cleavage energy is about 0.37 J/m . This tells us that it isabout 4-5 times easier to exfoliate graphene from graphite compared to our systems. Incontrast, for exfoliating quasi-two dimensional (more than one atomic layer thick) sheets,for example GeP layer from its bulk, the cleavage energy is 1.14 J/m , which is about0.68 J/m (0.37 J/m ) higher than that we have observed for Ti C (Ti C ). Although thecleavage energy for exfoliating Ti C (Ti C ) is larger than those observed for exfoliation of2D layers from different van der Waals solids, we would like to mention that very recentlylayered 2D materials have been exfoliated from non-van der Waals solids also. For example,Balan et al. have synthesized a novel 2D material “hematene” from natural iron-ore hematite( α -Fe O ) using liquid exfoliation technique. Using a sonification-assisted liquid-phase ex-foliation method Yadav et al. demonstrated that it is possible to synthesize magnetic 2Dmaterial “chromiteen” from naturally occurring mineral chromite (FeCr O ). For boththese cases, the exfoliation results in cleavage of strong covalent bonds. This suggests thatusing similar experimental techniques, it is possible to exfoliate Ti C and Ti C MXenesfrom their corresponding layered bulk phases. We note that in this case the exfoliationwould involve breaking of weaker metallic bonds between the Ti atoms of two interactingTi-C-Ti or Ti-C-Ti-C-Ti layers depending on the systems.
Conclusions
In summary, we have proposed a novel method to synthesize pristine Ti C and Ti C MX-enes by exfoliation of, respectively, Ti-C-Ti and Ti-C-Ti-C-Ti layers from their correspondinglayered bulk phases. Based on our computed cleavage energy and some recent experimental10eports on synthesis of layered magnetic 2D materials from non-van der Waals solids usingsonification-assisted liquid-phase exfoliation method, we suggest that use of similar meth-ods in this case will enable experimentalists to exfoliate highly desired pristine Ti C andTi C MXenes. We hope that our results will motivate experimentalists to use our proposedmethodology to try synthesizing pristine Ti C and Ti C MXenes.
Acknowledgments
PG would like to acknowledge Dr. Nirmalya Ballav, IISER Pune for helpful discussions. KMand PG would like to acknowledge Department of Scinece and Technology, India Grant No:EMR/2016/005275 for funding. PG would like to acknowledge Department of Science andTechnology-Nanomission, India Grants No: SR/NM/NS-15/2011, SR/NM/NS-1285/2014and SR/NM/TP-13/2016 for funding.
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Adv. Mat. Inter. , ,1800549. 16 uplementary of Exfoliation of Ti C and Ti C Mxenesfrom Bulk Phases of Titanium Carbide: A TheoreticalPrediction b a Figure S1: Different stable phases of bulk Ti C, (a) Cubic, and (b) TrigonalTable 1: Comparison of our computed results with those of the reported values.
Thevalues within the parenthesis indicate the experimental data taken from ref. The resultsobtained with the van der Waals correction are given within the square brackets.Cubic Trigonalour results reported our results reportedE form -0.66 [-0.71] -0.68 [-0.70] -0.64 -a(˚A) 8.64 [8.62] 8.64 (8.60) 3.08 [3.09] 3.09 (3.06)c(˚A) - - 14.45 [14.48] 14.45 (14.91)
Slab Convergence Test
It is found that the five layers of Ti C, which we named as Slab5, is required to achievethe convergence of the thickness of the slab along (0001). In Figure S2 we have plotted thedensity of the states (DOS) of the middle layer of this slab along with that of the bulk Fromthe Figure S2(a) it can be observed that the density of the bulk closely matches with thatof the middle layer in slab5. This clearly indicates that the Slab5 can mimic a piece of bulk17i C. For the case of Ti C , it is found that the three layers of Ti C , which we named as (a)(b) Figure S2: Density of states of (a) Ti C and (b) Ti C .Slab3, is required to achieve the convergence of the thickness of the slab along (0001). InFigure S2(b) we have plotted the density of the states (DOS) of the middle layer of this slabalong with that of the bulk From the Figure S2 (b) it can be observed that the density ofthe bulk closely matches with that of the middle layer in slab3. This clearly indicates thatthe Slab3 can mimic a piece of bulk Ti C . Exfoliation of Ti C MXene
We have investigated the exfoliation of Ti-C-Ti-C-Ti layer from the trigonal phase of Ti C .For this purpose we have chosen the (0001) surface of the bulk phase, which is representedby a slab with a thickness of 4 layers (Slab4) (see Figure S3). From this slab, we gradually18 i2C Ti3C2 Figure S3: Exfoliation of Ti C and Ti C2