Solid State Communications 303–304 (2019) 113739

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New predicted two-dimensional MXenes and their structural, electronic andlattice dynamical propertiesBerna AkgencDepartment of Physics, Kirklareli University, 39060, Kirklareli, Turkey

A R T I C L E I N F O

Keywords:MXenes2D materialsDensity functional theoryStructural propertiesElectronic PropertiesVibrational Properties

A B S T R A C T

MXenes, transition metal carbides and nitrides, are a bourgeoning class of two-dimensional (2D) materialsdue to their tunable electronic and magnetic structures, rich surface chemistry and thermal stability. Here, weperform structural, electronic, vibrational and thermal properties of six transition-metal carbides (Re2C, Tc2C,Mo2C, W2C, Os2C, Ru2C) both 2H and 1T phases by first-principle calculations within density functional theory.Although physical and thermal properties of some pristine MXenes put forward to understanding tunableelectronic and magnetic properties, many of 1T-phase and almost never of 2H-phase are not investigated indetailed. Firstly, the atomic structure of six MXenes both 1T and 2H phases are optimized, and their respectivedynamical stabilities are discussed. Secondly, electronic band structure calculations reveal that the pristineMXenes are metallic. Finally, phonon calculations of pristine MXenes are computed with the density functionalperturbation theory and reported. Raman-active modes are predicted and to assign them to specific atomicmotions. Ab-initio molecular dynamic simulations (AIMD) are also performed to check the thermal stabilityof these MXenes. Our results clearly proved that while 2H-W2C, 2H-Mo2C, 2H-Re2C and 1T-W2C can keepthe stabilities at very high temperature (1500 K). The results suggest that these pristine MXenes combiningwith outstanding properties such as non-magnetic metallic state and high-temperature thermal stability wouldprovide promising candidates for using from energy storage to spintronic applications.

1. Introduction

Following the synthesis of graphene in 2004 [1,2], 2D materialshave received particular attention for next generation electronic andoptoelectronic applications [3–5]. The physical properties of 2D ma-terials are usually different from their conventional bulk materialsbecause of providing a new degree of freedom. Due to the weaknessof interlayer interaction, synthesis of the single-layer or few-layers 2Dmaterials are possible. 2D materials show unique properties such asvery thin atomic thickness [6], transparency [7] and flexibility [8]. Inthe past decade, a large number of 2D materials such as group III-V bi-nary compounds (h-BN, h-AlN) [9–11], silicene [12], germanene [13],arsenene [14], transition-metal dichalcogenides (TMDs) [15,16], andtransition metal oxides [17] have been extensively investigated intheoretical and experimental.

MXenes, a new family of 2D transition metal carbides, just re-cently entered the research area since the discovery of titanium carbide(Ti3C2) in 2011 [18]. They have generated huge interest in mechanical,thermal, optical, electronic and magnetic engineering fields becauseof metallic conductivity, hydrophilicity, high light transmission, bio-compatibility and large surface area [19–21]. Depending on their

E-mail address: berna.akgenc@klu.edu.tr.

constituent elements, MXenes are suggested as energy storage [22],electromagnetic interference (EMI) shielding [23], electrochemical ac-tuators [24], photocatalysis [25], sensors [26] and many other appli-cations [27,28]. Their chemical compositions are given by the formulaM𝑛+1AX𝑛 (n=1,2,3), M indicates early transition metal, A representsA-group elements (mostly groups 13 and 14) and X can be carbon ornitrogen. They can be easily produced by selectively etching ‘‘A’’ layersout from the parent MAX bulk phase due to the chemical bonds betweenA–M elements are weaker than M-X-M bonds. After their exfoliationfrom the MAX phase, the surfaces of these layers MXenes are chemicallysurface terminated/functionalized with a selective groups such as –O,–F and –OH. Comprehensive MXene-related reviews were recently pub-lished [29,30]. Close to 30 MXenes have been experimentally reported,and more than dozens have been studied theoretically. Combining with4d or 5d transition metals and low atomic mass elements (i.e: B, N andC) are of great scientific importance for searching high temperatureoxidation resistance, high hardness and resistance to chemical attack.

Siriwardane et al. are predicted two stable rhenium carbide mono-layer namely r-ReC2 and h-Re2C among the several optimized Re–Cmonolayers [31]. Comparing to other 2D materials, they have found

https://doi.org/10.1016/j.ssc.2019.113739Received 9 May 2019; Received in revised form 3 September 2019; Accepted 24 September 2019

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very high elastic constants and Young’s modulus. Technetium (Tc) liesdirectly above Re in the periodic table and their valence electron num-bers are same so it is worth to studying as 2D monolayer MXene. Zhanget al. have predicted a hexagonal P63/mmc structure of Tc2C with aPSO technique for crystal structure prediction [32,33]. The calculatedmechanical properties show that Tc2C is a ultra-incompressible andsuperhard material. Ru2C and Os2C were synthesized at a high pressureand ambient pressure with high temperature, respectively [34,35].They have predicted ultra-incompressible metals due to their strongcovalent bonding. Wu et al. have demonstrated tungsten carbide (W2C)has a high negative Poisson’s ratio in two-dimensional material, whichusing numerous promising engineering applications such as auxeticmaterial [36]. We have also investigated Mo2C and compared withour results with Mo2C, which is well-known carbide in the scientificplatform [37–39].

The exploration of new 2D MXenes with interesting novel propertiesis aimed of this study to using fascinating applications. We have sug-gested MXenes (M = Re, Ru, Tc, Os, Mo, W) can be formed well-known1T and 2H phase from the 4d/5d binary carbides. Among them, weillustrate that Mo2C, W2C, Re2C, Os2C with both 1T and 2H phases,Ru2C at 2H phase are dynamically stable at 0 K, and these materialscan be experimentally synthesized.

Surface functionalization and mechanical strain play a key rolein MXenes’ electronic properties. Some MXenes change from metalto semiconductor upon surface functionalization or mechanical strain.Here, the study provides a guide for researchers who are exploringthose properties of MXenes.

2. Computational methodology

Density functional theory based calculations were performed withinthe plane-wave basis projector-augmented wave (PAW) [40] method asimplemented in the Vienna ab initio Simulation Package (VASP) [41,42]. The exchange–correlation potential energies was described bythe generalized gradient approximation (GGA) via Perdew–Burke–Ernzerhof (PBE) [43] functional. The plane-wave basis set was takenas energy cutoff of 600 eV. The convergence criterion for the totalenergy difference between sequential steps in the iterations was takenas 10−5 eV and the Fermi level Gaussian smearing factor was taken as0.05 eV. The integration in the k-space was performed using 16 × 16 × 1𝛤 k-point for the primitive unit cell. In order to avoid any interactionbetween the periodic images (the single layer and its images along the𝑧-direction), calculations were performed with a large unit cell includ-ing ∼20 Å vacuum space. The electronic band structure calculationswere presented more sensitive; the Brilliouin zone (BZ) integration wasincreased to twofold.

The phonon calculations were performed by using the small dis-placement methodology. The force constant matrix was constructed byslight displacements of 4 × 4 × 1 supercell whose BZ was sampled with6 × 6 × 1 k-point by implementation PHONOPY [44] code. We havealso increased the electronic degrees of freedom to 10−8 eV to ensure areasonable convergence. The ab-initio molecular dynamic simulations(AIMD) were performed with a 4 × 4 × 1 supercell in the NVT ensemblewith fixed particle number, volume and temperature. The time stepwas set to 2 fs (1000 steps) with a total simulation time of 2 ps. AIMDcalculations was carried out five different temperature. The simulationtime was increased to 10 ps for all different temperatures.

3. Results and discussion

3.1. Structural and energetic

We have started to investigated the structural properties of mono-layer MXenes in the 1T and 2H phases. The ground state structure ofpristine 1T phase M2C (M = transition metal atoms) is found to behexagonal crystal structure (P63/mmc symmetry) as shown in Fig. 1(a).

Fig. 1. (Color online) Crystal structure of 2D monolayer MXenes. Top and side viewsof (a) 1T phase (b) 2H phase The purple spheres stand for M atoms (Re, Tc, Mo, W, Os,Ru) and the brown spheres stand for C atom. (c) and (d) Schematics of three differentmagnetic structures: FM, AFM1 and AFM2 for 1T and 2H phases, respectively.

Table 1The calculated parameters for the monolayer MXene; the lattice constants, a and d;cohesive energy, E𝑐𝑜ℎ., energy difference of 1T and 2H phases are given with 𝛥E.

Phase a d𝑀−𝐶 d E𝑐𝑜ℎ. 𝛥E(Å) (Å) (Å) (eV/atom) (eV)

Mo2C 2H 2.84 2.13 2.70 6.41 01T 2.99 2.09 2.35 6.31 0.10

W2C 2H 2.80 2.12 2.75 8.47 01T 2.82 2.12 2.72 8.18 0.29

Tc2C 2H 2.79 2.07 2.62 6.71 01T 2.82 2.06 2.54 6.58 0.13

Re2C 2H 2.73 2.10 2.79 8.33 01T 2.66 2.16 3.05 8.09 0.24

Ru2C 2H 2.69 2.09 2.79 6.42 01T 3.16 2.04 1.85 6.27 0.15

Os2C 2H 2.67 2.11 2.90 7.65 0

The unit cell include two transition metal atoms and one carbon arelocated at (2/3, 2/3, z), (1/3, 1/3, -z) and (0, 0, 0) on the Wyckoff sites.The ground state structure of pristine 2H phase M2C is also found to behexagonal as shown in Fig. 1(b). The unit cell include three atoms, twotitanium and one carbon are located at (1/3, 2/3, z), (2/3, 1/3, -z) and(0, 0, 0) on the Wyckoff sites. The optimized lattice parameters of thestructure are given in Table 1. Each C atom in the crystal covalentlybonds with M atoms, the bond length between M and C atom is givend𝑀−𝐶 . For comparison, we have showed energy difference of 1T and2H phases, energetically favorable structure was set to 0 eV.

Cohesive energy, which is defined as the energy required to separatecondensed material into isolated free atoms, is one of the most impor-tant physical parameters in quantifying the stability of materials. Thecohesive energy per atom was calculated using the following equation:

𝐸𝑐𝑜ℎ = ((𝑛𝑀𝐸𝑀 + 𝑛𝑋𝐸𝑋 ) − 𝐸𝑀𝑋𝑒𝑛𝑒𝑠)∕𝑛𝑡𝑜𝑡 (1)

where 𝐸𝑀 and 𝐸𝑋 represent the energies of isolated single M atoms(Re2C, Tc2C, Mo2C, W2C, Os2C, Ru2C) and C atom; 𝐸𝑀𝑋𝑒𝑛𝑒𝑠 representsthe total energy of the MXene; 𝑛𝑀 , 𝑛𝑋 and 𝑛𝑡𝑜𝑡 stand for the number ofM atoms (𝑛𝑀=2), number of C atom (𝑛𝑋=1), and total number of atoms(𝑛𝑡𝑜𝑝=3), respectively. The cohesive energy per atom of 2D MXenes is

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calculated and listed in Table 1. The energy difference of 2H and 1Tphases are given with 𝛥E. 2H phase is found lowest energy structure inall calculations.

3.2. Electronic and magnetic properties

Regardless of stable structures, we have calculated electronic prop-erties of 1T and 2H phases 2D MXenes. They exhibits metallic proper-ties in taken into account spin-polarized case, according to Fig. 2. Thespin–orbit coupling (SOC) effect is not included in these calculations.Having 3d orbitals in transition metal atoms, we have expected intrinsicmagnetism on these MXenes. The single atoms of W, Mo, Ru, Os, Tc andRe have 4.00, 6.00, 1.92, 3.98, 5.00 and 3.00 𝜇𝐵 magnetic moments,respectively. We have calculated magnetic properties of six differentMXenes in 2H and 1T phases. Our calculation demonstrated that only2H-Ru2C has magnetic moments 1.72 𝜇𝐵 and the rest of them arenon-magnetic material. Though transition metal atoms have intrinsicmagnetization, interaction with carbon atom made them non-magneticmaterial. The main reason of the effect stem from hybridization be-tween transition metal atoms (3d orbital) and carbon atom (2p orbital).Well-know Mo2C MXene has showed non-magnetic material in theprevious theoretical work [38,45]. According to our best knowledge,there is no experimental evidence of magnetic properties for thesestructures.

To investigate the energetically most stable structure of these MX-ene, we have calculated spin-polarized and spin-unpolarized statesof MXenes. In order to checked for possible magnetic coupling ofMXenes with fully relaxed spin-polarized calculations. We have con-structed 2 × 1 supercell that contains four transition metal atoms. Wehave obtained three different magnetic states including ferromagnetic(FM), antiferromagnetic in two different configurations, which calledAFM1 and AFM2 (see Fig. 1(c) and (d)). We have observed that thenon-magnetic state possesses the lowest energy in all ordering except2H-Ru2C.

It is well-known, Ti3C2 MXene undergoes a metallic to semicon-ductor transition with the functionalization –F, –O or –OH terminalgroups. Zhang et al. have deeply analyzed the electronic properties ofmonolayer Mo2C and its functionalized ones [37]. They have improvedthat for chalcogen functionalized monolayer Mo2C, its superconductiv-ity can be modified. The functionalization is important issue at MXenes,which is beyond the scope of the present work and the study will guidefor further studies.

3.3. Vibrational and thermal properties

Basically, the Raman theory deal with inelastically scattered photonoriginates from the oscillating dipoles of the crystal correspond to theRaman active vibrational modes of the crystal [46,47]. Raman activephonon modes of novel monolayer 2D materials are critical for newpredicted materials. According to our best knowledge, there is no studywhich covers dynamical properties with Raman active frequencies forthese structure. The dynamical stability of each 1T and 2H phase ofbinary MXenes are examined by calculating the corresponding phononband structure through the whole BZ. The phonon dispersion curvescalculated along the high symmetry points (𝛤 , M, K). It is clearlyshow that, Mo2C, W2C, Re2C, Os2C with both 1T and 2H phases andRu2C at 2H phase are dynamically stable with no significant imaginaryfrequencies. Even if materials which are low-dimensional, vibrationalproperties require the high computational cost. The reason limited usto use fairly small unit cells, which makes it difficult to carry outsimulations. Small negative frequencies in the out-of-plane acousticmodes near the 𝛤 point are attributed to numerical artifacts whichare stream from by small inaccuracies of the FFT grid. The vibrationalphonon mode frequencies at the 𝛤 point were calculated using thefinite-difference method as implemented in VASP. From the detailedanalysis of the phonon spectra, the 9 phonon modes are inferred as 3

Table 2The calculated Raman active frequencies for the 2H and 1T phases of monolayer MXene.

Phase E′′ /E1𝑔 A1/A1𝑔 E′ /E2𝑔(cm−1) (cm−1) (cm−1)

Mo2C 2H/1T 157/113 272/239 478/637W2C 2H/1T 131/99 234/167 603/585Re2C 2H/1T 119/76 182/163 483/393Ru2C 2H 21 333 391Os2C 2H 49 195 480

acoustical and 6 optical branches as illustrated in Fig. 3. There are 3acoustical modes which are doubly degenerate the in-plane transversalacoustical (TA) and the in-plane longitudinal acoustical (LA) phononbranch at the 𝛤 point for 2H and 1T symmetries. Raman spectrumof 2H and 1T symmetries possess D3ℎ point-group symmetry with 5Raman active modes. E′ and E′′ which are doubly degenerated Ramanactive modes have in-plane optical phonon modes. Out-of plane opticalmode A1 is Raman active. Another out-of plane optical mode, A′′

2 is theonly Raman inactive mode for the 2H symmetry. 2H symmetry of E′,E′′, A1 and A′′

2 Raman modes given as E1𝑔 , E12𝑔 , A1𝑔 and A1

2𝑔 Ramanmodes for 1T symmetry. The Raman active frequencies are calculatedfor dynamically stable structure as shown in Table 2.

Additionally, thermal stability of monolayer MXenes are furtherexamined by the ab-initio molecular dynamic (AIMD) simulation. Thecalculations are carried out on a 4 × 4 × 1 supercell which containing48 atoms and 4 × 4 × 1 k-points. The thermal dynamic investigationsare started with the optimized structure of 2D MXenes at 0 K [48,49].The temperature was increased to 1500 K with 300 K steps. Thestructure snapshots are taken at the end of the each simulation in theevery temperature steps; 300 K, 600 K, 900 K, 1200 K and 1500 K.Additionally, the evolution of free energy for these MXenes during thesimulation time is shown in Figs. 4 and 5. Since the given realisticrange of the thermal dynamic investigation, we have terminated thesimulation when the thermal dynamic stability was breakdown. As anexample, 1T phase of Re2C shows thermal dynamic stability at 300 K,the deformation occurs at 600 K. It kept their original structure at the300 K, which is the highest temperature for it Fig. 4. On the otherhand, 2H phase of Mo2C confirms that it thermally is stable to 1500K Fig. 5. Eventually, 2H-Os2C is found unstable at 300 K, 2H-Re2Cis found unstable at 600 K, Our results show that they are promisingmonolayer materials with good thermal stability.

4. Conclusions

By employing density functional theory calculations including abinitio molecular dynamic simulation, a pristine transition-metal car-bides are theoretically predicted with 1T and 2H symmetries. Theelectronic structure results showed that the metallic feature. Among thesystems studied here, we identify Mo2C, W2C, Re2C, Os2C with both 1Tand 2H phases and Ru2C at 2H phase as possible to synthesize in futureexperiments. AIMD calculations suggest that the 2H-W2C, 1T-W2C, 2H-Mo2C and 2H-Re2C MXenes possess good thermal stability, and theycould hold their structure up to temperature of 1500 K. Our futureresearch will focus on exploring effect of surface functionalization andmechanical strain. Because of some of them (Mo2C and W2C) areauxetic and the rest of them should investigate the further studies. Weexpect that our theoretical study will stimulate further experimentalresearch on this material in the future.

Acknowledgments

Computational resources were provided by TUBITAK ULAKBIM,High Performance and Grid Computing Center (TR-Grid e-Infrastr-ucture). The author acknowledges financial support the KLU-BAP,Turkey under the project number 189.

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Fig. 2. (Color online) Band structure of 2D monolayer 1T and 2H phase MXenes (Re2C, Tc2C, Mo2C, W2C, Os2C, Ru2C).

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Fig. 3. (Color online) (a) Phonon dispersion of T and H phase of Mo2C monolayer and their phonon modes. 𝛤 (0, 0, 0), M(1/2, 0, 0), and K(2/3, 1/3, 0) refer to the specialpoints in the first Brilliouin zone in reciprocal space.

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Fig. 4. (Color online) Snapshots of for AIMD simulation of geometrical structure for the 1T-Re2C at the temperature of (a) 300 K and (b) 600 K. Variation of free energy in AIMDsimulation at (a) 300 K and (b) 600 K during the timescale of 2 ps.

Fig. 5. (Color online) Snapshots of for AIMD simulation of geometrical structure for the 2H-Mo2C at the temperature of (a) 300 K, (b) 600 K, (c) 900 K, (d) 1200 K and (e) 1500K. Variation of free energy in AIMD simulation at (a) 300 K, (b) 600 K, (c) 900 K, (d) 1200 K and (e) 1500 K during the timescale of 2 ps.

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Appendix A. Supplementary data

Supplementary material related to this article can be found onlineat https://doi.org/10.1016/j.ssc.2019.113739.

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