Intrinsic Structural, Electrical, Thermal and Mechanical Properties of ...

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Intrinsic Structural, Electrical, Thermal, and Mechanical Properties of the Promising Conductor Mo2C MXene Xian-Hu Zha,† Jingshuo Yin,† Yuhong Zhou,† Qing Huang,† Kan Luo,† Jiajian Lang,† Joseph S. Francisco,‡ Jian He,§ and Shiyu Du*,† †

Engineering Laboratory of Specialty Fibers and Nuclear Energy Materials, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo, Zhejiang 315201, China ‡ Departments of Chemistry and Earth and Atmospheric Science, Purdue University, West Lafayette, Indiana 47906, United States § Center for Translational Medicine, Department of Biotechnology, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, Liaoning 116023, China ABSTRACT: Mo2C, the newly synthesized MXene with a large lateral size and superconductivity property, has attracted increasing interest in material science. Employing first-principles density functional calculations, its intrinsic structural, electrical, thermal, and mechanical properties are investigated in this work. It is found that this MXene is nonmagnetic with a small molar volume. The electrical conductivity is predicted in the order of 106 Ω−1m−1, and its value is significantly influenced by doping. For thermal conductivity, both of the electron and phonon contributions are studied. At room temperature, the Mo2C’s thermal conductivity is determined to be 48.4 Wm−1 K−1, which can be further enhanced by increasing temperature and introducing n-type dopants. The specific heat and thermal expansion coefficient are also assessed, and their values at room temperature are calculated as 290 Jkg−1 K−1 and 2.26 × 10−6 K−1, respectively. Moreover, the thermal contraction of the MXene is found at low temperatures. Under biaxial strains, the elastic modulus is predicted as 312 ± 10 GPa, and the ideal strength is determined to be 20.8 GPa at a critical strain of 0.086. In view of the small molar volume, superhigh electrical conductivity, favorable thermal conductivity, low thermal expansion coefficient, and high mechanical strength, the Mo2C MXene generally merits more widespread applications besides superconductors, such as applying to substrates for other layer materials, and candidate materials for batteries and supercapacitors.

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INTRODUCTION MXenes, a new family of two-dimensional materials, have attracted extensive attentions in recent years.1,2 Since the discovery of Ti3C2Tx in 2011 (Tx referring to surface terminations, which generally are fluorine, hydroxyl and oxygen functional groups),3 over 10 MXene members have been successful synthesized: Ti2CTx, Ta4C3Tx, (Ti0.5Nb0.5)2CTx, (V0.5Cr0.5)3C2Tx, Ti3CNTx,4 Nb2CTx, V2CTx,5 Nb4C3Tx,6 Mo2TiC2Tx, Mo2Ti2C3Tx, Cr2TiC2Tx,7 Zr3C2Tx,8 pristine Mo2C,9 Mo2CTx,10,11 and Ti4N3Tx.12 Most existing MXenes are prepared by etching corresponding MAX phases and relatives13 with various etchants, such as concentrated hydrofluoric acid,3 ammonium bifluoride (NH4HF2),14 and the combination of common hydrochloric acid and lithium fluoride.15 By means of the etching approaches, various surface groups Tx generally form, and their compositions are related to the choice of etchants and the experimental conditions.16,17 Because the intrinsic physical properties of the MXenes are found to be significantly dependent on their surface groups,18,19 variations of surface terminations become an obstacle that hinder MXenes’ practical applications. Recently, Xu et al. successfully synthesized a stable and clean Mo2C MXene.9 In © 2016 American Chemical Society

contrast to previous approaches, the Mo2C MXene was prepared though the traditional chemical vapor deposition (CVD) method in which methane was adopted as the carbon source and a copper foil was chosen as the substrate for a molybdenum foil. Using this CVD approach, the lateral size of the synthesized Mo2C MXene was measured to be larger than 100 μm, and its surface was found to be clean without any functional groups. Additionally, the MXene was determined to present superconductivity under 2.85 K. Considering the large lateral size, simple and stable configuration, and superconductivity characteristics, the Mo2C MXene has potential applications in the future. For example, a recent theoretical work implied that the Mo2C monolayer is a competitive anode material.20 However, up to date most intrinsic physical properties of the Mo2C MXene are still unavailable. It is difficult to design functional or structural materials using Mo2C without the important physical properties being obtained. Therefore, to better understand and to utilize this new material, Received: April 26, 2016 Revised: June 28, 2016 Published: June 30, 2016 15082

DOI: 10.1021/acs.jpcc.6b04192 J. Phys. Chem. C 2016, 120, 15082−15088

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The Journal of Physical Chemistry C

⎛ Mωmax,j υj 3 ⎞1/2 ⎟ minimum frequency is redefined as ωmin, j = ⎜⎜ 2 ⎟ ⎝ 2kBTL γj ⎠ with kB representing the Boltzmann’s constant. The thermal expansion coefficient is investigated based on the Grüneisen approximation32−34

the intrinsic structural, electrical, thermal and mechanical properties of the Mo2C MXene are studied in this work. Moreover, this work provides some critical data for the MXene, which shows promise for a number of practical applications.

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COMPUTATIONAL DETAILS First-principles calculations are implemented in the plane-wave VASP code.21 The generalized gradient approximation (GGA) of the Purdue−Burke−Ernzerhof (PBE) approach22 is adopted to describe the exchange-correlation functional on the basis of the projected augmented wave (PAW). Plane-waves with energies up to 500 eV are employed to describe the electronic wave functions in which the C 2s2, 2p2 and Mo 4p6, 5s1, 4d5 electrons are considered as valence states. During optimization, all of the structures are relaxed until the forces on each atom are smaller than 1.0 × 10−3 eV/Å, and the criterion for energy convergence is chosen as 1.0 × 10−6 eV/cell. A Γ-centered sampling of 12 × 12 × 1 grid is used in describing the Brillouin zone (BZ). Spin-polarization calculations are performed. To eliminate the interactions of neighboring layers, a 30 Å lattice parameter in the c-axis perpendicular to the MXene surface is adopted. To obtain the electrical conductivity and the electron thermal conductivity, we perform the semiclassical Boltzmann transport calculations within the constant relaxation time approximation (τ = 5.52 × 10−15 s). The constant relaxation time τ for the Mo2C MXene was determined according to Xu’s work.9 The transport calculations are undertaken by the BoltzTraP code.23 The electronic structure for transport properties are calculated using a very fine k-mesh of 42 × 42 × 1. In the BoltzTraP calculation, the original k-mesh is interpolated onto a mesh 20 times as dense, and the tetrahedron scheme is adopted to obtain the density of states. In regard to the vibrational properties, the phonon spectrum is calculated based on the density functional perturbation theory,24 which is implemented by the combination of the VASP and the Phonopy softwares.25 A 6 × 6 × 1 k-points mesh based on a 4 × 4 × 1 supercell is employed for calculating the dynamical matrix, and a 120 k-points grid is adopted for plotting the phonon dispersion for various directions and the entire BZ. The phonon thermal conductivity is calculated in the framework of the Klemens theory26−28 ρ κp = T

∑ j

υj

α=

γj2 ωmax, j

ln

here ρ is mass density, which equals to ρ =

M

(

)

ℏωj , k 2

( )

c v (j , k ) = k B

(2)

kBT

ℏωj , k

( ) ⎡ exp ) − 1⎤⎦⎥ ⎣⎢ ( exp

k BT

ℏωj , k

2

with ℏ denoting the

k BT

reduced Planck’s constant. Specific heat33,35,36 is proportional to the heat capacity, which is calculated as 1 c = N M ∑j , k c v(j , k). k

To predict the elastic modulus and the ideal strength under biaxial strains, the calculations on stretching strains up to 12.5% with an increment of 0.5% are conducted. To be more precise, a smaller increment of 0.1% in the vicinity of the critical strain is undertaken. Because of the vacuum layer, the elastic constants of the MXene is rescaled by h/d with h being the lattice parameter in c-axis (30 Å in this work). All the structures and electronic density distributions are visualized in the VESTA code.37 All the computational parameters and methods have been well tested. For example, the methods and relevant parameters for calculating the thermal properties have been adopted in our previous works.28,33 In our benchmark calculations, the predicted thermal conductivities of graphene and ZnSb (4756 and 3.099 W m−1 K−1 at room temperature, respectively) by the current methods have been shown to be in excellent agreement with the measurements.38,39 Moreover, to verify the semiclassic Boltzmann calculations implemented in the BoltzTraP code we have calculated the transport coefficient σxx/τ, equal to the electrical conductivity divided by the scattering time, of the monolayer Sc2C(OH)2. The value at room temperature is predicted to be 1.98 × 1020 Ω−1 m−1 s−1 at a chemical potential of −0.5 eV, which is consistent with that of the Khazaei’s work.40

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RESULTS AND DISCUSSION In order to investigate intrinsic physical properties, the structure and the fundamental electronic properties of the Mo2C MXene are investigated first. As shown in Figure 1, the top- and side-views of the MXene are presented in Figure 1a,b, respectively. A central carbon layer is sandwiched by two molybdenum monolayers, and a molybdenum atom is on the top-site of the center of three neighboring carbon atoms. The space group is determined to be P3̅ml (No. 164), and its corresponding BZ is given in Figure 1c. As seen from the figure, the high symmetry routes ΓM and ΓK in BZ are correspond to the armchair and zigzag directions in the real-space.28 For the Mo2C MXene, the hexagonal lattice parameter in the xy-plane is optimized to be 3.00 Å. Through the optimization of the multilayer configuration, the monolayer thickness is determined to be 4.64 Å, which is approximately twice that of the bare layer thickness (2.34 Å).41 Evidently, both of the lattice parameter

(1) 3 2 ad 2

j,k

here Nk is the k-point number adopted in plotting the phonon spectrum, which equals to 120 in our calculations; Es is the strain energy; cv (j, k) is the (j, k) mode contribution to the heat capacity, whose expression is

ωmax, j ωmin, j

∑ c v (j , k )γ (j , k )

∂a

4

1

1 1 2 ∂ Nk a 2 Es | 0 2 0

with M

being the mass of the unit cell,27 and a and d denoting the hexagonal lattice constant in the xy-plane and the monolayer thickness in the z-direction, respectively. In order to obtain the layer thickness, the multilayer Mo2C MXene is optimized, and d is chosen as the monomer thickness, similar to the definition for monolayer MoS2.29 Because the van der Waals correction is crucial in describing layer interactions,30 a damped VDW correction (DFT-D3)31 is adopted in the optimization of multilayer configuration. T denotes temperature; υj and γj are the group velocity28 and Grüneisen parameter32 of the j-branch in phonon spectrum, respectively; ωmin,j and ωmax,j are the minimum and maximum circular phonon frequency, respectively, of each branch. Because of the flake length L, the 15083


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for the Mo2C MXene system and is not considered in the following sections. On the basis of the optimized structure and electronic characteristics, the electrical conductivity and the electron thermal conductivity of the Mo2C MXene are further investigated. It is revealed that the two quantities are isotropic in the plane of the monolayer regardless of the temperatures and chemical potentials. To facilitate elaboration, the transport coefficients defined by the electrical conductivity and electron thermal conductivity divided by the scattering time (σxx/τ and κxx/τ), as functions of chemical potentials at various temperatures, are provided in Figure 2. As shown in Figure 2a, σxx/τ is

Figure 1. (a,b) The top-view and side-view of the Mo2C MXene. (c) The Brillouin zone of the 2D hexagonal lattice, in which the high symmetry routes ΓM and ΓK correspond to the real-space armchair and zigzag directions, respectively. (d) The electronic DOS of the MXene in which the projected DOS of each atomic orbital is provided. The inset presents the electronic wave functions with energy in the range of −0.2−0.2 eV with the Fermi level is adjusted to 0 eV. Figure 2. Transport coefficients (a) σxx/τ and (b) κxx/τ, as functions of the chemical potentials at various temperatures.

and the layer thickness are smaller than those of functionalized Mo2CT2 (T = O, F, OH) MXenes.19 On the basis of the small lattice parameter and thin layer thickness, the Mo2C MXene generally possesses a small molar volume. Meanwhile, these structural parameters imply that the molybdenum atoms bond strongly with carbon atoms. To test the bond strength and stability of the Mo2C MXene, the binding energy is also assessed (Ebinding = (2EMo + EC − EMo2C)/3, where EMo and EC are the energies of separated molybdenum and carbon atoms, respectively, and EMo2C denotes the total energy of Mo2C unit cell), which is determined to be 6.46 eV. This large and positive value partially implicates the stability of the Mo2C MXene. On the basis of the optimized structure, the electronic density of states (DOS) is studied and presented in Figure 1d. It shows that the Mo2C MXene is a nonmagnetic and metallic system with a large DOS around the Fermi level. This is markedly different from its fluorine functionalized Mo2CF2 MXene with a small band gap.40 By further analization with the projected DOS, the DOS in the vicinity of the Fermi level is determined to be mainly contributed by the electrons of the molybdenum atoms, especially those valence electrons in the 4d orbitals. The large DOS implies that there exist a high number of migration channels for electrons. For visualization, the electronic wave functions with energy in the range of −0.2−0.2 eV that significantly influenced the electrical conductivity are plotted and provided as an inset in Figure 1d. Wave packets can be seen around the molybdenum atoms, which are mainly related to the high degeneracy of the 4d orbitals. The high DOS near Fermi level is a reflection of the superconductivity of the Mo2C MXene.9 It is worth mentioning that we have also considered the influence of spin−orbit coupling (SOC) in the electronic energy bands. It shows that the energy bands calculated with SOC corrections change little from those without them. Therefore, the contribution of SOC may not be significant

generally independent of the increasing temperatures without considering the temperature effect on the chemical potential, which is similar to the behaviors in other metallic MXenes.40 Conversely, the chemical potential plays an important role in regulating the electrical conductivity. At zero chemical potential, the σxx/τ value is determined to be 6.51 × 1020 Ω−1 m−1 s−1 (using τ = 5.52 × 10−15 s, the σxx value is calculated as 3.59 × 106 Ω−1 m−1), which is substantially consistent with the experiment result (σ is calculated to be 8.99 × 106 Ω−1 m−1 based on a layer thickness of 8.3 nm at 10 K).9 With a positive chemical potential up to 0.684 eV, σxx/τ increases with increasing chemical potential, and its maximum value at 0.684 eV is determined to be 10.6 × 1020 Ω−1 m−1 s−1 (corresponding σxx is 5.87 × 106 Ω−1 m−1). Because the positive chemical potential is mainly caused by n-doping, it is a demonstration that the n-doping is beneficial to increase the MXene’s electrical conductivity. Although a higher chemical potential corresponds to a lower electrical conductivity, it has been beyond the applicability of the current model. In contrast to the circumstance with a positive chemical potential, the negative chemical potential can be induced by introducing ptype dopants and increasing temperature.42 The σxx/τ value first decreases with the increasing absolute value of the negative chemical potential, and the minimum value is found to be 5.00 × 1020 Ω−1 m−1 s−1 at −0.24 eV. Thereafter, the σxx/τ value increases. It is interesting to point out that the lowered Fermi energy by p-doping causes the increase in density of states according to the DOS plot shown in Figure 1d, however, it can be seen the value of σxx/τ decreases when the chemical potential is slightly lowered. This indicates the electron mobility is lowered when low amount p-doping occurs. In general, the predicted electrical conductivity is much higher 15084


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Figure 3. (a,b) The phonon dispersions in the zigzag and armchair directions, respectively. (c,d) The phonon thermal conductivities along these two directions.

Figure 4. (a) The phonon dispersion in the entire Bollouin zone; (b) the specific heat as a function of temperature; (c) the thermal expansion coefficient as a function of temperature; and (d) the Grüneisen parameter in the entire BZ.

m−1 K−1 s−1 at room temperature (κxx is calculated as 26.4 W m−1 K−1). The corresponding value at 500 K is 80.9 × 1014 W m−1 K−1 s−1. At the higher chemical potential of 0.684 eV, the room temperature κxx/τ increases to 77.4 × 1014 W m−1 K−1 s−1, and the value at 500 K reaches 127 × 1014 W m−1 K−1 s−1 (corresponding κxx are 42.7 and 70.2 W m−1 K−1, respectively). Interestingly, the electron thermal conductivity can be further

than those of Mo2CT2MXenes.40 In regard of the κxx/τ values as shown in Figure 2b, the function of κxx/τ with different chemical potentials is similar to that for σxx/τ. A remarkable difference is that κxx/τ is proportional to the increasing temperature. As a consequence, the metallic Mo2C MXene satisfies the Wiedemann−Franz Law.43 At zero chemical potential, the κxx/τ value is determined to be 47.8 × 1014 W 15085


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temperature is low, and it expands afterward. The negative thermal expansion coefficient with the largest absolute value is determined to be −3.27 × 10−6 K−1 at 25 K, and the maximum thermal contraction is found at 125 K where the thermal expansion coefficient reaches zero. After that, the value of the thermal expansion coefficient is positive and increases with increasing temperature. At 800 K, the value is determined to be 3.65 × 10−6 K−1. Evidently, the magnitude of the thermal expansion coefficient is much smaller than those of most metals, such as copper and nickel.46 In order to gain a deeper understanding of the thermal expansion behavior, the Grüneisen parameter γ,32,34 shown in each mode contribution in the entire BZ, is investigated and presented in Figure 4d. This figure shows that the absolute values of γ for acoustic modes are much larger than those of optical modes, which implies that the acoustic modes undertake the main contributions. The ZA mode shows large negative γ near the BZ center, and positive values at the BZ boundary. Thus, this mode both contributes to the thermal contraction and expansion of the Mo2C MXene. In contrast to the ZA mode, the TA mode mainly contributes to the thermal contraction, and the LA mode generally causes the thermal expansion. On the basis of the predicted low thermal expansion coefficient of the Mo2C MXene, a large thermal mismatch is expected to appear between the Mo2C MXene and the pure molybdenum,47 which probably is the main reason that we can obtain the clean Mo2C MXene free from Mo nanoparticles by a rapid cooling approach.9 Moreover, the relatively low thermal expansion coefficient can be beneficial in the Mo2C’s practical applications because the structure is robust to temperature variations. Because biaxial strains can inevitably emerge due to existence of substrates when using layer materials, it is interesting to investigate the mechanical properties of the Mo2C MXene under the biaxial strains. Figure 5 shows the relationship

enhanced by increasing the temperature. Evidently, the Mo2C MXene possesses superhigh electrical conductivity and favorable thermal conductivity. To describe the thermal conductivity more precisely, the phonon thermal conductivity of the Mo2C MXene is also investigated. Figure 3a,b shows the phonon dispersions along the zigzag (ΓM) and armchair (ΓK) directions, respectively. Three acoustic modes [out-of-plane acoustic (ZA), longitudinal acoustic (LA) and transversal acoustic (TA) modes] are denoted in black rectangles, red circles, and blue triangles, respectively. The ZA mode shows the lowest phonon frequency. Meanwhile, the phonon dispersions of the TA and LA modes are nearly superposed, especially along the armchair direction. It is worth mentioning that the LA mode is slightly softened at the M high-symmetry point along the zigzag direction. On the basis of the phonon dispersions and a flake length of 5 μm, the phonon thermal conductivities along the zigzag and armchair directions are calculated and provided in Figure 3c,d, respectively. From these two graphs, we find that the phonon thermal conductivity is mainly contributed by the LA mode, and its value decreases with increasing temperature in the range of 100−500 K investigated. At room temperature, the phonon thermal conductivity is determined to be 9.72 W m−1 K−1 in the zigzag direction in which the ZA, TA, and LA mode’s contributions are 1.50, 1.93, and 6.29 W m−1 K−1, respectively. Correspondingly, the phonon thermal conductivity in the armchair direction is calculated as 16.2 W m−1 K−1. The lower thermal conductivity in the zigzag direction can be ascribed to the softening of the LA mode at the M point, which introduces a smaller group velocity and a higher Grüneisen parameter. In general, a long flake of a 2D material may reduce boundary scattering of phonons, leading to high thermal conductivity. With a larger flake length of 100 μm approaching to the experimental result,9 the phonon thermal conductivities increase to 12.9 and 22.0 W m−1 K−1 in the zigzag and armchair directions, respectively. Considering both of the electron and phonon contributions, the thermal conductivity at room temperature is predicted as 48.4 W m−1 K−1 in the armchair direction, which increases to 64.7 W m−1 K−1 by means of a heavy n-doping (with chemical potential equal to 0.68 eV). Moreover, a higher temperature will further enhance the thermal conductivity. For example, the value is determined to be 92.2 W m−1 K−1 at 500 K in view of the n-doping, which is proximately close to that of pure iron.44 As to the thermal conductivity in the zigzag direction, the value is approximately 9 W m−1 K−1 lower at room temperature. Because the Mo2C MXene shows excellent electrical and favorable thermal conductivities, it is capable as a conductive material at various temperatures. Herein, the thermal expansion coefficient and the specific heat become two crucial factors in determining its practical applications. On the basis of the phonon dispersion in the entire BZ as shown in Figure 4a, these two quantities of the Mo2C MXene are also investigated. The specific heat and thermal expansion coefficient as functions of the temperatures are given in Figure 4b,c, respectively. As seen from the figures, the specific heat increases with increasing temperature in the entire range of temperatures investigated, and its room temperature value is determined to be 290 J kg−1 K−1. At 800 K, which is the highest temperature investigated, the specific heat reaches 351 J kg−1 K−1. With respect to the thermal expansion behavior, the Mo2C MXene is distinct from those of functionalized MXene and many bulk systems.45−47 This MXene contracts with the increasing temperature when

Figure 5. Calculated stress versus biaxial strain for the Mo2C MXene. The inset shows the linear regression of the initial stress strain curve for calculating the elastic modulus.

between the stress and the biaxial strain. By fitting the stress strain function based on linear regression up to 1.50% (as shown in the inset), we obtained a biaxial elastic modulus Y2D = 312 ± 10 GPa, which is slightly higher than that of monolayer MoS2.29,48 Incidentally, the large elastic modulus can be attributed to the strong interactions between the molybdenum and carbon atoms. With increasing strains, the stress increases up to the critical strain of 0.086, and then the MXene shows a creep deformation. The ideal strength at the critical strain is 15086



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determined to be 20.8 GPa. Interestingly, the predicted ideal strength also approaches that of the monolayer MoS2 (23.8 GPa), though the critical strain is smaller than that of MoS2(0.195).29 These data imply that the Mo2C MXene is a virtually strong elastic 2D material which is robust to applied strains. From this work, the structure, electrical, thermal, and mechanical properties of the Mo2C are comprehensively studied. It is found that the MXene presents a small molar volume, superhigh electrical conductivity, favorable thermal conductivity, low thermal expansion coefficient, and strong mechanical strength. These properties suggest that this MXene may have broader applications. For example, the Mo2C MXene can be used as conductive material based on its superhigh electrical conductivity and favorable thermal conductivity. Moreover, it may be used as a substrate for other layer systems49 due to its strong conductivity and the structure robustness to temperature variation and strains. Considering the strong capacity on adsorption of ions,50 small molar volume, and superhigh conductivity, the Mo2C MXene can also act as a good candidate material for batteries and supercapacitors.

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CONCLUSIONS In summary, we have investigated various intrinsic physical properties of the promising Mo2C MXene. The MXene is found to present a small molar volume, superhigh electrical conductivity, and favorable thermal conductivity. Moreover, it is robust to temperature variations and strains. Explicitly, the lattice parameter in the xy-plane is determined to be 3.00 Å, and the layer thickness is predicted as 4.64 Å. The electrical conductivity is of order of 106 Ω−1 m−1. The thermal conductivity increases with the increasing temperature; the intrinsic value at room temperature is predicted to be 48.4 W m−1 K−1, which increases to 64.7 W m−1 K−1 by introducing a heavy n-doping. The maximum thermal expansion coefficient is determined below 3.65 × 10−6 K−1 in the entire range of temperatures up to 800 K. The biaxial elastic modulus is predicted as 312 ± 10 GPa by a linear fitting, and the ideal strength is found to be 20.8 GPa at the critical strain of 0.086. On the basis of these predicted properties, the Mo2C MXene merits promise for a number of potential applications.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the support of the Division of Functional Materials and Nanodevices, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, the National Natural Science of Foundations of China (Grant Nos. 51372046, 51479037, and 91226202), the Ningbo Municipal Natural Science Foundation (Nos. 2014A610006 and 2016A610272), ITaP at Purdue University for computing resources, and the key technology of nuclear energy, 2014, CAS Interdisciplinary Innovation Team. 15087


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