Ti2CO2 Nanotubes with Negative Strain Energies and Tunable Band

Letter pubs.acs.org/JPCL

Ti2CO2 Nanotubes with Negative Strain Energies and Tunable Band Gaps Predicted from First-Principles Calculations Xun Guo,† Ping Zhang,*,†,§ and Jianming Xue*,‡,∥ †

Institute of Applied Physics and Computational Mathematics, Beijing 100094, People’s Republic of China; State Key Laboratory of Nuclear Physics and Technology, School of Physics, §Center for Applied Physics and Technology, and ∥ CAPT, HEDPS, and IFSA Collaborative Innovation Center of MoE College of Engineering, Peking University, Beijing 100871, People’s Republic of China

‡

S Supporting Information *

ABSTRACT: MXenes, a series of two-dimensional (2D) layered early transition metal carbide, nitride, and carbonitride, have been prepared by exfoliating MAX phases recently. In addition to 2D planar MXene, one-dimensional tubular formsMXene nanotubesare also expected to form. Herein, we design atomic models for Ti2C as well as Ti2CO2 nanotubes in the 1−4 nm diameter range and investigate their basic properties through density functional theory (DFT). It is shown that though the strain energy of Ti2C nanotubes are always positive, Ti2CO2 nanotubes have negative strain energies when diameter beyond 2.5 nm, indicating that they could possibly folded from 2D Ti2CO2 nanosheets. Moreover, the band gap of Ti2CO2 nanotubes decrease with the growing diameter and the maximum band gap can reach up to 1.1 eV, over 3 times that of their planar form. Thus, tunable band gaps provide strong evidence for the effectiveness of nanostructuring on the electronic properties of Ti2CO2 nanotubes.

O

maintain its shape, but after surface decoration the stability would be greatly improved. Two kinds of MXene nanotubes, Ti2C and its O-functionalized form Ti2CO2, are studied as the representative in this article due to the following reasons: (1) In 2011, Naguib et al. already prepared the Ti2C nano scroll with minimal diameter no more than 20 nm experimentally,12 which means this kind of MXene can be possibly rolled up. (2) The newly exfoliated MXenes often decorated by functional groups, including H, O, and F,13−15 often named as functionalized MXenes (fMXene),14,16,17 and planar Ti2CO2 was proved to be a semiconductor with band gap about 0.4 eV.14 What’s more, other Ti2CO2-based nanomaterials also exhibit good electrical property, such as Ti2CO2 nanoribbon.18 So it is reasonable to believe that Ti2CO2 nanotubes would also have good electrical properties. In this work, we employ first-principles calculations based on density functional theory (DFT) to study the properties of 1D MXene nanotubes. The diameter dependent strain energy and band gap are explored for both Ti2C and Ti2CO2. Our results show that Ti2C nanotubes have positive but small strain energies, which follow the D−2 relation strictly. While for Ti2CO2, the strain energies become negative when diameter is beyond 2.5 nm, and the band gap of Ti2CO2 nanotube decreases with the growing diameter. Our results demonstrate that surface decoration can not only improve the stabilities of

ne-dimensional (1D) materials have great potential for applications in nanoelectronics and nanospintronics due to their unique quantum confinement effects. For example, carbon and MoS2 nanotube exhibit different electronic and magnetic properties compared with their corresponding 2D planar forms.1−3 However, the preparation of 1D nanotube is always a difficult problem, so it is also very important for a nanotube to have low formation energy, customarily instead by strain energy. Recently, a new serials of free-standing two-dimensional (2D) materials with a chemical formula Mn+1Xn, where M represents a transition metal element and X is C or N,4,5 which are well-known as MXenes, have been successfully isolated by exfoliating MAX phasesa large family of layered ternary transition-metal carbides or nitrides with Mn+1AXn (n = 1, 2, or 3) structures then remove the A atom layer (mostly IIIA or IVA group element). These MXenes exhibit many extraordinary properties in the field of electronic device and ion adsorption anode,6−8 so it is reasonable to expect that their tubular form, MXene nanotube, would also have unique performance. Early in 2005, Enyashin and Ivanovskii proposed theoretical models for TiC nanotubes, and investigated their stability and electronic properties with the density functional theory tightbinding (DFTB) method.9 Later in 2012, they predicted the exist and stability of Ti2C and Ti3C2 MXene nanotube, because of their low strain energies.10 After that, a new kind of MXene nanotube based on Sc2C with band gap greater than 1 eV was investigated by Xu Zhang et al. computationally.11 They confirmed that bare Sc2C nanotube is not stable enough to © XXXX American Chemical Society

Received: November 2, 2016 Accepted: December 5, 2016 Published: December 5, 2016 5280

DOI: 10.1021/acs.jpclett.6b02556 J. Phys. Chem. Lett. 2016, 7, 5280−5284

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calculations were performed for (n, n) and (n,0) MXene nanotubes as a function of n with outer diameter (D) ranging from 0.8 to 3.5 nm, which correspond to index (n, n)-(n,0) from (6,6)-(6,0) to (20,20)-(20,0). The geometrical structures, including diameters of the nanotubes and lattice parameters c0 of relaxed Ti2C and Ti2CO2 nanotubes are present in Table 1. It could be found

bare MXene nanotube, but also greatly improve their electrical properties. Thus, these nanotubes will have profound implications for the application of MXenes. All calculations were carried out based on DFT as implemented in the Vienna ab initio simulation package (VASP).19,20 The exchange correlation energy is described by the generalized gradient approximation (GGA) in the scheme proposed by Perdew Burke-Ernzerhof (PBE),21 and electron− ion interactions are described by projector augmented wave pseudopotentials.22 Meanwhile, the optPBE method is used to account for the effect of van der Waals (vdW) interaction,23,24 and DFT+U correction was used during our calculations,25 with the consideration of 3d electron in Ti and V. According to previous studies, the U value for pure transition metals (from Ti to Cu) should be in the range of 2−4 eV,26,27 so in our calculations the value of U was set to 3 eV. Periodic boundary condition is applied along the z direction, and a large spacing of more than 20 Å in both x and y direction is used, which is far enough to avoid interaction between nanotube and its mirror image. The tube axis are set along z direction, and the lattice parameters c can be defined as the length of unit cell along z axis, as shown in Figure 1. The total

Table 1. Outer Diameter D (in nm), Inner Diameter d (in nm), Lattice Parameters c0 (in Å) and Bond Length l (in Å) of Ti2C and Ti2CO2 Nanotubesa chirality

D

d

c0

lTi1−C

lTi2−C

lTi1−O1 lTi2−O2

Ti2C (6,6) Ti2C (8,8) Ti2C (12,12) Ti2C (16,16) Ti2C (6,0) Ti2C (8,0) Ti2C (12,0) Ti2C (16,0) Ti2CO2 (8,8) Ti2CO2 (12,12) Ti2CO2 (14,14) Ti2CO2 (16,16) Ti2CO2 (20,20) Ti2CO2 (16,0) Ti2CO2 (20,0) Ti2CO2 (30,0)

1.26 1.61 2.26 2.95 0.904 1.09 1.47 1.86 2.06 2.65

0.818 1.15 1.78 2.47 0.542 0.708 1.01 1.38 1.13 1.77

3.27 3.19 3.12 3.01 5.44 5.49 5.37 5.37 3.14 3.06

2.12 2.12 2.11 2.12 2.08 2.06 2.08 2.10 2.05 2.12

2.25 2.22 2.19 2.18 2.13 2.19 2.21 2.22 2.31 2.23

1.94 2.14

2.04 1.96

2.87

1.98

3.11

2.23

2.15

2.03

1.95

3.18

2.28

3.10

2.24

2.14

2.03

1.95

3.78

2.85

3.14

2.26

2.08

2.01

1.95

2.25

1.33

5.18

2.07

2.22

1.89

1.92

2.52

1.61

5.22

2.13

2.18

1.95

1.92

3.44

2.54

5.37

2.19

2.16

2.11

2.03

a

Ti1 and O1 respresent the atoms in the outer layer, while Ti2 and O2 respresent the atoms of the inner layer.

Figure 1. Structure of (10,10) armchair (left) and (10,0) zigzag (right) Ti2CO2 nanotube sample, respectively. The vacuum slab in the a, b direction is over 20 Å, which means the lattice parameter can only be defined as the length of unit cell along the c axis.

that the lattice parameter c0 of Ti2CO2 and zigzag Ti2C nanotubes are not obviously influenced by the tube diameters, with the maximal relative difference within 2% and the changing is irregular. However, for Ti2C, c0 decreases 8% dramatically as diameter grows from 1.26 to 2.95 nm. At the same time, the changing of bond length is also no more than 5% for both Ti2C and Ti2CO2 nanotubes. So we can conclude that these MXene nanotubes can basically maintain their structures during scrolling. For all kinds of nanotubes, the relative difference of bond lengths between inner layer atoms are always higher than outer ones. For example, lTi1−C changes within 0.5% (armchair Ti2C), 2% (zigzag Ti2C), 10% (armchair Ti2CO2) and 3% (zigzag Ti2CO2), respectively, while corresponding lTi2−C values are 3, 4, 11, and 3%, mostly higher than outer layer bonds. This phenomenon can also be seen in Ti−O bonds, indicating that there are stronger interactions between inner layer atoms. Because of these strong interactions, the calculations to locate the proper stable structure of Ti2CO2 with smaller diameter become more difficult. So in this Letter, we only investigate Ti2CO2 with diameter larger than 2.06 nm, and in fact, this range is complete enough to represent the properties of these nanotubes. Figure 2 shows that the calculated strain energies follow strictly a D−2 behavior whether for the armchair or zigzag structure, just as previous studies.10 It could been found that

energy was converged to better than 10 meV for a plane wave cutoff of 500 eV, and 1 × 1 × 15 Monkhorst−Pack k points sampling for the Brillouin zone. After structural optimization, the density of states (DOS) and electronic properties are calculated using denser 1 × 1 × 30 k points. For geometry relaxation we used the method of conjugate gradient energy minimization, and the convergence criterion for energy was 10−5 eV between two consecutive steps. The maximal force exerting on each atom is less than 0.01 eV/Å upon ionic relaxation. Following previous studies, strain energy was taken into account to take the place of formation energy.2,28−30 The strain energy per unit formula for MXene nanotube is defined as Estrain = Etubular − Eplanar

(1)

where Etubular is the total energy per formula of the MXene nanotube, Eplanar is the total energy per formula of MXene monolayer. A lower Estrain value means higher stability of MXene nanotube under this definition. To denote the structure of MXene nanotubes, we also use the notation of Ti2C (m, n) and Ti2CO2 (m, n) in accordance with previous research. In the following research, different sizes of armchairs and zigzag nanotubes were studied for both Ti2C and Ti2CO2. Our 5281

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Table 2. A Brief Comparison of Typical Negative Strain Energy Nanotubesa name Ti2CO2 nanotube SrTiO3 nanotube31 anatase(001) 3 ML nanotube32 imogolite nanotubes33

composition per unit

minimal strain energy (eV/atom)

Ti2CO2 SrTiO3 Ti3O6

−0.18 −0.091 −0.053

(HO)3Al2O3SiOH

−0.038

a

Note that Ti2CO2 nanotube has the least number of atoms in a unit and lowest strain energy per atom.

Figure 2. Calculated strain energies (Estrain in eV) of nanotubes as a function of the nanotube outer diameter (D in nm). The strain energies Ti2C follow the 1/D2 relation strictly. However, for Ti2CO2, the strain energy decreased until the diameter reached 3.2 nm, then increased with growing tube diameter. The minimal strain energy of Ti2CO2 can be as low as −0.91 eV.

the strain energy for Ti2C nanotube with 1 nm diameter is about 0.88 eV/formula, which corresponds to 0.07 and 0.1 eV/ atom according to Figure 2. This value is almost 1 order of magnitude smaller than that of a MoS2 nanotube with similar diameter (about 0.7 eV/atom),28 and basically the same as carbon nanotubes whose strain energy is about 0.1 eV/atom when D = 1 nm,30 which means the stability of Ti2C nanotube is much higher than tubular MoS2’s and quite close to carbon nanotubes. So we are quite optimistic for the emergence of MXene nanotubes, since tubular carbon and MoS2 have already been prepared experimentally. While for Ti2CO2 nanotubes, the strain energy curve decreases from 0.19 to −0.91 eV/formula until D reaches 3.2 nm, then rises with the increasing diameter, which means Ti2CO2 nanotubes with D = 3.2 nm diameter has the most stable structure. Additionally, the Estrain value is positive when tube diameter smaller than 2.5 nm, indicating that the size of Ti2CO2 nanotubes can be hardly lower than this value. What’s more, Ti2CO2 tube with diameter lower than 2.0 nm is quite difficult to locate the stable structure, so in the following article, we did not consider more nanotubes with smaller or larger size. Comparing with other nanotubes who also have negative strain energies, such as SrTiO3 nanotubes,31 imogolite nanotubes33 and anatase(001) 3 ML nanotubes,32 the calculated strain energy of Ti2CO2 nanotube could be low as −0.18 eV/atom, which means Ti2CO2 nanotube is quite possible to be prepared experimentally because the Ti2CO2 nanosheet has already proved to exist, and tubular Ti2CO2 has lowest strain energy compared with other negative Estrain nanotubes as discussed in Table 2. The band structures of all Ti2CO2 nanotube samples are plotted in Figure 3 in the range of growing diameter. Mostly, Ti2CO2 nanotubes have indirect band gaps whether with armchair or zigzag structure. However, it is very interesting that when tube diameter approaches the transition point of strain energy from positive to negative, the band gap transforms into a direct one shortly, and then returns to an indirect band gap as diameter continues increasing. In fact the transition process is already started in (8,8) nanotube, because the bottom of its conduction band is nearly flat as shown in Figure 3. The highest point is only 0.06 eV

Figure 3. Band structure near the Fermi level (EFermi = 0) of Ti2CO2 nanotubes with growing diameter. Tubes with direct band gap are plotted with yellow lines, while red lines represent indirect band gap.

higher than the lowest point, which means, quite possibility, that an electron can transit at the Z point directly. So we believe that Ti2CO2 nanotubes with diameter near 2.5 nm could be all direct band gap semiconductor, while the others are indirect ones. The total and partial density of states (DOS) of a typical armchair and zigzag Ti2CO2 nanotube compared with that of a planar Ti2CO2 monolayer and Ti2C nanotube is shown in Figure 4. The DOS reveals that all the Ti2CO2 nanotubes are nonmagnetic just as their planar forms, while Ti2C nanotubes are magnetic and metallic, which is well consist with a previous study.10 More DOS plots are listed in Figure S1 in the Supporting Information due to the length limit, and it seems that the DOS of a Ti2CO2 nanotube is not significantly influenced by tube structure and diameter. The band gaps of Ti2CO2 nanotubes possessing different diameters were also calculated and shown in Figure 5. In order to check the validity of our present calculations, the band gap of planar Ti2CO2 monolayer was calculated as 0.36 eV, which is very close to the present result 0.4 eV.6 It can be shown that the band gap curve is discontinuous at the transition point when strain energy from positive to negative. The band gap reaches 5282

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Figure 4. Total and partial density of state (DOS) of planar Ti2CO2 monolayer, (12,12) Ti2C nanotube, comparing with Ti2CO2 nanotube with armchair (12,12) and zigzag (20,0) structure. The Fermi level has been set to zero. The density of electron (DOE) of (a) (16,16) and (b) (20,0) Ti2CO2 nanotube were also plotted on the right side.

nanotube, with corresponding relative diameter difference no more than 5%. However, for other MXene nanotubes, such as Sc2C(OH)2 with similar relative diameter difference, the relative band gap difference is only about 3−8%.11 So measuring the band gap of Ti2CO2 nanotube might be a effective way to estimate the tube diameter. What’s more, this valuable property makes it possible to produce Ti2CO2 nanotube with specific band gap value as needed by changing the tube diameter, which is very useful in the semiconductor industry. In this Letter, we established the atomic model to investigate the strain energy and electronic properties of Ti2C and Ti2CO2 MXene nanotubes with different diameters and structures. Our calculations show that these two kinds of MXene nanotubes have relatively low strain energy compared with other 1D tubular materials. Especially, Ti2CO2 nanotubes with certain size have negative strain energies, which might contribute to the understanding of their creation method. What’s more, the band gap of Ti2CO2 nanotube with negative strain energy decreases monotonically with the growing diameter, whether for armchair or zigzag structure. This phenomenon is very valuable not only for the measurement, but also provides a perspective of potential applications of these tubular structures.

Figure 5. Variation of band gap (G in eV) with diameter of Ti2CO2 nanotubes, the structures of these tubes are as labled. The dashed line represents the band gap of planar MXene from our calculation.

the highest value when D = 2.52 nm, then decreased as te growing tube diameter dramatically, and can be even lower than the G value of planar Ti2CO2 when D is over 3.1 nm. The largest band gap among all the calculations can be as high as 1.1 eV, over three times higher than the G value of planar Ti2CO2’s, which means scrolling into nanotube can significantly enlarge the band gap of Ti2CO2 monolayer to a sizable level. It could be noted that the band gap of Ti2CO2 nanotubes is also independent of the tube structure, just as their strain energies. Figure 5 shows that the band gap of a Ti2CO2 nanotube is very sensitive to the changing of diameter. For example, the band gap drops 47% from (20,0) to (12,12)

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b02556. Total and partial density of state (DOS) of (8,8), (16,0), (12,12), (16,16), and (20,20) Ti2CO2 nanotubes (PDF) 5283

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Xun Guo: 0000-0002-8424-2618 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported by NSFC (Grant No. 91226202 and 91426304) and the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase).

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