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Dandan Wang^{a},
ZhongHui Sun^{ab},
DongXue Han*^{a},
Lei Liu^{c} and
Li Niu^{a}
^{a}State Key Laboratory of Electroanalytical Chemistry, c/o Engineering Laboratory for Modern Analytical Techniques, Changchun Institute of Applied Chemistry, Chinese Academy of Science, Changchun, 130022, Jilin, P. R. China. E-mail: dxhan@ciac.ac.cn; Fax: +86 4318526 2800; Tel: +86 4318526 2425
^{b}University of Chinese Academy of Sciences, Beijing, 100049, P. R. China
^{c}State Key Laboratory of Luminescence and Applications, CIOMP, Chinese Academy of Sciences, No. 3888 Dongnanhu Road, Changchun, 130033, Jilin, P. R. China

Received
12th January 2017
, Accepted 10th February 2017

First published on 17th February 2017

The discovery of graphene and other two-dimensional (2D) materials has set the foundation for exploring and designing novel single layered sheets. The family of 2D materials encompasses a wide selection of compositions including almost all the elements of the periodic table and they have the potential to play a fundamental role in the future of electronics, composite materials and energy technology. Therefore, searching for new 2D materials is a big challenge in materials science. In this work, we theoretically designed a monolayer of Ti_{3}BN following the strategy of “atomic transmutation”. The Ti_{3}BN monolayer can be considered as three Ti-atomic layers being interleaved with one N-atomic layer and one B-atomic layer, in the sequence of Ti_{1}–N–Ti_{2}–B–Ti_{3}. The moderate cohesive energy, positive phonon frequencies and high melting point are the best guarantees for good stability of Ti_{3}BN. Based on a global minimum structures search using the particle-swarm optimization (PSO) method, Ti_{3}BN is the lowest energy structure in 2D space, which holds great promise for the realization of layered Ti_{3}BN in experiment. Based on density functional theory (DFT) calculations, Ti_{3}BN is intrinsically metallic and its electronic properties can be modulated by varying the surface groups, such as OH or F-termination. If realized in experiment, it may find applications in many aspects.

Recently, a new family of graphene-like 2D materials termed as MXenes were successfully synthesized by selectively extracting the “A” element from the layered MAX phases (A is an A-group element, mostly Al or Si) in the aqueous HF.^{10} MAX phases are a large (>60 members) family of layered ternary early transition-metal carbides, nitrides, and carbonitrides with P6_{3}/mmc symmetry.^{11} To date, several MXenes have been synthesized successfully, including Ti_{3}C_{2},^{12} Ti_{2}C,^{13} Ta_{4}C_{3},^{14} V_{2}C,^{15} TiNbC,^{16} Nb_{2}C^{17} and Mo_{2}C.^{18}

With the increasing interest in MXenes, a mass of experimental and theoretical efforts related to their synthesis, structures, properties and potential applications have been made experimentally and theoretically.^{19,20} Among the as-synthesized MXene phases, the most studied MXene is Ti_{3}C_{2}, prepared by immersing Ti_{3}AlC_{2} in HF solutions at room temperature.^{12} Ti_{3}C_{2} was predicted theoretically to be good electrical conductors and its electrical conductivities can be tuned by different surface terminations.^{21} What's more, Ti_{3}C_{2} have been proved to be very promising as anode materials for Li-ion batteries and as hydrogen storage media.^{22,23}

Motivated by the Ti_{3}C_{2} monolayer, which is composed of three Ti-atomic layers being interleaved with two C-atomic layers, herein we designed a new 2D material of Ti_{3}BN by performing density functional theory (DFT) calculations following the strategy of “atomic transmutation”, which means substituting certain types of elements with their neighboring elements in the periodic table but the total number of valence electrons is kept unchanged.^{24,25} A major breakthrough has been made in finding and designing novel materials. For example, if one were to substitute the oxide ions in ZnO with N and F, one would ultimately obtain Zn_{2}NF whose conduction and valence band edges are more favorable for water splitting.^{26} When two C atoms in graphene were transmutated with one B atom and one N atom, h-BN with wide band gap and new functionalities will be obtained.^{27} Therefore Ti_{3}BN monolayer can be thought of as obtained by substituting the two C-atomic layers of Ti_{3}C_{2} monolayer with one nitrogen-atomic layer and one boron-atomic layer, respectively, in consideration of that nitrogen and boron are two nearest-neighbors of carbon in the periodic table and Ti_{3}BN is isoelectronic to Ti_{3}C_{2}.

The thermal stability of Ti_{3}BN monolayer was assessed by first-principles molecular dynamics (MD) calculations using the PAW pseudo-potential and PBE functional as implemented in VASP.^{34} For each temperature, a preheating for 1 ps was applied for the initial geometry structure. And the MD calculations were in NVT ensemble, lasting for 10 ps with a time step of 1.0 fs. To control the temperature, Nosé–Hoover method was applied.^{35}

The global minimum structure for Ti_{3}BN monolayer was searched by particle-swarm optimization (PSO) method within the evolution algorithm which was implemented in CALYPSO code.^{36–38} The population size was set as 30, and the number of generation was maintained at 25. Unit cells containing 5, 10, and 15 atoms were considered. The structure relaxations during the PSO searching were carried by using PBE functional as implemented in VASP.

To elucidate the chemical bonding and stabilization mechanism of Ti_{3}BN monolayer, the deformation electronic density^{39} has been calculated. As shown in Fig. 1(b), there is remarkable electron transfer from Ti atoms to N atoms and from Ti atoms to B atoms, indicating the electronically stabilization in the Ti_{3}BN monolayer. Bader charge analysis shows that the net charges on N and B atom are −1.65 e and −1.57 e and those on Ti_{1}, Ti_{2}, and Ti_{3} atom are 0.97 e, 1.34 e and 0.91 e, respectively. The electron localization function^{39} of Ti_{3}BN monolayer is also calculated to highlight the electron distribution. As seen from the isosurfaces of electron localization functions presented in Fig. S1,† the electrons are complete delocalized around the Ti atoms, and widely distributed in the N and B frameworks, which also suggests the electron transfer from Ti atoms to N and B atoms.

Although Ti_{3}BN monolayer possesses similar structure properties with Ti_{3}C_{2} monolayer, the question whether Ti_{3}BN monolayer is as stable as Ti_{3}C_{2} or not need to be answered. The cohesive energy of Ti_{3}BN monolayer is a useful argument for evaluating its stability, defined as E_{coh} = (xE_{Ti} + yE_{N} + zE_{B} − E_{Ti3BN})/(x + y + z), where E_{Ti}, E_{N}, E_{B} and E_{Ti3BN} are the total energies of a single Ti atom, a single N atom, a single B atom and Ti_{3}BN monolayer, x, y and z are the number of Ti, N, and B atoms in the supercell, respectively. Based on our DFT calculations, the cohesive energy of Ti_{3}BN monolayer is 7.46 eV per atom, which is a little smaller than that of graphene (7.95 eV per atom)^{40} and higher than that of Ti_{3}C_{2} (about 7.00 eV).^{13} The relatively large cohesive energy of Ti_{3}BN monolayer indicates that Ti_{3}BN monolayer is a stable phase with strong chemical bonds. What's more, the small cohesive energy difference between Ti_{3}BN monolayer and Ti_{3}BN bulk (7.46 eV per atom vs. 7.82 eV per atom) means that it’s favorable to obtain Ti_{3}BN monolayer from its bulk phase. The elastic constants of Ti_{3}BN monolayer were then calculated to be C_{11} = C_{22} = 202.11 N m^{−1}, C_{12} = C_{21} = 59.24 N m^{−1}, which satisfy the mechanical stability criteria, indicating that the Ti_{3}BN monolayer is also mechanically stable.

The kinetic stability of Ti_{3}BN monolayer has been further confirmed by its phonon dispersion along the high-symmetry directions in the first Brillouin zone. As shown in Fig. 2(a), there is no appreciable imaginary frequency in the phonon dispersion curves, implying the good kinetic stability of Ti_{3}BN monolayer. The highest frequency of Ti_{3}BN monolayer is 653.60 cm^{−1}, higher than that of the widely studied MoS_{2} monolayer (473 cm^{−1})^{40} and silicene (580 cm^{−1}).^{40} The high frequency suggests that the related bonds in Ti_{3}BN monolayer are strong.

Fig. 2 Phonon dispersion curves of (a) bare Ti_{3}BN monolayer; (b) Ti_{3}BN(OH)_{2}-IV monolayer; (c) Ti_{3}BNF_{2}-I monolayer. |

Finally, the thermal stability of Ti_{3}BN monolayer was investigated by first-principles molecular dynamics (MD) calculations. A 5 × 5 supercell containing 125 atoms was used here and three individual MD calculations for Ti_{3}BN monolayer at temperatures of 500 K, 800 K, and 1000 K were performed. Fig. 3 presents the snapshots of Ti_{3}BN monolayer at the end of 10 ps MD calculations. These snapshots show that Ti_{3}BN monolayer can maintain its structural integrity throughout a 10 ps dynamical calculation up to 800 K, however will be disrupted at the temperature of 1000 K. Those results reveal that the Ti_{3}BN monolayer has good thermal stability and the melting point of Ti_{3}BN monolayer is between 800 K and 1000 K.

As shown in Fig. 4, in which the relative energy per atom is presented, the global minimum structure is Ti_{3}BN-I, which is just the above discussed Ti_{3}BN monolayer. Interestingly, Ti_{3}BN-II is also crystallized in the space group P3m1 (no. 156). The geometric construction, thickness, atomic layer distances of Ti_{3}BN-II is similar with that of Ti_{3}BN-I, while the biggest difference between them is the N-atomic layer just located above the B-atomic layer and the Ti_{1}-atomic layer above the Ti_{3}-atomic layer in Ti_{3}BN-II monolayer. The length of Ti_{1}–N, N–Ti_{2}, Ti_{2}–B, and B–Ti_{3} bond in Ti_{3}BN-II monolayer is 2.043 Å, 2.202 Å, 2.254 Å, and 2.116 Å, respectively. Considering structure Ti_{3}BN-III, it is 0.057 eV per atom higher in energy than Ti_{3}BN-I. This high energy might be due to the more nonbonding electrons of Ti_{1} atoms.

The structural stability of different Ti_{3}BN(OH)_{2} and Ti_{3}BNF_{2} configurations can be estimated by comparing their relative total energies. For Ti_{3}BN(OH)_{2}, configuration IV is energetically most favorable. Ti_{3}BN(OH)_{2}-IV is energetically lower than Ti_{3}BN(OH)_{2}-I, Ti_{3}BN(OH)_{2}-II and Ti _{3}BN(OH)_{2}-III by 0.047, 0.320, and 0.382 eV per unit cell, respectively. While for Ti_{3}BNF_{2}, configuration I is energetically most favorable, with its energy lower than that of Ti_{3}BNF_{2}-II, Ti_{3}BNF_{2}-III and Ti_{3}BNF_{2}-IV by 0.584, 0.507, and 0.054 eV per unit cell, respectively. Phonon dispersions of Ti_{3}BN(OH)_{2}-IV and Ti_{3}BNF_{2}-I has been further calculated to investigate their kinetic stability, as shown in Fig. 2(b) and (c). As expected, there are no imaginary frequencies in the phonon dispersion curves. The phonons at about 3654.56 cm^{−1} and 3620.86 cm^{−1} for Ti_{3}BN(OH)_{2}-IV should be dominated by the OH groups, and the phonons at about 744.73 cm^{−1} for Ti_{3}BNF_{2}-I should be due to the F groups. These high-frequency phonons indicate the strong bond nature of the related bonds (Ti–O and Ti–F).

In comparison with bare Ti_{3}BN, the OH or F-terminated Ti_{3}BN monolayer have smaller lattice constants. With terminal groups, the bond lengths of N–Ti_{2} and Ti_{2}–B shrink, while the bonds between the Ti_{1}–N and B–Ti_{3} are elongated except the Ti_{1}–N bonds of Ti_{3}BNF_{2}-I and Ti_{3}BNF_{2}-III. Those results imply that the surface groups strongly interact with the original Ti_{3}BN block, in accordance with the corresponding phonon dispersions. For clearance, the calculated lattice constants and bond lengths are presented in Table S1.†

Though the Ti_{3}BN monolayer is metallic, its hydroxylated or fluorinated derivatives may be narrow-gap semiconductors or metals, depending on the geometrical arrangements of surface F and OH groups. Seen from Fig. 7(a), for Ti_{3}BN with surface OH groups, the most favorable Ti_{3}BN(OH)_{2}-IV has a semiconducting character, with a direct band gap of 0.09 eV. Ti_{3}BN(OH)_{2}-II also shows the electronic properties of direct semiconductor, and the band gap is 0.16 eV. However, Ti_{3}BN(OH)_{2}-I and Ti_{3}BN(OH)_{2}-III is metallic. For Ti_{3}BN with F-termination (Fig. 7(b)), the most stable configuration of Ti_{3}BNF_{2}-I and the metastable configuration of Ti_{3}BNF_{2}-III are metals. On the contrary, the band structures of Ti_{3}BNF_{2}-II and Ti_{3}BNF_{2}-IV demonstrate their indirect semiconducting characters, with the band gap of 0.07 eV and 0.37 eV, respectively. Those theoretical results prove that the electronic structure of Ti_{3}BN monolayer can be modulated by varying the surface functional groups.

Fig. 7 Band structures of the hydroxylated and fluorinated Ti_{3}BN monolayer obtained from hybrid functional calculations: (a) Ti_{3}BN(OH)_{2}; (b) Ti_{3}BNF_{2}. |

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## Footnote |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7ra00483d |

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