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Applied Surface Science

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Two-dimensional tetragonal Ti2BN: A novel potential anode material for Li-ion batteries

Yi-Yuan Wua,b,c, Tao Boa,b, Xueliang Zhua,b, Zhiguang Wangd, Junwei Wue, Yuhong Lic,⁎,Bao-Tian Wanga,b,f,⁎

a Institute of High Energy Physics, Chinese Academy of Sciences (CAS), Beijing 100049, Chinab Spallation Neutron Source Science Center, Dongguan 523808, Chinac School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, Chinad Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, Chinae Shenzhen Key Laboratory of Advanced Materials, Department of Materials Science and Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, Chinaf Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China

A R T I C L E I N F O

Keywords:Ti2BN monolayerAnode materialsFirst principles

A B S T R A C T

In this work, we theoretically design a new class of two-dimensional (2D) ternary transition-metal compound,namely, tetragonal Ti2BN monolayer sheet. The first-principles calculations proved that this system exhibitsgood dynamic and thermal stability, inherent metal properties and good mechanical properties. Additionally, weinvestigate the suitability of 2D Ti2BN as host materials in Li-ion batteries (LIBs). Our results show that thediffusion barrier of Li on surface (24 meV) and interlayer (165 meV) of Ti2BN monolayer are extremely low. At300 K, their corresponding diffusion coefficient of Li are 6.08 × 10−3 and 0.028 × 10−3 cm s−1, respectively.Besides, it also exhibits extremely high theoretical capacity (889 mA h g−1) and low average open circuit voltage(0.24 V). All these advanced properties indicate that Ti2BN monolayer is a promising negative electrode materialfor LIBs. In order to facilitate the experimental synthesis of this material, we theoretically predicted that Ag(1 0 0), Au (1 0 0) and Sn (1 0 0) may be good growth substrates for Ti2BN sheet.

1. Introduction

New energy technologies are crucial to achieve sustainable energydevelopment in the future. Recyclable Li-ion batteries are becoming thenext generation of advanced energy storage devices due to their highsafety and specific capacity [1–3]. LIBs are mainly composed of positiveelectrode, negative electrode, electrolyte and diaphragm, among whichthe choice of anode materials will directly affects the energy density ofthe batteries [4,5]. Therefore, it is always a great challenge to developanode materials with better performance.

Graphite has occupied the main market of anode materials for LIBsdue to its low and stable lithium potential (0.01–0.2 V), high theoreticalspecific capacity (372 mAh/g), low cost and environmental friendliness[6,7]. However, in order to meet the increasing demands for high-power and high-energy-density, people have been looking for new andbetter anode materials. In recent years, using 2D materials present newopportunities in LIBs, because of the exceptionally high energy densityand charge-discharge efficiency [8]. Compared with bulk materials,novel 2D layered materials have large specific surface area and unique

electronic properties, which make it possible for rapid ion diffusion andhigh ion capacity [9,10]. Among them, several representative 2Dlayered materials have shown great potentials as anode materials forLIBs, such as: (i) transition metal oxide (TMO) [11,12]; (ii) transitionmetal carbides and nitrides (MXenes) [13,14]; (iii) transition metaldichalcogenides (TMD) [15,16]. Recently, two new types of 2D struc-tural materials, namely hexagonal transition metal borides [17,18] andtetragonal transition metal carbides and nitrides [19,20], have beenfound by the Crystal structure AnaLYsis by Particle Swarm Optimiza-tion (CALYPSO) technology [21,22]. The following first-principlescalculations proved that they have excellent lithium electrical proper-ties. Indeed, the search for optimal electrode materials is still in itsinfancy, and designing new anode materials is a challenging task.Combined structural prediction and theoretical research can provideguidance for finding high-quality anode materials. For example, Eret al. [23] theoretically demonstrated that Ti3C2 MXene has a highercapacity than graphite and is suitable as an anode material for LIBs.Later, Sun et al. [24] synthesized Ti3C2 by immersing Ti3AlC2 in 49%HF, and suggested that it is a promising anode material for Li+

https://doi.org/10.1016/j.apsusc.2020.145821Received 29 December 2019; Received in revised form 11 February 2020; Accepted 15 February 2020

⁎ Corresponding authors at: Institute of High Energy Physics, Chinese Academy of Sciences (CAS), Beijing 100049, China.E-mail addresses: liyuhong@lzu.edu.cn (Y. Li), wangbt@ihep.ac.cn (B.-T. Wang).

Applied Surface Science 513 (2020) 145821

Available online 17 February 20200169-4332/ © 2020 Elsevier B.V. All rights reserved.

T

intercalation. However, the advance theoretical researches can provideguidance for the experiments. In our previous study, we predicted anew class of 2D tetragonal vanadium carbide and nitride, and verifiedthat they were potential anode materials [19]. Based on this work, wetheoretically design a new class of 2D ternary transition-metal com-pounds with tetragonal structure, namely TM2BN (TM = Ti, Zr, V andNb), using the strategy of “atomic transmutation”. The phonon dis-persion relations illustrate that Ti2BN and Zr2BN have good lattice vi-brational stability.

Considering that 2D titanium compounds, such as Ti2B2 [18], Ti2C[25], Ti2N [26] Ti3C2 [23], Ti3BN [27] and Ti3CN [28] have showngreat application potentials in LIBs. Here, we choose the Ti2BN mono-layer as a representative and investigate its performance as negativematerials for LIBs. It’s shows that the Ti2BN monolayer is a promisingelectrode anode material for LIBs. This is especially meaningful andindicates that the 2D Ti2BN monolayer we designed provide un-precedented opportunity to develop new high-performance electrodematerials.

2. Computational methodology

In this work, all of our calculations were based on density functionaltheory (DFT) in conjunction with the projector augmented wave (PAW)potentials [29], as implemented in the Vienna ab initio simulationpackage (VASP) [30]. The exchange-correlation energy was describedby the generalized gradient approximation of Perdew–Burke–Ernzerhof(GGA-PBE) [31]. Through testing, we find that the difference betweenadsorption energy of Li on 2 × 2 and 3 × 3 super-cell is very small, sothe 2 × 2 cell was used to study the adsorption and diffusion of Liatoms on Ti2BN. The Brillouinzone (BZ) integration was performedusing 11 × 11 × 1 k-point grids. To avoid interlayer interactions, a15 Å vacuum was set along the z direction. The valence electrons in-cluded Ti: s1d3, B: 2s22p1, N: 2s22p3, and Li: 2s12p0. Carefully tested,the effect of spin-polarization effect on adsorption energy was negli-gible. Thus, we didn’t consider it. The spin-orbital coupling effects arenegligible for band structures [as seen in Fig. S1 in the electronicsupplementary information (ESI)], which are not considered in allcalculations. The energy cut-off was set to 550 eV. The criterion ofconvergence for total energy was set as 10−5 eV. The geometricstructures were relaxed until the forces on atoms were less than0.001 eV Å−1. k grids of 15 × 15 × 1 was employed in the BZ tocalculate the electronic density of states (DOS). Especially, the optB86b-vdW exchange functional [32] was employed, so as to better describethe van der Waals interactions of adsorption models.

PHONOPY package [33] basing on the density functional pertur-bation theory (DFPT) [34] was used to obtain the phonon dispersioncurve. ab initio molecular dynamics (AIMD) simulations [35] wereperformed using a 2 × 2 × 1 super-cell with the NVT ensemble. Theclimbing image nudged elastic band (CI-NEB) method [36,37] wasemployed to get the diffusion paths and diffusion energy barrier of Li onthe Ti2BN sheets. Number of NEB images between the fixed endpoints is7 and the force convergent criterion is set as 0.02 eV Å−1.

The cohesive energy of Ti2BN monolayer is defined as:

= − + + + +[ )E E xE yE zE x y z( ]/( )coh Ti BN Ti B N2 (1)

where ETi BN2 is the total energy of Ti2BN monolayer. ETi, EB and EN arethe total energies of a single Ti, B and N atom, respectively. ×, y and zrepresent the number of Ti, B, and N atoms in this monolayer, respec-tively.

The adsorption energy (Eab) of Li on the Ti2BN monolayer is ob-tained from:

= − −E E E nEab total Ti BN Li2 (2)

where n, Etotal, ELi and ETi BN2 are the number of Li atom absorbed, theenergy of Ti2BN after Li adsorption, the energy of a single Li atom (in

the bulk phase) and the energy of isolated Ti2BN, respectively.To quantify the stability of Ti2BN monolayer after adsorbing mul-

tilayer Li atoms, the average adsorption energy is calculated by thefollowing equation:

= − −−E E E mE m/ave ntotal n total( 1) Li (3)

where Entotal and E(n−1)total are the total energies of Ti2BN with n and(n − 1) adsorbed Li layers, respectively. m represents the number ofadsorbed Li atoms in each layer.

The charge density difference Δρ is defined as:

= − −ρ ρ ρ ρΔ total Ti BN Li2 (4)

where ρtotal, ρTi BN2 and ρLi are the total charges of the Li-adsorbedTi2BN system, the Ti2BN monolayer, and the Li atom, respectively.

The formation energy is calculated by:

= − − +( )E x E E xE x( ) /( 1)f Ti BNLi Ti BN Lix2 2 (5)

where ETi BNLix2 and ETi BN2 are the energies of the Ti2BNLix compoundand pristine Ti2BN monolayer, respectively.

For every concentration x of the Ti2BNLix compound, the opencircuit voltage (OCV) is evaluated by:

= − − − − − =V E E x x E x x( ( ) )/e( ) (M Li, Na)x x 1 2 M 1 22 1 (6)

where Ex1 and Ex2 are the total energies of the Ti2BNLix at two adjacentconcentration x1 and x2, both x1 and x2 are the stable concentration.

The theoretical capacity (CA) can be obtained from:

=C czF M/A Ti BN2 (7)

where c is the number of adsorbed Li atoms, z is the valence number ofLi, F is the Faraday constant (26801 mA h mol−1), and MTi BN2 is themolar weight of Ti2BN.

3. Results and discussion

3.1. Crystal structure and stability of Ti2BN

Using the strategy of “atomic transmutation”, we design a new 2DTi2BN monolayer, whose crystal structure shows in Fig. 1(a) and (b). Itis similar to the 2D tetragonal vanadium carbides and nitrides mono-layer proposed in our previous work [19]. Ti2BN belongs to the spacegroup of P4/nmm (No. 129) and each unit cell contains two Ti, one Band one N atoms. Different from Ti3BN monolayer [27], Ti, B and Natoms in Ti2BN are arranged in a tetragonal lattice, where B and Natoms are located in different atomic planes. The optimized latticeparameters are a = b = 3.02815 Å, and the length of TieB and TieNbonds are 2.16926 and 2.10874 Å (2.15113 and 2.14617 Å) along thevertical (horizontal) direction, respectively. Similar to the length ofTieB (2.117 and 2. 249 Å) and TieN (2.195 and 2. 054 Å) bonds inTi3BN monolayer. In order to effectively evaluate the stability ofstructure, we firstly consider the cohesive energy of Ti2BN [as definedby Eq. (1)]. Based on the DFT calculations, we obtain the cohesiveenergy of Ti2BN (−4.89714 eV per atom), which is smaller than that ofTi2B2 (−0.195 eV per atom) [18] and Ti2N (−0.370 eV per atom) [26].The relatively lower cohesive energy indicates that Ti2BN monolayerhave a more stable crystal structure.

To examine the dynamical stability, we calculate the phonon dis-persion curves of Ti2BN monolayer. As seen in Fig. 1(c), all vibrationalmodes are found to be positive in the first Brillouin zone along the high-symmetry directions (Γ-X-M-Γ). This means that Ti2BN monolayer aredynamically stable. Phonon spectra of other compounds, namelyTM2BN (TM= Zr, V and Nb), are shown in Fig. 2. All vibrational modesof Zr2BN monolayer are positive, but the phonon spectra of V2BN andNb2BN have virtual frequencies. This suggests that the V2BN and Nb2BNmonolayers may be unstable. To further confirming the mechanicalstability of Ti2BN monolayer, we assess the effect of lattice distortion onstructural stability. The elastic stiffness constants of Ti2BN are obtained

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by fitting the energy curves of the uniaxial and equal biaxial strains.The data fitting process is performed on the VASP calculation datathrough the VASPKIT code [38]. The 2D Young’s moduli (in-planestiffness) for strains in × and y directions are Yx = C11C22-C12

2/C22 andYy = C11C22-C12

2/C11 [39]. All results are summarized in Table 1. Theelastic constants of Ti2BN satisfy the criterion of C11C22 - C12

2 > 0 andC66 > 0 [40], indicating that Ti2BN is mechanical stability. Besides,we find that the 2D Young’s modulus of Ti2BN is larger than that of SiCand GeC [41]. All the discussions indicate that Ti2BN monolayer isstable enough to form a free-standing membrane.

Next, to examine the stability of Ti2BN monolayer at room tem-perature (300 K). We perform AIMD [35] simulation at 300 K with atime step of 1 fs. As shown in Fig. 1(d), the free energy of this systemremaining almost invariant during the simulation time. Besides, thecrystal structure of Ti2BN monolayer keep well after heated for 10 ps.We further increase the temperature up to 1200 K [as show inFig. 1(e)], and find that the structure can maintain stable free energyand survive. Fig. 1(f) shows the radius distribution function (RDF) ofTi2BN at 300 K. All the Ti-Ti, Ti-N, Ti-B, N-N, N-B and B-B RDF of Ti2BNhave two sharp peaks between 1 and 5 Å, which are consistent withtheir corresponding bond lengths. Each peak is broadened due to thevibration of the particles around the lattice points. These relativelyindependent RDF spikes indicate the long-range order of this structureafter annealing. In summary, Ti2BN has high-temperature thermal sta-bility, which provides a guarantee for its application to anode materialfor LIBs.

3.2. Electronic properties of Ti2BN monolayer

As an ideal anode material for LIBs, it needs to have good electronicconductivity. In order to study the conductivity of Ti2BN monolayer, wecalculate its electronic band structures, total density of states (TDOS)and orbital resolved partial density of states (PDOS). As illustrated inFig. 3(a), there are multiple bands that pass through the Fermi level,and these bands are contributed by Ti-d orbitals. The PDOS analysisalso shows that the high density of states near the Fermi level aremainly contributed by the Ti-d states, whereas the B-p and N-p stateshave only a small contribution. The high density of states means thatthere are many available carriers contribute to the high electric con-ductivity of the Ti2BN monolayer. Furthermore, considering that theelectrode materials need to keep metallic after lithiation. Thus, wecalculate the TDOS and PDOS of the Ti2BN monolayer adsorbed withone layer of Li atoms. As shown in Fig. 3(b), the TDOS clearly suggestthat the Ti2BN monolayer maintain metallic character after lithiation.

Fig. 1. (a) Side and (b) top views of the optimized structure of monolayer Ti2BN; (c) Phonon dispersion curves of Ti2BN; The variation of free energy with time inAIMD simulations at (d) 300 K and (e) 1200 K; (f) The radius distribution function (RDF) of Ti2BN at 300 K.

Fig. 2. Phonon dispersion curves of (a) Zr2BN, (b) V2BN and (c) Nb2BN.

Table 1Calculated elastic stiffness constants Cij (GPa·nm) and Youngs’s Modulus Y(GPa·nm) of Ti2BN along the x and y directions. The results of the materials (SiCand GeC) used for comparison are from Ref. [42].

C11 C22 C12 C66 Yx Yy

Ti2BN 227.92 227.92 79.22 25.70 200.40 200.40SiC42 179.70 179.70 53.90 62.90 163.50 163.50GeC42 154.70 154.70 47.50 53.60 140.10 140.10

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The PDOS analysis shows that the metallic feature is mainly contributedby Ti-d orbits, but the contribution from the B-p, N-p and Li-p orbitals islimited.

The electron localization function (ELF) of Ti2BN is shown inFig. 3(c) and (d). It can be used to analyze the classification and sta-bility mechanism of chemical bonds. It is not difficult to find that thered region is mainly distributed around B and N atoms with ELF valuesclose to 0.80 and 0.83, respectively. However, the region around Tiatoms is blue with ELF values close to 0, indicating that the electronshere may be highly delocalized (or may not have electron distribution).Here ELF values correctly reflect the ionic bond properties of TieB andTieN. Besides, the corresponding value of the green area on the ELFdiagram is about 0.5, which indicates that the electrons in this regionare in a uniform electron gas state. This is consistent with the goodelectronic conductivity of Ti2BN.

3.3. Storage and transportation of Li on Ti2BN monolayer

The working process of LIB includes intercalation-deintercalation ofLi ions between the electrodes. During the charging and dischargingprocess, the LIB stores and delivers direct current (DC) respectively.Therefore, it is important to comprehensively study the storage andtransmission behaviors of Li atoms on Ti2BN monolayer. We first in-vestigate the adsorption behaviors of a single Li atom on the surface ofTi2BN. Three high symmetry sites are considered on the upper (B-layer)and lower (N-layer) sides of Ti2BN, respectively. The correspondingsites are shown in Fig. 4(a) and (b). As shown in Fig. 4(c), we calculatethe adsorption energies of Li atom on these sites [as defined by Eq. (2)].On the B-layer of Ti2BN, the S1 site (above the middle-point of B and Tion the surface) has the lowest adsorption energy (−0.767 eV). But onthe N-layer, the lowest adsorption energy on the S5 site (on the top ofN). The adsorption energies on S4 (0.6127 eV), S5 (0.406 eV) and S6(1.072 eV) are positive, which indicates the Li atom is not possible toappear on these sites. In addition, we test the effect of optB86b-vdW,optB88-vdW, DFT-D2 and D3 correction on the adsorption energy of Li,

and compared them with the results of PBE (see Fig. S2 in ESI). We findthat the difference between their values is small and both are smallerthan the results of PBE. Besides, their trends are consistent, whichmeans that judgment of Li adsorption behavior will not be affected.Then, we study the adsorption behaviors of Li with higher concentra-tion. As can be seen in Fig. 4(d), as the concentration of Li (x) increases,the average adsorption energy increases (From −0.426 to −0.106 eV/atom). But their values remain negative at all times. This indicates thatthe adsorption configurations of Li atoms are still stable at high con-centration.

To further understand the adsorption behavior of Li on the surfaceof Ti2BN, we calculate the difference charge density (as summarized inFig. 5). On the N-layer (B-layer), the electrons tend to accumulate be-tween Li and its neighbor N (B) atoms, forming the LieN (LieB)bonding. Those chemical bonding between Li atoms and Ti2BN help toprevent the forming of Li cluster. Thereby preventing the formation of“dead lithium” in the actual application process, improving the safetyand availability of LIBs. Furthermore, to study the interaction me-chanism of Li and B/N atoms, we calculate the p-projected DOS of B[seen Fig. 6(a)] and N [seen Fig. 6(c)] atoms on the Ti2BN, and the p-projected DOS of Li, B [seen Fig. 6(b)] and N [seen Fig. 6(d)] atoms onthe adsorption configurations of S2 and S5, respectively. The con-tribution of the B (N) atom in S2 (S5) increases around−2.5 (−4.5) eV,which coincides with the p orbital of a Li atom. This indicate that theremay be some hybridization between the B (N) and Li atom in the S2(S5). This also shows that the LieN (LieB) bond may be formed.

Generally, a high charging/discharging rate is extremely necessaryperformance of LIBs. Therefore, a low Li diffusion barrier is highlydesirable. It is necessary to investigate the behavior of Li hopping be-tween the various possible sites of Ti2BN monolayer. In order to un-derstand the migration behavior of Li more comprehensively, we con-sider the diffusion of Li atoms on Ti2BN surface and between layers.Five diffusion pathways are considered according to symmetry. Path-1:S1-S2-S1; Path-2: S1-S1; Path-3: S5-S6-S5; Path-4: S5-S5; Path-5: S1-S3-S1 (S4-S5-S4). These diffusion paths and corresponding diffusion

Fig. 3. (a) Orbital-resolved band structure and DOS with the contributions of Ti-d, B-p and N-p orbits for the Ti2BN monolayer. The Fermi energy is set to 0 eV. (b)DOS of the Ti2BN monolayer adsorbed with one layer of Li atoms. The corresponding electron localization function (ELF) maps of (c) B-layer and (d) N-layer viewedfrom the horizontal and vertical directions. The values of ELF lie by definition between zero (blue) and one (red). (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)

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barriers are shown in Fig. 7. Their diffusion paths have short lengthsbetween 2.5 and 5.1 Å. The corresponding diffusion energy barriers are32.2 (Path-1), 32.0 (Path-2), 67.1 (Path-3), 24.0 (Path-4) and 165.0(Path-5) meV, respectively. The diffusion energy barriers of Ti2BN are

much lower than some well-established anode materials, such as gra-phite (400 meV) [6], Ti3C2 (68 meV) [23] and graphene (277 meV)[41]. In particularly, when Li atom diffuses between two layers ofTi2BN monolayer, the diffusion barrier is only 165.0 meV. Such lowenergy barrier indicates that the 2D Ti2BN possesses high rate cap-ability for Li diffusion, which provides a necessary condition for prac-tical application. In addition, we estimate the diffusion coefficient of Liatoms through the equation as D ≈ d2ν0exp(−Ea/kBT), where d is thehoping distance; ν0 is the vibration frequency which approximates to1013 s−1

; Ea is the diffusion barrier; kB is Boltzmann constant; T = 300 Kis temperature (From Wert-Zener 's theory [42]). This formula is widelyused to calculate the diffusion coefficient of Li atoms [6,43-45]. Allcalculations are summarized in Table 2. It is found that the extremelylow diffusion barrier of path-4 resulting the highest diffusion coefficientwith 6.08 × 10−3 cm s−1.

3.4. Average open circuit voltage and theoretical specific capacity

As the core component of LIBs, the anode material usually needs tomeet the following conditions in application: (i) embedded lithiumpotential is low and stable, to ensure higher output voltage; (ii) higherspecific capacity. In order to get all the stable intermediate states in thelithium process, we calculated their formation energies (Ef) by formula(5). The tendency of Ef along with increasing the concentrations of Liatoms are show in Fig. 8(a). Here, the red solid lines connect the lowestforming energies and form convex hulls. The structures located on thered convex hulls represent the thermodynamically stable states whilethe structures on the black hollow square are the metastable states. Wecan see that the compounds of Ti2BNLix (x = 0.25, 0.5, 1.0, 2.0, and 4)lie on the red convex hull. This indicates that Ti2BNLi0.25, Ti2BNLi0.5,Ti2BNLi1.0, Ti2BNLi2.0, and Ti2BNLi4.0 are stable intermediate phases.All adsorption configurations are presented in Fig. S3 in ESI. We can seethat during the process of lithiation the structure of the Ti2BN mono-layer doesn't change at all. In order to further verify the stability ofTi2BN in the lithium process at high temperature, We chose the

Fig.4. (a) Upper- (B-layer) and (b) lower-views (N-layer) of Ti2BN with three high-symmetry sites, respectively. S1 site: abovethe middle-point of B and Ti on the surface;S2 site: on the top of B; S3 site: on top of Ti;S4 site: above the middle-point of N and Tion the surface; S5 site: on the top of N; S6site: on the top of Ti; (c) Correspondingadsorption energies of those sites; (d)Average absorption energies of Ti2BNLix,where x represents the concentration of Liatoms.

Fig. 5. Top- and side-views of the difference charge density for Li-combinationon the different absorption sites of Ti2BN monolayer. The yellow and blue areasdenote electron gains and loses. (For interpretation of the references to colourin this figure legend, the reader is referred to the web version of this article.)

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saturated film (Ti2BNLi2) to perform AIMD simulation at 300 and1000 K. Analyzing the final trajectory of the AIMD simulation (asshown in Fig. S4 ESI) can well confirm that the Ti2BN monolayer is wellmaintained, and adsorption of Li adatoms will not cause structural

damage.The open circuit voltage (OVC) of the Ti2BN for the LIBs are cal-

culated by formula (6). [As shown in Fig. 8(b)]. There are five mainplateaus: Ti2BN → Ti2BNLi0.25, Ti2BNLi0.25 → Ti2BNLi0.5, Ti2BNLi0.5 →

Fig. 6. Comparison of the partial density of states (PDOS) of B and N atom inTi2BN and the adsorption configurations of S2 and S5, respectively.

Fig. 7. Energy profiles of lithium diffusion along (a) Path-1, (b) Path-2, (c) Path-3, (d) Path-4 and (e) path-5 for Ti2BN. The corresponding top view of the Li diffusionpathway on the Ti2BN monolayer is inserted below.

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Ti2BNLi1.0, Ti2BNLi1.0 → Ti2BNLi2.0 and Ti2BNLi2.0 → Ti2BNLi4.0. TheOCV for these five plateaus are 0.76, 0.53, 0.43, 0.35, and 0.24 V, re-spectively, which definitely meet a generally accepted standard(0.1–1.0 V) [46]. The average OCV of the Ti2BN for the LIBs is 0.24 V.Such low-discharge platform enables the Ti2BN monolayer to be co-operate with a cathode material to form a secondary battery with a highdischarge voltage. In addition, we obtain the theoretical Li capacity ofTi2BN by formula (7). To evaluate the superiority of the Ti2BN mono-layer we studied as anode material for LIBs, we compare their theore-tical specific capacity, diffusion barrier and average OCV with otherpotential anode materials. As summarized in Table 3, the theoreticalcapacity of Ti2BN is 889 mA h g−1, which are superior to other anodematerials such as graphite (372 mA h g−1) [6], Ti3C2 (448 mA h g−1)[23] and VS2 (466 mA h g−1) [47]. Although its capacity is smaller thanthat of silicene (954 mA h g−1) [48] and borophene (2040/1984 mA h g−1) [49,50], it has smaller diffusion barrier and averageopen-circuit voltage, which is also important for anode materials. Insummary, all calculations show that 2D Ti2BN monolayer has good li-thium battery performance.

3.5. Growth substrate

Experimental growth of crystals is usually done by chemical vapordeposition (CVD) method, which often requires finding a suitablesubstrate. For example, Geng et al. selected graphene as substrate togrow 2D Mo2C [51]. In this work, we choose the widely used substratessuch as Ag(1 0 0), Au(1 0 0), Sn(1 0 0), and InAS(1 0 0) as examples ofgrowing the 2D Ti2BN sheet. Their lattice mismatch (δ) is defined by[(LTi BN2 − Lsub)/LTi BN2 ] × 100%, where LTi BN2 and Lsub are the latticeconstant of Ti2BN and substrates, respectively. The adsorption energy(Ead) is defined by (Etotal − ETi BN2 − Esub)/n, where Etotal, ETi BN2 andEsub are the total ground state energy of the 2D Ti2BN adsorbed on thesubstrates, 2D Ti2BN and substrates, respectively. The geometricalconfiguration of the Ti2BN with substrates are summarized in Fig. 9,and the corresponding δ and Ead are listed in below. δ and Ead are thekey parameters used to evaluate the suitability of the substrates. Ex-perimentally, a smaller lattice difference is beneficial to crystal growth,and a more negative adsorption energy indicates that the structure ismore likely to form. It is generally believed that the δ less than 5% isreliable. Besides, the adsorption energies of Ti2BN on four considered

substrates are negative, indicating that such adsorption configurationsare stable. After comprehensive consideration of lattice mismatch andadsorption energy, it should be desirable to grow Ti2BN sheet on Ag(1 0 0), Au (1 0 0) and Sn (1 0 0).

4. Conclusions

In summary, we design a new class of 2D tetragonal structure of

Table 2Hoping distance (d), Diffusion barrier (Ea) and diffusion coefficient (D) of Liatoms in the Ti2BN structure.

Path d (Å) Ea (meV) D (cm s−1)

Path-1 3.06 32.2 2.69 × 10−3

Path-2 2.39 32.0 1.66 × 10−3

Path-3 5.08 67.1 1.92 × 10−3

Path-4 3.92 24.0 6.08 × 10−3

Path-5 4.08 165.0 0.028 × 10−3

Fig. 8. Calculated (a) formation energy and (b) open circuit voltage (OCV) profile as a function of Li concentration in the Ti2BN monolayer.

Table 3Theoretical specific capacity (mA h g−1), diffusion barrier (meV), and averageOCV of anode materials for the LIBs.

Specific capacity Diffusion barrier OCV

Materials Theo. Theo. Theo. Refs.

Ti2BN 889 24 0.24 This work.graphite 372 400 0.23 [6]Ti3C2 448 68 0.46 [23]VS2 466 22 0.93 [43]Silicene 954 60 – [44]Borophene1 2040 69 ~1.0 [6]Borophene2 1984 66 1.09 [45]

Fig. 9. Side views of Ti2BN on (a) Ag(1 0 0), (b) Au(1 0 0), (c) Sn(1 0 0) and (d)InAs(1 0 0), respectively. The corresponding lattice mismatch (δ) and adsorp-tion energy (Ead) are given in below.

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TM2BN (TM= Ti, Zr, V and Nb). Their phonon spectra show that Ti2BNand Zr2BN monolayer exhibit dynamically stable, but V2BN and Nb2BNhave virtual frequency. We choose Ti2BN as example and investigate itslithium battery properties. Further first-principle calculations showedthat Ti2BN has low diffusion barrier (24 meV), high diffusion coefficient(6.08 × 10−3 cm s−1) and theoretical capacity (889 mA h g−1), whichare conducive to being next-generation LIB anode material. In addition,we encourage experimental research on the tetragonal phase of Ti2BNand provide some theoretical data for experimental synthesis. We be-lieve that our designed TM2BN materials will provide a major referencefor finding new 2D anode materials.

CRediT authorship contribution statement

Yi-Yuan Wu: Conceptualization, Methodology, Software,Investigation, Writing - original draft. Tao Bo: Validation, Formalanalysis, Visualization, Software. Xueliang Zhu: Validation, Formalanalysis, Visualization. Zhiguang Wang: Resources, Writing - review &editing, Supervision, Data curation. Junwei Wu: Resources, Writing -review & editing, Supervision, Data curation. Yuhong Li: Writing -review & editing. Bao-Tian Wang: Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financialinterests or personal relationships that could have appeared to influ-ence the work reported in this paper.

Acknowledgements

This research was supported by the National Natural ScienceFoundation of China (Grant No.11504312, 11775102), National BasicResearch Program of China (No. 2015CB921103), China PostdoctoralScience Foundation (Grants No.2018M641477), Guangdong ProvincialDepartment of Science and Technology, China (No.2018A0303100013), National Natural Science Foundation of China(No. 11805088) and Supported by the Fundamental Research Funds forthe Central Universities (Lanzhou University, No. lzujbky-2018-19).The calculations were performed at Supercomputer Centre in ChinaSpallation Neutron Source.

Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.apsusc.2020.145821.

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