Improved Transport Properties and Novel Li Diffusion Dynamics in van

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C: Energy Conversion and Storage; Energy and Charge Transport

Improved Transport Properties and Novel Li Diffusion Dynamics in van der Waals CN/Graphene Heterostructure as Anode Materials for Lithium Ion Battery: A First Principles Investigation 2

Yingchun Ding, Bing Xiao, Jiling Li, Qijiu Deng, Yunhua Xu, Haifeng Wang, and Dewei Rao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11044 • Publication Date (Web): 16 Jan 2019 Downloaded from http://pubs.acs.org on January 16, 2019

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The Journal of Physical Chemistry

Improved Transport Properties and Novel Li Diffusion Dynamics in van der Waals C2N/graphene Heterostructure as Anode Materials for Lithium Ion Battery: A First Principles Investigation Yingchun Ding,ac Bing Xiao,*b Jiling Li,c Qijiu Deng,c Yunhua Xu,c Haifeng Wangd and Dewei Rao*e

aCollege

of Optoelectronics Technology, Chengdu University of Information Technology, Chengdu, 610225, China bState Key Laboratory of Electrical Insulation and Power Equipment & School of Electrical Engineering, Xi’an Jiaotong University, Xi’an , 710049, P.R. China Email: [email protected] cSchool of Materials Science and Engineering, Xi'an University of Technology, Xi’an 710048, China dDepartment of Physics, College of Science, Shihezi University, Xinjiang, 832003, China eSchool of Materials Science and Engineering, Jiangsu University, Zhenjiang 212013, P. R. China. E-mail: [email protected] ABSTRACT: In this paper, we report a theoretical investigation of the electronic structures, electron/phonon transport properties and electrochemical parameters of C2N/graphene bilayer. The p-type C2N/graphene bilayer, with direct band gap of 0.2 eV at Γ-point, exhibits the promising electric conductivity similar to that of graphene monolayer. In addition, it also shows excellent lattice thermal conductivity of 1791.1 W/m·K, compared to 82.22 W/m·K of C2N monolayer. The theoretical capacity of C2N/graphene in Li-ion battery is found to be 490.0 mAh/g. For Li diffusion, the energy barriers for the energetically favourable diffusion pathways are found to be in the range of 0.2 eV ~ 0.5 eV for both C2N monolayer and C2N/graphene bilayer. The planar diffusion coefficients of Li atom on C2N and C2N/graphene materials are predicted as 2.97 × 10-11 m2/s and 4.74 × 10-11 m2/s at 300 K, comparable to that of graphene monolayer. With the help of FPMD simulations at low temperature, it has been revealed that the Li atoms either absorbed or intercalated in C2N/graphene hetero-structure, which could migrate easily in the vertical direction through the large hole of C2N atomic layer, and these ascended Li atoms together with absorbed Li atoms on the upper surface of C2N monolayer are able to hopping further away from the substrate, giving the strongly absorbed inner Li layer and weakly attached outer Li layer on the top of C2N atomic layer. The outer Li atoms are mainly responsible for the ionic diffusion at room temperature. The hopping process between the nearest adsorption sites, which is obtained from routine NEB calculations, is only seen in FPMD simulations at high temperature (> 800 K).

1. INTRODUCTION

Graphene, an unique two-dimensional atom-thick honeycomb carbon material, has been regarded as the promising anode candidate6 owing to its high mechanical strength, excellent thermal conductivity (3500 W/m·K), high surface area (2630 m2/g) and ultra-high electronic mobility (10000 cm2/V·s).7-11 All those unique properties should enhance the performance of graphene as the anode material, leading to high energy density and rate capability. Previous theoretical work found that graphene possesses a maximum capacity of 740 mAh/g on the basis of double-layer adsorption configuration.6 However, further study reported that pristine graphene has lower capacity than graphite.12 It has been explained that the repulsion forces between Li+ ions at both sides of the graphene decreased the Li

The utilization of renewable energies such as wind and solar powers has been attracting tremendous attentions in the last decade. And high energy density batteries are indispensable for the development of these intermittent energies. Besides, the demands of rechargeable batteries have been greatly expanded with the increasing of various portable devices and large-scale energy storage industries.1-3 Unfortunately, graphite, the most widely used anode material of lithium-ion battery (LIB), cannot satisfy all these demands due to its low theoretical capacity (372 mAh/g) and poor rate capability.4,5 Consequently, it is essential to develop new electrode materials with high energy density.

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adsorption ability.12,13 Although few layered graphene could slightly improve its performance as anode material, the experimental capacity is still far below the theoretical values.6, 14 Very recently years, single layer (2D) transition metal dichalcogenides or Mxenes 15-17 and several new 2D-carbon nitrides (C3N4, C2N and C3N et.al) have been explored for their potential application in rechargeable LIBs.18-22 Noticeably, C2N monolayer was also investigated for other interesting applications, for example high-performance FETs and metal-free photocatalytic materials for water splitting 23 and catalyst 24-27. Nevertheless, the limited rate capability and short cycling stability have seriously impeded their application. Moreover, the re-stacking and agglomeration of these 2D-materials during cycling process could also heavily deteriorate the overall performance of anode. Finally, the electronic states of many 2D carbon nitrides at Fermi level mainly consists of the long-pair orbital of N atoms, leading to the very large effective masses for hole or electron and the low electric conductivity. As a result, various bilayer or heterostructures have been proposed to improve the electrochemical properties. It has been demonstrated that the formation of the van der Waals bilayer or heterostructure could tune materials properties deliberately, including transport properties (electrical and thermal conductivities), adsorption capacities for small molecules or atoms, and the diffusion dynamics of the absorbed ions. Improving those properties are considered to be essential for developing the advanced anode materials for LIBs. For example, Natalya and Peng et al. found that VS2/graphene and black phosphorene/TiC2 heterostructures have high Li adsorption capacities, and which could be used as the promising anode material for Li-ion batteries.28,29 The lithium ion batteries can release a lot of heat during charging/discharging cycle. Due to the very low thermal conductivity of carbon black (< 1 W/m·K),30 which is one of the main materials used to produce the battery, the accumulation of the heat in the interior of the cell could deteriorate the quality and the performance of the battery or in the worst case which may cause the catastrophic failure of the device (for example the explosion of Samsung Galaxy Note7). Currently, the dispersion of heat in the commercial LIBs is achieved with the help of the complex structural design of the battery. However, improving the thermal conductivity of electrodes has been considered as a novel and effective strategy to manage the heat dissipation of LIBs.31-34 Previous works also showed that graphene-based heterostructures could possess high electric and thermal conductivities, which are highly desired for anode materials used in lithium ion battery.23,28-29,35-50 In this paper, we designed a new heterostructure that consists of graphene and C2N (C2N/G) monolayers. It is found that this heterostructure shows the improved transport properties (thermal and electric conductivities), compared to those of intrinsic C2N 2D material. Additionally, the C2N/graphene bilayer exhibits the better adsorption ability for Li atoms than that of graphene monolayer. From the CI-NEB calculations in combination with first principles molecular dynamics simulations, it has been revealed that the C2N/graphene bilayer also has the desired Li ion diffusion dynamics at room

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temperature. Our findings in present work could helpful to deeply understand the adsorption energetics and diffusion process of Li atom in graphene-based heterostructures, and which can also provide more guidance for the rational designing of highperformance electrode materials for rechargeable LIBs.

2. COMPUTATIONAL DETAIL

METHOD

AND

2.1 First-principles calculations All first principles calculations were carried out using Vienna ab initio simulation package (VASP) software based on density functional theory (DFT), employing the projector augmented plane wave (PAW) basis and periodic boundary conditions (PBCs). We used 500 eV for kinetic energy cut-off value for plane wave expansion in reciprocal space. For the numerical integration of total energy in the Brillouin zone, the Gamma-centred k-mesh of 5×5×1 was used in all calculations. The exchange-correlation energy was calculated by PerdewBurke-Ernzerhof (PBE) density functional.51 PBE is known to predict the reliable energetic parameters such as formation enthalpy and binding energy.52 Nevertheless, the van der Waals interactions are not properly described by the semilocal density functionals like PBE or LDA. Those weak interactions are considered to be important both for structural properties and energetics of layered structures and the absorbent on the surface. In our calculations, the van der Waals interactions were calculated using the pair-wise like potentials in terms of PBE+D2 scheme, as proposed by Grimme and co-workers.53 We performed both spin polarized and spin non-polarized calculations for the adsorption energies of Li atoms at the different adsorption sites on C2N monolayer, it was found that the spin polarization has no significant effect on the obtained values (See Supporting Materials Table S1). Therefore, the spin non-polarized method was employed throughout this work. The spin-orbital coupling (SOC) effects are negligible for light elements (Li, C and N), and which were not considered in all calculations. Using the current computational parameters, the total energy was converged to 10-6 eV. The Hellmann-Feymann force acting on the atom was reduced to 0.001 eV/Å. For all supercell models, the vacuum layer employed to separate the periodic images in the z direction was 20 Å. 2.2 Lattice thermal and electrical conductivity The lattice thermal conductivity is calculated by ShengBTE code with the IFCs includes harmonic (second order) and anharmonic (third-order) IFCs. In this paper, the third-order IFCs were extracted from second order IFCs using a real-space finite difference method as implemented in ShengBTE code.54 The harmonic IFCs were investigated using the Phonopy code.55 The k-grids tested were 20×20×1 in ShengBTE code. Increasing the k-mesh further would change the calculated lattice thermal conductivity by less than %1. Therefore, the well-converged 20×20×1 q-meshes are used for the C2N and graphene. And the electrical conductivity ws calculated using BoltzTrap code based

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on a semi-classic Boltzmann transport theory.56 The electrical transport parameters were calculated based on the eigenvalues from PBE functional. Although, the reliable fundamental band gap might be obtained from other more accurate methods such as HSE06 and GW, it is not mandatory in our case. The correct band gap is required for calculating the optical conductivity which is originated from the direct or indirect electronic transitions between valence and conduction bands. However, the electric conductivity of the p-type insulator or semiconductor under the external electric field is solely determined by the electronic states very near the Fermi level. Many previous works have shown that the curvature of the band dispersions at the top of valence band or at the bottom of conduction band could be described accurately by the semilocal functional.57-59 Therefore, for computing the electrical conductivity of graphene, C2N and C2N/graphene systems, the PBE functional was used to predict the band dispersions, and no post-correction to the band gap was applied to all structures. To accurately predict the transport parameters, much denser k-mesh (20×20×1) was used for the integrations in 1st BZ.

Here, the factor

refers to the two equivalent diffusion

𝑬𝒂𝟏

𝐥𝐧 𝑫(𝑻) = 𝐥𝐧 𝑫𝟎 ― 𝒌 𝑻 (3) 𝑩 In eq 3, the D0 represents the prefactor in the original exponential form of Arrhenius expression, and the Boltzmann constant is given by kB. Meanwhile, the parameter Ea might be denoted as the apparent activation energy of the diffusion, and which could be obtained from first principles method as Ea = Evib + kBT + Eb, where Evib is the change of the phonon vibrational energy and Eb is known as the diffusion barrier height.63 We should note that the magnitude of either Evib or kBT term is significantly smaller than that of Eb. Thus, one can see that Ea ≈ Eb. In this paper, Ea is simply treated as the fitting parameters. Once the fitting parameters such as D0 and Ea are determined, the diffusion coefficient can be extrapolated to room temperature using the eq 3. 2.5 Open circuit voltage and theoretical capacity The lithiumation reaction between Li metal and C2N/G hetero-junction can be expressed as eq 4.

𝑪𝟐𝑵/𝑮 + 𝒏𝑳𝒊 + +𝒏𝒆 ― = 𝑪𝟐𝑵/𝑮–𝑳𝒊𝒏

(4) The Gibbs free energy change for the above reaction is written as eq 5.

2.4 Planar diffusion coefficient We performed first principles molecular dynamics (FPMD) simulations for the large supercells of Li-C2N structure (Li40(C2N)24) and Li-C2N/G heterojunction (Li48(C2N)24C96) between 400 K and 1200 K with an increment of 200 K to evaluate the planar diffusion coefficient of Li atoms. For the FPMD simulations, the NVT ensemble was employed and the standard Nosé-Hoover thermostat was used.61-62 The total duration of the FPMD run was 15 ps with the time step 1.0 fs at each temperature. The vacancies were introduced intentionally in the supercells for initiating the diffusion process of Li in the C2N/G hetero-junction and C2N monolayer. From the obtained trajectory of the FPMD simulation, the mean square displacement (MSD) was calculated by Eq. (1) for Li atoms.

∆G = ∆U - P∆V - T∆S (5) Here, the second and third terms on the right hand side of eq 5 are considerably small even at finite temperature, compared to that of the first term. Since we evaluated the reaction Gibbs free energy at 0 K in this work, it is simply calculated as the total energy difference between the product and reactants, as shown in eq 6.

𝜟𝑮(𝟎𝑲) = 𝑬𝑪𝟐𝑵/𝑮

― 𝑳𝒊𝒏

― 𝑬𝑪𝟐𝑵/𝑮 ― 𝒏𝑬𝑳𝒊

(6) We should note that the last terms on the right hand side of eq 6 refers to the total energy of a single Li atom in the Li metal. The electron motive force or the open circuit voltage can be computed from the Nernst equation, as shown in eq 7.

𝟏

𝑵 𝑴𝑺𝑫(𝒕) = 𝑵∑𝒊 = 𝟏⟨𝒓𝒊(𝒕) ― 𝒓𝒊(𝒕𝟎)⟩•⟨𝒓𝒊(𝒕) ― 𝒓𝒊(𝒕𝟎)⟩

(1) Where, the position of the i atom in the supercell is denoted as

Vocv  

r ri ; t0 represents a reference time, and which can be set as t0 = 0

G (0 K ) neF

(7)

In eq 7, the total number of electron transferred during the discharging process is given as ne, and the Faraday constant F. The theoretical capacity is determined from the calculated adsorption energy as a function of the total number of Li atoms in C2N/G hetero-junction, using eq 8. 𝑬𝒂𝒅(𝒙𝑳𝒊) = 𝑬(𝑪𝟐𝑵/𝑮–𝑳𝒊𝒙) ― 𝑬(𝑪𝟐𝑵/𝑮) ― 𝒙𝑬(𝑳𝒊) + ∆𝝁𝑳𝒊 (8)

in the calculation. Obviously, the maximum t for computing MSD is limited by the duration of the FPMD run. For the planar diffusion process, only the x and y components of MSD are required to estimate the diffusion coefficients. The relationship between MSD and diffusion coefficient is given by eq 2.

D =

𝟐

directions in x or y axis. Using the x and y components of MSD(t), the in-plane diffusion coefficients were calculated for Li atoms in the C2N/G hetero-junction. Since, the kinetics of the diffusion of Li atom in C2N/G heterojunction was found to be sluggish below 600 K in our FPMD simulations, the diffusion coefficients of Li atoms at the room temperature (300 K) cannot be obtained from FPMD simulations using eq 1 and 2. For such purpose, the Arrhenius relationship between temperature and diffusion coefficient must be applied, as shown in eq 3.

2.3 CI-NEB for diffusion barrier height The climbing-image nudge elastic band (CI-NEB) method60 was used to calculate the activation energy for diffusion and also to predict the minimum energy diffusion path. For all CI-NEB calculations, five intermediate images were created between the initial and final structures to provide a relatively smooth diffusion path between them. The structures of all images were relaxed until the tangential force imposed on each of them was converged to 0.001 eV/Å.

𝟏 MSD (𝒕) 𝐥𝐢𝐦 𝒕 𝟐t→∞

𝟏

Where, the term ∆μLi might be referred to the chemical potential of Li atom, and which varies between -1.8948 eV (Li metal) and -0.02 eV (isolated single Li atom). With the addition of Li atom

(𝟐)



excellent lattice match between C2N and graphene layers can be obtained in the orientations employed in current work, i.e., C2N: u [100]-v [010] (1×1) || graphene: u [1-10] –v [120] (2√3 × 2√3) and C2N (0001)|| graphene (0001), as shown in Figure 1.

to the C2N/G hetero-junction, the adsorption energy is gradually increased, and which may also change the sign from negative number to positive one. As defined in eq 8, the positive adsorption energy indicates the structure is unstable, and no more Li atom can be accommodated in the hetero-junction further. Thus, the theoretical capacity of the C2N/G hetero-junction is estimated as the maximum number of Li atoms adsorbed in the structure when the adsorption energy approaches to zero. Formally, the theoretical capacity is calculated from eq 9. 𝒙𝒎𝒂𝒙𝒛𝑭

𝑸 = 𝑴𝑪 𝑵/𝑮–𝑳𝒊 𝟐

(9) 𝒙

In eq 9, the charge state of Li is denoted as z, and its value is unity; the Faraday constant is given by F (26.810 Ah/mol); the M represents the molar mass of lithium saturated C2N/Graphene hetero-junction in the unit of g/mol.

Figure 1. The crystallographic orientations of graphene (a) and C2N (b) employed to build the coherent C2N/graphene bilayer structure with a lattice misfit value of 0.5%. For graphene, the default orientations for a primitive cell are indicated as ou`[𝟏00] and ov`[010]. Meanwhile, the new orientations used to match with those of C2N monolayer (ou[100] and ov[010]) are ou [𝟏10] and ov[120], and the corresponding primitive lattice is referred to the blue lines.

3. RESULTS AND DISCUSSIONS 3.1 Optimized structural parameters Using PBE+D2 method, the optimized planar lattice parameters of C2N and graphene are 8.476 Å and 2.447 Å, respectively. For C2N monolayer, the lattice parameters reported in the literatures are 8.330 Å ,64-65 8.29 Å66 and 8.32 Å,67 and which are smaller than that of present calculation. On the other hand, the planar lattice parameters of single layer graphene are given as 2.464 Å and 2.46 Å in previous studies,13,68 compared to 2.447 Å of this work. Overall, our calculation gives the lateral lattice constant of graphene in agreement with previous literatures.69-71 Other characteristic structural parameters such as C-C, C-N bond lengths, their values are listed in Table 1 for graphene, C2N and C2N/graphene structures. In the case of C2N monolayer, the bond lengths are C-C (1.429 Å, 1.470 Å), C-N (1.337 Å) in Ref 66, and C-C (1.430 Å, 1.460 Å), C-N (1.330 Å) in Ref 49, compared to C-C (1.440 Å, 1.446 Å) and C-N (1.397 Å) in Table 1. For the graphene, the calculated length of C-C bond is 1.413 Å, and which is in excellent agreement with 1.42 Å of Ref 56.

3.2 Electronic structures and transport properties of C2N/Graphene heterojunction The excellent lattice transport properties of graphene have been extensively investigated before.69-70,72 For example, the lattice thermal conductivity of single layer graphene was reported as 3500 W/m·K at 300 K, compared to 2200 W/m·K of natural occurring crystalline flake graphite at the same temperature and 2800 W/m·K of single crystalline graphite in-plane conductance at 80 K.73 Meanwhile, the theoretically predicted inner-plane lattice thermal conductivity of free-standing C2N single layer was 82.22 W/m·K.67 Although, the lattice heat conductance of C2N layer is less prominent than that of graphene and graphite, the inner-plane lattice thermal conductance of C2N/graphene heterojunction might be still sufficiently large for the practical use as the anode materials in lithium ion battery. The overall thermal conductance of C2N/graphene junction can be simplify estimated from eq 10 for the weakly coupled bilayer structure.74

Table 1 Optimized lattice parameters and bond lengths of graphene, C2N and C2N/graphene structures using PBE+D2 method. Structure a (Å) Bond type Bong Length (Å) Graphene C2N C2N/graphene

2.447 8.476 8.477

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C-C C-C C-N C-C (C2N) C-N (C2N) C-C (graphene)

1.413 1.440 1.397 1.498 1.347 1.414

𝑨𝑪𝟐𝑵

𝑨𝑮𝒓

𝜿 = 𝜿𝑮𝒓𝑨𝑮𝒓 + 𝑨𝑪 𝑵 + 𝜿𝑪𝟐𝑵𝑨𝑮𝒓 + 𝑨𝑪 𝟐

(10)

𝟐𝑵

In eq 10, the cross sections areas of graphene and C2N single layers are given by 𝑨𝑮𝒓 and 𝑨𝑪𝟐𝑵, and their corresponding

1.445

lattice thermal conductivities are denoted as

𝜿𝑮𝒓 and

𝜿 𝑪 𝟐𝑵

(see Figure S1). The cross section area of a two-dimensional material might be estimated either from the calculated electron localization function (ELF) or by using the van der Waals radii of N (1.55 Å) and C (1.70 Å) atoms. In this our case, we plot the ELF for the cross section part of the monolayer. Since the ELF decreases rapidly to zero in the vacuum region next to surface, the thickness of the monolayer is estimated as the vertical distance between the isovalue contour (0.001) of the upper surface and that of the lower one. The determined thickness of C2N monolayer is very similar to that of graphene, i.e., 3.57 Å and 3.59 Å, respectively. In the C2N/Graphene heterojunction,

1.443 1.414

As can be seen from Table 1, the planar lattice constant of C2N/graphene bilayer is fixed to that of C2N monolayer (8.476 Å). The lattice misfit value for C2N and graphene in the standard orientations (C2N: u [100]-v [010] (1×1) || graphene: u [100]-v [010] (4 × 4) or (3 × 3) and C2N (0001) || graphene (0001)) with respect to either C2N or graphene layer is found to be larger than 13 %, resulting in a non-coherent bilayer. Fortunately, the

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. The value is

found to be 1791.1 W/m·K. The lattice thermal conductivity of C2N/Graphene bilayer structure is significantly improved, compared to that of C2N monolayer. The excellent thermal conductance of C2N/Graphene is considered as an advantage for the use as the anode material in the lithium ion battery. We first show the calculated electronic band dispersions of C2N, graphene and C2N/Graphene heterojunction in Figure 2. Obviously, the single layer C2N (2D-C2N) shows a direct band gap of 1.5 eV at Γ-point in the Brillouin zone. The semilocal density functional like PBE employed here is well-known to underestimate the band gap. Therefore, C2N could be regarded as a wide band gap semiconductor.71,72 Interestingly, both the bottom of conduction band and top of valence band of 2D-C2N mainly consists of flat bands, as illustrated in Figure 2(a). The flat bands at the top of VB are originated from the electron long pairs of N atoms. The long pair occupies one of the sp2 hybridized orbitals of each N atom, and which is pointed toward the center of the large inner planar hole. On the other hand, the flat CB band is attributed to the anti-π bonding orbitals of N atoms, i.e., the 2pz orbital which is perpendicular to the C2N atomic plane.70 The flats bands at conduction band minimum (CBM) or valence band maximum (VBM) results in the heavy electron or hole mass, leading to the small electric carrier mobility. In Figure 2(b), the band structure of graphene is also displayed. The linear band dispersions and Dirac cone at Γ-point can be clearly seen in the graph. For the C2N/Graphene heterojunction, the band structure is depicted in Figure 2(c). The hetero-junction exhibits a small direct band gap as 0.20 eV at Γpoint, which is agreement well with the previous result.66 The originations of CBM and VBM are differ from free-standing C2N or graphene layer. In the case of C2N/Graphene, the top of VB is dominated by the π-bonding state of graphene layer. Meanwhile, the bottom of CB is determined by the anti-π bonding state of C2N layer. Thus, the formation of C2N/Graphene hetero-junction alters both the band orders and band gap. In contrast to single layer graphene, the upper and lower Dirac bands split at the Γpoint in heterojunction, giving a small band gap of the magnitude of 0.5 eV.61 Engineering the band gap of graphene through the formation of heterojunction has been reported before.66,75 The size of the resulting band gap of graphene can be explained using the π-electron tight binding model of the biparticle lattice. The dispersion relation for the Dirac bands near the Fermi surface is given by eq 11.

(b)

4

5

5 4

3

3

3

2

2

2

1 0 -1

1 0 -1

1 0 -1

-2

-2

-2

-3

-3

-3

-4

-4

-5

-5



K

M

K

-4

K

-5



K

M

10

K

M

30

TDOS

(e)

TDOS

20 15



K

15

25

(d)

(c)

4

(f)

10

TDOS

20

Figure 2. The band dispersions of C2N (a), graphene (b), and C2N/graphene (c) bilayer. -4

-3

-2

-1

0

1

2

3

4

5

C-2s C-2p

15 10 5 0

25

-5

-4

-3

-2

-1

0

1

2

3

4

10

5

0

-5

-4

-3

-2

-1

0

1

2

3

4

5

Energy(eV)

15

C-2s C-2p

5 10

0

10

-5

-4

-3

-2

-1

0

1

2

3

4

5

C-2s C-2p

5

0 -5 10

-4

-3

-2

-1

0

1

2

3

4

5

N-2s N-2p

8

N-2s N-2p

20

Density of State(DOS))

5

0 -5 25 20

B

𝟐

5

Energy(eV)

(𝜿𝑮𝒓 + 𝜿𝑪𝟐𝑵)

Energy(eV)

Eq. (10) can be approximated as 𝜿 =

(a)

Energy(eV)

the lateral cell length is the same for both layers. Therefore, the total lattice thermal conductivity of the bilayer structure using


From the obtained band structures, we predict the electric conductivities of free-standing C2N, graphene and C2N/graphene C2N/Graphen Graphene 2N BoltzTrap code structures Cusing which is based on the semiclassical Boltzmann transport theory.56 The results are shown in Figure 3 for p-type dopant at 300 K. We should note that for ntype C2N/graphene hetero-junction, the electric current is only carried by C2N layer. As can be seen from Figure 3, the pure C2N layer shows very poor electric conductivity for the low hole concentration. Its hole conductance can be greatly boosted only in the heavily doped case, i.e., nh > 5.0 × 1021 1/cm3. The electric conductivities of graphene and p-type C2N/graphene are significantly higher than that of intrinsic 2D-C2N for the considered range of the hole concentration. Moreover, the predicted electric conductivity of p-type C2N/graphene is similar to that of free-standing graphene, because the mobility of holes in both structures is determined by the electronic bands of graphene. Our results indicate that the poor electrical conductance of 2DC2N could be significantly improved due to the formation of C2N/graphene heterojunction especially for the p-type dopant. 15

5

10

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10  m s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



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C2N Graphene C2N-Graphene

20

10

21

-3

10

22

n(cm ) Figure 3. The calculated electric conductivities of C2N, graphene and C2N/graphene structure as a function of hole concentration at 300 K.

3.3 Theoretical capacity In order to determine the theoretical capacity of C2N/graphene bilayer as the anode material for Li ion battery, we would like to address the energetics of adsorption/intercalation of Li atoms in C2N/graphene heterojunction. Previous studies have already concluded that the free standing graphene is not considered as a promising anode materials due its unexpected weak interaction with the absorbed Li atoms, compared to that of Li atom in bulk phase.13 However, other theoretical works indicated that the adsorption of Li on graphene layer was actually exothermic and strong.12 In this work, we first perform the FPMD simulations for an artificial supercell model for the graphene single layer saturated with the Li absorbent at 300 K. In the initial condition, the graphene layer was placed in the middle of supercell between four 15-atom Li layers (Li120C48). We ran the

|𝑬(𝒌)| = ± 𝜟𝟐 + (ℏ𝒗𝑭𝒌)𝟐 (11) Where, the k the wave vector and vF is the Fermi velocity; the onsite energy (potential) difference between two sublattices (C2N and Graphene) is characterized by the quantity Δ. Since the electrostatic potential of C2N is different to that of graphene, the intrinsic build-in electric field is created between C2N and graphene layers. At the Γ-point, the induced band gap between upper and lower Dirac bands is roughly estimated as E+ - E- = 2Δ.



𝜟𝑬𝒊𝒏 𝑳𝒊

MD simulation for 5ps with a time step of 1fs in NVT ensemble. The resulting structure is displayed in Figure 4(a). We find that the average distance between graphene and Li atoms in the nearest layers is 2.50 Å, indicating graphene monolayer could absorb Li atoms. From Figure 4(a), it is estimated that totally 30 Li atoms are accommodated on the surfaces of graphene monolayer, and that gives a theoretical capacity of 1024.8 mAh/g. The value is larger than that of experimental one (945 mAh/g) by 7.7 %. In the cases of C2N monolayer and C2N/graphene bilayer, the snapshots in the FPMD simulations are illustrated in Figure 4(b) and Figure 4(c) at 300 K. For C2N monolayer, Li atoms are separated into different layers in terms of their distances within the substrate. The shortest distance between Li and C2N monolayer is found to be less than 2.5 Å. Using the distance between Li atom and C2N monolayer as the criterion to distinguish the absorbed and free Li atoms (rcut=3.0 Å), the maximum number of Li atoms chemically attached to the upper and lower surfaces of C2N monolayer is estimated as,29 providing the theoretical capacity of 1181.9 mAh/g. Experimentally, it has been shown that the C2N 2D framework could exhibit the very high reversible capacity of 933.2 mAh/g.17 Obviously, the capacity is overestimated by the procedure, compared to the experimental value. As displayed in Figure 4(c), C2N/G heterojunction could accommodate 40 Li atoms which give a theoretical capacity of 818.4 mAh/g. Overall, the FPMD simulations predict that the theoretical capacity of C2N/graphene bilayer is smaller than that of either graphene or C2N monolayer. We should note that one must be very cautious when using the FPMD results (See Figure 4) to estimate the theoretical capacity. Although, one can always define the cut-off distance to distinguish the absorbed Li atoms and the remaining free Li layers, the definition of maximum distance is actually arbitrary. Calculating the adsorption energy is the better way to determine the theoretical capacity.

t

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= 𝑬[𝒔𝒖𝒓 + 𝒏𝑳𝒊] ― 𝑬[𝒔𝒖𝒓 + (𝒏 ― 𝒎)𝑳𝒊] ―𝒎𝝁𝑳𝒊

(12) Where, E[sur+nLi] and E[sur+(n-m)Li] represent the total energies of the n and n-m Li atoms adsorbed structures, respectively. Specifically, the m in the eq 12 refers to the degeneracy of a particular adsorption site. The chemical potential of Li atom is denoted as μLi, and the energy of bulk Li metal is used in our calculations. In Figure 5, the obtained differential adsorption energies of Li-C2N and Li-C2N/graphene structures are shown as a function of the number of adsorbed Li atoms. By increasing the theoretical capacity, the magnitude of adsorption energy decreases, and which eventually approaches to zero at the maximum theoretical capacity. For the C2N monolayer, the maximum number of Li atoms accommodated by the structure is found to be 13 or equivalently 1095.2 mAh/g. The value now is in close agreement with the experimental capacity (933.2 mAh/g).20 Meanwhile, we find the C2N/graphene bilayer could absorb 11 Li atoms and which gives a theoretical capacity of 490.0 mAh/g. Clearly, the FPMD simulation significantly overestimates the theoretical capacity of C2N monolayer, compared to that of calculated one using eq 12 or experimental value for the same structure. Although, the experimental adsorption capacity for C2N/graphene is not available at the moment, the conclusion could be also applied to the bilayer structure. It might be interesting to compare the theoretical Li adsorption capacities of C2N/G and C2N structures with other 2D materials. Using the FPMD simulation, the theoretical capacity of borophene as the anode for Li ion battery was estimated as 3306 mAh/g.76 The value is roughly three times higher than that of C2N monolayer, and eight times bigger than that of C2N/G bilayer structure. Other 2D materials such as graphene, MoS2 and graphdiyne, the specific capacities were found to be 945 mAh/g (exp),77 1062 mAh/g (exp)78 and 1120 mAh/g (cal).79 Yu and coworkers investigated the electrochemical properties of TiC3 monolayer which is a new MXene based 2D material, using the first principles method.80 The reported theoretical capacity of TiC3 2D structure was 1278 mAh/g. The specific capacity of C2N monolayer is predicted to be less prominent than that of borophene, but the value is comparable to other well-known 2D materials (graphene and MoS2). On the other hand, the theoretical capacity of C2N/graphene is significantly smaller than that of C2N monolayer. In terms of their theoretical capacities as anode for Li ion battery, C2N, MoS2, graphdiyne, borophene and TiC3 are the promising candidates as the anode materials. However, the electrical conductivity of C2N monolayer is predicted to be significantly lower than that of C2N/graphene bilayer. In addition, the theoretical capacity of C2N/graphene (490.0 mAh/g) is still superior to that of graphite (~370 mAh/g). Therefore, C2N/graphene bilayer could be used as the anode material for LIBs.

Figure 4. The last snapshot of Li saturated supercell models from the FPMD simulations at 300 K: (a): Li-graphene (Li120C48); (b): Li-C2N (Li120C24N12); (c): Li-C2N/graphene (Li126(C2N)12/C48). The Li atoms located in the region of red-bashed square in each graph are considered to be effectively absorbed, and which contribute to the adsorption capacity. We now determine the theoretical capacity from the calculated differential adsorption energy of Li on C2N monolayer or C2N/graphene bilayer. The differential adsorption energy is defined as eq 12.

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-0.5 -1.0 -1.5 -2.0 -2.5 -3.0

interacts with the absorbed Li atoms more strongly than the graphene. In order to further reveal the binding mechanism of Li atom at CN3 site, the electron density difference is calculated for Li (CN3)-C2N structure using eq. 13.

0.0

(a)

C2N monolayer 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Li adsorbed number (n)

Differential adsorption energy(eV)

0.0

Differential adsorption energy(eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(b)

-0.5 -1.0 -1.5

𝜟𝝆 = 𝝆(Li - C𝟐𝑵) ― ∑i = Li,C,N𝝆𝒊

-2.0 -2.5

C2N/Graphene heterosructure

-3.0 0

1

2

3

4

5

6

7

8

(13)

Where, the electron density of Li-C2N is represented by 𝝆(Li C𝟐𝑵), and which is determined from the self-consistent calculation of the total energy of the optimized atomic structure. The summation refers to the total atomic density of the noninteracting atoms. The valence electron density difference is illustrated in Figure S(4-6) in terms of the 3-dimensional isovalue contour. We clearly observe the depletion of valence electron density of Li atom at CN3 site. Meanwhile, the electron density is increased in the regions between Li atom and other two nearest N atoms, suggesting the formation of directional Li-N bonds at CN3 site. For those two Li-N bonds, their lengths are roughly the same (2.14 Å). In the bulk α-Li3N crystal structure, the typical Li-N bond length is about 2.13 Å for the six-fold coordinated Li atom.68,69 The ionic radii of Li+ and N3- are 0.90 Å and 1.32 Å, giving the length of 2.12 Å for the ideal ionic Li-N bond. As a result, the Li-N bonds in Li-C2N structure at CN3 site are similar to those of α-Li3N phase. We also performed the Bader charge analysis (see Table S4) for the relevant N and Li atoms in the same adsorption geometry. It is found that Li atom carries a very large positive charge as +0.91 e, and the value is very close to that of Li+. On the other hand, the two N atoms, which form the Li-N bonds with the absorbent, show more negative nominal charges (-0.18 e and -0.20 e) than other N atoms (~-0.11 e) in C2N structure. Therefore, the above analysis confirms the formation of strong directional Li-N bonds at CN3 site for LiC2N structure. In contrast, the Li atom absorbed either at CN1 or CN2 site is situated right above the central of hexagons of C2N atomic layer. For CN1 and CN2 sites, the distances between Li and the nearest C are about 2.26 Å and 2.20 Å, respectively. Furthermore, the Li-N has a length of 2.15 Å in the latter adsorption site. The computed bond lengths for Li-N and Li-C bonds for CN1, CN2 and CN3 sites are consistent with the order of their relative stability.

9 10 11 12

Li adsorbed number (n)

Figure 5. The calculated differential adsorption energies of LiC2N (a) and Li-C2N/graphene (b) structures as a function of the number of the accommodated Li atoms 3.4 Lithium adsorption site preference on C2N/graphene bilayer 3.4.1 Single Li adsorption In the actual Li ion battery, the electric potential difference between the anode and the cathode results in the changing of chemical potential of Li atom in the different regions of electrodes. Therefore, the calculated adsorption energy of Li atom in the anode is dependent on the latter quantity, as indicated in eq 8. In our paper, we assume the chemical potential of Li is constrained in the range from the value of bulk Li metal (-1.8948 eV) to the energy of an isolated Li atom (-0.02 eV). We first investigate the adsorption of Li atom on graphene and C2N structures. Since the atomic structure of graphene monolayer is high symmetric, the most stable adsorption site of Li atom on graphene is uniquely located in the centre of carbon hexagon. In this work, it is denoted as G1. By varying the chemical potential of Li atom, the calculated adsorption energy of Li at G1 site is situated in the range from -1.3385 eV/atom (Li atom) and 0.53 eV/atom (Li metal)(see Table S2). The cohesive energy of Li metal is found to be -1.63 eV/atom. Therefore, the free standing graphene flakes could absorb certain amount of Li atoms, as suggested by experiments. However, the cohesive energy of Li metal is always more negative than the adsorption energy of Li on graphene for the considered range of chemical potential of Li atom. The dendrites of Li metal are expected to form during the charging process. Particularly, from the predicted adsorption energy, the adsorption of bulk Li metal on graphene monolayer is endothermic as implied by its positive value. The atomic structure of C2N monolayer consists of like C-C and unlike C-N hexagons. The coplanar hole has a diameter of 8.30 Å. In our calculations, three stable adsorption sites are revealed for the absorbed Li atom on C2N monolayer. Those energetically favoured adsorption sites are indexed as CN1 (the central of the like C-C hexagon), CN2 (the central of the unlike C-N hexagon) and CN3 (off-central position in the large hole), and which are also illustrated in Figure 6(a). We show the calculated adsorption energies as a function of the chemical potential of Li atom in Figure 6(b). Obviously, the Li atom strongly prefers to occupy the site CN3 on C2N monolayer, as indicated by its very negative adsorption energy, compared to those of CN1 and CN2 sites. CN2 gives a slightly more negative adsorption energy than that of CN1. When the chemical potential of Li atom is equal to that of Li metal, the adsorption process at CN1 site becomes endothermic on C2N monolayer. From the calculated adsorption energies, we conclude that C2N monolayer



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bashed horizontal line represents the boarder for the endothermic and exothermic adsorption processes. For C2N/G bilayer structure, the predicted adsorption energies for all possible high symmetry adsorption sites are plotted in Figure 6(c). In addition to G1, CN1, CN2 and CN3 sites, the intercalated Li atom between C2N and graphene is found to be stable at GCN1 (mid-point between C2N and graphene, right below CN1 site), GCN2 (the same to GCN1, but right below CN2 site) and GCN3 (right below CN3 site and that of C2N atomic plane) sites. Among all investigated adsorption sites, CN3 and GCN3 exhibit the most negative adsorption energies. Moreover, the adsorption energy of GCN3 site is almost the same as that of CN3 site. For GCN3 site, the bonding mechanism of Li atom with the C2N atomic layer is found to be very similar to that of CN3 site discussed before. For the two LiN bonds, their lengths are calculated to be 2.15 Å, and which are slight longer than those of the same bonds at CN3 site. The calculated Bader charges of Li and other two N atoms are again the same as those of CN3 site(see Table S4). In general, the chemical bonding mechanism at CN3 and GCN3 sites is considered to be identical to each other. It is also found the Li atom placed at either GCN4 or GCN5 site is not favoured in energy. During the structural optimization, the Li atom at those two sites could move to GCN3 site. Finally, we should note that for the lower graphene layer, the most stable adsorption geometry of Li atom is the same as that of free standing graphene monolayer (G1). Since the formation of C2N/graphene bilayer structure is mainly attributed to the relatively weak van de Waals interactions, the chemical property of lower graphene layer is not altered significantly.

3.4.2 Li13-C2N and Li11-C2N/graphene structures In Figure 7, both C2N monolayer and C2N/graphene bilayer absorbed with the maximum numbers of Li atoms are illustrated. The degree of the saturation of the absorbed Li atoms in both structures is carefully monitored by calculating the differential adsorption energy using eq 12. As can be seen from Figure 7 (a) and (c), the C2N monolayer could absorb 13 Li atoms. The upper and lower surfaces do not exhibit the same adsorption capacity, i.e., 9 Li atoms on the former surface and 4 on the lower one. Besides Li-12 and Li-13, other remaining Li atoms prefer to occupy CN3 and CN1 sites. The calculated differential adsorption energy of Li atom on CN2 site is positive (0.2-0.3 eV/atom), suggesting that the adsorption of Li atom on the site is no longer favoured in energy. Interestingly, in the previous discussions, we have shown that the adsorption energy of CN2 site is actually more negative than that of CN1 site in the case of Li-rich condition for the monatomic adsorption case, as displayed in Figure 7(c). Obviously, the overall landscape of adsorption energy is altered due to the accumulation of Li atoms at different sites gradually on C2N monolayer especially the CN3 sites. From Figure 7(c), we also find that Li atoms absorbed on the upper surface of C2N monolayer are separated into two different major layers. The atoms Li-12 and Li-13, which are situated roughly below CN2 and CN3 sites, are weakly absorbed on C2N

Figure 6. The adsorption sites (a) and predicted adsorption energies of single Li atom at the different absorption sites of C2N or graphene monolayer (b) and C2N/graphene bilayer heterojunction (c). The chemical potential of Li is defined as 𝝁𝑳𝒊 ― 𝝁𝒂𝒕𝒐𝒎 ,𝝁𝒂𝒕𝒐𝒎 ], and its value varies , where 𝝁𝑳𝒊 ∈ [𝝁𝒎𝒆𝒕𝒂𝒍 𝑳𝒊 𝑳𝒊 𝑳𝒊 𝒂𝒕𝒐𝒎 between 0 eV (𝝁𝑳𝒊 = 𝝁𝑳𝒊 ) and -1.8948 eV (𝝁𝑳𝒊 = 𝝁𝒎𝒆𝒕𝒂𝒍 ). In 𝑳𝒊 graph (a), the large “hole” in the C2N atomic layer is indicated by the blue-dashed circle. The mid-plane between C2N and graphene layers is represented by the grey-horizontal plane. The red-

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monolayer (also see Figure 7 (a)). In the case of C2N/graphene bilayer, the total number of Li atoms intercalated between C2N and graphene is found to be 7 for the modelling structure. The remaining 4 Li atoms are absorbed on the upper surface of C2N layer. From Figure 7(b) and (d), one can see that all intercalated Li atoms could occupy all possible stable adsorption sites such as GCN1, GCN2 and GCN3. Meanwhile, those Li atoms absorbed on upper surface of C2N layer are only found at CN3 and CN1 sites. The lower surface of the bottom graphene layer dose not absorb any additional Li atom.

absorbed. Finally, we should point out that the site preference determined from the monoatomic adsorption energy provides the invaluable information regarding all energetically favourable adsorption sites on C2N monolayer or C2N/graphene bilayer in the initial stage. However, the interactions between absorbed Li atoms and substrate could significantly change the order of the occupation at those adsorption sites. The saturation of Li atoms in C2N or C2N/graphene structure must be determined from the calculated differential adsorption energy profile. Consequently, the calculation of differential adsorption energy provides a reliable methodology to estimate the theoretical capacities of C2N monolayer and C2N/graphene bilayer as the anode materials for LIBs.

Figure 7. Li atoms saturated structures of C2N monolayer and C2N/graphene bilayer: (a) and (c): top and side views of Li13-C2N structure; (b) and (d): top and side views of Li11-C2N/graphene bilayer. Different adsorption sites are indicated as CN1, CN2, CN3, GCN1, GCN2 and GCN3 for both structures.

Figure 8. The structural evolutions of C2N monolayer ((a) and (c)) and C2N/graphene bilayer ((b) and (d)) saturated with Li atoms obtained from first principles molecular dynamics simulations at 400 K. The initial conditions for both supercell models are represented by ball-and-stick models. The dotted lines illustrate the time-series for Li atoms during the whole FPMD simulations. The stable adsorption sites are also indicated in the graphs ((a) and (b)).

3.4.3 Li saturated structures at finite temperature We also perform the FPMD simulation at the 400 K for C2N monolayer and C2N/graphene bilayer which are saturated with Li atoms. The duration of the FPMD simulations is about 16 ps with a time step of 1 fs. The trajectories of Li atoms are depicted for Li-C2N and Li-C2N/graphene structures in Figure 8. Since the FPMD simulation is performed at finite temperature, few Li atoms are able to overcome the energy barrier for the diffusion due to the thermal energy. The migration paths of Li atoms are clearly seen in all graphs in Fig. 8 as the dotted curves. For LiC2N system, the FPMD simulation predicts that the Li atoms are strongly attached to CN3 and CN1 sites, as shown in Figure 8 (a) and (c). Meanwhile, most CN2 sites do not absorb Li atom. In the case of C2N/graphene bilayer, Li atoms are preferred to occupy GCN3/CN3 and CN1/GCN1 sites. Most GCN2 and CN2 sites are left empty. Interestingly, the above finds are consistent with the adsorption site preferences and Li-saturated monolayer or bilayer structure predicted at 0 K by means of differential adsorption energies. Furthermore, we also find that the absorbed Li atoms are separated into two layers on the upper surface of C2N layer from Figure 8 (b) and (d). The average distance between the outer Li layer and the substrate is found to be 4.50 Å, and which is significantly larger than that of inner Li layer (2.15 Å). The absorbed Li atoms in the outer layer do migrate easily on the substrate in our FPMD simulations, showing no site preference on their diffusion pathways. The FPMD simulations also confirm that the order of the adsorption of Li atoms in the two structures at different sites follow the very simple rule, i.e., the more negative the adsorption energy is, the more Li atoms are

3.5 Diffusion Pathways and Barrier Height 3.5.1 Single Li adsorption case The rate of charging or discharging process of the lithium ion battery is solely determined by the diffusion energetics of Li atom in the electrodes. Here, we would like to investigate the diffusion mechanism of Li atom on C2N monolayer and C2N/graphene bilayer using the CI-NEB method. The main migration path of Li atom on graphene layer is indicated as G1-to-G1. On the path, the middle point represents the saddle point in the total energy. This diffusion mechanism has been well-understood and investigated in previous works.12,13 The calculated diffusion barrier in our work for this particular migration path is about 0.30 eV(see Figure S2), and which is in excellent agreement with other literatures.12 Now, for both C2N monolayer and C2N/graphene bilayer, the possible diffusion paths are CN1-CN3, CN2-CN3, CN1CN2-CN3 and CN1-CN2-CN1 (with CN3 preoccupied by Li atom) for adsorption of Li atom on the C2N surface. In the previous section, we have shown that the adsorption energy is always more negative for CN3 site than that of either CN1 or CN2 site. Thus, the Li atom strongly tends to bond with C2N monolayer at CN3 site. In Figure 9, the migration paths and their



energy profiles are displayed for C2N/graphene bilayer. The similar results for C2N monolayer are provided in supporting materials (Figure S2). Here, our discussions will be mainly focused on CN3-CN2-CN1-CN2-CN3 (Figure. 9(d) and (g)), CN3-CN1-CN3 (Figure 9(e) and (h)) and CN1-CN2-CN1 (Figure 9(f) and (i)) pathways. The diffusion barrier heights for either CN3-CN2 or CN3-CN1 migration path is larger than 2.0 eV. Consequently, the lithium atom trapped at CN3 site has very low mobility, compared to that of absorbed at CN1 and CN2 sites. The energy profile of the migration path CN3-CN2-CN1-CN2CN3 clearly also implies that the energy barrier for the pathway CN2-CN1-CN2 (or CN1-CN2-CN1) is roughly ten times smaller than both CN3-CN1 and CN3-CN2 cases. Once all CN3 sites are preoccupied with Li atoms, we would suggest that the CN1-CN2CN1 is the most likely migration path for the absorbed single Li atom on C2N monolayer. As one can be seen from Figure 9(c), the diffusion barrier is found to be 0.25 eV. Therefore, as long as the CN3 site is preoccupied, the diffusion energetics of Li atom on C2N monolayer is comparable to many other 2D structures, i.e., graphene (0.3 eV or 0.33 eV in Ref 70), MoS2 (0.25 eV),84 VS2 (0.22 eV),85 borophene (0.01 ~ 0.6 eV),76 phosphorene (0.076 ~ 0.624 eV)86 and TiC3O-MXene (0.20 ~ 0.25 eV).80 Although, C2N monolayer is regarded as a possible candidate for the LIBs, it has a very poor electric conductivity. On the other hand, the electric and lattice transport properties of graphene are much superior to those of C2N single layer. However, the specific capacity of graphene is relatively small.

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migration paths GCN3-GCN1 and GCN3-GCN2 are extremely high, i.e., 2.5 eV. As a result, similar to CN3 site, the GCN3 would also trap the Li atom and suppress its diffusion process. Nevertheless, the migration energy barrier for GCN2-GCN1GCN2 steps on the entire GCN3-GCN2-GCN1-GCN2-GCN3 pathway is turned out to be 10 times smaller. Therefore, with the preoccupation of Li atom at the available GCN3 site, the diffusion energetics for the path GCN1-GCN2-GCN1 (or equivalently GCN2-GCN1-GCN2) is again on the magnitude of 0.25 eV, as shown in Figure 10(c). We may compare the calculated most favoured diffusion barrier of C2N/graphene to other bilayer 2D materials, i.e., VS2/graphene (0.20 eV),28 MoS2/graphene (0.10 ~ 0.23 eV),44 Si/graphene (0.36 ~ 0.40 eV),45 graphene/blue-phosphorus (0.22 ~ 0.23 eV),46 phosphorene/graphene (0.09 ~ 0.79 eV).35 Overall, the diffusion energetics of Li atom in C2N/graphene is in the desired range as the anode material for the LIBs.

Figure 10. The diffusion energy profiles and migration pathways of the intercalated Li atom in C2N/graphene bilayer for GCN3GCN2-GCN1-GCN2-GCN3 ((a), (d) and (g)), GCN3-GCN1GCN3 ((b), (e) and (h)) and GCN1-GCN2-GCN1 ((c), (f) and (i)).

Figure 9. Diffusion energy profiles and the corresponding migration pathways of Li atom on the upper surface of C2N/graphene bilayer for CN3-CN2-CN1-CN2-CN3 path ((a), (d) and (g)), CN3-CN1-CN3 path ((b), (e) and (h)) and CN1CN2-CN1 path ((c), (f) and (i)). For intercalated Li atom, the energy profiles for GCN3GCN2-GCN1-GCN2-GCN3, GCN3-GCN1-GCN3 and GCN1GCN2-GCN1 (with preoccupied Li at GCN3 site) are shown in Figure 10 (a), (b) and (c). The actual diffusion images in the CINEB calculations are displayed in Figure 10 right below each migration energy profile. GCN3 and CN3 sites are considered to be identical from the point of view of chemical bonding mechanism with Li atom, and also from the calculated adsorption energy (See Figure 10(a)). The diffusion barriers for the

Finally, one should note that the migration paths and energy barriers discussed here have been obtained only for single Li atom or very few Li atoms absorbed on the corresponding structures. For the actual anode materials of LIBs, the planar diffusion process might be either hindered or assisted due to the simultaneously existence of many other absorbed Li atoms on the surface of electrode. The FPMD simulations performed at lower temperature (400 K) also reveal other energetically favourable migration paths in the vertical direction (or z-direction of modelling cell) which cannot be simply suggested based on the geometries of adsorption sites. Nevertheless, the FPMD simulations at high temperature (> 800 K) indeed agree very well with the migration paths of Li atoms shown in Figure 9. 3.5.2 Li saturated C2N and C2N/graphene structures Using the CI-NEB calculation to predict the migration energy barrier for Li saturated structures is not straightforward,

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because the possible diffusion pathways are difficult to visualize from the modelling structures. In our methodology, we first run the standard FPMD simulations at finite temperature (400 K) for Li-C2N and Li-C2N/graphene supercell models in the NVT ensemble with a duration of 16 ps. The time series of each Li atom in the supercell model is tracked by our home-made post processing codes.86 By calculating the mean square displacement (MSD) and the diagonal components of diffusion coefficient for each Li atom, the diffusion pathways might be obtained for the interested atoms in the supercell model. Several typical diffusion pathways are illustrated in Figure 11 for Li-C2N and LiC2N/graphene structures. We find that for the C2N monolayer, the migration of Li atom involves a fast vertical movement in the z-direction at the room temperature (CN3-CN1-CNx or CN3CNx). As a result, the absorbed Li atoms form two layers on the surface of C2N monolayer. The inner Li layer is strongly attached to the C2N substrate with relatively low diffusivity. Meanwhile, the upper Li atoms are weakly absorbed and they exhibit relatively high planar diffusion coefficient. For example, the diffusion coefficients of Li atoms in the inner layer are found to be in the range from 10-10 m2/s to 10-11 m2/s in x-y and z directions at 400 K. On the other hand, the values for the Li atoms in the outer layer are estimated as 10-9 m2/s in the x-y plane at the same temperature. In the case of C2N/graphene, the observed migration paths show both the planar (GCN1-GCN3) and vertical diffusions (GCN3-CN3) as displayed in Figure 11(b) and (d). The estimated diffusion coefficients for intercalated Li atoms are between 10-10 m2/s and 10-11 m2/s at 400 K. The order of the magnitude is the same to that of the absorbed Li atoms in the inner layer on C2N substrate. It might be interesting to point out that intercalated Li atom could migrate vertically through the large hole of C2N monolayer (GCN3-CN3). Consequently, the migration paths shown in Figure 11(a) and (c) may also apply to those ascended Li atoms which originally are intercalated between C2N and graphene layers. Based on the previous FPMD simulations for Li-C2N and Li-C2N/graphene supercell structures, we investigate further the diffusion barriers for the conjectured migration paths shown in Figure 12(a) using CI-NEB calculation. We should note that all CI-NEB calculations were carried out using the supercell models built from Li-saturated structure shown in Figure 11. In the calculation, the energy profile for each migration pathway was obtained by creating 12 images between the initial and final positions of the selected single Li atom on the path. The atomic positions of all other Li atoms and the framework of substrate were actually fixed in the NEB method. Meanwhile, no such constraints have been applied to the modelling structure in our FPMD simulations. Therefore, the migration energy profiles presented in Figure 12(b) using the standard CI-NEB method are not expected to be fully consistent with the FPMD simulations. As can be seen from Figure 12(a), the vertical diffusion pathways, which is observed in our FPMD simulations at 400 K, is referred to GCN1-GCN3-CN3-CNx path. Since, GCN3 and CN3 are the energetically preferred adsorption sites, the migration of Li from GCN1 to GCN3 is spontaneous, as shown in Figure 12(b). In addition, the diffusion barrier from GCN3 to CN3 is less than 10 meV. However, the energy barrier predicted for CN3-CNx path is relatively high (~1.0 eV), using the CI-NEB method. For other two migration pathways (GCN1-GCN3-GCN1

and CN1-CN3-CN1), the barrier heights are very large (> 2.0 eV). The mobility of Li atom at either GCN3 or CN3 site is expected to be very low. This conclusion is in good agreement with previous CI-NEB results illustrated in Figure 9 and 10 for a single Li atom case. Interestingly, Figure 12(b) does imply two energetically favourable migration paths for the absorbed and intercalated Li atoms in C2N/graphene bilayer, i.e., GCN1GCN3-CN3-CNx and CN1-CN3-CNx. Those two migration pathways are indeed consistent with FPMD simulations.

Figure 11. The diffusion pathways of Li atom obtained from the FPMD simulations at 400 K for C2N monolayer ((a) and (c)) and C2N/graphene bilayer ((b) and (d)). The colours scale with the zcoordinate of atoms in the structure. For the clarity, other Li atoms in the supercell models are not shown in all graphs. The notations for the stable adsorption sites on the migration paths are also indicated. CNx and CNxx refers to the adsorption sites in the outer layer.

Figure 12. The calculated energy profiles for different diffusion pathways using CI-NEB method for C2N/graphene bilayer structure at 0 K: (a): the three migration pathways are displayed in the graph as GCN1-GCN3-GCN1 (blue line), GCN1-GCN3CN3-CNx-CNxx (red-dashed line) and CN1-CN3-CN1-CNxCNxx (green line); (b): the migration energy profiles for GCN1GCN3-CN3-CNx, GCN1-GCN3-GCN1 and CN1-CN3-CN1 pathways. Different adsorption sites are indicated in graph (a), and particularly the bonding mechanism at GCN3 or CN3 site is implied by the black solid lines. 3.6 Diffusion coefficients The CI-NEB calculations only provide the diffusion barrier for the suggested diffusion pathways. In order to obtain the inplane diffusion coefficients, we conducted the first principles molecular dynamics simulations (FPMD) at finite temperature for the supercell models of Li-C2N and Li-C2N/graphene structures. Using the time series, we are able to calculate the diffusion coefficients of each individual Li atom in the supercell models (totally 40 and 48 Li atoms in our supercell models for


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Li-C2N and Li-C2N/graphene structures) in x, y and z directions and their general averages at a specific temperature using our own post-processing software.86 We would like to point out that the integrity of the either Li-C2N or Li-C2N/graphene structure is retained at the highest temperature (1200 K) in our FPMD simulations. Using eq 1 and 2, the predicted general averages of the in-plane diffusion coefficient are plotted in Figure 13 between 600 K and 1200 K for both models. As expected, the inplane diffusion coefficient increases rapidly with the increasing of the temperature. For Li-C2N/graphene bilayer, by fitting the Arrhenius equation to the calculated diffusion coefficient as a function of temperature, the prefactor D0 is found to be 4.31×10-7 m2/s, and the apparent diffusion activation energy (Ea) is 23.88 kJ/mol or 0.25 eV/atom. In our CI-NEB calculations, the computed diffusion barrier (0.25 eV/atom) is in excellent agreement with the value given by FPMD simulations. Using the obtained fitting parameters in the Arrhenius equation (See eq 3), the in-plane diffusion coefficient of Li atom in C2N/graphene bilayer is predicted to be 2.97 × 10-11 m2/s or 2.97 × 10-7 cm2/s at 300 K. In the case of Li-C2N model, the fitting parameters are obtained as D0 =2.12×10-7 m2/s and Ea = 20.95 kJ/mol or 0.22 eV/atom. The planar diffusion coefficient of Li atom at 300 K is calculated to be 4.74 × 10-11 m2/s or 4.74 × 10-7 cm2/s. Due to the relatively smaller activation energy of Li atom on C2N monolayer than that of C2N-graphene bilayer, the diffusion is predicted to be slightly faster in the former structure at room temperature. However, as can be seen from Figure 13 absorbed Li atoms on C2N/graphene bilayer exhibit larger average diffusion coefficient above 400 K in FPMD simulations than that of C2N monolayer. It might be interesting to compare the calculated diffusion coefficients of Li atom in the C2N and C2N/graphene models to that of Li-graphene or Li-graphite systems. The diffusion coefficient of Li on graphene was reported as 2.0 × 10-11 m2/s at the room temperature.87 In the graphite, the calculated diffusion coefficients of Li atom at room temperature were 1.0 × 10-11 cm2/s for the interstitial mechanism and 1.0 × 10-10 cm2/s for vacancy mechanism in Ref 63. For the same material, the experimentally measured diffusion coefficient is in the range from 10-7 cm2/s to 10-12 cm2/s at room temperature.63 Therefore, the diffusion dynamics of Li atom in either C2N or C2N/graphene bilayer structure are somehow similar to that of graphene monolayer, and which is superior to that of Li-graphite case.

D (m2/s)


4.0x10

-8

3.0x10

-8

2.0x10

-8

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-8

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C2N/G C2N

400

600

800

1000

1200

Temperature (K) Figure 13. The calculated general average of the in-plane diffusion coefficients as a function of temperature between 400 and 1200 K for the Li-C2N and Li-C2N/graphene system. The statistic error of the data at each temperature is indicated by the size of error bar. The solid-black/red line represents the fitting to the FPMD data by Arrhenius equation. 3.7 Open circuit voltage (OCV) The OCV is related to the adsorption energy by eq 6. For the anode material in LIBs, the desired OCV value should be in the range from 0 V to 1.0 V, preventing the formation of dendrite during the charging/discharging cycle.83 Here, we first calculate the OCV values for the C2N monolayer as a function of the specific capacity using eqs 4-7. As shown in Figure 14(a), the OCV decreases with the increasing of the absorbed Li atoms. The largest OCV is achieved for Li-C2N structure when all absorbed Li atoms are located at CN3 sites at the initial stage of lithiation. The calculated OCV profile for Li-C2N/graphene structure is illustrated in Figure 14(b), the highest value (V vs. Li/Li+: 3.10 V) is found to be slightly larger that of Li-C2N case (V vs. Li/Li+: 2.90 V). Similar to Li-C2N structure, occupying GCN3/CN3 sites provides the highest OCV in Li-C2N/graphene system. Since the adsorption energies of CN3 and GCN3 sites are very negative, the reversibility of insertion/extraction of Li atoms from those sites is expected to be relatively low. Therefore, the highest OCV for either C2N monolayer or C2N/graphene bilayer, which can be achieved in any practical LIBs, should be smaller than our predictions here. Regarding the OCV versus theoretical capacity, the 63.6 % of total capacity has the OCV below 1.0 V for C2N monolayer, and that value for C2N/graphene bilayer is 78.0 %. Interestingly, the percentages given here can be compared to those of MXenes reported in Ref 88, i.e., MoTiC2Tx (85 %) and Nb2CTx (66.0 %). For both C2N monolayer and C2N/graphene bilayer, the average OCV is estimated as 1.50 V. In Ref 76, the average voltages for other ion batteries based on borophene are reported as 2.37 V (LIB: V vs. Li/Li+), 1.70 V (NIB: V vs. Na/Na+), 1.48 V (KIB: V vs. K/K+), 0.91 V (MIB: V vs. Mg/Mg2+) and 1.32 V (AIB: V vs. Al/Al3+), respectively. For the phosphorene with various defects, the theoretical OCVs are found to be in the range from 0.23 V to 1.36 V in Ref 76. Therefore, the overall electrochemical performance of C2N monolayer or C2N/graphene

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bilayer is comparable to many other 2D materials which are widely investigated for the anode materials of LIBs.

AUTHOR INFORMATION Corresponding Authors

3.0

C2N monolayer

(a)

2.5 2.0 1.5 1.0 0.5 0.0 0

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(b) C2N/Graphene heterostructure

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Open Circuit Voltage (V)

Open Circuit Voltage (V)

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1000

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2.5

*B.X.: e-mail, [email protected]; tel, (0)29-82664000. *D.R.: e-mail, [email protected] ; tel, (0)25-88797783

2.0 1.5 1.0 0.5 0.0

ORCID 0

-1

Capacity (mAhg )

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200

300

400

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-1

Capacity (mAhg )

Bing Xiao: 0000-0002-1284-7386

Figure 14. The calculated open circuit voltage (OCV) as a function of theoretical capacity: (a): C2N monolayer; (b): C2N/graphene bilayer.

Notes

4. CONCLUSIONS

The authors declare no competing financial interest.

In this paper, we first calculated the electronic and lattice transport properties of C2N monolayer and C2N/graphene bilayer using density functional theory. It was found that the electrical and lattice thermal conductivities of C2N/graphene bilayer are much superior to those of C2N monolayer at room temperature (300 K). For the electrochemical properties, the theoretical capacity of C2N monolayer was found to be 220 % of C2N/graphene bilayer (490 mAh/g). The predicted open circuit voltage (OCV) of C2N/graphene was slightly larger than that of C2N monolayer. Using the NEB calculation, the migration energy barriers of both C2N monolayer and C2N/graphene bilayer were found to be suitable for the use as the anode materials of LIBs. Moreover, the predicted average planar diffusion coefficient of Li-C2N/graphene was 4.74 × 10-11 m2/s, and which is slightly better than that of C2N monolayer. We would suggest that both C2N monolayer and C2N/graphene bilayer might be used as the anode materials in LIBs. By applying the first principles molecular dynamics (FPMD) simulation in combination with CI-NEB method, it has been shown that the migration paths of Li atom at the room temperature could be described as the two-step process in C2N/graphene bilayer: the energetically favourable migration path in the z-direction for the intercalated Li atom through the large hole of C2N atomic layer or also refereed to vertical diffusion process, and the subsequent planar diffusion mechanism for the outer Li atoms absorbed on C2N upper surface. Nevertheless, the migration paths predicted by standard CI-NEB calculations were qualitatively correct, and which were in agreement with FPMD simulations at high temperature (> 800 K).

ACKNOWLEDGMENTS The work was carried out at LvLiang Cloud Computing Center of China, and the calculations were performed on TianHe-2. This work was supported by the Foundation Department of Education of Sichuan Province (No. 2017Z031). We would like to acknowledge the National Science Foundation (NSF) of China for the financial support (No. 51807146, 51801075).

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ASSOCIATED CONTENT Supporting Information

Convergence tests for adsorption energies, electrical conductivity of graphene/C2N heterostructure, the energy barrier of lithium diffusion pathways along the difference sites of monolayer C2N and Graphene (Figures S1−S2) and charge density difference of chosen adsorption sites of graphene/C2N heterostructure (Figures S3−S5).

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Improved Transport Properties and Novel Li Diffusion Dynamics in van

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