Defect-Mediated Lithium Adsorption and Diffusion on Monolayer Molybdenum Disulfide

Monolayer Molybdenum Disulfide (MoS2) is a promising anode material for lithium ion batteries because of its high capacities. In this work, first principle calculations based on spin density functional theory were performed to investigate adsorption and diffusion of lithium on monolayer MoS2 with defects, such as single- and few-atom vacancies, antisite, and grain boundary. The values of adsorption energies on the monolayer MoS2 with the defects were increased compared to those on the pristine MoS2. The presence of defects causes that the Li is strongly bound to the monolayer MoS2 with adsorption energies in the range between 2.81 and 3.80 eV. The donation of Li 2s electron to the defects causes an enhancement of adsorption of Li on the monolayer MoS2. At the same time, the presence of defects does not apparently affect the diffusion of Li, and the energy barriers are in the range of 0.25–0.42 eV. The presence of the defects can enhance the energy storage capacity, suggesting that the monolayer MoS2 with defects is a suitable anode material for the Li-ion batteries.

With increasing demand for lithium ion batteries (LIBs) to be smaller and lighter, but still to have a higher energy density, extensive research is needed to find advanced electrode materials which can provide high specific capacity, long cyclic stability, high-rate capability and safety 1,2 . Higher capacities of 600 to 1000 mAh/g of mono-layer graphene and their composites 3,4 compared to that of the bulk counterpart of graphite (372 mAh/g) 5 inspired researchers to search for other monolayer anode materials for the LIBs, such as graphdiyne 6 , molybdenum disulfide (MoS 2 ) 7 , boron carbon nitride nanosheets 8 , and monolayer V 2 O 5 9 , etc. MoS 2 has a layered structure, in which the atoms are covalently bonded to form two-dimensional layers that are stacked together through weak van der Waals interactions 10 . The weak interactions between interlayers allow foreign ions or molecules to be introduced among the interlayers through intercalation without causing significant volume changes. Therefore, MoS 2 could be developed as an intercalation host material to form a promising anode material for high energy density LIBs with a capacity of ~600 mAh/g 11 . Recently, nanostructured MoS 2 has been attracted much attention for the anode of the LIBs, and preliminary results showed it has a higher specific capacity than that of the bulk MoS 2 [12][13][14] . The nanoflower MoS 2 anode decorated with crumpled reduced graphene oxides exhibited a high specific capacity (1225 mAh/g) and an excellent cycling performance (680 mAh/g) after 250 cycles 13 . Ultrathin MoS 2 nano-layers on N-doped carbon shells showed a high specific capacity of ~1000 mAh/g 14 . MoS 2 /graphene nanocomposite showed a high specific capacity of 1400 mAh/g in the first cycle and remained a specific capacity value of 1351 mAh/g after 200 cycles 12 .
Recently, two-dimensional (2D) MoS 2 monolayer has been synthesized using different methods. It can be easily synthesized by a top-down methods by exfoliation from bulk materials, such as scotch tape based micromechanical exfoliation 15,16 , intercalation assisted exfoliation [17][18][19] , and liquid exfoliation 20,21 . The 2D MoS 2 monolayer can also be synthesized using different bottom up approaches, such as transition metal sulfurization 22,23 , molybdenum oxide sulfurization 24,25 , physical vapor deposition 26 , and hydrothermal synthesis 27,28 . Defects are inevitably introduced during these fabrication processes, and could significantly affect the physical, chemical and electrical properties of the two-dimensional MoS 2 material. The presence of defects in the monolayer MoS 2 has been proven experimentally, and the types of defects were found to be dependent on the synthesized methods [29][30][31][32] . The dominant category of common defects could be changed from sulphur vacancy in the mechanical exfoliation and chemical vapor deposited samples to molybdenum antisite in the physical vapor deposited samples 30,32 . MoS 2 monolayer with large areas could be synthesized using chemical vapor deposition (CVD) 29 . However, the obtained monolayer MoS 2 is often polycrystalline in nature; thus dislocations and grain boundaries (GBs) normally appear in this monolayer 23,31,33,34 . The effects of intrinsic point defects (including various vacancies and antisite defects) and grain boundaries on the electronic and magnetic properties of the MoS 2 monolayer have been investigated [34][35][36] .
The performance of the LIBs is significantly dependent on electrochemical properties of the cathode and anode materials 37 . The energy density is determined by the reversible capacity and operating voltage, which are generally determined by the electrode material chemistry, i.e., effective redox couples and maximum lithium concentration in active materials 37 . The rate capability and cycling performances are determined by the electronic and ion mobilities in the electrode materials. Apart from high energy density and fast ion mobility, electrode materials should be cheap, and also have good thermal stability which is related to the safety of LIBs 38 . Theoretical studies revealed that the Li can be stably adsorbed onto the MoS 2 monolayer with low diffusion barriers 7,39 . The intrinsic point defects (including various vacancies and antisite defects) and grain boundaries appear on the MoS 2 monolayer, however, their effects on the Li adsorption remain unexplored. In this report, for the first time as far as we know, we perform density functional theory (DFT) calculations of Li adsorption and diffusion on pristine and MoS 2 monolayers with various intrinsic point defects and grain boundaries. To be good anode materials for the LIBs, the diffusion barriers of the Li ion in the MoS 2 should be small, which can realize a fast charging rate. At the same time, the MoS 2 should have a large exothermic reaction energy with the lithium so that the anode materials have a large energy storage capacity.

Results
MoS 2 monolayer has a sandwich-like structure with the Mo layer sandwiched between two layers of S. There are two polymorphs of MoS 2 , i.e., trigonal phase (1T) and hexagonal phase (2H). At room temperature, the MoS 2 monolayer prefers to crystallize in a hexagonal phase 19 . The metal-stable 1T-MoS 2 phase upon lithium and sodium intercalation has been observed by in-situ transmission electron microscopy (TEM) measurements [40][41][42] . The real mechanism of the 2H-1T phase transition is not well addressed. As discussed below, the defect formation energies in the metastable 1T-MoS 2 have negative values, indicating that the 1T phase is not stable. Therefore, our investigations were focused mainly on the hexagonal phase structure. The calculated lattice parameters of monolayer 2H-MoS 2 are: a = b = 3.22 Å. The Mo-S bond lengths have a constant of 2.448 Å, which is in a good agreement with experimental results 43 and other simulation values 44 .
We considered the commonly observed point defects in the monolayer MoS 2 30,32 , including Mo (V Mo ) and S (V S ) single vacancies, S2 double vacancies (V S2 ), a vacancy complex of Mo and nearby three sulfur (V MoS3 ), a vacancy complex of Mo and three nearby disulfur pairs (V MoS6 ), and antisite defects where a Mo atom substituting a S atom (Mo S ) or a S atom substituting a Mo atom (S Mo ). The optimized defect structures from the DFT calculations in the 2H-MoS 2 and 1T-MoS 2 are shown in Fig. 1(b,c), respectively. The defects of atomistic structures for all the point defects including V Mo , V S , V S2 , V MoS3 , V MoS6 Mo S and S Mo in 2H-MoS 2 show a 3-fold symmetry nature. Except for the point defects, an extended line defect GBs often appears in the samples prepared by a CVD method 23,31,33,34 . Based on direct mapping results of grain boundaries 45,46 in the monolayer MoS 2 using transmission electron microscope, the grain boundary is considered to be consisted of pentagon/heptagons (5-7) pairs with low energy configurations. The pentagon/heptagons (5-7) pairs are the basic components of GBs in the other layers materials, as evidenced by the TEM in graphene 46,47 . Therefore, we modeled the Li interaction with a grain boundary consisting of 5-7 polygons in the monolayers as shown in Fig. 1(a), with the GBs showing a mirror image symmetry. Each repeated grain boundary cell is composed of a Mo-rich structure with a homoelemental Mo-Mo bond, and a reversed grain boundary with a sulfur-rich structure with two S-S bonds. (1) in a thermal equilibrium are defined by: (1) the values that prevent the formation of pure elements of Mo and S, in which the chemical potential cannot be higher than the energy of bulk materials of this species; (2) a thermal equilibrium with MoS 2 chemical potential of Mo and S, which should satisfy the equation μ MoS2 = μ Mo + 2μ S . The defect formation energies as a function of S chemical potential, over a wide range of conditions from Mo-rich to S-rich for the 2H-MoS 2 , are shown in Fig. 2(a), where the 2H-MoS 2 can remain stable with respect to the formation of bulk Mo (μ S = − 1.5 eV) or bulk alpha-S (μ S = 0 eV). It can be seen that the V S has the lowest formation energy, which is consistent with the experimental observation that the V S is frequently observed 30 . V S2 is defined as a missing pair of S atoms aligned along the c-axis of the MoS 2 lattice. The formation energy of the V S2 is about twice that of Vs, suggesting that the V s does not tend to combine together. This can be supported by the fact that randomly distributed V s was more frequently observed than the V S2 30 . The formation energy of the V Mo is higher than 4.59 eV even in the S-rich condition. Under the Mo-rich condition, V MoS3 has a lower defect formation energy than that of the V Mo , which means that once the V Mo is formed, the S atoms surrounding it become loose. The formation energy of large defects becomes higher as can be seen from Fig. 2(a), and the formation energy of V MoS6 is larger than that of V MoS3 for the whole chemical potentials. In the case of antisites, both the S Mo and Mo S have fairly low formation energy values for S-rich and Mo-rich conditions, respectively. The intrinsic defects can affect the electronic properties of the monolayer MoS 2 , thus much related work has been done to understand this effect 30,32,35,44 .

Defects in MoS 2 monolayer. The chemical potentials of Mo and S in equation
The defect formation energies as a function of S chemical potential over the range between Mo-rich and S-rich on 1T-MoS 2 are shown in Fig. 2(b). All the defects have negative formation energies for the 1T-MoS 2 in the whole S chemical potential range. The negative formation energy indicates that the defective 1T-MoS 2 structures are more stable than the pristine ones. It is also reported that the critical value of lithium required for the stabilization of the 1T phase is estimated to x ≈ 0.4 in Li x MoS 2 48 , now we will focus on how the defects affect the adsorption and diffusion the Li on the 2H-MoS 2 .   The pristine monolayer 2H-MoS 2 shows semiconductor properties. The valence band maximum (VBM) and conduction band minimum (CBM) are mainly composed of Mo 4d and S 3p states as seen from the projected density of states (PDOS) for both the Mo and S as shown in Fig. 4. As the Li atom is adopted on the pristine monolayer MoS 2 , the adsorption has no effect on the change of band gap and the near band edge band structure, except that the Fermi energy level moves upward into the conduction band. As the Li 2s state is ~3.7 eV, which means that Li is located above the CBM, the Li donates its electron to the CBM, thus pushing the Fermi level further upward. The Li adsorbed system shows an n-type doping state, which agrees well with the previous reports 49 . The electron transfer from the adatom to the substrate has been reported in other systems 5,49-51 . A charge transfer from K to the C layers is 0.57 electron for K adsorbed on graphene 49 . It was reported that a charge transfer of ~0.83 and 0.44 electron as Li atom adsorbed on the silicene 51 and graphene 50 , respectively. The charge transfer will give rise to an n-type doping of the substrate 49 . Some peaks appear in the bandgap for the monolayer MoS 2 with point defects, indicating that the point defects induce defect energy levels within the band gap. The Li 2s state locates at an energy higher than this defect levels, and the Li donates the 2s electron to the point defects. Therefore, the Li ion has a positive charge and the defect has a negative charge, and the adsorption was enhanced due to a strong coulomb interaction. The enhancement of Li adsorption in the defective graphene is also attributed to the same mechanism of coulomb interaction 52 .

Adsorption of Li on 2H-MoS 2 monolayer with grain boundaries.
The calculated formation energy of grain boundary is 0.20 eV/Å. The adsorption energies for a Li atom adsorbed at the different T and H sites of the monolayer 2H-MoS 2 with a grain boundary are shown in Fig. 5. For most of the tested sites, the Li adatom prefers to occupy the T site rather than the H site in the monolayer MoS 2 with the grain boundary. It can be seen that a Li adatom energetically prefers the adsorption sites near the grain boundary with a Mo-Mo bond, which indicates that the grain boundaries can significantly enhance the Li atom adsorption. For example, the Li adsorption energy at the T1 site is 0.33 eV, which is lower than that at the T12 site, indicating that Li is preferred to stay at the T1 site.   The site projected density of states indicates that the localized states within the band gap come from the Mo and S atoms located at the grain boundaries. The adopted Li donates its electron to the localized states, thus increasing the adsorption between the Li ion and monolayer 2H-MoS 2 .

Diffusion of Li on 2H-MoS 2 monolayer with defects.
As the charging rate of the LIBs relies on the Li ion mobility in the anode material, we studied the Li diffusion on the 2H-MoS 2 monolayer with defects. As discussed above, V S has the lowest formation energy in all the S chemical potential over the range between Mo-rich and S-rich, and S Mo and Mo S have fairly low formation energy values for S-rich and Mo-rich conditions, respectively. These defects have previously been confirmed from TEM observation 30 . We investigated the Li diffusion around the V S , S Mo , Mo S and GBs defects. The nudged elastic band method (NEB) 53 is a good choice for calculating the energy barriers, yet it needs large computation efforts. We used a constrained method to calculate the diffusion barriers. The diffusion pathway of the Li atoms was determined by moving the Li atoms along different paths with a small constant distance; and the total energy was recorded at each position. The Li atom was constrained in the direction along the path, but it is free to move in the directions perpendicular to the path, which enable the Li atom to find its optimized position. As the stable adsorption site for the Li in pristine 2H-MoS 2 monolayer is T site, the diffusion of Li occurs from one T site to a nearest T site by passing an H site, as shown in insert of Fig. 6(a). The calculated diffusion barrier for the Li in pristine 2H-MoS 2 monolayer is 0.23 eV, which agrees well with NEB results of 0.21 54 and 0.24 eV 55 . Clearly, the constrained method is reliable to be used to calculate the diffusion barrier of Li in 2H-MoS 2 monolayer. Two diffusion paths were considered for the Li diffusion in 2H-MoS 2 monolayer with V S defect, and the energy curves as a function of relative diffusion coordinates are shown in Fig. 6(b,c). The V S defect does not affect the diffusion away from the defect; the energy barrier is 0.23 eV as Li diffuse from position 0 to 2. The energy barrier increases about 0.08 eV compared with the value in pristine MoS 2 through path 1 in Fig. 6(b), and increases about 0.01 eV through path 2 in Fig. 6(c). The appearance of Mo S defect does not significantly affect the diffusion behavior of Li in 2H-MoS 2 monolayer, which can be concluded from Fig. 6(d). The S Mo defect induces the increase of energy barriers up to about 0.09 eV. The energy barriers are kept at 0.23 eV as in the pristine 2H-MoS 2 monolayer when the GBs appear. It can be seen from the energy curves in Fig. 6, the Li atom tends to diffuse to the defect position, therefore the diffusion barriers for backward diffusion of Li atoms were slightly increased. The maximum diffusion barriers are 0.37, 0.26, 0.42 and 0.30 eV for backward diffusion of Li atoms in 2H-MoS 2 monolayer with V S , Mo S , S Mo and GBs defects, respectively. From these results we can conclude that the V S , Mo S , S Mo and GBs defects can enhance the adsorption of Li, but do not significantly affect the diffusion behavior of Li.

Discussion
Defects will exist in real anode materials for LIBs, therefore, the effect of defects on the adsorption and diffusion Li in graphene 52,56-59 and silicene 60 has been investigated before. It was shown that the defects appear in graphene and silicene can enhance the adsorption of Li, thus can improve the Li storage capacities 56 . Together the results from this study, we can conclude that the presence of structural defects is beneficial for adsorption of Li atom in the two-dimensional materials. Li is bound to silicene with adsorption energies between 1.89 and 3.85 eV as the single vacancy, double vacancy and Stone-Thrower-Wales defects are presented 60 , which are higher than the values of 0.99-2.71 eV for the Li adopted on a defective grephene 58 . Our calculation shows that the Li can be strongly bounded to the defective 2H-MoS 2 monolayer with adsorption energies in the range between 2.81 and 3.80 eV. The presence of the single-vacancy in graphene leads to a backward diffusion barrier of 0.56 eV 52 , and the presence of divacancy and Stone-Wales in the graphene leads to backward diffusion barriers of 0.37-0.54 eV 58 , which is higher than our calculated values of 0.26-0.42 eV for the Li in 2H-MoS 2 monolayer with defects. The Li atom may be trapped by the defects in the graphene, thus cannot participate in the following electrochemical process. The presence of GBs in graphene leads to a decrease of about 0.92 eV in the adsorption energy of a Li adatom with diffusion barriers between 0.254 and 0.535 eV 59 . Our simulation results showed that the presence of GBs in the 2H-MoS 2 monolayer leads a decrease of 1.2 eV in the adsorption energy of a Li adatom, and keeps the low diffusion barrier of 0.23 eV as in the pristine 2H-MoS 2 monolayer. As the adsorption energy is higher than that in the defective graphene and the diffusion barriers are lower than that in the graphene, MoS 2 monolayer should be a better anode material for the LIBs compared to graphene.

Conclusion
The adsorption and diffusion of Li atom on the monolayer MoS 2 with defects was studied using spin density functional theory. All the defects including single-and few-atom vacancies, antisite, and grain boundary can enhance the adsorption of Li atom on the monolayer MoS 2 . The donation of Li 2s electron to the defects causes a strong coulomb interaction, thus enhances the adsorption. High adsorption energies and small diffusion barriers for the Li in the defective MoS 2 suggested that a monolayer MoS 2 with defects is a suitable anode material for the Li-ion batteries.
Simulations Details. All the calculations were performed using the spin density functional theory as implemented in the SIESTA code 61 . The electron exchange-correlation was processed using the generalized gradient approximation (GGA) with the parametrization scheme of Perdew-Burke-Ernzerhof (PBE) 62 , and the projector augmented wave (PAW) method 62 was used to describe electron-ion interaction. Tests with a local density approximation (LDA) gave similar results for GGA in the calculations of the lattice parameters and band structures. Therefore, only the exchange-correlation potentials treated within GGA are applied for all the calculations. Electrons were described with norm-conserving Troullier-Martins pseudo-potentials 63 . The valence electron wave functions were expanded using double-ζ basis set plus polarization functions. The charge density was projected on a real space grid with a cutoff of 150 Ry to calculate the self-consistent Hamiltonian matrix elements.
A 5 × 5 hexagonal supercell of monolayer MoS 2 was employed to model the point defects and the Li adsorption. A large spacing of 25 Å between the monolayers of MoS 2 was used to prevent interlayer coupling. The Brillouin zone integration was modeled using a special k-point sampling of the Monkhorst-Pack scheme with a Г-centered grid. For the structural relaxation, a 3 × 3 × 1 k-grid was adopted for the calculations. All atomic positions and lattice constants were optimized using the conjugate gradient method until the maximum Hellmann-Feynman force acting on each atom was less than 0.02 eV/Å.
The defect formation energy E f of defect α was calculated from the following expression 64 : where E(α) is the total energy of the supercell containing a relaxed defect (vacancy, vacancy complex and antisite), E(pristine) is the total energy of the same supercell without defects, μ i is the chemical potential of species i. n i is the number of exchanged particles between the supercell and the reservoirs in forming the defect cell. The formation energy of grain boundary was calculated using E f = (E grainbounary − E pristine )/L GB , where E grainboundary and E pristine are the total energy values of a pristine MoS 2 monolayer and the one with the grain boundary having the same number of MoS 2 atoms pairs, and L GB is the length of the grain boundary.
To analyze the stability of Li adsorbed on MoS 2 with point defects, the adsorption energy of a Li adatom was calculated using where − E MoS Li 2 and E MoS 2 are the total energies of MoS 2 with and without Li-adsorption, respectively. E Li is the energy of an isolated lithium atom. According to the definition, a more negative binding energy indicates a more favorable exothermic reaction between the monolayer MoS 2 and Li.