Origin of Structural Transformation in Mono- and Bi-Layered Molybdenum Disulfide

Mono- and multi-layered molybdenum disulfide (MoS2) is considered to be one of the next generation anode materials for rechargeable ion batteries. Structural transformation from trigonal prismatic (2H) to octahedral (1T) upon lithium or sodium intercalation has been in-situ observed experimentally using transmission electron microscope during studies of their electrochemical dynamics processes. In this work, we explored the fundamental mechanisms of this structural transformation in both mono- and bi-layered MoS2 using density functional theory. For the intercalated MoS2, the Li and Na donate their electrons to the MoS2. Based on the theoretical analysis, we confirmed that, for the first time, electron transfer is dominant in initiating this structural transformation, and the results provide an in-depth understanding of the transformation mechanism induced by the electron doping. The critical values of electron concentrations for this structural transformation are decreased with increasing the layer thickness.

the 2H-MoS 2 by intercalating alkali metals 25 . Using in-situ transmission electron microscopy (TEM) technique, a real time imaging characterization of the electrochemical process at the atomic level was performed to investigate the atomistic mechanisms of the 2H-1T/1T' transition in the MoS 2 upon lithium or sodium intercalation [26][27][28] . A shear mechanism of the 2H-1T/1T' phase transition has been identified by probing the dynamic phase boundary movement 27 . The stability of the 2H-and 1T-LiMoS 2 has also been investigated as functions of the Li content and intercalation sites 29,30 , and results showed that the critical content of lithium, required for the initialization of the 2H→ 1T phase transition, was estimated to be x ≈ 0.4 in Li x MoS 2 29 . Apart from the alkali metals, whose intercalation could induce 2H→ 1T/1T' phase transition, the phase transition in the MoS 2 was also reported to be caused by the substitutional doping of Mo by Re atom 31 , in which Re has one more valence electron than Mo. The 2H-1T' phase transition was also reported to be induced by using a high dose electron beam irradiation during heating the MoS 2 monolayer 32 or by using hot electrons generated by plasmonic nanoparticles deposited onto a MoS 2 monolayer 33 .
However, currently the mechanisms of the structural transformation from 2H→ 1T/1T' induced by various methods, such as alkali metals intercalation, Re-doping, electron irradiation and hot electron doping, are not fully understood. As the metastable 1T-MoS 2 shows enhanced magnetism 34 and can be used as electrode materials for supercapacitors 35 , understanding the mechanisms of these structural transformations is crucial to improve the battery performance, material design and practical applications.
The MoS 2 shows layer-dependence electronic properties [36][37][38] . The valence bands of the monolayer MoS 2 are distinctly different from those of few-layer and bulk MoS 2 , and the valence band maximum of a MoS 2 monolayer is located at K point of the first Brillouin zone (BZ), rather than at Г point in a bulk MoS 2 36 . Electrocatalysis of the MoS 2 for hydrogen evolution also showed this layer dependent behaviour 39 . If the layered MoS 2 is used in the anode materials for rechargeable ion batteries, the interstitial sites between the adjacent layers provide different adsorption sites compared with those of a monolayer MoS 2 . The MoS 2 materials studied in the literature have various properties of size, morphology and number of layers [19][20][21][22][23] . The dependence of structural transformation on the layer number has not been investigated. Therefore, it is imperative to obtain a comprehensive understanding of the structural transformation in different layered MoS 2 .
In this paper, for the first time, the origin or mechanism of the structural transformation of mono-and bi-layers MoS 2 was investigated using a density functional theory (DFT). Based on the results from the first principle calculation, we concluded that the electron transfer is the key reason for the structural transformation of the 2H→ 1T' in the MoS 2 .

Results
The lattice parameters of the 2H-MoS 2 mono-and bi-layers after a full structural optimization using the DFT are a = b = 3.19 Å, which are consistent with the previously calculated values of 3.18-3.19 Å 40,41 and experimental value of 3.20 Å 42 . Those of the 1T'-MoS 2 are a = b = 3.18 Å. It was reported that there are several types of stacking sequences for the bilayer MoS 2 synthesized using chemical vapour deposition method [43][44][45] . Changing the stacking sequence can tune the electronic properties of the bilayer MoS 2 . The DFT simulations showed that the bilayer MoS 2 with AA' stacking sequence is energy favorable than the other types of stacking sequences 46 . In AA' stacking sequence, the top layer Mo (S) atoms align vertically with the bottom layer S (Mo) atoms. In this work, we modeled the structural transformation of the bilayer MoS 2 with AA' stacking sequence.
2H→1T' phase transition in MoS 2 upon electron doping. A 2 × 2 hexagonal supercell of the MoS 2 layers was used to study the stability of both the 2H-and 1T'-MoS 2 . The 1T-MoS 2 monolayer can maintain its structure with a 1 × 1 supercell, however, it will change into the 1T' structure when a 2 × 2 supercells was used. This phenomenon was also reported by Kan et al. 47 . First principles analysis shows that the instability of the 1T-MoS 2 is caused by the instability of phonon dispersion at M-point 48 . A distorted structure of 1T-MoS 2 phase, i.e. the 1T'-MoS 2 , can be stabilized by dimerization of Mo atoms [48][49][50] , as shown in Fig. 1(c). The calculated three nearest Mo-Mo distances are 2.775, 3.193, and 3.825 Å, which agree with the previous simulation values of 2.769, 3.175 and 3.808 Å 51 . Based on the analysis, we did not find any layer dependent dimerization of the Mo atoms. The 1T'-MoS 2 is 0.26 eV per formula unit (eV/f.u.) energy lower than that of the 1T-MoS 2 for both mono-and bi-layers. To investigate the stability of both the 2H-and 1T'-LiMoS 2 , extra numbers of electrons were injected into the MoS 2 lattices instead of the traditional method of increasing the Li adsorption to characterize the modified electron density 29,30 . Figure 2 shows the energy difference per MoS 2 molecule between the 2H-and 1T'-phases, Δ E = E 1T' − E 2H , as a function of extra electron concentration. The 2H-phase is more stable than 1T'-phase at lower electron concentrations, and it is also energetically stable (with an energy difference value of 0.54 eV/f.u.) than the 1T'-phase without addition of electrons, which agrees well with the value of 0.55 eV/f.u. reported by Esfahani et al. 30 and 0.51 eV/f.u. reported by Kan et al. 47 . The 1T'-phase becomes more stable with increasing the electron concentration, i.e. a 2H→ 1T' phase transition will occur by increasing the electron concentration. The critical values of adding extra electron concentrations to trigger the 2H→ 1T' phase transition were calculated to be 0.78 and 0.55 e/f.u. for the mono-and bi-layers, respectively. For the bulk Li x MoS 2 , the critical value of x was predicted to be 0.4 for the 2H→ 1T structural transformation 29 . Therefore, our results showed that the critical electron concentration for the 2H→ 1T' phase transition decreases with the increase of thickness of MoS 2 layers.

Table 1. Calculated adsorption energies (in eV) versus vacuum (V) and bulk metal (B) reference states for Li and Na in mono-and bi-layers MoS 2.
Scientific RepoRts | 6:26666 | DOI: 10.1038/srep26666 Adsorption of Li/Na on 2H-MoS 2 . Li/Na adsorptions on the mono-and bi-layers 2H-MoS 2 were investigated using a 6 × 6 MoS 2 hexagonal supercell to avoid periodical image interactions. All the previous investigations 41,42 showed that both the Li and Na prefer to occupy the top of the molybdenum site (T) compared with center of the hexagon site (H) on the mono-layer of the 2H-MoS 2 . There are two preferred positions for the Li/ Na intercalation into the interlayer spaces for MoS 2 bi-layers: (1) an octahedral site enclosed by six S atoms; and (2) a tetrahedral site enclosed by four S atoms. These interstitial sites are corresponding to the T and H sites in the monolayer MoS 2 . Figure 3 shows the side-view and cross-section view of the adsorption sites. We calculated the adsorption energy values of Li/Na on the MoS 2 using E ads = E MoS2+Li/Na − E MoS2 − E Li/Na , where E MoS2+Li/Na and E MoS2 are the total energies of MoS 2 with and without Li/Na adatom adsorption, respectively. The adsorption energy can be calculated reference to adatom either in vacuum (modeled as an isolated atom in a supercell of size 30 × 30 × 30 Å 3 ) or in bulk metal. E Li/Na is the energy of an isolated Li/Na atom or half of the energy body center cubic Li/Na bulk metal. A negative value of the adsorption energy indicates a thermodynamic favorable intercalation process. The calculated adsorption energies of the Li/Na in the monolayer and bilayer 2H-MoS 2 are listed in Table 1. The calculated adsorption energies are − 1.8 and − 1.6 eV for the Li to be adsorbed at T and H sites on mono-layer 2H-MoS 2 , respectively, which agree well with the previous report of Li prefer to occupy the T site 52,53 . The adsorption energy of the Na adsorbed at the T site on the 2H-MoS 2 is −1.3 eV, which is 0.1 eV energy lower than that adsorbed at the H site. It was reported that the Na cannot penetrate through the surface monolayer of MoS 2 , and it prefers to stay on the surface of (0001) of MoS 2 54 . whereas K can be intercalated into the interlayer spaces of MoS 2 crystal 55 .
It was found that the adsorption energy value of the octahedral site is 0.12 eV lower than that of the tetrahedral site for Na adsorbed in the bi-layers of the 2H-MoS 2 . However, the Li prefers to occupy the tetrahedral site. It was also obtained that the Li and Na all prefer to occupy the interlayer position than the surface of the 2H-MoS 2 . Previous simulation results also showed that the Li prefers to be in the interlayer space than on the surface in bi-layers graphene 56 .

Charge distribution in MoS 2 upon electron doping and Li/Na adsorption.
The effects of extra numbers of electrons by the electron injection were studied using the equation (1) based on the differences in charge densities in the MoS 2 with and without electron doping, with without where ρ r ( ) with and ρ r ( ) without are the charge densities of the MoS 2 with and without electron injection at position r, respectively. The electron injection was performed by adding electrons into the cell, and a compensating background was used to achieve the charge neutrality 57 . This was done by immerging the original charged system into a jellium background which fills the cell, and then neutralizing the charge to keep the net charge to be zero 58 . The redistribution of charge densities of Li/Na adsorbed MoS 2 systems was calculated using the equation (2),  Fig. 4(a-c). The red and green surfaces correspond to gains and loss of charges, respectively. There is no apparent redistribution of charge for the MoS 2 doped with electron injection concentrations of 0.25 e/f.u. or below. With increasing the electron injection concentrations, there is an apparent loss of electronic charges from the Mo-S bonds, whereas there is a net gain of electronic charge surrounding the Mo atoms. The distribution of electronic charge on the Mo atom shows an orbital characters of dz 2 59 , indicating that the doped electrons and the lost electrons from the Mo-S bonds all fill the Mo dz 2 orbital. The phenomenon of electron doping leading to occupation of the conduction band minimum (CBM) was also reported by Chakraborty et al. 60 . The transfer characteristic of the top-gated single-layer MoS 2 transistor device showed an on-off ratio of ~10 5 and a field-effect mobility of 50 cm 2 /Vs with electron doping of ~2 × 10 13 /cm 2 60 . The differences of charge densities for the Li and Na adsorbed MoS 2 systems are shown in Fig. 4(d,e), respectively. The electronic charge surrounding Li/Na decreases, resulting in a net loss of electronic charge of the Li/Na. There was a charge loss on the Mo-S bonds at the Li/Na adsorption site on MoS 2 . A net gain of electronic charge in the Li/Na-S bonds and Mo dz 2 orbital can be observed. The Li/Na donate their electrons to the CBM of the 2H-MoS 2 61 , which results in an n-type doping character of Li/Na adsorbed 2H-MoS 2 systems. The same phenomenon has been reported Li-doped graphene systems [62][63][64][65] . The bonding of Li/Na adatoms appears to be primarily ionic bonding 66 , which is same with that in Li intercalated graphene system 67,68 .
The charge distributions of the bi-layers 2H-MoS 2 injected with 0.25, 0.75, and 1.00 e/f.u. electron and Li/Na adsorption are shown in Fig. 5, which shows the same characteristics as those of the mono-layer 2H-MoS 2 .

Discussion
Within the framework of crystal field theory, the energy of the 4d orbitals of Mo ions will be affected by the arrangement of surrounding negative ions. The five 4d orbitals are initially degenerate (have the same energy). Placing six negatively charged ions at the vertices of an octahedron does not change the average energy of the 4d orbitals, but will remove their degeneracy. As the Mo atom is in trigonal prism coordination sites in the 2H-MoS 2 , the five degenerate 4d orbitals are split into (1) one singly degenerate state dz 2 (filled), (2) two doubly-degenerate states dx 2 − y 2 , dxy (empty), and (3) two doubly-degenerate states dxz, dyz (empty), as shown in Fig. 6(d). Whereas the Mo 4d orbitals of an O h -MoS 6 unit in the 1T-MoS 2 can be separated into two groups: (1) three degenerated dxz, dyz and dxy orbitals occupied by two electrons; and (2) non-occupied dz 2 and dx 2 − y 2 as shown in Fig. 6(f). Incomplete occupation of the degenerated orbitals leads to the metallic ground state of the 1T-MoS 2 , and also decreases lattice stability compared with that of the 2H-MoS 2 69 . As the 1T-MoS 2 is doped with electrons, the extra electrons will occupy the dxz, dyz and dxy orbitals, thus increasing the stability of the 1T-MoS 2 . When such kind of doping occurs in the semiconducting 2H-MoS 2 , the extra electrons occupy the dx 2 − y 2 and dxy states, thus resulting in a metallic-like character of the electronic structure and destabilization of the lattice 31 .
The partial density of states (PDOS) of 2H-and 1T'-monolayer MoS 2 are shown in Fig. 6(a,b), respectively. The 2H-monolayer MoS 2 shows a semiconductor character with a band gap of 1.70 eV. The electronic states near the valence band maximum (VBM) and CBM are mainly composed of Mo 4dz 2 , 4dx 2 − y 2 and 4dxy, whereas the Mo 4dxz and 4dyz orbitals do not contribute to the energy states near the VBM and CBM, which agrees with the literature 17,18,70 . The 1T'-monolayer MoS 2 shows a metallic-like character. The extra electrons either from injection or from ion intercalation doping occupy the Mo 4dz 2 , and induce loss of charges from the Mo-S bonds, which will destabilize the lattice of the 2H-MoS 2 as shown in Fig. 6(c). On the contrary, there is no loss of charge from the Mo-S bonds in the 1T'-MoS 2 .
From the charge distribution shown in Fig. 6(e), the extra electrons occupy the S 3p and Mo orbitals of dxz, dyz and dxy 59 . This explains the stabilization of the 1T' structure upon Li/Na adsorption or electron doping. The electron doping destabilizes the crystal structure of the 2H-MoS 2 , and causes the structural transformation into the 1T' phase through the re-distribution of the Mo 4d orbitals.

Conclusion
The stability of 2H-and 1T'-MoS 2 for both the mono-and bi-layers upon electron doping was investigated using the density functional theory, and then linked with that for Li/Na intercalation process. After doping with electrons, the 2H-and 1T'-MoS 2 show semiconductor and metallic characters, respectively. The extra electrons either from charge injection or from ion intercalation doping occupy the Mo 4dz 2 in 2H-MoS 2 , and induce loss of electronic charge from the Mo-S bonds. Whereas, the extra electrons occupy the S 3p and Mo orbitals of dxz, dyz and dxy in the 1T'-MoS 2 without apparent loss of electronic charge from the Mo-S bonds. Whereas electron doping destabilizes the crystal structure of the 2H-MoS 2 , and causes its structural transformation into the 1T' phase through the redistribution of the Mo 4d orbitals. The critical values of electron concentrations for the 2H→ 1T' phase transition decrease with increasing the layer thickness.
Simulation details. The stability of 2H-and 1T'-MoS 2 and Li/Na adsorption behavior in the two polytypic structures were investigated using first principles plane-wave simulations based on DFT as implemented in the Vienna ab initio simulation package (VASP) 71 . Electron-ion interaction and electron exchange-correlation were described using the projector augmented wave (PAW) method 72 and the generalized gradient approximation was described using the Perdew-Burke-Ernzerhof (PBE) function, respectively. An energy cutoff of 520 eV was used for the plane wave basis sets. Spin-polarization was considered applied for all the simulations.
A 2 × 2 supercell of MoS 2 monolayer was used to investigate the stability of 2H-and 1T' phases with monoand bi-layers of MoS 2 . A 6 × 6 supercell of MoS 2 monolayer was used to investigate the adsorption of Li/Na. A 25 Å vacuum space were constructed to avoid the periodical image interactions between two adjacent MoS 2 layers. The Brillouin zone was integrated using the Monkhorst-Pack scheme 73 with 5 × 5 × 1 k-grid. All the atomic positions and cell parameters were relaxed until the force on each atom is less than 0.02 eV/Å. Electron concentrations of 0.125-1.00 e/f.u., i.e. 0.14-1.13 × 10 15 /cm 2 and 0.28-2.26 × 10 15 /cm 2 were injected into the mono-and bi-layer MoS 2 , respectively, to investigate the stability of 2H-and 1T'-MoS 2 .