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Adsorption and Diffusion of Lithium on Monolayer Transition Metal Dichalcogenides (MoS Se ) Alloys 2(1-x)

2x

Fatih Ersan, Gökhan Göko#lu, and Ethem Akturk J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b09034 • Publication Date (Web): 04 Dec 2015 Downloaded from http://pubs.acs.org on December 5, 2015

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The Journal of Physical Chemistry

Adsorption and Diffusion of Lithium on Monolayer Transition Metal Dichalcogenides (MoS2(1−x)Se2x) Alloys ˘ ‡ and Ethem Aktürk∗,†,¶ Fatih Ersan,† Gökhan Gökoglu,

Department of Physics, Adnan Menderes University, Aydn 09010, Turkey, Department of Physics, Karabük University, 78050 Karabük, Turkey, and Nanotechnology Application and Research Center, Adnan Menderes University, Aydn 09010, Turkey E-mail: [email protected]

Phone: +902562130835-1894;. Fax: +902562135379

To whom correspondence should be addressed Department of Physics, Adnan Menderes University, Aydn 09010, Turkey ‡ Department of Physics, Karabük University, 78050 Karabük, Turkey ¶ Nanotechnology Application and Research Center, Adnan Menderes University, Aydn 09010, Turkey ∗ †

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)>IJH=?J Based on rst-principles plane-wave calculations, we examine the adsorption and diusion of lithium on the hexagonal MoS2(1−x) Se2x monolayers with variation of x for 0.00, 0.33, 0.50, 0.66, and 1.00. We nd that the lowest energy adsorption positions of Li adatom is at the top site of Mo atom in both MoS2 and MoSe2 monolayers, while Li moves through the Mo-S bond for MoS2(1−x) Se2x . While bare MoS2(1−x) Se2x compounds are nonmagnetic semiconductor and its energy band gap varies with x, they can be metallized by Li adsorption. NEB calculation results show that their energy barriers make them suitable for using in electrode materials. The lithium adsorption energy is sensitive to the external strain, when we elongate the lattice constants, the adsorption energy decreases quickly. We also examine the penetration energy barrier for single lithium atom to pass through the MoS2(1−x) Se2x monolayers, this barrier is decreasing from ≈2.5 eV to ≈1.3 eV with increasing selenium concentration. Introduction

The transition-metal dichalcogenides (TMDs) have attracted a considerable attention owing to their typical layered structures and their band gaps. While they possess weak Van der Waals forces between layers, they have a strong chemical bonding within the layers, since these structures are suitable for exfoliation to 2D materials. After this process, their indirect band gaps that they have in 3D forms (see Supporting Information ), turn to direct gaps between 1-2 eV 1,2 . These materials with band gaps corresponding to the visible region of the spectrum have potential applications for a variety of electronic and optoelectronic applications and also in solar cells. 35 There have been several studies about TMDs to investigate their properties in various situations. 68 Especially, they are suitable materials for energy storage, 9,10 such as lithium ion battery (LIB), 11 supercapacitors, 12 and also for hydrogen evolution reactions. 13,14 For example, monolayer MoS 2 has lower Li ion diusion barrier compared to graphene, 15 and has high energy capacity of 1200 mAh/g 16,17 while graphene 2


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has that of 600-900 mAh/g. 18,19 This make it potential material for anode of LIB 20,21 , and also MoS2 nanoribbon as a promising cathode material for rechargeable Mg batteries. 22 Recently, mesoporous MoSe 2 has been synthesized and it has a reversible lithium storage capacity of 630 mAh/g for at least 35 cycles. 23 Hui Wang et al. showed that nanocrystaline MoSe2 can be anode materials for high performance lithium ion battery. 24 Single layer TMDs alloys such as MoS 2(1−x) Se2x , 25 Mo1−x Wx S2 , 26,27 and also Nbx Mo1−x S2 28 with honeycomb structure have been a subject of active study in order to develop an ecient medium of energy storage. The experimental and theoretical studies show that there exist stable ordered structures for monolayer MoS 2(1−x) Se2x alloy which have x=1/3, 1/2, and 2/3 concentrations. 29 These alloys have intriguing results with changing the ratio of the components. Their electronic properties can be modied by systematic variation in ratio. For instance, the band gaps decrease while ratio of Se atoms increase in MoS 2(1−x) Se2x and WS2(1−x) Se2x alloys, but the direct gap property doesn't change. 29,30 Jadczak et. al. obtained from Raman scattering measurements that the splitting of A 1g mode for increasing composition of x in MoSx Se2−x alloy is related with the weight of atoms. 31 The measurements of Klee et. al. showed that photocurrent at xed wavelength is decreasing with increasing Se atoms in MoS2(1−x) Se2x alloys. 32 According to Kiran et. al., few layer molybdenum sulphoselenides can serve to higher hydrogen evolution (HER) activity compared to pristine MoS 2 and MoSe2 . 33 In this respect, it will be important to examine how lithium interacts and diuses on monolayer MoS 2(1−x) Se2x alloys while selenium concentration increases. Therefore, in this work, we carry out a detailed study on the lithium adsorption on MoS 2(1−x) Se2x compounds based on rst-principles investigation. We also present diusion path of lithium to predict the possible applications for LIB. We display an extensive analysis of electronic structure and charge density. We nd that lithium adatom is bound to MoS 2 and MoSe2 at top site (top of a Mo atom), while this atom bounds to MoS 2(1−x) Se2x compounds at bridge site above a Mo-S bond. All investigated MoS 2(1−x) Se2x compounds are found to be nonmagnetic semiconductor. However, the same compounds become metallized upon the 3



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adsorption of lithium atom.

Computational Details Our calculations are based on the rst-principles spin polarized plane wave method within density functional theory (DFT) using ultrasoft pseudopotentials. The valence states of the atoms are as follows: Mo: 4d 2 5s1 5p0 , S:3s2 3p4 , Se:4s2 4p4 , Li:1s2 2s1 . The exchange correlation functional is approximated with generalized gradient approximation using Perdew-BurkeErnzerhof parametrization !" including van der Waals (vdW) correction. !# All numerical calculations are carried out by using Quantum Espresso software. !$ In the self-consistent eld potential and total energy calculations, Brillouin Zone (BZ) is sampled using (3 ×3×1) Monkhorst-Pack special k-points mesh for (3 ×3) monolayer MoS2(1−x) Se2x cell. !% A planewave basis set with kinetic energy cuto of h ¯ 2 | k + G |2 /2m = 1088 eV is used. All atomic positions and lattice constants are optimized by using the BFGS method, where the total energy and atomic forces are minimized. !& The convergence criterion for energy is chosen as 10−5 eV between two successive iteration steps, and the maximum Hellmann-Feynman forces exerted on each atom is reduced to less than 0.05 eV/Å upon ionic relaxation. The maximum pressure on the unit cell is reduced to less than 0.5 kbar. Methfessel-Paxton type smearing method is used with a smearing width of 0.01 eV. Two MoS 2(1−x) Se2x layers are separated by a distance of 20 Å vacuum region to avoid interlayer interactions. Bader analysis !' is used for determination of the charges on the atoms. To seek the minimum energy path and saddle points between determined initial and nal positions we use climbing image nudged elastic band (CI-NEB) method. "

Results and Discussion For the sake of comparison, we rst carried out the properties of three-dimensional layered structure of MoS2 and MoSe2 . The calculated structure parameters and related properties of 4


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2H-MoS2 and 2H-MoSe2 are given in Supporting

Information .

We next consider 1H-MoS 2

and 1H-MoSe2 structures. The lattice constants of the optimized structure in equilibrium are calculated to be a = 3.198 Å and a = 3.328 Å, respectively. In order to consider the lithium adatom as isolated dopant, we use 3 ×3 supercells of bare and alloy structures. This lattice dimension provides sucient distance to avoid interactions between lithium adatoms. To construct MoS2(1−x) Se2x alloys, we choose stable structures as obtained in literature.

'

We rstly examine electronic and structural properties of bare MoS 2 , MoSe2 , and their alloys to verify the chosen pseudopotentials. The obtained parameters are given in Table 1 and the variation of lattice constant with increasing Se atoms is also given in Fig.1. As can be seen in this gure, the lattice constants of the systems are enhanced with increasing number of Se atoms due to larger ionic radius of Se compared to S atom in agreement with literature. We evaluate the cohesive energy as follows:

Ecoh = [nM o EM o + nS ES + nSe ESe − EM oS2(1−x) Se2x ]/9

(1)

where EM oS2(1−x) Se2x is the total energy of the bare TMD monolayer, EM o , ES , and ESe are the energies of isolated free atoms of Mo, S, and Se, respectively. nM o , nS , and nSe are the numbers of Mo, S, and Se atoms in the supercell, respectively. The coecient 9 is for trio of MoX2 as included in (3×3) supercells. We nd that the cohesive energies of the systems are inversely proportional with lattice constants, while it is directly proportional with their band gaps. All of the systems have direct band gaps between 1.624-1.428 eV and the gaps decrease through x=0.00 to x=1.00 (see

Supporting Information ).

Band-gaps

are actually predicted correctly by DFT-PBE for this material system. For MoS 2 system, 0.60 electrons are transferred from Mo atoms to sulphur atoms, this value increases to 0.69 electrons with increasing selenium content. This situation occurs in an opposite manner for Mo and Se atoms, in bare MoSe 2 system while 0.48 electrons are transferred from Mo to Se, this value decreases to 0.41 electrons with decreasing Se atom in TMDs alloys. All of S, Se

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atoms form p-d hybridization with Mo atoms and constitute ionic bonds. This gives a clue about where lithium atom can prefer to bind in TMDs structure. After the examination of pristine TMDs and their alloys, we start to investigate the interaction of lithium atom with these monolayers. In order to determine the most stable adsorption site, we use adsorption energy formula as follows:

Eads = EM oS2(1−x) Se2x +Li − EM oS2(1−x) Se2x − ELi

(2)

where EM oS2(1−x) Se2x +Li is the energy of total system, EM oS2(1−x) Se2x is the energy of (3×3) bare hexagonal TMD structure, and ELi is the energy of free lithium atom. We also use this formula to determine the binding energy for strain and penetration calculations that will be mentioned later. We dene the stability by more negative values. The obtained results are given in Table 1. According to our results, lithium prefers to bind over molybdenum atom for MoS2 and MoSe2 systems, while lithium adsorption site is deviating slightly along some Mo-S bond for alloys. These results are also in agreement with charge transfers that occur in bare monolayers. The lattice constants are enhanced approximately 0.7% by lithium adsorptions as seen in Fig.1. The charge dierences are also shown at right side of Fig.1. The charge dierence isosurfaces are determined as below;

Δρ = ρtotal − ρM oS2(1−x) Se2x − ρLi

(3)

where ρtotal is the total charge of total system, ρM oS2(1−x) Se2x is the charge of (3×3) pristine TMD monolayer, and ρLi is the charge of Li adatoms. All charge densities are plotted by using VESTA programme " with isosurfaces 0.002 electrons/Å 3 . According to Bader charge analysis, ≈0.90 electrons transfer from lithium to around atoms for all the systems. While S and Se atoms are bounded with lithium, each of them take 0.20 electrons, the remaining electrons are shared with Mo atoms. These electron transfers between constituents turn nonmagnetic semiconductors into nonmagnetic metallic materials. The emerging metallic 6


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systems with single lithium adsorption make them favorable as the electrode material due to good electrical conductivity compared to bare MoS 2 and MoSe2 systems. Because LIB performance is closely related with electrode materials conductivity, so the electron contributions are important to examine electrodes in details. This situation can be seen in density of states (DOS) in Fig.2 which are related with one lithium adsorption upon Mo atoms. The bare MoS2(1−x) Se2x systems (i.e. without Li adsorption) are nonmagnetic semiconductors with an electronic gap restricted by Mo-d states. Lithium s orbitals contribute the systems at conduction bands around 2 eV. These contributions occupy the unoccupied conduction bands in systems and slip them below Fermi level, so these crossing bands make the system metal. DOS graphs show that s-p hybridization occurs between Li and S or Se atoms. Proportional with the number of chalcogenides in the systems, their electron contributions increase or decrease. Therefore, the electronic conductivity would be good even though single lithium atom is adsorbed. Despite the fact that electrical conductivity is important to determine the rate performance of electrode materials, it is not enough by itself. The ion diusion characters should also be known. Thus the diusion of lithium adatom on TMDs and on their alloys is investigated in the present study. To seek the minimum energy path and saddle points, we use climbing image nudged elastic band (CI-NEB) method. 40 Cause of the energetic favorability, we choose two nearest neighboring molybdenum atoms (T 1 and T2 ). Before the CI-NEB calculation, rstly initial and nal images of the structures are fully optimized and then nine intermediate images with equal intervals are linearly chosen between them as seen in Fig.3. For MoS2 and MoSe2 systems, there are two energy minima, one of them is absolute energy minimum where the lithium is adsorbed on top sites of Mo atoms, and the other one is a local minimum corresponding to the lithium above the hollow sites of hexagonal rings. The calculated energy barrier for this path of a lithium adatom is 0.194 eV and 0.237 eV for MoS2 and MoSe2 , respectively. These energy barriers are lower than pristine graphene and silicene sheets. 42,43 This high mobility prediction implies that rate performance of MoS 2 and

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MoSe monolayers can be better than graphene and silicene. If we examine the diusion paths of TMD alloys, we will see two antisymmetric maxima. The alloys with x=0.33 and x=0.66 have one local and one global minima, while x=0.50 alloy has two local minima and one global minimum. From these diusion paths, we understand that lithium prefers to bind with sulphur atoms, local minima occur when the lithium approaches to sulphur atoms. In x=0.50 alloy global minimum occurs with increasing S atoms binding with Li. 0.125 eV energy dierence occurs between two Mo atoms. The energy barriers of these alloys are 0.319 eV, 0.541 eV, and 0.391 eV for x=0.33, 0.50, 0.66, respectively. These results may be higher than graphene and silicene, but lower or comparable with commercial electrode materials such as pyrophosphate (Li FeP O ), sulphate cathodes Li M(SO ) (M=Fe, Mn, Co) or 1T-MoS . Namely, these energy barriers could be acceptable for using these materials in LIBs as the electrodes. We also investigate the external strain eects on TMDs and their alloys. It can be seen from Fig.4 that the adsorption energy decreases quickly with elongating lattice constants. This indicates that the binding energy is highly sensitive to the elongation. In the next and nal part of this study, we focus on the possibility of lithium atom pass through hollow site (at the center of hexagon) of the MoS Se monolayers. Recently, this investigation has been performed for MoS monolayer. It will be important to examine the penetration barrier while Se concentration varies. For that purpose, we calculate the binding energy at a xed dierent heights from molybdenum layer. For this calculation we consider (3 ×3) cell of MoS Se monolayers, and the height of the lithium atom from Mo layer is kept constant by xed z-axis of the Li and the 3 closest Mo atoms during relaxation. We made this work until the pressure on the atoms decrease below 1 kBar. At left side of Fig.5, we present the obtained binding energies of single Li atom on bare MoS Se layers for various xed heights. As can be seen from Fig.5, the barrier energy (sucient energy for penetrate) decreases with changing concentration from x=0.00 to x=1.00. One of the reasons of this is the increasing of lattice constant with increasing selenium concentration 2

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in the systems.

Increasing of lattice constant ensures the expanding of hexagon ring, so

repulsive forces between Li and Mo atoms decrease.

While, x=0.00 barrier energy is 2.452

eV, it is reduced approximately fty percent and becomes 1.283 eV for x=1.00. These values are still so big, and indicate that the adsorptions of Li atoms will primarily occur at upper parts of the layers.

This situation is similar to that encountered in MoS 2 system.

"$

The

charge transfer between Mo and S atoms creates an electrical eld towards from side of Mo atoms to side of S atoms.

When the Li atom try to penetrate the MoS 2 layer, its energy

states split due to this electrical eld as same as Stark eect. This splitting is shown at the right side of Fig.5 by density of states of Li atom for the various heights on MoS 2 layer.

Summary and Conclusions In conclusion, we performed DFT calculations to examine the lithium adsorption and diffusion on the hexagonal MoS 2(1−x) Se2x monolayers with variation of x for 0.00, 0.33, 0.50, 0.66, and 1.00.

All semiconductor bare structures become metal upon lithium adsorption.

Their energy barriers, which are obtained by NEB calculations, make them suitable materials for using in electrode materials. It is found that lithium prefers to bind on top site of Mo atom, and for alloys Li slightly slips through the Mo-S bonds. The external strain aects the lithium adsorption energy remarkably, with increasing tensile strain the adsorption energy is decreasing very quickly. The energy barriers are very big to pass through the MoS 2(1−x) Se2x layers, but it is decreasing with the increasing of Se atoms.

Acknowledgments Computing resources used in this work were provided by the TUBITAK ULAKBIM, High Performance and Grid Computing Center (Tr-Grid e-Infrastructure).

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Supporting Information The lattice parameters and band structures of 2H-MoS 2 and 2H-MoSe2, the optimized structural parameters of the MoS2(1−x)Se2x systems before and after adsorption; neighbour distance (dM −X ), angle between bonds (θ) and band gap of bare TMDs (E g ).

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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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(40) Henkelman, G.; Uberuaga, B. P.; Jonsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths.

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J. Appl. Crystallogr. , 44,

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(42) Zhou, L.-J.; Hou, Z. F.; Wu, L.-M. First-Principles Study of Lithium Adsorption and Diusion on Graphene with Point Defects.

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15


J. Phys. Chem. C

#, 119,


o

Lattice Constants (A)

Δρ0

Mo

9.9

x=0.00

9.8

Se 9.7 9.6 1.65

MoS2(1-x)Se2x

1.60

MoS2(1-x)Se2x Li (metal)

0.50

1.55

0.66

Band Gap (eV)

S

0.33

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

Page 16 of 28

1.50 1.45 1.40

0

0.2

0.4

0.8

0.6

1

x=1.00

Concentration x

Figure 1: The variation of lattice constants and band gaps with and without lithium adsorption as given in left part. At the right side, the charge density isosurfaces are given, blue represents Δρ < 0 and red for Δρ > 0.

16


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


Mo - d

40

S- p

Se - p

EF

Li - s x=0.00

20

0 40 x=0.33

20

P-DOS (states/eV)

Page 17 of 28

0 40 x=0.50

20

0 40 x=0.66

20

0 40 x=1.00

20

0 -6

-4

-2

0

2

4

Energy (eV)

Figure 2: The partial density of states of (3 ×3) MoS2(1−x) Se2x Li including majority orbital contributions.

17



0.2

T2

T1 Mo

0.1

x=0.00

E0= -1.919 eV T1

T2

Se

S

0.3 0.2

E-E0 (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

Page 18 of 28

0.1 E0= -1.831 eV

0 0.4

0 0.4 x=0.33 0.3 0.2 E0-1= -1.730 eV 0.1 0 -0.1 x=0.66

x=0.50

E0-2= -1.855 eV

x=1.00

0.2

0.3

E0= -1.605 eV

0.2

0.1

0.1

E0= -1.731 eV

0

0 0

0.2

0.4

0.6

0.8

1

Diffusion Path

0

0.2

0.4

0.6

0.8

1

Diffusion Path

Figure 3: The lowest energy diusion paths of a single lithium atom and calculated energy proles along the paths for one Li atom-adsorbed on the TMDs monolayer.

18


Page 19 of 28

0

x=0.00 x=0.33 x=0.50 x=0.66 x=1.00

-0.5

Binding 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


-1

-1.5

-2 0

1

2

3

4

5

Elongating percentage (%)

Figure 4: The binding energies of a single lithium atom as the function of elongation (as percentage) of the lattice constant.

19


3

4

7

s - up s - down

2

2 1.849 eV

1

0

-8

0

-4

4

o

0 1

1.635 eV 1.283 eV

2.452 eV 1.975 eV

Binding 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

Page 20 of 28

Density of States (states/eV)


0

d=3 A o

d=1.5 A

0 o

x=0.00 x=0.33 x=0.50 x=0.66 x=1.00

-1 -2

0.1

d=0 A

0

-6

-4

-2

0

o

2

4

6

-8 -4

Distance (A)

0

4

8

Energy (eV)

Figure 5: Left side: Binding energies of a single lithium atom when it approaches and penetrates a bare MoS2(1−x) Se2x monolayers from innity (right). Right side: Density of states of single lithium atom on MoS 2 with dierent heights. Little DOS graph in the top right-hand corner illustrates for the single isolated lithium atom.

20


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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


Table 1: The optimized structural and energetic parameters of the systems before and [after] adsorption, respectively ([], sign separates them from each others); neighbour distance (dLi−X ) [after] Li adsorption, cohesive energy of bare systems (Ecoh) before Li adsorption, excess charge on the atom before[after] Li adsorption (ρ*, where negative sign indicates excess electrons), adsorption energy (E ads), band gap (Egap) of the systems before [after] Li adsorption. System x=0.00[+Li] x=0.33[+Li] x=0.50[+Li] x=0.66[+Li] x=1.00[+Li]

dLi−X (Å) Ecoh (eV) Li-S=[2.38] 15.750 Li-Mo=[2.97] Li-S=[2.35] 15.263 Li-Se=[2.53] Li-Mo=[3.01] Li-S=[2.33] 15.014 Li-Se=[2.52] Li-Mo=[3.06] Li-S=[2.33] 14.767 Li-Se=[2.51] Li-Mo=[3.07] Li-Se=[2.49] 14.262 Li-Mo=[3.14]

ρ* (electron) Eads (eV) S=-0.6[-0.82] -1.919 Li=[0.89] S=-0.65[-0.85] -1.831 Se=-0.41[-0.62] Li=[0.89] S=-0.65[-0.85] -1.730 Near Se Se=-0.41[-0.61] -1.855 Near S Li=[0.88] S=-0.69[-0.89] -1.731 Se=-0.42[-0.62] Li=[0.88] Se=-0.48[-0.68] -1.605 Li=[0.88]

21


Egap (eV) 1.624[Metal] 1.555[Metal] 1.527[Metal] 1.498[Metal] 1.428[Metal]


x

0.4

+

x

+

x

0.3

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

0.1 + xıı 0o

+ o

o

ıı + o

ıı

ıı

+

x

ıı

MoS2(1-x)Se2x +

o

o

ıı

0.2

Page 22 of 28

o x + ıı

o ıı x

x

x=0.00 x=0.33 x=0.50 x=0.66 x=1.00

+ o ıı x

Mo

+ o ıı

Li S, Se

-0.1

x

0

0.2

0.4

0.6

0.8

Diffusion Path

For Table of Contents Only

22


1

Page 23 of 28

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


Figure1 193x174mm (300 x 300 DPI)



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

Figure2 276x857mm (300 x 300 DPI)


Page 24 of 28

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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


Figure3 177x171mm (300 x 300 DPI)



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

Figure4 170x123mm (300 x 300 DPI)


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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


Figure5 114x60mm (300 x 300 DPI)



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

graphical abstract 188x143mm (300 x 300 DPI)


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Adsorption and Diffusion of Lithium on Monolayer ... - ACS Publications

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