Computational Study of the Enhancement of Graphene Electrodes for Use in Li–Ion Batteries via Forming Superlattices with Transition Metal Dichalcogenides

In our study, we examined nine transition metal dichalcogenide (TMDC)–graphene superlattices as potential Li–ion intercalation electrodes. We determined their voltages, with ScS2–graphene in T- and R-phases showing the highest at around 3 V, while the others ranged from 0 to 1.5 V. Most superlattices exhibited minimal volumetric expansion (5 to 10%), similar to NMC (8%), except for SnS2-T and NiS2-T, which expanded up to nearly 20%. We evaluated their capacities using a stability metric, EIS, and found that ScS2-T, ScS2-R, and TiS2-T could be intercalated up to two Li ions per MX2 unit without decomposing to Li2S, yielding capacities of 306.77 mA h/g for both ScS2 phases and 310.84 mA h/g for TiS2-T, roughly equivalent to LiC2. MoS2-T could accept Li up to a limit of a = 15/16 in LiaMoS2Cb, corresponding to a capacity of 121.29 mA h/g (equivalent to LiC4). Examining the influence of graphene layers on MoS2-T, we observed a voltage decrease and an initial EIS decrease before effectively flat lining, which is due to charge donation to the middle graphene layer, reducing the electron concentration near the TMDC layer. As graphene layers increased, overall volume expansion decreased with Li intercalation, which is attributed to the in-plane expansion changing. Our results underscore the potential of TMDC–graphene superlattices as Li–ion intercalation electrodes, offering low volumetric expansions, high capacities, and a wide voltage range. These superlattices all show an increase in the capacity of the graphene.


∆H(MS
where ∆H(A) is the enthalpy of formation of compound A, E(A) is the energy of compound A and µ 0 B = E(B) is the chemical potential of the element B when it is in its elemental bulk structure and M represents transition metal.Thermodynamic equilibrium requires that where ∆µ B = µ B − µ 0 B with µ B being the chemical potential of the element B in Li a MS 2 C b .
This states that the energy of the intercalated superlattice is the sum of the chemical potentials of its constituent atoms.This can be restated as We also require that MS 2 C b , Li 2 S and the bulk forms of the constituent elements do not form, thus ∆µ Li,M,S,C ≤ 0. (S8) Substituting (S5) into (S6) and rearranging which is our first thermodynamic limit on the chemical potential of lithium that determines when lithium intercalated into MS 2 C b is more favourable than MS 2 C b and bulk lithium.
Substituting (S5) into (S7) provides which is our second thermodynamic limit on the chemical potential of lithium that determines when Li 2 S does not form.Together these describe the boundary conditions on the chemical potential of lithium based on the formation energies and chemical potentials of relevant products and elements.Given that we have removed all dependence on the chemical potential of the chalgogen (sulphur for all TMDCs investigated), these are dependent only on ∆µ Li , ∆µ M and ∆µ C .
If we consider the relative change in ∆µ Li between these two boundaries, Equations(S9) and (S10), at ∆µ M = ∆µ C = 0, we can quantise a region of stability using a single value E IS .
We define this quantity such that a positive value means that there is a region of stability and a negative means there is not, E IS is thus defined as This can also be used for TMDCs without graphene by simply setting b = 0.
The values of E IS for the TMDC-graphene superlattices at a = 1 and a = 2 and the TMDCs without graphene at a = 1 are given in Table S S1.

Formation of LiC 6
In addition to the formation of LiS 2 , we have also considered the formation of LiC 6 from the intercalated superlattices.We can state this as which has limits of These represent when there is no LiC 6 formed in the limit there is no additional carbon.Between these limits we found that Li a MS 2 C b was more favourable for all investigated TMDC-G superlattices.Tables SS2

Supercells
The in-plane and out of plane lattice constants for the TMDC-graphene superlattices at a = 0, 1 and 2 are given in Table S S5 and the in plane lattice constant for the bulk TMDCs are given in Table S S6.For the TMDC-graphene superlattices these are for the overall supercell and not transition metal to transition metal distances.These values for the superlattices are plotted in the main manuscript in Figures 2(c) and 2(d).The supercells for a = 1 were constructed by taking the fully relaxed supercells for a = 2 and uniformly removing lithium.For the a = 1 structures where all the lithium was on one side of the TMDC layer this meant that all the lithium on one side was removed.For structures where the lithium is equally spread over both sides of the TMDC layer, lithium from every other lithium site.An example of this is shown in Figure SS1.
Table SS7 show the strain on the TMDC and graphene layers in the superlattices along with their respective formation energies.These were all calculated from graphene supercells of the same size as the superlattices and a single unit cell of the TMDCs, the only exception to this is MnS 2 -T.Within the table, MnS 2 T* is the strain and formation energy as calculated with the above method and MnS 2 -T uses a supercell of the TMDC layer instead.This was done as manganese's potential spin states are complex and numerous.To provide a direct comparison of the spin states, in this case we used the same supercell for the bulk TMDC

Voltages
The voltages for the TMDC-graphene superlattices for a = 0 → 1 and a = 1 → 2 and the TMDCs without graphene for a = 0 → 1 are given in Table S S8.These values for the TMDC-graphene superlattices are plotted in the main manuscript in Figure 2(a).
Table S7: The ratios of MX 2 to C along with the strain associated with each layer for the 9 supercells generated using the ARTEMIS 1 package and the formation energies per unit area.The strains are calculated for the TMDCs with no lithium compared with their superlattices with no lithium (a = 0).

Volumetric expansion
The volumetric expansion the the TMDC-graphene superlattices for a = 0 → 1 and a = 1 → 2 and the TMDCs without graphene for a = 0 → 1 are given in Table S S9.These values for the TMDC-graphene superlattices are plotted in the main manuscript in Figure 2(b).

Effect of additional Graphene
The voltages, E IS , % volumetric expansion and % local expansion for MoS 2 -T as the number of graphene layers are increased are given in Table S S10.These are calculated for lithium contents of a = 0 and a = 1 in Li a MoS 2 C b and are plotted in the main manuscript in Figure 4.
The local expansion for bulk MoS 2 -T is the distance between the closest sulphur atoms in the two neighbouring TMDC layers, this effectively includes the change in the TMDC layer itself and the change in the van der Waals gap both above and below it as lithium is added.For the superlattices we have used the distance from the graphene layer above the TMDC to the one below, also capturing the change in the TMDC layer and the two van der Table S8: Voltages for TMDC-Graphene superlattices and their respective TMDCs without graphene.Table S9: Volumetric expansion for TMDC-Graphene superlattices and their respective TMDCs without graphene.

Charge Analysis
A Bader charge analysis 2-5 was carried out on various MoS 2 -T systems.Table S11 shows the Bader charges of the different species present in MoS 2 -T with graphene as the concentration of carbon is increased without any lithium.Also included are the base TMDC without graphene and graphene without the TMDC.
Table S12 shows the Bader charges of the different species present in Li a MoS 2 -T with graphene as the concentration of carbon is increased with lithium at at a = 1.Also included

Additional MoS 2
We present the results of including an extra layer of MoS 2 -T in these MoS 2 -T -graphene superlattices, this is equivalent to b = 1.6875.However, there are multiple potential configurations for the Li within this system, and we have presented only one configuration (shown in Fig. S2 (d)).In this structure, the forces for this system are converged to ≈ 0.659 eV/Å (whereas in the main manuscript the forces are converged to 0.01 eV/Å).Figure S2 (a-c

Diffusion barriers
For large supercells such as these, the number of unique diffusion pathways that one could consider is significantly larger than in a normal bulk unit cell.For example, in the MoS 2graphene supercell, the number of Li sites (adjacent to the sulphur) is 32, meaning that one would need to consider 32 pathways for Li diffusion to just compare the diffusion between the two adjacent Li sites.When considering the larger cell, these pathways become significantly more complex.As a single case study, for the SnS 2 -graphene system, which is the smallest of the systems considered, we have investigated one of the possible diffusion pathways.This pathway is shown in Figure S3, this pathway has a diffusion barrier of ≈ 0.257 eV.This is roughly half the diffusion barrier that was found for bulk SnS 2 (of ≈ 0.5 eV) found by Price et al., 6 a reduction compared to the bulk is observed by others as well. 7However this one diffusion pathway may not fully describe the full diffusion of Li through these systems and further study is warranted to explore this fully.

AIMD stability analysis
The systems considered in this article are large supercells consisting of 100's of atoms.For a full consideration of AIMD, one would normally want multiple picoseconds of simulation to carry out a full stability analysis.For these systems, this remains unfeasible with current HPC resources.We can state here that the SnS 2 -T -Graphene and LiSnS 2 -T -Graphene systems are stable for approximately 0.1 ps, but this is vastly insufficient to state that these systems are truly phonon stable.However, in our previous works 6,8 we have shown the TMDCs individual phonon stability (without graphene) for select systems.As the interaction here is weak, we believe this would remain to be true, but a full phonon dynamics calculation (taking into account interplanar interactions) would be required.

Figure S1 :
Figure S1: The structure of one of the TMDC-graphene superlattices for a = 1 where the lithium is spread over both sides of the TMDC.
) the voltage and E IS of the 2 layer MoS 2 -T -1 layer graphene structure is compared to the other MoS 2 -T/Graphene supercells investigated.The voltage is ≈ 1.588 V and the E IS is ≈ −0.141 eV, and as expected, these lie between the results for 1 layer of MoS 2 -T with 1 layer of graphene and bulk MoS 2 -T.

Figure S2 :
Figure S2: (a) The Open Circuit voltage and (b) E IS for MoS 2 -T as the number of layers of graphene is increased for a lithium content of a = 0 and a = 1.(c) shows both the total volumetric expansion in green and the local expansion in the z-axis in black.For the superlattices this is measured from the graphene layer below the TMDC to the graphene layer above, for the TMDC on its own we have used the distance between the closest sulphur atoms in the two neighbouring TMDC layers.The red crosses on the voltage and E IS plots are for the 2 layer MoS 2 -T -1 layer graphene system and (d) shows the structure of this system.

Figure S3 :
Figure S3: Schematic of the Li NEB pathway within the SnS 2 -graphene superlattice.

Table S1 :
The values of E IS for the TMDC-graphene superlattices at a = 1 and a = 2 and the bulk TMDCs at a = 1.

Table S2 :
, SS3 and SS4 show the formation energy of Li a MS 2 C b from all compounds on the right hand side of equation S12.A negative formation energy shows that the formation of Li a MS 2 C b is more favourable, so LiC 6 won't form.All tables show negative formation energies indicating LiC 6 will not form.The energetic costs of forming Li a=1 M S2C b from LiC 6 and various other compounds, based upon equation S12.

Table S3 :
The energetic costs of forming Li a=2 M S2C b from LiC 6 and various other compounds, based upon equation S12.

Table S4 :
The energetic costs of forming Li a=1 M oS2C b from LiC 6 and various other compounds, based upon equation S12, for the differing number of graphene layers (b = 3.375, 6.750 and 10.125 corresponding to 1, 2 and 3 layers of graphene).

Table S5 :
In plane and out of plane lattice constants for TMDC-Graphene superlattices in Angstroms.These values are for the supercells considered, not the primitive unit cell values.The values of a correspond to the relevant levels of filling discussed in the main article.

Table S6 :
The in plane lattice constant for the bulk TMDCs for differing levels of intercalation (none, a = 0 and partially filled, a = 1).The graphite supercell average carbon-carbon bond lengths in Angstroms.

Table S10 :
The voltage, E IS , % volumetric expansion and % local expansion for MoS 2 -T as the number of graphene layers are increased.

Table S11 :
The average charge on the different species present in the MoS 2 -T graphene superlattices without lithium as b is increased.b = ∞ is AA stacked graphite.

Table S12 :
The average charge on the different species present in the MoS 2 -T graphene superlattices with lithium as b is increased.b = ∞ is AA stacked graphite with 2 Li to 16 C.