First-Principles Study of 3R-MoS₂ for High-Capacity and Stable Aluminum Ion Batteries Cathode Material

Abstract

Currently, exploring high-capacity, stable cathode materials remains a major challenge for rechargeable Aluminum-ion batteries (AIBs). As an intercalator for rechargeable AIBs, Al³⁺ produces three times the capacity of AlCl₄⁻ when the same number of anions is inserted. However, the cathode material capable of producing Al³⁺ intercalation is not a graphite material with AlCl₄⁻ intercalation but a transition metal sulfide material with polar bonding. In this paper, the insertion mechanism of Al³⁺ in 3R-MoS₂ is investigated using first-principles calculations. It is found that Al³⁺ tends to insert into different interlayer positions at the same time rather than occupying one layer before inserting into another, which is different from the insertion mechanism of AlCl₄⁻ in graphite. Ab initio, molecular dynamics calculations revealed that Al³⁺ was able to stabilize the insertion of 3R-MoS₂. Diffusion barriers indicate that Al³⁺ preferentially migrates to nearby stabilization sites in diffusion pathway studies. According to the calculation, the theoretical maximum specific capacity of Al³⁺ intercalated 3R-MoS₂ reached 502.30 mAg h⁻¹, and the average voltage of the intercalation was in the range of 0.75–0.96 V. Therefore, 3R-MoS₂ is a very promising cathode material for AIBs.

1. Introduction

Energy storage batteries have always been the focus of attention. Currently, metal-ion batteries have attracted significant attention from researchers due to their small size and high efficiency. Lithium-ion batteries (LIBs) are a widely utilized energy storage solution due to their high energy density, charge/discharge voltage, and capacity [1,2]. However, in comparison to other metal resources, lithium metal reserves are relatively limited (0.0017 wt%), and the cost of LIBs has been on an upward trajectory. Furthermore, safety concerns, such as the formation of lithium dendrites, are becoming increasingly prominent [3,4,5,6,7]. In this context, Aluminum-ion batteries (AIBs) have emerged as a highly promising option due to their abundance of energy storage, high energy density, and extensive reserves [8]. However, AIBs still lack cathode materials with high capacity and stability [9,10].

In 2015, Dai et al. developed ultra-fast charging AIBs comprising an anode of metallic aluminum and a cathode of three-dimensional foam graphite, a material that exhibits an ultra-fast charging rate but a low capacity [11]. This was due to the intercalation and deintercalation of AlCl₄⁻ in the electrode material, which did not utilize the properties of Al³⁺. Furthermore, the large size of the chloroaluminum anion causes volume expansion [12]. Al³⁺ carries more charge than AlCl₄⁻, which means that when the same amount of AlCl₄⁻ is inserted, Al³⁺ can produce more capacity. Currently, transition metal oxides with polar bonds are considered potential cathode materials for Al³⁺ inserted [13]. In 2011, Jayaprakash et al. reported for the first time that V₂O₅ nanowires could serve as cathode materials for Al³⁺ intercalation. The cell obtained a capacity retention of 273 mAh g⁻¹ after 20 cycles at a current density of 125 mA g⁻¹. However, the high charge density on the Al³⁺ surface produces strong Coulombic ion−lattice interactions that hinder the diffusion of Al³⁺ in the lattice, limiting the rate performance and cycling stability of the AIBs [13,14]. To reduce this strong Coulombic ion–lattice interaction, transition metal sulfides (TMDs) with weak Coulombic interactions have been used for extensive studies [15,16]. In 2018, Li et al. first prepared a rechargeable aluminum ion battery consisting of MoS₂ microsphere cathode, aluminum anode, and ionic liquid electrolyte, demonstrating the feasibility of MoS₂ as a cathode for AIBs [17]. In 2019, Tu et al. synthesized hierarchical flower-like MoS₂ microspheres as AIBs cathodes by a simple hydrothermal method and showed that the structure of MoS₂ was stabilized during Al³⁺ intercalation/deintercalation by density functional theory calculations [18]. All the above studies are based on 2H-MoS₂. However, 3R-MoS₂, which is also a semiconductor phase with a stable thermodynamic ABC stacking mode (unlike 2H-MoS₂ AB stacking), lacks studies specifically on electrochemical behavior [19,20].

This study systematically investigates the structural stability, electronic properties, theoretical capacity, and average voltage of Al³⁺ intercalation/deintercalation 3R-MoS₂ electrodes using first-principles calculations. Furthermore, the thermal stability of 3R-MoS₂ is examined using the Ab Initio Molecular Dynamics (AIMD) method, and the diffusion path of Al³⁺ in the 3R-MoS₂ layer is investigated in detail. Our findings were benchmarked against the most recent experimental data on AIBs. Furthermore, we conducted a detailed investigation of the Al³⁺ inserted MoS₂ system to elucidate the cation insertion mechanism in MoS₂, with the objective of facilitating the design of superior electrodes in the future.

2. Results and Discussions

2.1. Single Al³⁺ Inserted in 3R-MoS₂

A comprehensive examination of all potential inserted locations for Al³⁺ within MoS₂ has been conducted. Two preferred insertion positions of Al³⁺ in 3R-MoS₂ were envisioned based on the study of potassium ion intercalation at the 2H-MoS₂ site (Figure 1): positions A and B (named PA and PB) [21]. At PA, the Al³⁺ is situated within an octahedron comprising six S atoms. It occupies a bridging position between two nonbonding S atoms, thereby forming six Al–S bonds. At PB, the Al³⁺ is situated within a tetrahedron of four S atoms, and Al³⁺ also occupies a bridging position between two non−bonded S atoms, forming four Al–S bonds. According to binding energy studies, these two positions are very favorable, and the two energies are very close. (Table S1). The binding energy for PA is less than that of PB, indicating that PA is the more stable site for Al³⁺ intercalation (consistent with the stabilization site in 2H-MoS₂ [18]). The subsequent section of this study focuses on the insertion of an Al³⁺ at PA. The energies associated with the intercalation of an Al³⁺ into the top, middle, and bottom layers of PA exhibit minimal variation. This indicates that the initial insertion of the Al³⁺ is random with respect to the layer in question.

The thermal stability of Al³⁺ inserted into the 3R-MoS₂ structure was investigated with AIMD (Figure S1). The most stable PA was selected for the simulation. Initially, the structure was subjected to a heating process, reaching a temperature of 300 K over a time interval of 1 fs to 5 ps. It was observed that the ABC stacking of 3R-MoS₂ remained unaltered from the snapshot taken at 5 ps. The structure remained intact, and the embedded Al³⁺ exhibited minimal displacement within the PA. Furthermore, simulations were conducted using the NVT system at temperatures of 400 K, 500 K, and 600 K with a time step of 1 fs and a time step of 5 ps. It was observed that 3R-MoS₂ also maintains the ABC stacking at temperatures between 300 K and 600 K. There is no significant displacement at the PA, and the changes in bond lengths and bond angles are not significant. The results demonstrate that intercalation in the PA is stable in AIMD simulations conducted at temperatures between 300 K and 600 K. Additionally, the Al³⁺ can diffuse rapidly into 3R-MoS₂ due to the unaltered chemical bonding nature of the latter.

2.2. More Al³⁺ Inserted in 3R-MoS₂

As shown in Figure 2 and Figure S2, we simulated three different interpolation stages (stages 1–3), each using four different concentrations. 3, 6, 9 and 12 Al³⁺ are inserted in MoS₂ for stage-1, 2, 4, 6 and 8 Al³⁺ are inserted in MoS₂ for stage-2. 1, 2, 3 and 4 Al³⁺ are inserted in MoS₂ for stage-3. A 3 × 3 × 2 supercell consisting of 24 S atoms and 12 Mo atoms was constructed for the calculations of stage-1, stage-2, and stage-3. It should be noted that the system was modeled using a pure 3R-MoS₂ ABC-stacked structure comprising three MoS₂ layers with an interlayer spacing of 2.80 Å. It is, therefore, believed that the MoS₂ model is more suitable for simulating real experimental observations in ultra−fast AIBs.

It has been found that good cathode materials for AIBs require suitable interlayer spacing as well as reasonable Al binding strength. Therefore, MoS₂ with these two characteristics happens to be a potential cathode for AIBs. We first investigated the structural deformation in MoS₂ due to Al³⁺ inserted. There are three interlayer distances in the unit cell named Ind1, Ind2, and Ind3, shown in Figure S3. All distances are projected onto the C-axis and listed in

Table 1. Interlayer distance (Ind1, Ind2, Ind3), average open-circuit voltage (OCV), and binding energy (BE) per Al³⁺ for all stages with different content considered.

Stages	No. of Al	OCV (V)	BE (eV)	Ind1 (Å)	Ind2 (Å)	Ind3 (Å)
Stage-1	3	0.96	−2.87	3.16	3.19	3.16
	6	0.94	−2.85	3.13	3.19	3.31
	9	0.94	−2.83	2.42	2.51	3.26
	12	0.77	−2.71	3.23	2.86	3.15
Stage-2	2	0.94	−2.83	3.15	2.78	3.22
	4	0.86	−2.69	3.33	2.79	3.23
	6	0.86	−2.65	3.19	2.78	3.05
	8	0.81	−2.60	3.17	2.80	3.22
Stage-3	1	0.92	−2.76	2.78	3.21	2.78
	2	0.82	−2.61	2.79	3.15	2.75
	3	0.79	−2.53	2.77	3.21	2.78
	4	0.75	−2.46	2.81	3.18	2.77

. The layer spacing in pure MoS₂ (2.80 Å), which is very close to the experiment data 2.98 Å and corresponds to the (006) diffraction plane of MoS₂ (JCPDS No. 17–0744), is larger than the covalent radius of Al (1.18 Å) [22]. The results show that the interlayer spacing expands with the insertion of Al³⁺ at first for all the stages. All the expansion layers spacing are about 3.2 Å. This is due to the electrostatic interaction between Al and Mo ions. And the distance shrinks 0.1–0.5 Å for the layer without Al³⁺ inserted. After the interlayer spacing expands, further intercalation becomes smooth. Thus, with more Al³⁺ continuing to be embedded, the change in MoS₂ layer spacing becomes smaller. It can also be considered that the insertion of Al³⁺ will not cause a large change in layer spacing, which verified that the structure of 3R-MoS₂ is stable. The bonding of the Al and S atoms also prevents further expansion of the layer spacing. The increased interlayer spacing favors easier diffusion of Al³⁺ into MoS₂. However, when 9 Al³⁺ was inserted in MoS₂ in stage-1, and 6 Al³⁺ was inserted in MoS₂ in stage-2, the lattice changed much (Figure S2), and the interlayer spacing varied irregularly. For example, when 9 Al³⁺ is inserted in MoS₂ in stage-1, the Ind1 and Ind2 become smaller. This implies that the electrostatic interaction force is not uniform. However, the calculated expanded layer spacing for 3R-MoS₂ (1.1 Å) is smaller than the one of 2H-MoS₂ (1.9 Å), which indicates that the structure stability of 3R-MoS₂ is better than the one of 2H-MoS₂ [17,23].

2.3. Staging Mechanism

To further analyze the staging mechanism, the relative stabilities of stage-1, stage-2, and stage-3 with the same Al³⁺ concentration were compared. Divided into four sections, each inserted with the same concentration of Al³⁺, the optimized structures of stages 1, 2, and 3 are shown in Figure S4 and expressed in terms of relative energetics. The results show that stage-1 is more stable than stage-2 when the same concentration of 6 Al³⁺ is inserted, and stage-2 is again more stable than stage-3 when Al³⁺ is reduced to 4, and the same is true for subsequent reductions to 3 and 2. Thus, we believe that Al³⁺ prefers to insert into the galleries simultaneously rather than covering one gallery and then taking over the others. This is different from the mechanism of AlCl₄⁻ insertion in graphene [24]. This phenomenon can be explained by the ion−ion Coulomb attraction. As Al ion and S ion bond to each other, it is believed that Al³⁺ first binds to S, and with the Al³⁺ increasing, the repulsion between Al and Mo atoms increases. Thus, Al³⁺ will not cover one layer and then take over the other. That will increase the repulsive force between Al and Mo atoms. As the concentration of Al³⁺ increases, the repulsive force also rises, which may lead to lattice distortion, such as the formation of 6 Al³⁺. Nevertheless, if Al³⁺ is distributed uniformly throughout all layers, it will result in a reduction in lattice distortion, such as the presence of 6 Al³⁺ in stage-1. It is, therefore, postulated that the intercalation mechanism follows stage-1.

2.4. Binding Energy

To further assess the stability of the intercalated compounds, the binding energies calculated for all stages are listed in Table 1, and Figure S5 shows the variation of binding energy as a function of the weight percentage (wt%) of Al³⁺ intercalation in MoS₂ for all three stages. The calculated binding energies are observed to be negative in all cases, indicating that Al³⁺ is readily embedded in MoS₂ within the context of this study. This phenomenon can be attributed to the smaller atomic size of Al³⁺ in comparison to the spacing of the MoS₂ layers, which facilitates the insertion process. Moreover, the interaction between the intercalated Al³⁺ and the host MoS₂ layer is sufficient to overcome the van der Waals forces between the MoS₂ layers. In addition, the insertion of Al³⁺ in the already expanded MoS₂ main channel is facilitated by higher concentrations. This is due to an increase in the average interlayer distance, which results in a reduction in van der Waals forces between the MoS₂ layers. It can be demonstrated that the Al³⁺ binding energy in the bulk MoS₂ decreases with the amount of Al³⁺ in the same stage. Furthermore, the lower stages (stage-1) are more stable than the higher stages (stage-2, stage-3) for a given concentration of Al³⁺.

2.5. Electronic Properties

Conductive properties are very important for battery materials. The total density of states (TDOSs) and partial density of states (PDOSs) are calculated for Al³⁺ intercalated in MoS₂ of stage-1, as shown in Figure 3. Only DOSs near the Fermi level are meaningful. Thus, the DOSs between −10 and 15 eV are shown in Figure 3. Furthermore, the DOSs at the Fermi level can effectively reflect the conductivity of the material [25]. It can be seen that with no Al³⁺ intercalating, 3R-MoS2 has poor electrical conductivity. Because there are fewer electrons at the Fermi level. And the electrons are mainly from Mo 4d and S 3p, which can be found in Figure S6a. The parts from −10 eV to 0 eV mainly are Mo 4d and S 3p hybridization, forming the S–Mo bond. With Al³⁺ intercalating, the DOSs at the Fermi level increase, which means the electronic conductivity increases. The electronic conductivity increases are mainly from Al 3p, Mo 4d, and S 3p orbitals. It is supposed that when Al³⁺ intercalates, the electrons transfer from Al 3p to S 3p. Correspondingly, the charge transfer of the Mo 4d is reduced, which can be verified from the Hirshfeld charge analysis. Thus, during charge/discharge, Al³⁺ increases the electronic conductivity of the materials.

Hirshfeld charge analysis is performed to understand the charge transfer more intuitively. From Figure S7, it was found that with the insertion of Al³⁺, the positive charge of Al increases and the charge of Mo decreases, whereas the Al metal is conductive and tends to lose its outermost electrons, which also leads to the transfer of electrons from the outermost layer of Al to S, resulting in the formation of Al–S bonds. And the electron transfer of Mo is weakening. Thus, the Mo–S bond is weakening. The electrons mainly transfer from Al 3p to S 3p orbitals. Furthermore, part electrons of Al 3s jump to Al 3p. The same goes for S atoms. Thus, both s and p orbitals of Al and S are hybridized and participate in bonding, which can be verified from Figure 3 and Figure S6b. The electrons transfer for Mo are mainly from Mo 5s to S 3p orbitals. And part electrons of Mo 5s jump to Mo 4d. Thus, there are fewer electrons left in the Mo 5s orbital. Only Mo 4d bond with S 3p, which agreed well with the analysis of the DOSs above. The sudden increase in Hirshfeld’s charge is due to lattice distortion for 9 Al³⁺ inserted in MoS₂.

2.6. Diffusion of Al³⁺ in 3R-MoS₂

The charging/discharging rate of batteries is related to the diffusion of the intercalated species through the electrodes. Therefore, to study the Al³⁺ diffusion mechanism in the 3R-MoS₂ electrode, we have calculated barriers to finding energetically favorable diffusion paths. The PA site is the most stable. Hence, in this work, three favorable diffusion paths have been studied from a PA site to a neighboring A site. The first diffusion path, path 1, is from site PA to its nearest PA site, passing through a PB1 site (PA-PB1-PA); the second is path 2 involves the Al³⁺ diffusion from site A to another A site via site PB2 (PA-PB2-PA) and the third path, path 3, from site A to another nearest site A via site PB3 (PA-PB3-PA). All the diffusion paths and diffusion barriers are shown in Figure 4. From Figure 4, it is found that path 2 has the biggest barrier energy, as the diffusion path is the longest. Moreover, the barrier energies of path 1 and path 3 are closer and smaller than the ones of path 2. This can indicate that aluminum ions preferentially migrate to nearby stable positions. Moreover, the attraction of the S atom to Al³⁺ increased resistance and led to a higher barrier energy.

2.7. Electrochemical Properties of Al³⁺ Intercalated 3R-MoS₂

The open circuit voltage (OCV) is a valuable measure of a battery’s performance. The open-circuit voltage (OCV) is evaluated by the equation below [26]:

$$V=-(E_{x_2}-E_{x_1}-(x_1-x_2)E_{Al})/3e(x_1-x_2)$$

(1)

where $E_{x_1}$ and $E_{x_2}$ are the total energies of the Al_xMoS₂ at two adjacent stable systems of concentration x₁ and x₂, respectively.

Figure 5 represents the variation of average voltage with the weight percentage (wt%) of Al³⁺ for all three stages (stages 1–3), and the calculated values for different stoichiometries are listed in Table 1. The OCV varies in a range of 0.77 V to 0.96 V for stage-1, 0.81 V to 0.94 V for stage-2, and 0.75 V to 0.92 V for stage-3. Since Al³⁺ are inserted into each layer at the same time in stage-1, the Coulomb and van der Waals forces of each layer need to be overcome, but stage-2 and stage-3 do not, which results in a higher voltage plateau in stage-1 relative to stage-2 and stage-3 [17,27,28].

The theoretical gravimetric capacity has been calculated using the following equation [29]:

$$C=czF/M_{Mo{S}_2}$$

(2)

where c is the number of inserted Al³⁺, z is the number of chemical valences of Al³⁺, F is the Faraday constant (26,801 mA h mol⁻¹) and $M_{Mo{S}_2}$ is the molar mass of the MoS₂ cell. The calculated gravimetric capacities for stage-1, stage-2, and stage-3 are 502.30, 334.87, and 167.43 mAh g⁻¹, listed in

Table 2. The calculated theoretical specific capacity compared with other data.

Cathode	Theoretical Capacity	Initial Capacity (mA h g−1)/ Current Density (mA g−1)	Cyclic Capacity (mA h g−1)/ Cycle Number	Discharge Plateau (V)	Ref.
stage-1	502.30	−	−	0.77–0.96	−
stage-2	334.87	−	−	0.81–0.94	−
stage-3	167.43	−	−	0.75–0.92	−
2H-MoS2	−	253.6/20	66.7/100	0.5–0.9	[17]
2H-MoS2/N-doped carbon	−	−	232/500	0.4	[30]
2H-MoS2-Maxene	−	224/-	166/60	0.3, 0.9	[28]
2H-MoS2/RGO	−	278.1/1000	161.1/100	−	[31]
2H-MoS2	−	249.6/1000	80.9/100	−	[31]
Spongy MoS2	−	214.2/500	129.5/1000	0.5	[23]
Bi2S3/MoS2	−	274.3/375	132.9/100	0.8	[32]

. From Table 2, it is obvious that the theoretical capacity of 3R-MoS₂ stage-1 is higher than the experimental data of 2H-MoS₂. Furthermore, the discharge plateau is observed to be higher than that observed in the other experiments. Therefore, based on our research and analysis, 3R-MoS₂ is a potential cathode material for AIBs. The material’s stable layered structure enables it to maintain a long cycle life, high platform, and high capacity.

3. Computational Methods

The current calculations are based on Density Functional Theory (DFT) in the Cambridge Series of Total Energy Packets (CASTEP) plane wave code and on DS-PAW (Device Studio-Projected Augmented Wave) [33,34,35,36,37]. The Predew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) was used in the description of the exchange–correlation potential. Norm-conserving pseudopotentials were used to describe the interaction of ionic core and valence electrons. Valence states were considered in this study corresponding to Al 3s² 3p¹ Mo 4d⁵ 5s¹ and S 3s² 3p⁴. After convergence tests (Figure S8), the cutoff energy for plane waves is eventually identified as 1820 eV. The d orbitals in the Mo ions have been localized using the Hubbard corrected GGA (GGA + U) method (U value of 4 eV). All structures are optimized by fully relaxing the atomic and lattice positions until the Hermann−Feynman force for all atoms is less than 0.01 eV Å⁻¹. The numbers of K-points were set to 5 × 5 × 1. All systems are fully optimized, and the convergence criterion for the total energy is set to 5 × 10⁻³ eV. Van der Waals force interactions play an important role in the calculation of layered structures. Therefore, we have corrected the van der Waals force interactions using the DFT-3 method, which increases the potential energy and interatomic forces.

In this paper, a periodic structure was adopted. The unit cell of 3R-MoS₂ is of the R3m space group and exhibits a hexagonal structure (Figure S3). The 2 × 2 × 2 supercell was employed in the calculations, which included 12 Mo atoms and 36 S atoms. Following the completion of geometry optimization, the resulting geometry constants are presented in Table S1. As evidenced by Table S2, the findings align with those of other experimental and theoretical studies [38,39,40].

To calculate the electronic structure, a 4 × 4 × 4 K-point sampling was employed within the Brillouin region. Ab initio molecular dynamics simulations (AIMD) were conducted using a regular ensemble (NVT) with a fixed number of ions, volume, and temperature. The AIMD simulations were configured to be conducted at temperatures spanning the range from 300 to 600 K, with a time step of 1 fs and a duration of 5 ps. The temperature was maintained using a Nose thermostat model. The transition state search utilizes the fully optimized initial and final structures with RMS convergence set to 0.01 eV Å⁻¹. The activation barriers are calculated from the energy difference between the transition state and the initial state. The calculation of the diffusion potential incorporates corrections for entropy and zero−point energy. The binding energy after Al³⁺ intercalation into 3R-MoS₂ was calculated using the following equation [24]:

$$E_{binding}={\displaystyle \frac{E_{A{l}_{x}Mo{S}_2}-E_{Mo{S}_2}-x{E}_{Al}}{x}}$$

(3)

where $E_{A{l}_{x}Mo{S}_2}$, $E_{Mo{S}_2}$, $E_{Al}$ are the total energy of MoS₂ with x Al inserted, MoS₂ and single Al³⁺.

4. Conclusions

This paper presents an investigation into the electrochemical properties of 3R-MoS₂ and a discussion of its potential use as an AIB. The most stable configuration is one in which a single Al³⁺ is inserted into a PA octahedron comprising six S atoms. Moreover, the binding energy calculation revealed that the initial Al³⁺ insertion is random in the ABC stacking structure for 3R-MoS₂. The AIMD simulation results indicate that 3R-MoS₂ can retain a stable structure within a temperature range of 300 to 600 K. As the number of Al³⁺ inserted into 3R-MoS₂ increases, it is observed that the ions are more likely to be inserted into interlayer sites simultaneously rather than occupying only one interlayer site. The insertion of Al³⁺ resulted in an increase in the conductivity of 3R-MoS₂, accompanied by a transfer of electrons from Al atoms to S atoms, leading to the formation of Al–S ionic bonds. According to the calculation, the theoretical maximum specific capacity of Al³⁺ intercalated 3R-MoS₂ reached 502.30 mAg h⁻¹, and the average voltage of the intercalation was in the range of 0.75−0.96 V. Considering these findings, it can be concluded that 3R-MoS₂ has great potential as a cathode material for AIBs.