Two-dimensional Si₂C material exhibits efficient conductive properties and outstanding capacitance characteristics in Li/Na/K-ion batteries

Following precise structural optimization, the structure of the $3 \times 3$ Si₂C monolayer was comprehensively detailed, as shown in figure 1. This Si₂C monolayer is composed of 18 Si atoms and 9 C atoms, totaling 27 atoms. It exhibits a hexagonal structure within the P3m1 space group, with C atoms situated between two Si atoms. After the optimization, the C–Si bond length in Si₂C was determined to be 2.03 Å, while its lattice constants are a= b = 2.87 Å. To investigate the stability of the Si₂C monolayer structure more thoroughly, we utilized DFT for the calculation of its phonon spectrum, and conducted ab initio molecular dynamics simulations (AIMD) as a complementary analysis. The phonon spectrum of the Si₂C monolayer, as depicted in figure 2(a), showed no imaginary frequencies, indicating its dynamical stability. Concurrently, as figure 2(b) illustrates, both the energy and structural variations of the Si₂C monolayer were relatively minor, thereby affirming its thermodynamic stability. Furthermore, previous research on the electronic band structure of Si₂C reveals a bandgap of 0.08 eV when employing the PBE exchange-correlation functional, while adjustments using the HSE06 functional to address the underestimation by the GGA approximation yield a bandgap of 0.46 eV, suggesting the semiconducting characteristic of Si₂C [32].

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After confirming the electronic characteristics of the Si₂C monolayer, we further investigated the adsorption behavior of Li/Na/K-ions on the monolayer material. To determine the most stable adsorption sites, the adsorption energy was calculated using the following equation:

$$\begin{align}{E_{{\text{ads}}}} = {E_{{\text{substrate}} + {\text{M}}}} - {E_{{\text{substrate}}}} - {E_{\text{M}}}\end{align} \tag{ 1 }$$

where ${E_{{\text{ads}}}}$ represents the adsorption energy, ${E_{{\text{substrate}} + {\text{M}}}}$ is the total energy of the Si₂C configuration with adsorbed alkali metal atoms, ${E_{{\text{substrate}}}}$ is the energy of the Si₂C monolayer without any adsorbed atoms, and ${E_{\text{M}}}$ is the energy of a single alkali metal atom in a bulk metal. According to equation (1), a positive adsorption energy suggests that the adsorption process is endothermic, indicating that the reaction is non-spontaneous, whereas a negative adsorption energy indicates an exothermic reaction, implying that the reaction can occur spontaneously. Utilizing this method, researchers can accurately assess the adsorption stability of different alkali metal atoms on the Si₂C monolayer, providing crucial information for optimizing the performance of Si₂C monolayers as anodes in Li/Na/K-ion batteries.

To gain a comprehensive understanding of the adsorption of Li/Na/K-ions on Si₂C, multiple configurations and different adsorption sites were considered. Figures 3(a)–(c) showcase the adsorption models of Li/Na/K-ions on three potential adsorption sites: site-a, site-b, and site-c. Specifically, site-a is located above the empty space of a C atom, site-b above the empty space of a Si–C bond, and site-c above the empty space of a Si atom. Our computational results indicate that the adsorption of Li-ions and Na-ions at site-c is unstable, as they naturally migrate to site-a, similarly, the adsorption of K-ions at site-b and site-c also exhibits instability, ultimately moving to site-a. The adsorption energy results, displayed in figure 4, clearly demonstrate that for Li/Na/K-ions, the most stable adsorption site is site-a. Specifically, the adsorption energies at the most stable positions for Li and Na are approximately −1.41 eV, and for K, it is around −1.76 eV. These values are lower than the corresponding adsorption energies of Si₃C, which are −0.74 eV for Li-ion, −0.72 eV for Na-ion, and −1.14 eV for K-ion [33]. Of particular significance is the fact that a higher absolute value of negative adsorption energy corresponds to greater thermodynamic favorability, suggesting increased thermodynamic benefits for the adsorption process. This observation indicates that Si₂C exhibits more stable adsorption when dealing with single atoms.

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In this study, we conducted a comprehensive investigation of the adsorption behavior and charge transfer phenomena of Li/Na/K atoms on the Si₂C monolayer using Bader charge analysis and the charge density difference (CDD) method [34]. The CDD ${\Delta _\rho }{\text{ }}$ is calculated according to equation (2):

$$\begin{align}{\Delta _\rho } = {\rho _{{\text{sub}} + {\text{M}}}} - \left( {{\rho _{{\text{sub}}}} + {\rho _{\text{M}}}} \right)\end{align} \tag{ 2 }$$

where ${\rho _{{\text{sub}} + {\text{M}}}}$ represents the charge density of the Si₂C system with adsorbed alkali metal atoms, ${\rho _{{\text{sub}}}}$ is the charge density of the Si₂C monolayer without adsorbed alkali metal atoms, and ${\rho _{\text{M}}}$ is the charge density of the isolated alkali metal atoms. This methodology allows us to observe and analyze the charge transfer between the Si₂C monolayer and Li/Na/K atoms, thereby gaining a deeper understanding of their interactions and impact on electrochemical properties.

As shown in figure 5, the differential charge images indicate that the charge is primarily concentrated between the monolayer and the Li/Na/K atoms. This pattern of charge distribution suggests that the interaction between the sodium atoms and the monolayer exhibits characteristics of chemical adsorption. Through an in-depth analysis of Bader charge, we further understood the charge transfer between different cations and the Si₂C monolayer. Specifically, each lithium atom transfers about 0.89e worth of charge to the Si₂C monolayer, sodium transfers 0.83e, and potassium transfers 0.82e. These results reveal significant electron exchange between the alkali metal atoms and the Si₂C monolayer. The degree of charge transfer directly affects the material conductivity and electrochemical reaction activity. This comprehension is crucial for understanding the electrochemical performance and ion adsorption behavior of the material. This research carries substantial implications for assessing the potential of the Si₂C monolayer as an anode material.

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According to symmetry considerations, there should be three diffusion pathways on the surface of Si₂C. Ultimately, we identified three possible migration pathways for Li/Na/K-ions in Si₂C: path1 (site-a1 $\to$ site-b $\to$ site-a2), path2 (site-a1 $\to$ site-a2) and path3 (site-a1 $\to$ site-c $\to$ site-a2). These paths involve migration from one most stable position to another, potentially passing through one or two intermediate positions.

As depicted in figure 6, on the Si₂C monolayer, the diffusion energy barriers for Li/Na/K-ions are 0.14 eV, 0.065 eV, and 0.041 eV, respectively. Considering the influence of electronegativity on an atom's ability to attract electron pairs and consequently affect ion behavior, the strength of the ionic bonds formed between Li, Na, K, and the Si₂C substrate follows an order of b_Li > b_Na > b_K to some extent (b_Li, b_Na, b_K respectively represent the bonding strengths of Li/Na/K-ions with the substrate). Therefore, in terms of diffusion barriers, the order would be d_Li > d_Na > d_K. (d_Li, d_Na,d_K respectively represent the diffusion barriers of Li/Na/K-ions on the Si₂C monolayer).

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Moreover, compared to materials explored by other researchers, such as MoS₂ (0.27 eV) [35], InSe (0.23 eV) [36], Ti₂CS₂ (1.51 eV) [37], SnSe (1.65 eV) [38], SnO₂ (1.94 eV) [38], single layer graphene (0.31 eV) [39], the diffusion barrier for Li-ions in Si₂C, which is 0.14 eV, is relatively low. For Na-ions, their diffusion barrier in Si₂C is 0.065 eV, which is also lower than traditional 2D materials such as MoS₂ (0.22 eV) [40], Ti₂CC₂ (0.16 eV) [41], Ti₂CS₂ (0.095 eV) [41], CoS₂ (0.15 eV) [42], C-silicyne (0.57 eV) [43]. For K-ions, the energy barrier in Si₂C is 0.041 eV, which is lower than previously studied materials such as SrSnO₃ (0.44 eV) [44], C-silicyne (0.24 eV) [43], T-graphene (0.25 eV) [45], super-borophene (0.44 eV) [46] and graphite nanomesh with the hole density of 46% (0.19 eV) [47]. These comparisons highlight the advantages of the Si₂C monolayer as a material for Li/Na/K-ion batteries.

To establish Si₂C as an effective battery anode material, the key lies in its superior theoretical capacity and OCV performance, which are determining factors for battery efficiency. Therefore, this study focuses on evaluating the performance of the Si₂C monolayer in terms of theoretical capacity and OCV. Specifically, the theoretical capacitance is determined by the maximum adsorption concentration, while the OCV is calculated based on adsorption energy. The half-cell reaction can be represented by the following chemical equation:

$$\begin{align}{\text{L}} + x{{\text{M}}^{n + }} + n{{\text{e}}^ - } \leftrightarrow {\text{L}}{{\text{M}}_x}\end{align} \tag{ 3 }$$

where L represents the monolayer anode material, x indicates the concentration of adsorbed atoms, M is the type of adsorbed atoms, and n is the number of electrons transferred to the anode during atom adsorption. By calculating the maximum capacity of adsorbed cations, we determined the concentration x of adsorbed cations. We found that alkali metal atoms could be adsorbed on both sides of the Si₂C monolayer. To assess the effectiveness of one-by-one adsorption, we used the formula for the average adsorption energy ${E_{{\text{ave}}}}$:

$$\begin{align}{E_{{\text{ave}}}} = \frac{{{E_{{\text{L}} + {\text{M}}}} - {E_{\text{L}}} - n{E_{\text{M}}}}}{n}\end{align} \tag{ 4 }$$

where ${E_{{\text{L}} + {\text{M}}}}$ is the total energy of the system after atom adsorption, ${E_{\text{L}}}$ is the total energy of the initial substrate, ${E_{\text{M}}}$ is the energy of each adsorbed alkali metal atom in bulk metal, and n is the total number of adsorbed atoms.

In exploring the theoretical capacity of the Si₂C monolayer, we observed that the maximum adsorption quantity of Li, Na, and K atoms on the Si₂C monolayer is limited to a single layer. As shown in figures 7(a)–(c), the Si₂C monolayer can adsorb up to 5 Li atoms, 8 K atoms, and a maximum of 10 Na atoms. The interlayer adsorption energies for these different atoms on the Si₂C monolayer are −1.12 eV for Li, −0.62 eV for Na, and −0.83 eV for K. Notably, whether it is double-sided adsorption or the adsorption of additional Li/Na/K-ions on a single side, the adsorption energy becomes positive. Figures 7(d)–(f) show the electron localization function (ELF) maps of the Si₂C model with the maximum adsorbed states of Li/Na/K atoms. Here, '1' and '0' represent fully localized and fully delocalized electrons, respectively. Typically, ELF values below 0.5 suggest the presence of metallic or ionic bonding, whereas ELF values above 0.5 indicate the formation of covalent bonds. These images clearly demonstrate that covalent bonds are formed between Si and C in the Si₂C monolayer, while ionic bonds are formed between the alkali metal ions and the Si₂C monolayer.

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Upon determining the maximum adsorption capacity of the Si₂C monolayer, we proceeded to calculate its maximum theoretical capacitance using the following formula:

$$\begin{align}{\text{C}} = \frac{{nF}}{M}\end{align} \tag{ 5 }$$

where n represents the number of adsorbed atoms per unit cell, F is the Faraday constant (26 801 mAh g⁻¹), and M is the molar mass of the Si₂C monolayer. The results, as shown in figure 8, provide the maximum theoretical capacitance of the Si₂C monolayer. This calculation is crucial for evaluating the energy storage potential of Si₂C as an anode material in Li/Na/K-ion batteries, offering insights into its effectiveness in energy storage application.

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In LIBs applications, the Si₂C monolayer exhibits a high maximum theoretical capacitance of 174.7 mAh g⁻¹. This figure is notably superior compared to other materials such as Ti₃C₂F_x (123 mAh g⁻¹) [24], Ti₃C₂Cl_x (138 mAh g⁻¹) [24], and Ti₂NSSe (121.39 mAh g⁻¹) [48]. For potassium-ion batteries, the Si₂C monolayer's maximum theoretical capacitance reaches an impressive 349.4 mAh g⁻¹, significantly higher than Mo₂CrC₂ (154.88 mAh g⁻¹) [26], K₂C₆O₆ (217.8 mAh g⁻¹) [49], WSSe (156.0 mAh g⁻¹) [50], graphite (279 mAh g⁻¹) [51], and GeC (320 mAh g⁻¹) [51]. In the case of SIBs, the Si₂C monolayer stands out with an exceptional theoretical capacity of 436.8 mAh g⁻¹, showcasing a significant capacitance advantage compared to common materials like Na₂Ti₃O₇ (177 mA h g⁻¹) [52], MoS₂ (146 mA h g⁻¹) [53], Ti₂NS₂ (84.76 mA h g⁻¹) [54], V₂NS₂ (99.8 mA h g⁻¹) [54], WCrC (176 mA h g⁻¹) [25], and WCrCO₂ (155 mA h g⁻¹) [25]. Through these comparisons, the Si₂C monolayer demonstrates tremendous potential as an anode material for Li-ion, Na-ion, and K-ion batteries, marking an important direction for future research and development in battery materials.

By conducting detailed calculations of the OCV for Li/Na/K-ions in the Si₂C monolayer material, we also closely examined the voltage safety during the discharge process. The OCV can be calculated using the following formula:

$$\begin{align}V \approx \frac{{{E_{\text{L}}} + x{E_{\text{M}}} - {E_{{\text{L}}{{\text{M}}_x}}}}}{{n{e^ - }}}\end{align} \tag{ 6 }$$

where ${E_{{\text{L}}{{\text{M}}_x}}}$ is the energy of the substrate with adsorbed atoms, ${E_{\text{L}}}$ is the energy of the substrate without adsorbed atoms, ${E_{\text{M}}}$ is the energy of a single alkali metal atom in bulk metal, and x is the number of adsorbed atoms. An OCV below 1 V helps prevent the formation of dendrites within the battery, thereby enhancing its safety, and also implies a lower charging voltage requirement for the battery. As shown in figure 8, we observed different trends in OCV as the concentration of Li/Na/K-ions on the monolayer increases. In figure 8(a), with Li-ions concentration increasing from 1 to 4 atoms, the OCV ranges from 0.78 V to 1.41 V, with an average potential of about 0.95 V. In figure 8(b), as Na-ions concentration increases from 1 to 10 atoms, the OCV is between 0.22 V and 1.33 V, with an average potential of about 0.62 V. In figure 8(c), for K-ions concentration increasing from 1 to 8 atoms, the OCV ranges from 0.21 V to 1.68 V, with an average potential of about 0.83 V.

For the Si₂C monolayer, when adsorbing Li-ions, the average potential slightly exceeds 1 V but remains within a controllable range, sufficient to prevent lithium dendrite formation to some extent. In contrast, the average potentials for adsorbing Na-ions and K-ions are both less than 1 V, significantly reducing the risk of sodium and potassium dendrite formation. Moreover, the intercalation voltages of Li/Na/K-ions in the Si₂C anode exhibit a stable trend, further evidencing its safety during discharge.

Finally, we also calculated the changes in lattice constants of the Si₂C monolayer after adsorption of Li/Na/K-ions, to assess its structural stability during the charge-discharge processes of batteries. The results showed that after adsorption of Li/Na/K-ions, the lattice constant changes of the 3 $\times$ 3 supercell of the Si₂C monolayer were extremely minimal, indicating good structural stability during battery operation. Specifically, upon adsorption of Li-ions to their maximum capacity, the lattice constants a and b were both 8.59(6) Å, a change of about 0.21% compared to before adsorption. For Na-ions adsorbed to their maximum capacity, the lattice constants changed to a = b = 8.58(3) Å, a change of about 0.36%. And for K-ions adsorbed to their maximum capacity, the lattice constants were a = b = 8.60(1) Å, a change of about 0.15%. These results indicate that the lattice changes of the Si₂C monolayer are very small, whether lithium, sodium, or K-ions can be adsorbed. This suggests that even after adsorption of the maximum number of ions, the Si₂C monolayer maintains good structural integrity, which is a desirable characteristic for anode materials in battery applications.