English

• Sodium-ion batteries (SIBs) have emerged in recent years as a promising technology for large-scale energy storage due to the natural abundance of sodium resources as well as the close energy density and manufacturing processes to commercial lithium-ion batteries (LIBs) [1,2]. During battery operation, a thin passivating layer spontaneously forms on the anode due to the degradation reaction of the electrolyte. Such passivating layer is protective, allowing only ionic transport while preventing electron and solvent molecule transport [3-5], and has been proposed as the concept of solid electrolyte interface (SEI) [6-8]. The SEI layer is essential for inhibiting the sodium dendrite growth, thereby modulating the electrochemical performance of SIBs. Previous studies have focused on tailoring the composition, morphology, and thickness of the SEI on anode materials (e.g., hard carbon [9,10], graphite [11,12], graphene [13], and titanium dioxide [14]) to improve the efficiency of batteries, particularly in ether and carbonate electrolytes [15]. For instance, rational design of artificial SEI layers in ester-based electrolytes, i.e., uniform implantation of carbonyl groups to form a homogeneous SEI rich in inorganic components, significantly enhances the battery's rate capability and cycle stability [16]. The limited comprehension of the mesoscopic structure of SEIs is the primary bottleneck in the development of improved SIBs [17].

  It has been reported that in SIBs, the SEI layer consists of a mixture of organic and inorganic components, such as ROCO₂Na, Na₂CO₃, Na₂O, NaF [18,19]. These inorganic components are embedded in the organic components to form the so-called "mosaic-structure", similar to that of LIBs [20-23]. Inorganic components predominate in mosaic-structure SEIs and are believed to facilitate Na ion diffusion, enhance structural stability, and help improve the storage capacity of sodium [24,25]. Previous studies have demonstrated that the charge/discharge rate of SIBs can be improving by adjusting the content of NaF and Na₂CO₃ in SEI [26]. However, the role of different inorganic components on the diffusion of sodium ions remains controversial. Understanding the sodium ion transport mechanism in various possible SEI components is also crucial to the rational design of SEI [27]. It is worth noting that the diffusion of Li ions in SEI occurs mainly through paths along bulk phase surfaces and grain boundaries [28,29], it is natural to ask whether the diffusion path of sodium ions is the same as that of Li ions. Therefore, an in-depth understanding of the structure and ion transport mechanisms of inorganic components in SEI is essential for the potential utilization of SIBs.

  Earlier studies have shown that the transport of sodium ions in the SEI is largely dependent on the ion conductivity of the generated SEI products [30,31]. Crystalline inorganic SEI components, especially those containing salt such as fluoride and carbonate, may contribute to the accumulation of cations, resulting in the formation of adsorption layers and hindering the movement of sodium ions [32]. Recently, cryo-electron microscopy observations have demonstrated the presence of both crystalline and amorphous forms of the inorganic components within the SEI layers [33,34]. A similar observation has been found in LIBs, research indicates that the inorganic components of the SEI are more likely to exist in an amorphous state, particularly at the grain boundaries [35,36]. Hu et al. [37] investigated the diffusion mechanism of lithium ions in amorphous LiF and Li₂CO₃ by machine learning-assisted molecular dynamics (MD) simulations, and found that amorphous phases are not beneficial for lithium ion transport. However, in SIBs, amorphous SEI components may have better ion conductivity than crystalline components due to the isotropic properties that provide multiple pathways for ions and facilitate ion diffusion [31,38]. Nevertheless, the diffusion mechanism of sodium ions in the crystalline and amorphous phases of inorganic components remains largely unexplored. Conventional experimental techniques are challenging to achieve characterization of SEI in SIBs due to the electron beam, air sensitivity of Na metal. Therefore, MD simulations are expected to trace the diffusion pathway of Na ion in SEI and elucidate the effect of local amorphous environment on it.

  In this paper, MD simulations were performed to elucidate the diffusion behaviour of sodium ions within the main inorganic components of SEI layer, i.e., NaF, Na₂O and Na₂CO₃. Calculations were carried out separately for defect-free, interstitial/vacancy defects and amorphous inorganic components. The results have shown that amorphous SEI components significantly enhance the diffusion rate of sodium ions compared to crystalline components. Within these amorphous SEI components, we reveal that the diffusion coefficients of sodium ions in amorphous Na₂O and Na₂CO₃ are more than an order of magnitude higher than that of NaF. Moreover, voronoi tessellation analysis shows that the local amorphous environments help to facilitate Na ion diffusion. Our results provide a fundamental understanding of the transport properties of SEI in SIBs and propose a promising design strategy for artificial SEIs with amorphous structure.

  The present investigation explores SEI products including NaF, Na₂O and Na₂CO₃. Simulated box dimensions were set at 48.24 × 48.24 × 48.24 ų for NaF, 44.12 × 44.12 × 44.12 ų for Na₂O, and 44.84 × 42.61 × 42.26 ų for Na₂CO₃ (Figs. 1a-c). The calculated lattice parameters are in good agreement with experimental values, with errors of 0.1%−5.3% (Table S1 in Supporting information). We have also completed calculations for NaF, Na₂O, and Na₂CO₃ concentrations and found that variations in defect concentration have a minimal impact on the diffusion coefficients (Fig. S1 in Supporting information). Therefore, the point defect concentrations used in our study are consistent with those reported in previous literature [39]. Using ATOMSK [40], interstitial and vacancy defects were randomly introduced into each samples to establish the defect structures. According to previous results, NaF and Na₂O are considered to be energetically more favourable for vacancy defects than for interstitial defects, while Na₂CO₃ interstitial atoms are the main diffusion carriers [27,41,42]. Therefore, 16 Na atoms and 16 F atoms were removed in the NaF sample, and 16 Na atoms and 8 O atoms were removed in the Na₂O sample. For Na₂CO₃, 12 Na atoms were added as interstitial defects. Three-dimensional periodic boundary conditions were used for all SEI structures studied. For the amorphous samples, we obtained those models through rapid cooling of the NaF, Na₂O, and Na₂CO₃ samples at elevated temperatures with a cooling rate of 1 × 10³ K/ps. The local atomic structures of amorphous SEI are illustrated in Figs. 1d-f. To accurately replicate the different properties of NaF, Na₂O, and Na₂CO₃, a pre-study was conducted on defect-free crystal structures to evaluate the force field (Tables S2 and S3 in Supporting information). The crystal structures of each SEI component are verified to remain unaltered during energy minimization and equilibration at 300 K (Fig. S2 in Supporting information). Furthermore, the excellent consistency between the radial distribution function (RDF) curves derived from classical MD and ab initio molecular dynamics (AIMD) simulations demonstrates the accuracy of our model (Fig. S3 in Supporting information). Finally, we employed large-scale molecular dynamics simulations to investigate the diffusion of sodium ions in defect-free, interstitial/vacancy defects, and amorphous NaF, Na₂O, and Na₂CO₃ at variouzs temperatures. More computational details can be found in Supporting information.

  Figure 1

  

  Figure 1.  (a) Local structure of the NaF supercell with 4000 Na atoms and 4000 F atoms. (b) Local structure of the Na₂O supercell with 4096 Na atoms and 2048 O atoms. (c) Local structure of the Na₂CO₃ supercell, 2240 Na atoms, 1120 C atoms and 3360 O atoms. Local structures of (d) amorphous NaF, (e) amorphous Na₂O, and (f) amorphous Na₂CO₃. Na (blue), F (pink), O (red), C (gray).

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  We first analyse the RDF curves of the defect-free and amorphous samples in the range of 250 K to high temperature (1800 K for NaF, 1500 K for Na₂O, and 2400 K for Na₂CO₃) to characterize and compare the distribution of atoms in amorphous samples. RDF is the statistic average of two body correlation over the system, interpreting the short-range structure and chemical order [43]. It is well known that the atomic structure of amorphous is similar to liquid structure and shows great difference with crystal structure [44]. For NaF (Figs. 2a and b), the representative RDF curves were selected at 300, 1000, and 1600 K. At lower temperatures, the characteristic peaks corresponding to the crystals are still observed for amorphous NaF compared to the defect-free form after prolonged simulation period. Simultaneously, we observe that these peaks are shifted and the peak width becomes wider, indicating that the amorphous NaF has undergone a phase transition to a crystalline phase after a period of simulation, with only a few disordered structures remaining. As depicted in Fig. 2b, the characteristic peaks of amorphous structure gradually emerge and become sharper over time when simulated at 300 K for duration of 0.2, 0.6, and 5 ns, indicating that the amorphous NaF is undergoing a progressively transforming into its crystalline form. The total RDF of amorphous NaF (Fig. S4a in Supporting information) at 300 K also reveals its crystalline characteristics. Additionally, an analysis of the energy of NaF revealed a sudden change in energy, which further confirms the transition from an amorphous to a crystalline form (Fig. S5 in Supporting information). The transition from the amorphous to crystalline form is driven by the phase with lower potential energy, which is more favourable. Nevertheless, this transformation typically requires certain external factors, such as temperature, pressure, or alternative forms of energy input, to overcome the energy barrier between the amorphous and crystalline states. The spontaneous transition of amorphous NaF into the crystalline state at 300 K suggests that NaF has a pronounced tendency towards crystallization. This is consistent with extensive experimental observations, which also indicate that NaF primarily exists in crystalline form [16,45,46]. At 1000 K, the characteristic peaks of the defect-free NaF are both shifted and widened. However, these corresponding peaks can still be observed, indicating the presence of a significant amount of disordered structure within the crystal NaF. Despite this disorder, the model still maintains its crystalline phase. On the other hand, the g(r) of amorphous NaF is close to 1 in the long-range, indicating the liquid phase transition at this temperature. This is due to the increased structural disorder, which diminishes the strength of interatomic binding and thus lowers the melting point.

  Figure 2

  

  Figure 2.  Selected RDF for NaF, Na₂O, and Na₂CO₃. (a) For defect-free NaF at 300, 1000, and 1600 K: Na-F. (b) For amorphous NaF at 300, 1000, and 1600 K and in the 0.2, 0.6, and 5 ns at 300 K: Na-F. (c) For defect-free Na₂O at 300, 600, and 1200 K: Na-O. (d) For amorphous Na₂O at 300, 600, and 1200 K and in the 0.2, 0.6, and 5 ns at 300 K: Na-O. (e) For defect-free Na₂CO₃ at 300, 1400, and 2000 K: Na-C. (f) For amorphous Na₂CO₃ at 300, 600, and 1200 K and in the 0.2, 0.6, and 5 ns.

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  For Na₂O (Figs. 2c and d) and Na₂CO₃ (Figs. 2e and f), representative RDF curves at different temperatures were selected. In the RDF curves of Na₂O and Na₂CO₃ at low temperatures, the disappearance and alteration of the characteristic peaks were observed in the amorphous samples as compared to the defect-free samples. In addition, no significant changes in the characteristic peaks were observed at durations of 0.2, 0.6, and 5 ns, respectively, when simulating the amorphous samples of Na₂O and Na₂CO₃ at 300 K. Meanwhile, we observed a split in the second peak of the total RDF in Na₂O and Na₂CO₃ (Figs. S4b and c in Supporting information), which is characteristic of amorphous structures [47,48]. This indicates that the amorphous structures of Na₂O and Na₂CO₃ can maintain their amorphous configurations without crystallization transition at room temperature. In the RDF curves of Na₂O at 600 K and Na₂CO₃ at 1400 K, the characteristic peaks of both crystalline and amorphous samples are shifted and broadened. This indicates that the degree of disorder in defect-free Na₂O and Na₂CO₃ increases with rising temperature, and the degree of disorder in the amorphous Na₂O and Na₂CO₃ further increases. At high temperatures (1600 K for NaF, 1200 K for Na₂O, and 2000 K for Na₂CO₃), the RDF curves between the amorphous and defect-free samples exhibit similarities, with g(r) values approaching 1 over a wide range, suggesting that the simulated structures undergo a liquid phase transition at these temperatures. Overall, the analysis of the RDF curves for NaF, Na₂O, and Na₂CO₃ reveals that amorphous Na₂O and amorphous Na₂CO₃, which were obtained through rapid cooling, can maintain a stable amorphous structure over a long period of simulation. In contrast, amorphous NaF cannot maintain its amorphous structure and rapidly transitions to a crystalline state, demonstrating a pronounced tendency to crystallization.

  We also calculated the diffusion coefficients for defect-free, interstitial/vacancy defects and amorphous samples throughout a temperature range of 250 K to high temperatures (1800 K for NaF, 1500 K for Na₂O, and 2400 K for Na₂CO₃). Figs. 3a-c display the diffusion coefficients of the SEI products as a function of the reciprocal of temperature (1/T). Furthermore, Table S4 (Supporting information) provides a comprehensive compilation of the diffusion coefficients in 300 K, 500 K, and high-temperature ranges. The diffusion coefficient of sodium ions in defect-free samples is 4.02 × 10⁻¹⁶ m²/s for NaF at a low temperature of 300 K. Upon vacancy defects samples, the diffusion coefficient of sodium ions increases by an order of magnitude to 6.95 × 10⁻¹⁵ m²/s. This is consistent with many reports, where the introduction of defects has a significant impact on the material's properties [29,49]. This increase can be attributed to the fact that in the defect-free samples, sodium ions primarily vibrate near their equilibrium locations without effective diffusion. The introduction of vacancy defects allows for effective atomic diffusion rather than mere vibration, thus resulting in a substantial alteration of the diffusion coefficient of sodium ions. The diffusion coefficient of sodium ions in amorphous samples is found to be 9.41 × 10⁻¹⁴ m²/s, which is an order of magnitude higher than that in the vacancy defects NaF. Although RDF analysis of the amorphous NaF shows that they still retain the crystalline phase, the presence of significant structural disorder greatly improves the diffusion of sodium ions. The study reveals that the diffusion coefficient of sodium ions in amorphous NaF significantly exceeds that observed in the vacancy defects NaF. The diffusion coefficients of sodium ions in Na₂O at 300 K for defect-free, vacancy defects and amorphous samples are 2.52 × 10⁻¹⁵, 2.36 × 10⁻¹⁴, and 1.77 × 10⁻¹² m²/s, respectively. Similar to NaF, the diffusion coefficient of sodium ions in the vacancy defects Na₂O is an order of magnitude higher than in defect-free samples. Further, the diffusion coefficient in amorphous Na₂O is two orders of magnitude higher than in vacancy defects samples. RDF analysis of the amorphous Na₂O reveals that they maintain in the amorphous phase without crystallization. Consequently, the increase in the diffusion coefficient of amorphous Na₂O is higher than that of amorphous NaF. This result is expected since the diffusion mechanism in amorphous materials is primarily due to their disordered structure, which allows ions to move more flexibly, regardless the constraints of the lattice. The diffusion coefficients of sodium ions in defect-free samples, interstitial defects, and amorphous samples at 300 K for Na₂CO₃ are 1.19 × 10⁻¹⁵, 4.24 × 10⁻¹⁵, and 6.59 × 10⁻¹⁵ m²/s, respectively. The introduction of interstitial atoms into the crystalline samples results in a modest enhancement of sodium ions transport rate, but the improvement did not reach an order of magnitude. Similarly, the RDF analysis of the amorphous Na₂CO₃ demonstrated that they maintained their amorphous phase. As a result, the amorphous Na₂CO₃ have a higher increase in the diffusion coefficient compared to amorphous NaF. These findings suggest that the inherent disordered arrangement of amorphous Na₂CO₃ significantly facilitates the ion mobility compared to defect-free samples. Furthermore, we calculated the ionic conductivity using the diffusion coefficient of sodium ions, with specific data presented in Table S5 (Supporting information). The analysis of ionic conductivity is consistent with that of the diffusion coefficient, showing that the amorphous structure significantly enhances the ionic conductivity of sodium ions within the SEI. This is similar to findings in studies on amorphous Li₂O₂, where the amorphous structure greatly improves ionic conductivity. This further demonstrates that the amorphous structure facilitates more efficient sodium ion transport.

  Figure 3

  

  Figure 3.  The diffusion coefficients of (a) NaF, (b) Na₂O and (c) Na₂CO₃ were calculated at different temperatures. Diffusion pathway of sodium ions in (d) NaF, (e) Na₂O, and (f) Na₂CO₃. The sodium ions that migrate are shown in yellow, and the migration path is indicated by different colored arrows. Other Na (blue), F (pink), O (red), and C (gray).

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  In defect-free samples, sodium ions are constrained by the lattice and can only vibrate near their equilibrium locations, hindering the observation of a effective diffusion pathway. Hence, by introducing a small number of defects into the samples, we can observe the phenomenon of effective diffusion. Meanwhile, after the introduction of defects in the sample, we observed mainly the atomic vibrations caused by the temperature increase, making it difficult to identify the effective diffusion within the duration of the simulation. In contrast, as the temperature increases, the disorder of the local structure becomes more pronounced, and thus the diffusion of sodium ions can be observed more clearly. Therefore, temperatures of 1000, 600, and 1400 K were selected to investigate the diffusion mechanism of sodium ions in NaF, Na₂O, and Na₂CO₃ respectively. As shown in Fig. S6 (Supporting information), we used Ovito [50] to track the trajectories of all sodium ions in NaF, Na₂O, and Na₂CO₃. By analyzing these trajectories, we observed clear diffusion pathways of sodium ions. Based on these distinct diffusion routes, we identified the primary diffusion mechanisms in NaF, Na₂O, and Na₂CO₃ (Figs. 3d-f). Our simulation demonstrates that the diffusion of sodium ions in NaF primarily occurs through a vacancy diffusion mechanism, whereby multiple sodium ions migrate along lattice vacancies in a cascade fashion. When a Na ion jumps into a vacancy, a new vacancy is created, which is subsequently occupied by the nearest Na ion, resulting in a chain reaction or a cascade effect, as shown in Fig. 3d. Similarly, sodium ions diffuse mainly through a vacancy diffusion mechanism in Na₂O. When a sodium ion jumps into a vacancy, it creates a new vacancy, which is then occupied by the nearest sodium ion, leading to a chain reaction or a cascade effect (Fig. 3e). In Na₂CO₃, sodium ions primarily diffuse through both vacancy and knock-off diffusion mechanisms. In this process, sodium ions slightly deviate from their lattice positions, creating vacancies and interstitial sites. This allows subsequent atoms to replace their positions following the green arrows and further move into the interstitial sites. The displaced atom then follows the yellow arrows to knock-off its neighboring atom, moving it to the interstitial site. The interstitial atom, following the pink arrows, knock-off its adjacent atom into the interstitial, and so forth, leading to a cascade effect (Fig. 3f).

  Additionally, we analyse the evolution of sodium ions trajectories in both vacancy defects NaF and amorphous NaF, as shown in Fig. 4. Our results revealed that the effective diffusion pathways in amorphous NaF are significantly longer than those in vacancy defects NaF at temperatures of 300 K and 1000 K. At a temperature of 1600 K, the lengths of the trajectories are similar for the same period, since both are in the liquid state with a similar degree of disorder. This agrees well with the calculated diffusion coefficients: at low to mid-temperatures, the diffusion coefficient of amorphous NaF is much higher than that of vacancy defects NaF, while at high temperatures the two diffusion coefficients are very close to each other. It was also observed that at 300 K, the defect-bearing crystals mainly vibrate within the lattice, and only at higher temperatures does it exhibit more effective diffusion and larger effective diffusion distance. For Na₂O and Na₂CO₃ (Figs. S7 and S8 in Supporting information), similar to NaF, the effective diffusion pathways in the amorphous samples are significantly longer than in the interstitial/vacancy defects samples.

  Figure 4

  

  Figure 4.  At 300, 1000, and 1600 K, the evolution of sodium ions (represented by green spheres) trajectories in both vacancy defects (a-c) NaF and amorphous (d-f) NaF.

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  To further analyse the internal topological structure and atomic distribution of amorphous samples, we performed Voronoi tessellation analysis to character the local amorphous structure. The Voronoi tessellation technique is one of the most commonly used methods for characterizing the local structures of liquids and amorphous solids [51]. The method focuses on the study of local atomic configurations consisting of a central atom and its neighbouring atoms, known as Voronoi clusters [52]. These clusters are equivalent to the Voronoi polyhedron (VP) with the smallest volume [51]. Each VP can be labelled as <n₃, n₄, n₅, n₆, …, n_i, …>, where n_i represents the number of i-edged faces of VPs. The variable Z = ∑n_i represents the sum of the number of neighbours, which is also known as the coordination number (CN) of the central atom Z [53]. Fig. 5 illustrates the predominant VP and CN in amorphous NaF, Na₂O, and Na₂CO₃ at various temperatures. Table S6 (Supporting information) provides the overall proportion of VP in amorphous NaF at different temperatures. At 300 K, NaF in its amorphous state undergoes a rapid transition towards the crystalline state over time, eventually forming local crystal polyhedral with shape of <0, 6, 0, 0>, <0, 4, 2, 0>, <0, 5, 1, 0>, <1, 3, 3, 0>and <1, 5, 1, 0>as the main clusters (Fig. 5a and Fig. S9 in Supporting information). The proportions of these clusters are 37.1%, 16.6%, 4.2%, 3.8%, and 3.4%, respectively. The predominance of the first two clusters over the latter two suggests that the major structures in NaF are dominated by <0, 6, 0, 0>and <0, 4, 2, 0>clusters. In distinguishing the central atoms, both Na and F (Fig. S10 in Supporting information) show similarities in the local atomic cluster structures. The most prominent clusters are primarily <0, 6, 0, 0>and <0, 4, 2, 0>. In perfect crystal of NaF, the local structure is characterized by clusters featuring octahedra with six equivalent equilateral quadrangles, denoted as <0, 6, 0, 0>. The results indicate that the crystal structure essentially maintains its octahedral configuration when amorphous NaF transforms into the crystalline state. However, a large number of other characteristic clusters also exist, making it necessary to analyse the internal cluster structures in detail. Furthermore, it is worth noting that atoms with a CN of six account for 68.2% of amorphous NaF, providing further evidence of the dominance of the octahedral configuration in this structure (Fig. 5b). The <0, 6, 0, 0>and <0, 4, 2, 0>clusters decrease as the NaF temperature increases to 1000 K and 1600 K. In addition, the proportion of atoms with six coordination decreases to 8.0%, while there is a notable increase in the proportion of atoms with CN ranging from 8 to 11. These changes in local clusters and the increase in CN can be attributed to the fact that the structure becomes increasingly disordered as the temperature changes, eventually leading to a liquid state.

  Figure 5

  

  Figure 5.  Analysis of VP fractions and CN in amorphous NaF, Na₂O, and Na₂CO₃ at various temperatures. (a-c) The fractions of VP for NaF, Na₂O, and Na₂CO₃. (d-f) The fractions of CN. The analysis does not distinguish between central atoms in all panels.

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  In the ideal crystal structure of Na₂O, the octahedral VPs are formed around sodium atoms, as denoted by the Voronoi index <0, 0, 6, 0>. Similarly, the tetrahedral VPs are centred around oxygen atoms, as indicated by the Voronoi index <4, 0, 0, 0>. Table S7 (Supporting information) provides the overall proportion of VP in amorphous Na₂O at different temperatures. In the study at 300 K, the local structure of amorphous Na₂O remained largely unchanged over time (Fig. S11 in Supporting information). Notably, the most common clusters observed in the amorphous samples were icosahedral clusters. The ideal icosahedron cluster is <0, 12, 0, 0>, and several other clusters (e.g., <0, 2, 8, 2>, <0, 4, 4, 4>, <0, 1, 10, 2>, <0, 3, 6, 3>, and <0, 2, 8, 1>) are very similar to the <0, 0, 12, 0>cluster [54,55]. These types of clusters can be transformed into <0, 0, 12, 0>cluster from simpler structures, hence they are termed icosahedral-like clusters [53]. In amorphous Na₂O, the total proportion of these icosahedral clusters reaches 28.28%. Apart from the icosahedral, <0, 4, 4, 0>and <0, 3, 6, 0>are the most significant, yet they do not exceed 10% (Fig. 5c). When distinguishing the central atoms, the primary cluster structures of both Na and O atoms (Fig. S12 in Supporting information) are distinctly different. The Na-centred clusters predominantly occur in the coordination structures of 11–15, and the icosahedral structures are concentrated in the locally skewed structures of Na atoms. The O-centred clusters are mainly found in 7–10 coordination structures, such as <0, 4, 4, 0>and <0, 3, 6, 0>. Among the O-centred VPs, <0, 4, 4, 0>and <0, 3, 6, 0>account for 24% and 29.3% respectively. Both local structures centred on Na and O atoms are stronger constrained by the increase in the number of adjacent particles. This increased constraint makes it more difficult to adjust their locations, thereby enabling Na₂O to maintain a stable amorphous structure [56]. The above results show that although Na₂O is in an amorphous state, it still exhibits a relatively high degree of local ordering. As the temperature of Na₂O rises to 600 K and 1200 K, the proportion of each cluster begins to decline, losing their relatively stable captured structures. Atoms with CN of 8–14 still dominate, indicating that Na₂O (Fig. 5d) still maintains its amorphous structure at lower temperatures, and an increase in temperature will only add local disordering without significantly altering the CN of atoms. Table S8 (Supporting information) provides the overall proportion of VP in amorphous Na₂CO₃ at different temperatures. For Na₂CO₃, the local structure of amorphous Na₂CO₃ remained largely unchanged over time at 300 K (Fig. S13 in Supporting information). The statistical analysis of the VP index shows that the proportion value of all clusters is below 2%, and this remains the case even when different central atoms are used (Figs. 5e and f, Fig. S14 in Supporting information). The results indicate a lower degree of local ordering, suggesting the inability to form structures with a higher degree of local ordering. At elevated temperatures, the formation of clusters with greater proportions becomes challenging. The CN values are similar to those in Na₂O, where atoms with 9–12 coordination dominate and do not undergo significant changes with temperature variations.

  Fig. 6 illustrates a schematic of the prominent cluster structures in inorganic components of amorphous SEI and also examines the local structures of amorphous NaF, Na₂O, and Na₂CO₃. The schematic displays the main cluster structures in NaF (Figs. 6a-e), including <0, 6, 0, 0>, <0, 4, 2, 0>, <5, 1, 0>, <1, 5, 1, 0>, and <1, 3, 3, 0>. The octahedral clusters <0, 6, 0, 0>and <0, 4, 2, 0>are the most prominent clusters in NaF, forming the primary localized structures following the amorphization of NaF. As shown in Fig. S15a (Supporting information), the schematic of the <0, 4, 2, 0>octahedral structure indicates that the <0, 4, 2, 0>cluster can be formed by distortion of atoms in the <0, 6, 0, 0>cluster. Moreover, the clusters with smaller proportions, such as <0, 5, 1, 0>, <1, 5, 1, 0>, and <1, 3, 3, 0>, show interesting characteristics. The <0, 5, 1, 0>cluster remains structurally similar to the <0, 6, 0, 0>cluster (Fig. S15b in Supporting information). The <1, 5, 1, 0>and <1, 3, 3, 0>clusters can be formed by migration of the second nearest-neighbour atom to the first nearest-neighbour atom, resulting in hyper-coordinated structures (Figs. S15c and d in Supporting information). The analysis of these localized structures indicates that a large number of distorted structures like <0, 4, 2, 0>as well as some defect-like structures, such as <1, 5, 1, 0>and <1, 3, 3, 0>, are preserved in NaF. This elucidates the significant improvement in sodium ion diffusion, even following the crystallization of amorphous NaF. Figs. 6g-j display the five clusters in Na₂O with the highest proportions: <0, 4, 4, 0>, <0, 2, 8, 2>, <0, 3, 6, 0>, <0, 3, 6, 3>, and <0, 3, 6, 4>. The <0, 4, 4, 0>and <0, 3, 6, 0>are the main local structures centred on O atoms. The remaining clusters are centred on Na atoms. Unlike the crystal structures, where Na and O atoms are bound in octahedral and tetrahedral arrangements respectively, the amorphous local structures greatly reduce the lattice constraints and thus increase the mobility of atoms. Due to the relatively disordered local structure of Na₂CO₃ (Figs. 6k-o), the cluster structures also lack a regular local arrangement. The absence of regularity in the local structures of Na₂CO₃ suggests a higher degree of disorder, which facilitates the diffusion of sodium ions.

  Figure 6

  

  Figure 6.  The schematic diagrams of cluster structures in amorphous (a-e) NaF, (f-j) Na₂O, and (k-o) Na₂CO₃.

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  Before concluding, several remarks are in order. In this study, unlike the previous finding by Hu et al. [37] that amorphous LiF inhibits lithium ion diffusion, amorphous NaF significantly enhances sodium ion diffusion despite its strong crystallinity, which eventually crystallizes into a state primarily composed of octahedral structures. Considering that amorphous Li₂O₂ provides Li ion conductivity at a magnitude of 10⁻⁷S/m [57], we can speculate that inhibiting the crystallization of NaF could lead to better ion diffusion rates. As for the amorphous forms of Na₂O and Na₂CO₃, the study has directly observed specific local structures in the amorphous phase. Both the icosahedral structure of Na₂O and the disordered local structure of Na₂CO₃ play a significant role in facilitating Na ion diffusion.

  In summary, we employ MD simulations to study the diffusion mechanism of sodium ions within three main inorganic components of the SEI, namely NaF, Na₂O, and Na₂CO₃, as well as the local structures within amorphous inorganic components. Our simulations indicate that sodium ions diffuse mainly through vacancy mechanisms in NaF and Na₂O compounds. However, the predominant diffusion mechanisms observed were combination of vacancy and knock-off in Na₂CO₃. Notably, at room temperature, the diffusion rates of sodium ions in amorphous Na₂O and Na₂CO₃ are significantly enhanced, far surpassing their crystalline components. Within these amorphous SEI components, the diffusion coefficients of sodium ions in amorphous Na₂O and Na₂CO₃ are more than an order of magnitude higher than that of NaF. Our result suggests that amorphous Na₂O and Na₂CO₃ are more effective in facilitating sodium ion diffusion. This can be attributed to the predominantly disordered amorphous state of Na₂O and Na₂CO₃ at room temperature, characterized mainly by amorphous local structures. In contrast, amorphous NaF undergoes a spontaneous transition to spontaneously transformation into an ordered structure. These crystalline characteristics significantly restrict the diffusion of sodium ions, underscoring the critical influence of ordered structure on ionic transport properties. Therefore, the study reveals the superior functionality of amorphous Na₂O and Na₂CO₃ in promoting sodium ion diffusion, a critical factor for their application in SIBs technology. Overall, this research provides new insights at the atomic level into the diffusion behaviors of sodium ions in SEI films and highlights the potential of amorphous and defect states in enhancing the rapid diffusion of sodium ions.

  Declaration of competing interests

  The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  CRediT authorship contribution statement

  Yao Wang: Writing – review & editing, Supervision, Resources, Project administration, Investigation, Funding acquisition, Formal analysis. Jun Ouyang: Writing – original draft, Methodology, Investigation, Formal analysis. Huadong Yuan: Supervision, Investigation, Formal analysis. Jianmin Luo: Supervision, Investigation, Formal analysis. Shihui Zou: Supervision, Investigation, Formal analysis. Jianwei Nai: Supervision, Investigation, Formal analysis. Xinyong Tao: Supervision, Resources, Investigation, Funding acquisition, Formal analysis. Yujing Liu: Resources, Project administration.

  Acknowledgments

  The authors acknowledge financial support from the National Key Research and Development Project of China (No. 2022YFE0113800), the Natural Science Foundation of Zhejiang Province (No. LY23E020010), the National Natural Science Foundation of China (Nos. U21A20174 and 52225208). Y. Wang acknowledges the funding from China Postdoctoral Science Foundation (No. 2023M743098). The authors thank Beijing PARATERA Tech Co., Ltd. and Shanghai Hongzhiwei Tech Co., Ltd. for providing HPC resources.

  Supplementary materials

  Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cclet.2024.110412.

  
  
• 1. [1]

     T. Wang, Z. Huang, D. Wang, et al., Chin. Chem. Lett. 34 (2023) 107216. doi: 10.1016/j.cclet.2022.02.021

  2. [2]

     Y. Wang, Q. Xie, J. Zhang, et al., Comput. Mater. Sci. 211 (2022) 111523. doi: 10.1016/j.commatsci.2022.111523

  3. [3]

     G. Nazri, R. Muller, J. Electrochem. Soc. 132 (1985) 2050. doi: 10.1149/1.2114288

  4. [4]

     K. Xu, Chem. Rev. 114 (2014) 11503–11618. doi: 10.1021/cr500003w

  5. [5]

     P. Verma, P. Maire, P. Novák, Electrochim. Acta 55 (2010) 6332–6341. doi: 10.1016/j.electacta.2010.05.072

  6. [6]

     E. Peled, J. Electrochem. Soc. 126 (1979) 2047. doi: 10.1149/1.2128859

  7. [7]

     E. Peled, D. Golodnitsky, G. Ardel, J. Electrochem. Soc. 144 (1997) L208. doi: 10.1149/1.1837858

  8. [8]

     E. Peled, D. Golodnttsky, G. Ardel, et al., MRS Online Proc. Libr. 393 (1995) 209–221. doi: 10.1557/PROC-393-209

  9. [9]

     H. Wang, H. Chen, C. Chen, et al., Chin. Chem. Lett. 34 (2023) 107465. doi: 10.1016/j.cclet.2022.04.063

  10. [10]

      M. Ma, H. Cai, C. Xu, et al., Adv. Funct. Mater. 31 (2021) 2100278. doi: 10.1002/adfm.202100278

  11. [11]

      J. Zhang, D. Wang, W. Lv, et al., Energy Environ. Sci. 10 (2017) 370–376. doi: 10.1039/C6EE03367A

  12. [12]

      M. Goktas, C. Bolli, E.J. Berg, et al., Adv. Energy Mater. 8 (2018) 1702724. doi: 10.1002/aenm.201702724

  13. [13]

      M. Zhang, X. Liu, J. Gu, et al., Chin. Chem. Lett. 34 (2023) 108471. doi: 10.1016/j.cclet.2023.108471

  14. [14]

      G. Cha, S. Mohajernia, N.T. Nguyen, et al., Adv. Energy Mater. 10 (2020) 1903448. doi: 10.1002/aenm.201903448

  15. [15]

      C. Gong, S.D. Pu, S. Zhang, et al., Energy Environ. Sci. 16 (2023) 535–545. doi: 10.1039/d2ee02606f

  16. [16]

      M. Liu, F. Wu, Y. Gong, et al., Adv. Mater. 35 (2023) 2300002. doi: 10.1002/adma.202300002

  17. [17]

      N.T. Aristote, K. Zou, A. Di, et al., Chin. Chem. Lett. 33 (2022) 730–742. doi: 10.1016/j.cclet.2021.08.049

  18. [18]

      Y. Zhao, X. Sun, ACS Energy Lett. 3 (2018) 899–914. doi: 10.1021/acsenergylett.8b00145

  19. [19]

      Q. Liu, D. Mu, B. Wu, et al., RSC Adv. 7 (2017) 33373–33377. doi: 10.1039/C7RA04673A

  20. [20]

      J. Tian, T. Hu, S. Xu, et al., Chin. Chem. Lett. 34 (2023) 108242. doi: 10.1016/j.cclet.2023.108242

  21. [21]

      O. Sheng, J. Zheng, Z. Ju, et al., Adv. Mater. 32 (2020) 2000223. doi: 10.1002/adma.202000223

  22. [22]

      J. Zheng, Z. Ju, B. Zhang, et al., J. Mater. Chem. A 9 (2021) 10251–10259. doi: 10.1039/d0ta11444h

  23. [23]

      X. Zhu, Y. Mo, J. Chen, et al., Chin. Chem. Lett. 35 (2024) 109146. doi: 10.1016/j.cclet.2023.109146

  24. [24]

      J. Ge, C. Ma, Y. Wan, et al., Adv. Funct. Mater. 33 (2023) 2305803. doi: 10.1002/adfm.202305803

  25. [25]

      X. Dong, Y. Niu, Y. Ding, et al., Nanoscale Res. Lett. 12 (2017) 202. doi: 10.1186/s11671-017-1980-5

  26. [26]

      J. Fondard, E. Irisarri, C. Courrèges, et al., J. Electrochem. Soc. 167 (2020) 070526. doi: 10.1149/1945-7111/ab75fd

  27. [27]

      F.A. Soto, A. Marzouk, F. El-Mellouhi, et al., Chem. Mater. 30 (2018) 3315–3322. doi: 10.1021/acs.chemmater.8b00635

  28. [28]

      X.X. Ma, X. Sen, X. Chen, et al., Small Struct. 3 (2022) 2200071. doi: 10.1002/sstr.202200071

  29. [29]

      S. Shi, P. Lu, Z. Liu, et al., J. Am. Chem. Soc. 134 (2012) 15476–15487. doi: 10.1021/ja305366r

  30. [30]

      R. Dong, L. Zheng, Y. Bai, et al., Adv. Mater. 33 (2021) 2008810. doi: 10.1002/adma.202008810

  31. [31]

      E. Wang, Y. Niu, Y. Yin, et al., ACS Mater. Lett. 3 (2021) 18–41. doi: 10.1021/acsmaterialslett.0c00356

  32. [32]

      L. Raguette, R. Jorn, J. Phys. Chem. C 122 (2018) 3219–3232. doi: 10.1021/acs.jpcc.7b11472

  33. [33]

      B. Han, Y. Zou, Z. Zhang, et al., Nat. Commun. 12 (2021) 3066. doi: 10.1038/s41467-021-23368-6

  34. [34]

      S. Wan, K. Song, J. Chen, et al., J. Am. Chem. Soc. 145 (2023) 21661–21671. doi: 10.1021/jacs.3c08224

  35. [35]

      O. Borodin, G.D. Smith, J. Phys. Chem. B 110 (2006) 4971–4977. doi: 10.1021/jp056249q

  36. [36]

      M. Sulaiman, A.A. Rahman, N.S. Mohamed, Ionics 22 (2016) 327–332. doi: 10.1007/s11581-015-1548-2

  37. [37]

      T. Hu, J. Tian, F. Dai, et al., J. Am. Chem. Soc. 145 (2023) 1327–1333. doi: 10.1021/jacs.2c11521

  38. [38]

      J. Huang, X. Guo, X. Du, et al., Energy Environ. Sci. 12 (2019) 1550–1557. doi: 10.1039/c8ee03632b

  39. [39]

      L. Benitez, J.M. Seminario, J. Electrochem. Soc. 164 (2017) E3159. doi: 10.1149/2.0181711jes

  40. [40]

      P. Hirel, Comput. Phys. Commun. 197 (2015) 212–219. doi: 10.1016/j.cpc.2015.07.012

  41. [41]

      F.A. Soto, P. Yan, M.H. Engelhard, et al., Adv. Mater. 29 (2017) 1606860. doi: 10.1002/adma.201606860

  42. [42]

      H. Yildirim, A. Kinaci, M.K.Y. Chan, et al., ACS Appl. Mater. 7 (2015) 18985–18996. doi: 10.1021/acsami.5b02904

  43. [43]

      R.S. Liu, D.W. Qi, S. Wang, Phys. Rev. B. 45 (1992) 451–453. doi: 10.1103/PhysRevB.45.451

  44. [44]

      T. Egami, Y. Waseda, J. Non-Cryst. Solids 64 (1984) 113–134. doi: 10.1016/0022-3093(84)90210-2

  45. [45]

      Y. Wang, J. Lu, W. Dai, et al., Adv. Funct. Mater. 34 (2024) 2403841. doi: 10.1002/adfm.202403841

  46. [46]

      Z. Yang, X. Zhou, Z. Hao, et al., Angew. Chem. Int. Ed. 63 (2024) e202313142. doi: 10.1002/anie.202313142

  47. [47]

      A. Shvaika, M. Shpot, W. Schirmacher, et al., Phys. Rev. Lett. 127 (2021) 179601. doi: 10.1103/PhysRevLett.127.179601

  48. [48]

      S. Roorda, C. Martin, M. Droui, et al., Phys. Rev. Lett. 108 (2012) 255501. doi: 10.1103/PhysRevLett.108.255501

  49. [49]

      Y. Li, X. Liu, T. Ji, et al., Chin. Chem. Lett. 36 (2025) 109551. doi: 10.1016/j.cclet.2024.109551

  50. [50]

      A. Stukowski, Model. Simul. Mater. Sc. 18 (2010) 015012. doi: 10.1088/0965-0393/18/1/015012

  51. [51]

      Y.Q. Cheng, E. Ma, Prog. Mater Sci. 56 (2011) 379–473. doi: 10.1016/j.pmatsci.2010.12.002

  52. [52]

      Z.A. Tian, K.J. Dong, A.B. Yu, AIP Conf. Proc. 1542 (2013) 373–376. doi: 10.1063/1.4811945

  53. [53]

      P.H. Gaskell, Nature 276 (1978) 484–485. doi: 10.1038/276484a0

  54. [54]

      Y.D. Wei, P. Peng, Z.Z. Yan, et al., Comput. Mater. Sci. 123 (2016) 214–223. doi: 10.1016/j.commatsci.2016.06.030

  55. [55]

      E. Ma, Nat. Mater. 14 (2015) 547–552. doi: 10.1038/nmat4300

  56. [56]

      H. Zhang, Q. Zhang, F. Liu, et al., Phys. Rev. Lett. 132 (2024) 078201. doi: 10.1103/PhysRevLett.132.078201

  57. [57]

      Y. Zhang, Q. Cui, X. Zhang, et al., Angew. Chem. Int. Ed. 55 (2016) 10717–10721. doi: 10.1002/anie.201605228

• 

  Figure 1  (a) Local structure of the NaF supercell with 4000 Na atoms and 4000 F atoms. (b) Local structure of the Na₂O supercell with 4096 Na atoms and 2048 O atoms. (c) Local structure of the Na₂CO₃ supercell, 2240 Na atoms, 1120 C atoms and 3360 O atoms. Local structures of (d) amorphous NaF, (e) amorphous Na₂O, and (f) amorphous Na₂CO₃. Na (blue), F (pink), O (red), C (gray).

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  Figure 2  Selected RDF for NaF, Na₂O, and Na₂CO₃. (a) For defect-free NaF at 300, 1000, and 1600 K: Na-F. (b) For amorphous NaF at 300, 1000, and 1600 K and in the 0.2, 0.6, and 5 ns at 300 K: Na-F. (c) For defect-free Na₂O at 300, 600, and 1200 K: Na-O. (d) For amorphous Na₂O at 300, 600, and 1200 K and in the 0.2, 0.6, and 5 ns at 300 K: Na-O. (e) For defect-free Na₂CO₃ at 300, 1400, and 2000 K: Na-C. (f) For amorphous Na₂CO₃ at 300, 600, and 1200 K and in the 0.2, 0.6, and 5 ns.

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  Figure 3  The diffusion coefficients of (a) NaF, (b) Na₂O and (c) Na₂CO₃ were calculated at different temperatures. Diffusion pathway of sodium ions in (d) NaF, (e) Na₂O, and (f) Na₂CO₃. The sodium ions that migrate are shown in yellow, and the migration path is indicated by different colored arrows. Other Na (blue), F (pink), O (red), and C (gray).

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  Figure 4  At 300, 1000, and 1600 K, the evolution of sodium ions (represented by green spheres) trajectories in both vacancy defects (a-c) NaF and amorphous (d-f) NaF.

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  Figure 5  Analysis of VP fractions and CN in amorphous NaF, Na₂O, and Na₂CO₃ at various temperatures. (a-c) The fractions of VP for NaF, Na₂O, and Na₂CO₃. (d-f) The fractions of CN. The analysis does not distinguish between central atoms in all panels.

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  Figure 6  The schematic diagrams of cluster structures in amorphous (a-e) NaF, (f-j) Na₂O, and (k-o) Na₂CO₃.

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