Atomic-scale mechanism of alloy anodes mitigating polysulfide-induced degradation in lithium–sulfur batteries

Abstract

Polysulfide reactions at the lithium anode critically degrade the performance of Li–S batteries. Using density functional theory and molecular dynamics simulations, we unveil atomic-scale mechanisms of how alloying the lithium anode with Mg, Al, or Zn suppresses this degradation. In the lithium anode, weak Li–Li and Li–S bonds promote lithium migration into the electrolyte, accelerating polysulfide decomposition and structural collapse, along with the formation of a porous, unstable solid-electrolyte interphase (SEI). However, in Li–Mg alloy anodes, Mg atoms co-migrate with Li, forming a uniform, chemically stable Mg-rich SEI due to moderate Mg–S bonding. Li–Al and Li–Zn alloys have strong metal–metal bonds, leading to surface segregation of Al and Zn atoms that act as physical barriers to limit polysulfide access. S–S bond analysis shows that Li_1−xMg_x alloys suppress polysulfide decomposition most effectively at low concentrations (x = 0.05), while the suppression effects of Li_1−xAl_x and Li_1−xZn_x alloys are significantly enhanced at higher concentrations, eventually surpassing those of Li_1−xMg_x (x = 0.5). These distinct protection mechanisms offer design strategies for corrosion-resistant alloy anodes that enhance the long-term stability and performance of Li–S batteries.

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1. Introduction

Lithium–sulfur (Li–S) batteries exhibit a theoretical energy density of 2600 Wh kg⁻¹, offering more than eight times the energy storage capacity of currently commercialized lithium-ion batteries (250–300 Wh kg⁻¹).¹ Sulfur cathodes offer a high theoretical capacity of 1675 mAh g⁻¹, along with advantages such as abundant natural reserves, environmental friendliness, and cost-effectiveness,² while lithium metal anodes offer a low reduction potential of −3.04 V versus the standard hydrogen electrode (SHE) and a high theoretical capacity of 3860 mA h g⁻¹.³ These properties make Li–S batteries promising candidates for next-generation energy storage systems in electric vehicles, aerospace, and grid applications.⁴ The operating principle of Li–S batteries involves reversible electrochemical reactions in which lithium ions, oxidized at the anode, migrate to the sulfur cathode, where sulfur (S₈) undergoes stepwise reduction during discharge:⁵

S₈ → Li₂S₈ → Li₂S₄ → Li₂S₂ → Li₂S (1)

During charging, the reaction proceeds in reverse. Although this multi-step conversion process enables high energy density, it also introduces significant technical challenges. The most critical obstacle to commercialization is the shuttle effect of lithium polysulfides, which leads to severe corrosion of the lithium anode.⁶

During cycling, intermediate lithium polysulfides (Li₂S_n, n = 4–8), generated at the cathode, dissolve in the electrolyte. These species then migrate to the anode, where they react with the lithium surface to form insoluble Li₂S₂ and Li₂S precipitates.⁷ These continuous redox reactions cause structural damage to the anode surface and promote dendrite formation, increasing the electrolyte contact area and potentially penetrating the separator, risking internal short circuits.⁸

Additionally, a heterogeneous passivation-derived solid electrolyte interphase (SEI) layer forms on the anode surface, with accumulated reaction byproducts that hinder lithium-ion transport and increase the interfacial resistance.⁹ The impediment of lithium-ion transport results in the accumulation of electrochemically inactive (“dead”) lithium, significantly diminishing the reversible capacity and shortening the battery lifespan.¹⁰ Moreover, the persistent shuttle effect leads to the loss of active material from the cathode, thereby reducing the coulombic efficiency and overall energy density.¹¹

The repeated dissolution–deposition reactions during cycling also induce significant volume changes, generating mechanical stress that leads to cracking and delamination of the electrode surface. This exposes fresh lithium, further exacerbating side reactions.¹² In addition, the non-uniform distribution of current density promotes localized lithium deposition, accelerating dendrite growth and posing serious safety risks.¹³

To mitigate these issues, a wide range of strategies have been explored, including electrolyte additives (e.g., LiNO₃),¹⁴ protective coatings (Li₃N, LiF, BN, etc.),^15–17 and solid-state electrolyte interfaces.¹⁸ Additional efforts include composite electrode designs,^19–21 high-concentration electrolytes,²² low solubility electrolytes,²³ functional separators,²⁴ and cathode modifications.²⁵

Recently, lithium alloy anode systems have gained significant attention as a more fundamental solution to these challenges.²⁶ Compared to pure lithium, lithium alloy anodes demonstrate lower chemical reactivity, enhanced mechanical strength, and superior interfacial stability, effectively suppressing both corrosion and dendrite growth due to the intrinsic alloying-induced modifications in electronic and mechanical properties.^27–31 Multiple investigations have demonstrated the performance enhancement of lithium alloy systems, particularly highlighting their contributions to improved electrochemical stability and uniform SEI formation.^32–34 Studies have shown that the lithium–aluminum (Li–Al) alloys promote uniform lithium deposition and reduce polysulfide-induced corrosion,^35–37 while the lithium–magnesium (Li–Mg) alloys create more uniform SEI layers with improved lithium-ion diffusivity.^38–40

Despite recent progress, a fundamental understanding of how lithium-alloy anodes interact with polysulfides and inhibit polysulfide-induced degradation remains elusive. While numerous theoretical studies have examined the general electrochemical behavior of lithium anodes using Density Functional Theory (DFT) and Molecular Dynamics (MD) simulations, detailed investigations of lithium polysulfide decomposition and its impact on anode corrosion are limited.^41–45

This study investigates the decomposition of lithium polysulfides and the formation of a solid electrolyte interphase (SEI) at lithium alloy anodes through DFT and MD simulations employing the machine learning-based interatomic potential (M3GNet).^46,47 Magnesium, aluminum, and zinc were selected as alloying elements for lithium based on their favorable mechanical and electrochemical properties (SI Table 1). These elements exhibit significantly higher Young's moduli (Mg: 45 GPa; Al: 70 GPa; Zn: 80–90 GPa) compared to pure lithium (4.9 GPa), potentially enhancing the structural stability of lithium anodes. Additionally, their higher reduction potentials relative to lithium may inhibit reactions with lithium polysulfides, thereby improving stability under high-voltage conditions.

The positions of alloying elements and the spatial distribution of electrolyte and polysulfide molecules significantly influence interfacial reactivity. Therefore, analyzing only a few interface structures is insufficient to reliably elucidate the mechanisms of polysulfide decomposition and anode corrosion. To address this, we generated 400 distinct interface configurations for each alloy composition, enabling comprehensive sampling of the variability in corrosion behavior arising from atomic arrangements, elemental concentrations, and molecular orientations. This level of extensive sampling is computationally infeasible using DFT-based ab initio molecular dynamics (AIMD); thus, we employed the M3GNet potential, which allows large-scale MD simulations across diverse alloy–electrolyte interfaces with near-DFT accuracy.

We first examined the elastic properties of various alloy compositions using DFT. Subsequently, based on MD simulations involving multiple atomic configurations of alloy–electrolyte interfaces, we analyzed atomic displacements, bonding strengths, and bond lengths to compare how lithium polysulfide decomposition and SEI formation differ between alloyed and pure lithium anodes. Finally, we discussed, at the atomic scale, how lithium alloy anodes can more effectively suppress polysulfide-induced degradation in Li–S batteries.

2. Methods

2.1. Computational modeling

To model the solid–solution phase of lithium alloy anodes, the special quasi-random structures (SQS) method was applied. The body-centered cubic (BCC) lithium supercell, constructed as a 4 × 4 × 8 structure, consists of 256 atoms. The Li–M (M = Mg, Al, Zn) alloys were examined at M concentrations of 0, 5, 17, 33, and 50 at%, as illustrated in Fig. 1a. The SQS optimization was performed until the atomic pair correlation remained below 0.05, considering up to the fourth-nearest neighbor atoms within a distance of 1.42 times the BCC lattice constant.

Fig. 1 Structural models of alloy anodes and electrolyte components: (a) top and side views of Li_1−xM_x alloy configuration with varying x values (x = 0.05, 0.17, 0.33, and 0.50); (b) electrolyte components, including Li₂S₈ polysulfides, DOL solvent, LiTFSI salt, and anode–electrolyte interface view along the c-axis.

To obtain the structural and elastic properties of Li–M alloys, first-principles calculations were performed using the Vienna Ab initio Simulation Package (VASP),^48,49 based on DFT,^50,51 employing the projector augmented wave (PAW) method⁵² and the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA) exchange-correlation functional.⁵³ To ensure computational accuracy, the plane-wave energy cutoff was set to 650 eV. The convergence criteria for electronic and ionic relaxations were set to 10⁻⁵ eV and 0.02 eV Å⁻¹, respectively. A 4 × 4 × 2 Monkhorst–Pack mesh was used for k-point sampling of the bulk structure.⁵⁴

The elastic properties of the lithium alloy anode were determined using the stress–strain method with optimized high-efficiency strain matrix sets (OHESS) implemented in the ElasTool package⁵⁵ to calculate the elastic tensor of the SQS-modeled triclinic solid-solution structure. Moreover, bulk modulus values were calculated using the M3GNet potential by employing the Birch–Murnaghan equation of state, generating structures with varying volumes (±6% around equilibrium) for each alloy composition.

2.2. Interface construction and molecular dynamics simulations

To analyze the interfacial interactions between the lithium alloy anode and the electrolyte, a high-concentration lithium polysulfide electrolyte was constructed by randomly placing six lithium octasulfide (Li₂S₈) molecules, six 1,3-dioxolane (DOL) molecules, and two lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) molecules within an empty volume of 5000 ų⁴⁴ while enforcing a minimum intermolecular separation of 3 Å to avoid unphysical atomic overlaps, as illustrated in Fig. 1b. As a result of this initial placement constraint, the calculated electrolyte density (∼0.88 g cm⁻³) is lower than the experimentally reported values. However, the present setup is designed to prioritize robust sampling of interfacial chemical reactions rather than reproducing bulk volumetric properties of the electrolyte. Each molecule was structurally optimized using DFT within a cubic cell with 20 Å sides, employing a k-point sampling of 1 × 1 × 1.

The anode–electrolyte interface was constructed, as shown in Fig. 1b. The lithium alloy anode was modeled as a BCC 4 × 4 × 8 slab structure consisting of 8 atomic layers along the [001] direction. Eight different surface morphologies were considered (SI Fig. 1). Each of the eight layers exhibits distinct morphology, providing the basis for statistical sampling across diverse surface configurations. For statistical rigor, each morphology was combined with 50 unique electrolyte configurations, resulting in 400 interface structures per alloy composition. Ensemble MD simulations were performed at 300 K for 20 ps using the pretrained M3GNet potential for each of these configurations. The lower three layers of the superlattice structure were fixed to mimic bulk behavior, while the upper five layers of atoms were relaxed to facilitate reactions with lithium polysulfides.

2.3. Analysis methods

To quantitatively analyze the bond strength within the lithium alloy anode and the SEI layer, the Density Derived Electrostatic and Chemical (DDEC6) method was employed. Bond orders were computed based on the DDEC6 method via the Chargemol software.^56–58

3. Results

3.1. Structural and elastic properties of Li–M alloy anodes

Based on DFT simulations, the structural analysis of the optimized Li_1−xM_x alloys revealed distinct behaviors depending on the alloying element. The Li–Mg alloys, where lithium and magnesium possess similar atomic radii (see SI Table 1), maintained a stable BCC structure across all compositions with minimal lattice distortion. In contrast, the Li–Al and Li–Zn alloys, incorporating relatively smaller alloying atoms, exhibited noticeable changes in lattice parameters with increasing alloy concentration (Table 1). These alloys showed significant deviation from ideal BCC lattice positions, indicating potential structural instability (see SI Fig. 2).

Table 1 Structural parameters, formation energies, and elastic properties of Li_(1−x)M_x alloys for compositions x = 0.05–0.50 obtained from DFT calculations. Formation energies, bulk moduli, and sulfur adsorption energies were additionally predicted using M3GNet for validation. Values in parentheses represent standard deviations. B: bulk modulus; G: shear modulus; Y: Young's modulus; ν: Poisson's ratio; E_formation: formation energy; E_ads: sulfur adsorption energy

System	Stoichiometric formula	Lattice parameter (Å)	E formation,DFT (eV per atom)	E formation,M3GNet (eV per atom)	B DFT (GPa)	B M3GNet (GPa)	G DFT (GPa)	Y DFT (GPa	ν DFT	E ads,DFT (eV)	E ads,M3GNet (eV)
Pure Li	Li	3.432	0.000	0.000	14.09	12.86	2.05	5.87	0.43	−7.917	−7.840
Li–Mg system	Li0.95Mg0.05	3.424 (0.114)	−0.007	−0.007	15.48	14.12	8.97	22.56	0.26	−7.767 (0.151)	−7.755 (0.348)
	Li0.83Mg0.17	3.426 (0.126)	−0.021	−0.023	17.60	16.45	8.60	22.18	0.29	−7.643 (0.198)	−7.668 (0.222)
	Li0.67Mg0.33	3.436 (0.181)	−0.037	−0.040	21.69	19.69	12.35	31.13	0.26	−7.378 (0.421)	−7.187 (0.395)
	Li0.50Mg0.50	3.448 (0.093)	−0.047	−0.044	26.45	22.83	16.53	41.04	0.24	−7.139 (0.337)	−6.885 (0.276)
Li–Al system	Li0.95Al0.05	3.377 (0.091)	−0.023	−0.027	15.92	14.85	4.88	13.28	0.36	−7.718 (0.239)	−7.710 (0.349)
	Li0.83 Al0.17	3.290 (0.126)	−0.069	−0.071	21.03	18.25	8.53	22.55	0.32	−7.608 (0.353)	−7.661 (0.244)
	Li0.67 Al 0.33	3.208 (0.075)	−0.107	−0.125	29.93	21.32	18.66	46.34	0.24	−7.281 (0.529)	−7.428 (0.379)
	Li0.50 Al 0.50	3.208 (0.180)	−0.106	−0.144	37.07	27.91	8.41	23.45	0.39	−6.623 (0.423)	−6.905 (0.409)
Li–Zn system	Li0.95Zn0.05	3.376 (0.114	−0.021	−0.026	15.50	14.31	8.04	20.56	0.28	−7.729 (0.222)	−7.875 (0.331)
	Li0.83 Zn0.17	3.269 (0.140)	−0.065	−0.076	19.64	17.80	6.39	17.30	0.35	−7.560 (0.277)	−8.023 (0.400)
	Li0.67 Zn0.33	3.162 (0.161)	−0.122	−0.139	27.90	27.33	11.66	30.71	0.32	−7.314 (0.657)	−7.588 (0.351)
	Li0.50 Zn0.50	3.093 (0.069)	−0.150	−0.175	37.77	36.07	16.25	42.64	0.31	−6.797 (0.379)	−7.120 (0.339)

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The formation energy (E_formation) was calculated using eqn (2):

E_formation = E(Li_1−xM_x) – [(1−x)E(Li) + xE(M)] (2)

where E(Li_1−xM_x) represents the total energy of the alloy; E(Li) and E(M) are the energies of pure lithium and alloying metal in their standard states, respectively. The results showed negative formation energies for all alloy systems (Table 1), which became more negative as the alloy concentration increased. The Li–Zn system exhibited the most negative formation energy (−0.150 eV per atom at x = 0.50), suggesting thermodynamically favorable alloy formation. From a thermodynamic equilibrium perspective, Li–Mg alloys tend to remain in a solid solution state even with Mg additions up to 50 at%, whereas Li–Al and Li–Zn alloys favor the formation of intermetallic compounds with as little as 5 at% metal addition.⁵⁹ Recent experimental evidence shows that Li–Al alloys are kinetically stabilized in the β-LiAl (NaTl-type) phase under room-temperature electrochemical cycling, as Li-rich intermetallic phases beyond β-LiAl form only at extraordinarily slow lithiation rates and are therefore suppressed under practical conditions.⁶⁰ The β-LiAl phase exhibits a finite nonstoichiometric composition range, and its underlying atomic lattice corresponds to a body-centered cubic (BCC) arrangement when Li and Al atoms are not distinguished. Accordingly, in this study, Li–Al alloy systems are described using a solid-solution-like framework based on a BCC Li lattice with randomly distributed alloying elements. This approach is both physically motivated and computationally tractable, allowing us to capture diverse local Li–Al bonding environments as well as compositionally disordered surface states associated with Li, Li-poor β-LiAl, and Li-rich β-LiAl phases under kinetically stabilized, non-equilibrium conditions. A similar rationale applies to Li–Zn alloys, for which no Li-rich phase beyond β-LiZn exists, and nonstoichiometric β-LiZn has been reported.⁶¹

All lithium alloys exhibited significantly improved elastic properties compared to pure lithium (Table 1). The bulk modulus (B), shear modulus (G), and Young's modulus (Y) generally increased with the alloy concentration. However, for the Li_0.5Al_0.5 alloy, the shear and Young's moduli were found to be lower than those of the Li_0.67Al_0.33 alloy. This reduction can be attributed to increased internal lattice strain arising from the higher concentration of Al, whose atomic size differs significantly from that of Li. The higher elastic properties of lithium alloys compared to pure lithium are expected to enhance the structural stability of the anodes, which can be beneficial for achieving uniform lithium deposition and suppressing dendrite formation during the electrochemical cycling of Li–S batteries.^62–65

To validate the accuracy of the M3GNet machine learning potential, we calculated bulk modulus values and compared them against DFT results (Table 1). M3GNet reproduced the DFT results with good agreement, showing deviations mostly within 10%. In Li–Al alloys with high Al content, where substantial internal strain is expected, the discrepancy increased to nearly 30%. Nevertheless, the overall trends in mechanical behavior were well reproduced by M3GNet, and it remained predictive across different compositions. These results clearly demonstrate that M3GNet is a robust and reliable tool for modeling lithium alloy systems while dramatically reducing the computational cost compared to DFT.

To validate M3GNet's accuracy across multiple properties critical to our findings, we performed comprehensive benchmarking against DFT calculations for formation energies, bulk moduli, and sulfur adsorption energies (Table 1).

Formation energy validation: M3GNet reproduces DFT formation energies with excellent accuracy (mean absolute error: 0.010 eV per atom overall), with exceptional agreement for Li–Mg (0.002 eV per atom) and good agreement for Li–Al (0.016 eV per atom) and Li–Zn (0.015 eV per atom). Both methods show identical trends of increasingly negative formation energies with higher alloy concentrations, confirming thermodynamically favorable alloy formation.

Bulk modulus validation: M3GNet shows good overall agreement (MAE: 2.8 GPa, ∼13% relative error), with deviations mostly within 10%. The largest deviation (∼30% for Li_0.5Al_0.5) arises from severe internal lattice strain where the large atomic size mismatch creates significant elastic distortion (SI Fig. 2). Nevertheless, M3GNet correctly captures the concentration-dependent increase in elastic stiffness across all systems.

Sulfur adsorption energy validation: to validate M3GNet for interfacial chemistry―central to our study―we calculated sulfur atom adsorption energies on alloy surfaces using both methods. For each composition, calculations were performed on eight distinct surface configurations (SI Fig. 1) to capture surface morphology effects. The adsorption energy was calculated as:

E_ads = E(Surface + S) – E(surface) – E(S) (3)

where E(surface + S) and E(surface) were computed using the respective method (DFT or M3GNet), while the isolated sulfur atom reference energy E(S) = −0.057 eV was obtained from DFT calculations for both methods, as M3GNet cannot directly calculate single-atom energies. M3GNet reproduces DFT adsorption energies with good agreement (MAE: 0.12 eV for Li–Mg and Li–Al; 0.30 eV for Li–Zn). The magnitude of sulfur adsorption energy decreases systematically with increasing alloy concentration, reflecting the transition from pure lithium―where weak Li–Li bonds (0.07–0.09, Fig. 6) enable facile surface reconstruction―to alloy surfaces where stronger M–M bonds resist reconstruction despite forming intrinsically stronger M−S bonds (M = Mg, Al or Zn).

This comprehensive three-property validation confirms that M3GNet reliably predicts bulk thermodynamic stability, elastic properties, and interfacial bonding characteristics for Li–Mg and Li–Al systems, providing a robust foundation for our MD simulations.

3.2. MD simulations of the anode–electrolyte interfaces

First, we simulated the interactions between a pure Li anode and the electrolyte, with and without lithium polysulfides. Fig. 2 shows that lithium polysulfides significantly accelerate anode corrosion. In the absence of lithium polysulfides (Fig. 2a), the lithium anode surface retained its crystalline structure during the initial 3 ps, after which oxygen atoms from DOL and fluorine/carbon atoms from LiTFSI reacted with surface lithium to form a thin SEI layer. The underlying lithium lattice remained relatively intact through the 20 ps simulation.

Fig. 2 Surface corrosion evolution of the pure Li anode simulated using M3GNet molecular dynamics at 300 K over 20 ps: (a) without and (b) with lithium polysulfides.

In contrast, with lithium polysulfides (Fig. 2b), decomposition reactions markedly accelerated from the first picosecond. Li₂S₈ molecules reacted with surface lithium atoms, decomposing into Li₂S and promoting the detachment and migration of lithium atoms from the anode into the electrolyte. This process disrupted the crystalline lattice structure of the anode. Sulfur atoms from decomposed polysulfides penetrated into the vacancies left by the detached lithium atoms, further exacerbating the structural damage to the lithium anode.

As the simulation progressed, continuous polysulfide decomposition gradually thickened the passivation-derived SEI layer, primarily composed of Li₂S. The accumulation of Li₂S led to the formation of a porous and mechanically fragile SEI morphology, accompanied by a highly irregular and lithium-depleted anode surface. This unstable interface promotes inhomogeneous lithium electrodeposition during cycling, thereby accelerating dendrite growth and increasing the risk of internal short circuits in Li–S batteries. As electrochemically active lithium is irreversibly consumed through reactions with lithium polysulfides to form inactive SEI species, reduced coulombic efficiency and subsequent capacity fade can occur in Li–S batteries.

While pure lithium anodes exhibited rapid and destructive interfacial reactions upon contact with lithium polysulfides, such detrimental behavior was significantly suppressed in lithium alloy systems, as demonstrated in Fig. 3. However, the interfacial characteristics varied with the specific alloying element, reflecting the differences in how each alloy interacted with the polysulfide-rich environment.

Fig. 3 Surface corrosion evolution of Li_1−xM_x (x = 0.50) alloy anodes simulated using M3GNet molecular dynamics at 300 K over 20 ps: (a) Li_0.50Mg_0.50, (b) Li_0.50Al_0.50, and (c) Li_0.50Zn_0.50.

The Li–Mg alloy system (Li_0.50Mg_0.50, Fig. 3a) exhibited a distinctive interfacial behavior, forming a uniform and stable layer at the alloy–electrolyte interface. During early simulation stages (1–3 ps), magnesium atoms contributed to maintaining the structural stability of the lithium lattice while inhibiting rapid lithium detachment. Some magnesium atoms migrated alongside lithium into the electrolyte, contributing to the formation of a thin, uniform SEI layer that remained stable through the simulation period, which appears to inhibit further reactions with polysulfides.

The Li–Al and Li–Zn systems (Fig. 3b and c) showed notable aggregation of alloying elements at the surface. During the initial simulation stages, as lithium atoms began migrating away from the surface, aluminum and zinc atoms accumulated at the interface. This selective enrichment became increasingly distinct as the simulation progressed, ultimately forming dense interfacial layers. These segregated layers are thought to hinder further lithium migration and limit reactions with polysulfides by acting as a physical barrier at the anode–electrolyte interface.

SI Fig. 3 demonstrates that these protective effects are concentration-dependent across all three alloy systems, with higher alloy concentrations providing enhanced interfacial stability and anode protection. For the Li–Mg system (SI Fig. 3a), a progressive improvement in interfacial stability is observed with increasing Mg concentration. While lower Mg concentrations (x = 0.05, 0.17) show some degree of protection compared to pure lithium, the protective mechanism becomes more pronounced and visually apparent at higher concentrations (x = 0.33, 0.50), where magnesium atoms actively contribute to SEI formation, resulting in distinctly uniform, thin, and robust SEI layers. In contrast, Li–Al and Li–Zn systems (SI Fig. 3b and c) exhibited surface segregation behavior across all concentrations, with the segregation layer becoming progressively thicker as the alloy concentration increased. However, regardless of the concentration, the SEI formation in these systems remained similar to that of pure lithium anodes, showing the characteristic heterogeneous and porous structure, although the continued growth of the porous SEI is moderate compared to pure Li. This behavior indicates that the protective mechanism relies primarily on the physical barrier effect of the segregated metal layer rather than chemical improvement of the SEI quality. Notably, this trend is consistent with experimental observations for Li–Al anodes reported by Kim et al.,³⁵ who showed that both pure Li and Li–Al anodes form porous SEI layers, while the SEI on Li–Al exhibits a comparatively more compact structure than on pure Li.

3.3. Displacement of Li atoms in alloy anodes

To quantitatively assess how lithium atom migration behavior varies across different alloy anodes during interfacial reactions with polysulfide-containing electrolytes, we analyzed atomic displacement results from MD simulations and compared them with those of a pure lithium anode, as presented in Fig. 4. Using the simulation setup described in Section 2, we performed multiple independent MD simulations for each alloy composition to ensure statistical reliability. Variations in electrolyte and surface atomic configurations are critical, as the relative positioning of polysulfide and electrolyte molecules near the Li or Li–alloy surface strongly affects interfacial reactions and lithium displacement. To capture statistically meaningful trends, we generated 400 unique interface configurations for each alloy by combining 8 anode surface structures with 50 distinct electrolyte molecular arrangements. This approach, supported by SI Fig. 4, confirms that the observed trends are statistically robust and representative.

Fig. 4 Lithium atomic displacement analysis in Li_1−xM_x alloy systems. Shaded regions represent ±1 standard deviation. (a) Evolution of average Li displacement over 20 ps simulation time for varying Mg concentrations (x = 0.00–0.50); (b) time-dependent Li–M/pure Li displacement ratios for Li_1−xMg_x, Li_1−xAl_x, and Li_1−xZn_x alloy systems, respectively; (c) concentration-dependent Li–M/pure Li displacement ratio at 20 ps for three alloy systems, showing linear trend lines.

The migration distance (Δr_Li) of each lithium atom was calculated using eqn (4):

where dx, dy, and dz represent the displacement components along the x, y, and z directions, corresponding to the crystallographic a, b, and c axes, respectively.

The lithium atomic displacement analysis in Fig. 4 demonstrates a clear concentration-dependent protective effect across all lithium alloy systems. For the Li_1−xMg_x alloy system (Fig. 4a), pure lithium anodes (x = 0.00) exhibited the highest average lithium displacement (approximately 8 Å after 20 ps), with a characteristic logarithmic increase over time that rapidly rises in the initial phase (0–5 ps) before gradually approaching saturation. This behavior suggests that the system is highly prone to lithium displacement driven by interfacial reactions with polysulfides. With the addition of magnesium, Li_1−xMg_x systems showed progressively reduced lithium displacement with increasing magnesium concentration, with values decreasing systematically from approximately 7 Å at x = 0.05 to 4.5 Å at x = 0.50, confirming the effectiveness of magnesium in suppressing lithium migration.

The normalized displacement ratios (Fig. 4b) reveal distinct temporal behavior among the alloy systems. Li–Mg alloys consistently exhibited lower lithium migration ratios compared to pure lithium across all time points and concentrations, with final ratios ranging from 0.89 (x = 0.05) to 0.58 (x = 0.50). Interestingly, Li–Al and Li–Zn systems initially exhibited higher lithium migration before 10 ps, but later showed a decrease in migration rates. After 20 ps of MD simulations, the Li–Al system exhibited a 6 to 21% reduction in lithium migration, while the Li–Zn system showed a relatively smaller decrease, ranging from 0% to 7%. These results suggest that the suppression of lithium displacement becomes effective only after the surface atoms at the interface have undergone sufficient structural reorganization.

The concentration-dependent analysis (Fig. 4c) establishes a clear linear correlation between alloy content and migration suppression. The linear regression slopes indicate relative protective efficiencies: Li–Mg (−0.69) > Li–Al (−0.33) > Li–Zn (−0.18). Among the studied systems, Li–Mg alloys show the strongest suppression of lithium migration across the anode–electrolyte interface, followed by Li–Al and Li–Zn alloys with moderate and minimal effects, respectively.

3.4. Interfacial distribution of Li and alloying elements

In this section, we analyzed the spatial distribution of anode constituent elements at the anode–electrolyte interface. Fig. 5 displays the density distribution profiles along the c-axis after 20 ps of MD simulation. The density profiles were normalized such that the integrated density for pure lithium equals 1, while the Li_1−xMg_x alloy compositions were scaled according to their respective atomic fractions.

Fig. 5 Distribution density profiles along the c-axis after 20 ps of MD simulation: (a) Li atoms for the pure Li anode showing Li diffusion into the electrolyte; (b, d and f) alloying elements and (c, e and g) Li atoms for Li_1−xM_x alloys, where M = Mg, Al, and Zn at compositions x = 0.05–0.50. Shaded areas indicate initial anode regions.

Fig. 5a compares the lithium distribution before (0 ps) and after (20 ps) simulation in pure lithium. Initially, a well-ordered crystalline structure with 16 distinct density peaks extends to approximately 25.4 Å. After exposure to lithium polysulfides, while bottom layers (0–11 Å) remain relatively intact, the surface region undergoes severe disruption with most peaks collapsing. Substantial lithium migration into the electrolyte region (extending to ∼45 Å) indicates significant structural destabilization.

The Li_1−xMg_x alloy system (Fig. 5b and c, where Fig. 5b shows Mg distribution and Fig. 5c shows Li distribution) demonstrates concentration-dependent suppression of surface lattice disruption. Increasing magnesium concentration promotes the retention of lithium at defined lattice positions, thereby preserving the original crystal framework more effectively. SI Fig. 5–7 provide expanded views of the lithium and alloying element distributions for each composition, allowing clearer assessment of compositional effects. At low magnesium content (x = 0.05), significant collapse of the lithium crystalline structure occurs like pure lithium. However, at high concentrations (x = 0.50), most lithium density peaks remain well preserved. Notably, magnesium atoms migrate alongside lithium into the 25–33 Å region, forming a co-distributed interface layer that contributes to SEI formation.

Li_1−xAl_x and Li_1−xZn_x systems (Fig. 5d–g and SI Fig. 6 and 7) demonstrate a fundamentally different protective mechanism. While these alloys also exhibit concentration-dependent preservation of the lithium structure, aluminum and zinc atoms do not migrate significantly into the electrolyte. Instead, they concentrate at specific interface regions (20–25 Å for Al and 15–23 Å for Zn), forming physical barrier layers through surface segregation. Although less effective than the Li–Mg system, these surface-segregated barriers still suppress lithium anode structure collapse compared to pure lithium.

3.5. Bonding strength in alloy anodes and SEI layers

DDEC6 bond order analysis was performed to evaluate the atomic bonding strength within the alloy anode (Fig. 6a–c) and the SEI layer (Fig. 6d–f). SI Fig. 8 provides quantitative analysis of bonding characteristics based on bonds ≤3.0 Å identified in Fig. 6.

Analysis of bonds within the alloy anode revealed that Li–Li bonds in pure lithium exhibit extremely low bond orders (0.07–0.09), contributing to poor mechanical stability and facilitating easy detachment of lithium atoms. In contrast, alloy elements demonstrate significantly stronger bonding characteristics with the bond order progression: Li–Li < Li–M < M–M. In Li–Mg alloys (Fig. 6a), Mg–Mg bonds (bond order: 0.29 ± 0.02) and Li–Mg bonds (bond order: 0.15 ± 0.02) showed moderate strength with minimal variation. This bonding nature allows magnesium atoms to detach from the anode with lithium and participate in SEI formation, rather than remaining rigidly fixed or becoming easily leached. Li–Al and Li–Zn alloys (Fig. 6b and c) exhibited stronger but more variable bonding characteristics. The Al–Al, Zn–Zn, Li–Al, and Li–Zn bonds showed higher bond orders with substantial variability, which is accompanied by shorter bond lengths that reflect stronger bonding interactions. These strong yet inconsistent bonds alter the local bonding environment and induce noticeable distortion of BCC lattice positions (SI Fig. 2).

Fig. 6 DDEC6 bond order analysis of atomic bonding characteristics: bond order versus bond distance for (a–c) Li–M, Li–Li, and M–M bonds in Li–M alloy anodes (M = Mg, Al, Zn) and (d–f) Li–S and M−S bonds in the SEI layer.

Analysis of the SEI layer (Fig. 6d–f) revealed that M−S bonds consistently exhibit much higher bond orders than Li–S bonds (0.17–0.19). Mg–S bonds (0.42 ± 0.12) are approximately 2.4 times stronger than Li–S bonds and account for a much higher proportion of metal–sulfur interactions (Mg–S: 14.1% vs. Al-S: 2.4%, Zn–S: 1.0%). The high abundance of these moderately strong Mg–S bonds leads to the formation of a mechanically robust, magnesium-rich SEI layer that stabilizes the lithium structure and suppresses undesirable reactions with the electrolyte and soluble lithium polysulfides.

Although Al–S (0.77 ± 0.10) and Zn–S bonds (0.99 ± 0.27) demonstrate even stronger bonding potential than Mg–S bonds, their participation in SEI formation is minimal. The exceptionally strong M–M bonding in Al–Al (0.45 ± 0.12) and Zn–Zn (0.43 ± 0.11) systems causes these elements to remain anchored at the anode surface, leading to the formation of a surface-segregated layers instead of their incorporation into the SEI. Despite their superior bonding strength, the limited participation of Al–S and Zn–S bonds prevents significant improvement in SEI stability.

In addition, bond order analyses for oxygen and fluorine species from DOL and LiTFSI were performed to assess the contribution of electrolyte-derived species to SEI formation (SI Fig. 9). While DOL remains largely intact, LiTFSI decomposes at the anode–electrolyte interface, forming Li–O and Li–F bonds with similar characteristics across all alloy systems. Although these electrolyte-derived species do contribute to SEI formation, their interactions are weaker than metal–sulfur bonds, indicating that sulfur species play a more dominant role.

3.6. Polysulfide decomposition on alloy anode surfaces

To explore the chemical stability of lithium alloy anodes against polysulfide attack, we investigated the decomposition behavior of lithium polysulfides by analyzing the evolution of S–S bonds during MD simulations. Fig. 7a presents the changes in S–S bond lengths in the pure lithium anode system, revealing a non-uniform elongation pattern that can be classified into two distinct groups: bonds that exhibit significant elongation (S2–S3, S4–S5, and S6–S7) and those that elongate minimally (S1–S2, S3–S4, S5–S6, and S7–S8).

Fig. 7 S–S bond evolution analysis in Li₂S₈ polysulfides on Li alloy anodes: (a) individual S–S bond length changes in pure Li anodes; (b–d) average S–S bond length evolution across compositions (x = 0.00–0.50) for Li_1−xMg_x, Li_1−xAl_x, and Li_1−xZn_x systems.

Among these, the S2–S3 and S6–S7 bonds show the earliest and most pronounced elongation, suggesting that they serve as initial cleavage points during the decomposition of Li₂S₈ into smaller Li₂S_x fragments. Meanwhile, the terminal S–S bonds (S1–S2 and S7–S8), which are located in closest proximity to lithium atoms, exhibit minimal elongation and remain intact the longest, indicating that their strong interaction with lithium helps stabilize these bonds and delay their eventual cleavage. In pure lithium anodes, the decomposition of lithium polysulfides leads to the formation of a mechanically fragile and chemically uneven SEI layer, which fails to prevent further reactions with polysulfides or stabilize the lithium surface. As the decomposition reaction progresses toward the formation of Li₂S, this electrochemically inactive product accumulates on the surface, reducing active lithium utilization and ultimately degrades the performance of lithium–sulfur batteries.

The average S–S bond lengths across different lithium alloy systems and compositions are presented in Fig. 7b–d. A clear inverse relationship is observed between the alloy concentration and S–S bond elongation, with higher concentrations of alloying elements (x = 0.50) consistently showing reduced bond elongation compared to lower concentrations (x = 0.05). In the Li_1−xMg_x system (Fig. 7b), even a small amount of Mg (x = 0.05) meaningfully suppresses S–S bond elongation relative to pure lithium. However, this suppression effect does not improve further beyond x = 0.33, indicating that the ability of Mg to inhibit polysulfide decomposition reaches a saturation point at moderate concentrations. In contrast, the Li_1−xAl_x and Li_1−xZn_x systems (Fig. 7c and d) exhibit weaker suppression at low concentrations but a more pronounced reduction in the S–S bond length as the alloy content increases. At x = 0.5, both Li–Al and Li–Zn alloys outperform Li–Mg in decomposition inhibition, with Li_1−xAl_x demonstrating the most effective suppression overall.

This difference likely originates from the distinct inhibition mechanisms of each alloy system. In the Li–Mg alloy anode, even small amounts of Mg can migrate together with lithium into the electrolyte, contributing to the formation of a chemically stable SEI that effectively suppresses polysulfide decomposition. In the case of Li–Al and Li–Zn systems, Al and Zn atoms can inhibit polysulfide access by forming segregation layers, but the development of a robust and continuous segregation layer requires higher alloy concentrations. Once fully formed, these segregation layers are more effective than the Mg-derived SEI in blocking polysulfide decomposition reactions, due to the strong Al–Al and Zn–Zn bonds that stabilize the interfacial structure.

The spatially resolved S–S bond analysis presented in SI Fig. 10 further supports these mechanistic differences. Generally, Li₂S₈ species located near the anode interface undergo more rapid S–S bond elongation. The Li–Mg system exhibits a smaller gradient in S–S bond elongation across the electrolyte, compared to Li–Al and Li–Zn systems. This spatial consistency is attributed to the rapid co-migration of Mg with lithium into the electrolyte, which enables the prompt formation of a stable Mg-rich SEI that immediately inhibits polysulfide decomposition regardless of the distance from the anode. In the Li–Al and Li–Zn systems, a sharper gradient is observed along the distance away from the anode. Li₂S₈ molecules near the interface experience relatively greater S–S bond elongation and decomposition because the segregation of Al and Zn is not yet fully developed at the early stage. In contrast, Li₂S₈ located farther from the anode shows significantly reduced bond elongation, indicating more effective suppression by the progressively formed segregation layers. These findings suggest that while Mg acts rapidly through chemically stable SEI formation, Al and Zn require sufficient time and concentration to form protective segregation layers that inhibit polysulfide reactions more effectively.

Fig. 8 illustrates the spatial distribution of sulfur atoms (Fig. 8a–c) and their coordination numbers with alloying elements (Fig. 8d–f) after 20 ps of MD simulation. The sulfur atom distribution profiles show that lower alloy concentrations allow deeper sulfur penetration into the anode, indicating more active chemical reactions between sulfur species and the lithium alloy anode. As the alloy concentration increases, this penetration decreases markedly, confirming that alloying elements enhances the anode's resistance to such reactive species. The sulfur distribution in Li–Mg alloys shows a distinctive accumulation of sulfur atoms in the 23–35 Å region, where sulfur atoms exhibit a high coordination number with Mg. As previously discussed, these Mg–S bonds contribute to the formation of a mechanically robust SEI layer. Therefore, the elevated sulfur concentration observed in this region likely reflects the formation of a Mg-rich SEI, rather than unbound sulfur species diffusing through the electrolyte. Meanwhile, although the Mg concentration within the SEI region continues to increase from x = 0.33 to x = 0.50, the sulfur concentration in the same region remains nearly unchanged, indicating saturation of sulfur incorporation into the SEI. Consequently, further increases in Mg content do not lead to additional SEI chemical modification, which is consistent with the plateau in S–S bond elongation suppression observed beyond x = 0.33 in Fig. 7b.

Fig. 8 Sulfur distribution and coordination at Li_1−xM_x alloy interfaces: (a–c) S atom distribution along the c-axis for Li_1−xMg_x, Li_1−xAl_x, and Li_1−xZn_x alloys; (d–f) corresponding alloying element coordination profiles showing the average number of Mg, Al, and Zn atoms within 3 Å radius of sulfur atoms. Shaded regions indicate the initial anode domains.

Compared to the Li–Mg system, the Li–Al and Li–Zn systems show broader and less localized sulfur distributions across the electrolyte. Sulfur atoms exhibit low coordination numbers with aluminum and zinc, with these bonds confined to narrow interfacial zones (approximately 20–25 Å for Al and 15–23 Å for Zn). Even at high alloy concentrations, these coordination peaks remain relatively weak, indicating limited chemical interaction between alloying elements and sulfur. Instead of participating in SEI formation with sulfur, as observed in the Li–Mg system, aluminum and zinc enhance resistance against sulfur species-induced corrosion by forming physically stable segregation layers at the anode surface. These layers spatially isolate reactive sulfur species from the lithium interface, thereby reducing direct chemical interaction and effectively suppressing interfacial degradation.

While practical Li–S batteries often employ mixed solvents (e.g., DOL/DME) or alternative salts (e.g., LiFSI), the present study adopts a simplified DOL/LiTFSI electrolyte to isolate fundamental alloy–polysulfide interactions. Because the protection mechanisms identified here are governed by intrinsic bonding characteristics of the alloying elements, we expect their qualitative nature to remain valid across different electrolyte formulations, although quantitative kinetics may vary.

4. Discussion

Polysulfide-induced degradation in lithium–sulfur batteries manifests through several interrelated failure mechanisms: the formation of mechanically fragile and heterogeneous SEI layers and the structural collapse of the lithium anode due to lithium leaching, leading to the growth of lithium dendrites and continuous electrolyte consumption, and the irreversible loss of active lithium due to the accumulation of electrically isolated Li₂S, often referred to as dead lithium. These phenomena not only degrade the mechanical integrity of the anode but also reduce the coulombic efficiency and accelerate capacity fade.

Our multi-method simulations reveal that lithium alloying offers two distinct protective mechanisms to mitigate these degradation pathways. Li–Mg alloys operate primarily via a chemical protection mechanism, wherein magnesium atoms actively participate in the formation of the SEI by coordinating with sulfur. This leads to the development of a chemically robust Mg-rich SEI layer that effectively suppresses polysulfide decomposition and prevents structural collapse of the lithium anode. In contrast, Li–Al and Li–Zn systems exhibit a physical protection mechanism. Instead of forming part of the SEI through direct coordination with sulfur, aluminum and zinc atoms remain localized at the surface, forming dense interfacial segregation layers. These layers act as spatial barriers that restrict polysulfide access to the reactive lithium surface. While they do not significantly contribute to SEI composition, the physically stable nature of the segregation layers plays a critical role in preventing direct sulfur-induced attack on the lithium alloy anode.

Although the present simulations focus on the initial interfacial reactions during electrochemical cycling, the degradation-inhibition effects associated with the formation of Mg-rich SEI layers and Al/Zn surface segregation are expected to persist, at least in part, during continuous cycling. This expectation arises from the mechanical robustness of these interfacial structures, which is conferred by strong underlying atomic bonding. As a result, such protective layers are likely to withstand strain induced by repeated volume changes and surface morphology evolution during cycling, thereby continuing to suppress polysulfide-induced degradation after the initial reaction stage.

These distinct mechanistic roles predicted by simulation are consistent with experimental observations. Kong et al. showed that Li–Mg alloys formed stable SEI layers that enabled uniform lithium deposition and suppressed dendrite formation.³⁸ Specifically, they demonstrated that the SEI layer contained Mg sulfides and oxides, forming a robust passivation layer that could effectively suppress polysulfide attack and prevent further sulfur species adsorption. Their Li–Mg anodes retained surface integrity even after 7 days of electrolyte immersion, while pure lithium suffered rapid and severe corrosion. Using X-ray photoelectron spectroscopy (XPS), they observed a characteristic MgS peak at 1303.7 eV, on the basis of which they identified a Mg-rich SEI containing Mg–S bonding on cycled Li–Mg anodes. This experimental observation directly corroborates our simulation results, which predict the co-migration of Mg atoms and the formation of a chemically robust SEI dominated by strong Mg–S interactions.

Huang et al. reported that Li–Al alloys exhibit substantially improved corrosion resistance and electrochemical stability compared to pure lithium.³⁷ Their immersion tests revealed that pure lithium reacted completely within 10 seconds, whereas Li–Al reacted gradually over two hours. In addition, Li–Al alloy anodes maintained stable electrochemical cycling over hundreds of cycles, despite an extreme volume expansion of approximately 95%. These experimentally observed indicators of macroscopic interfacial stability are fully consistent with our simulations, which predict the formation of robust Al-rich segregation regions at the interface. Although such regions are only a few atomic layers thick and remain experimentally challenging to resolve directly, our simulations suggest that Al enrichment at the surface can function as an effective barrier, reducing direct contact between reactive Li, the electrolyte and lithium polysulfides and thereby increasing the energetic and kinetic resistance to parasitic chemical reactions.

While these chemical and physical mechanisms differ by alloy type, their protective effectiveness also evolves with alloying concentration, as revealed by our simulations. In Li_1−xMg_x systems, even low concentrations (x = 0.05) provide some degree of improvement due to the early formation of the SEI. As the Mg concentration increases, suppression of polysulfide decomposition and lithium displacement improves, but this effect saturates beyond x = 0.33, where further increases in Mg offer only limited additional suppression of degradation phenomena. As the alloy concentration increases, Li–Al and Li–Zn systems exhibit progressively stronger inhibition of polysulfide-induced degradation, driven by the gradual formation of robust physical barriers through surface segregation. Once the alloying concentration reaches x = 0.50, these systems even surpass the Mg-based alloy in suppressing polysulfide reactivity.

Although higher alloy concentrations can offer stronger inhibition of polysulfide-induced degradation phenomena, such as lithium structural collapse, unstable SEI formation, and active lithium loss, their practical implementation requires careful consideration from the perspective of lithium–sulfur battery performance. Elevated alloy content may promote intermetallic compound formation or induce undesired electrochemical side reactions that compromise long-term cycling stability or reversible capacity. Experimental data (SI Table 1) show that alloy anodes exhibit reduced specific capacities compared to pure lithium (3860 mAh g⁻¹), with Li–Mg alloys (10–30 at%) retaining ∼1930–2950 mAh g⁻¹, while Li–Al and Li–Zn alloys exhibit much lower capacities of ∼993 and ∼355 mAh g⁻¹, respectively, together with increased average electrode potentials that lead to 0.2–0.4 V output voltage loss in full cells. In the Li–Mg system, although moderate Mg alloying significantly enhances Li diffusion compared to pure lithium, high Mg concentrations (>20 at%) trigger a phase transformation during delithiation from the Li-rich β-phase to the Mg-rich α-phase, reducing Li diffusion coefficients from ∼10⁻⁷ cm² s⁻¹ to ∼10⁻⁹–10⁻¹⁰ cm² s⁻¹ and severely limiting Li⁺ extraction kinetics.^39,40 Therefore, identifying optimal alloying concentrations is crucial for effectively mitigating degradation mechanisms while preserving desirable battery performance.

Taken together, our findings provide atomistic insight into how lithium alloy composition and elemental identity govern degradation-inhibition mechanisms in lithium–sulfur batteries. Incorporating these mechanisms, whether through chemically integrated SEI formation or physically segregated barrier development, allows for the strategic design of alloy anodes that effectively mitigate polysulfide-induced degradation and enhance long-term battery performance. Further atomistic investigations over extended timescales, together with experimental validation, will be necessary to elucidate how the identified protection mechanisms influence long-term interfacial reactions beyond polysulfide-induced degradation, such as SEI evolution and lithium dendrite nucleation, during practical battery cycling.

5. Conclusion

In this study, we combined density functional theory and molecular dynamics simulations to elucidate how alloying strategies can mitigate polysulfide-induced degradation in lithium–sulfur batteries. Our results demonstrate that alloying the lithium anode with Mg, Al, or Zn fundamentally alters the degradation pathways by introducing distinct protection mechanisms. Li–Mg alloys provide chemical protection through the formation of chemically robust Mg-rich SEI layers, whereas Li–Al and Li–Zn alloys offer physical protection via surface segregation that blocks polysulfide access. The effectiveness of these mechanisms depends strongly on the alloying concentration. Low Mg content is sufficient to suppress polysulfide decomposition, while higher Al and Zn contents progressively enhance stability, eventually surpassing Mg at moderate concentrations. Overall, these findings provide mechanistic insights and practical guidelines for tailoring alloy anodes to achieve durable and high-performance lithium–sulfur batteries.

Author contributions

Il-Seok Jeong: formal analysis, investigation, validation, calculation, writing – original draft. Hidemi Kato: investigation, validation, writing – review & editing, funding acquisition. Byungki Ryu: investigation, validation, writing – review & editing. Eun-Ae Choi: conceptualization, methodology, formal analysis, investigation, validation, supervision, writing – review & editing, funding acquisition. Seung Zeon Han: methodology, formal analysis, investigation, validation, supervision, writing – review & editing, funding acquisition.

Conflicts of interest

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.

Data availability

Data will be made available on request.

Supplementary information (SI) is available. See DOI: https://doi.org/10.1039/d5ta07829f.

Acknowledgements

This work was supported by National Research Foundation of Korea (NRF) grants funded by the Korean government (MSIT) [Grant No. 2022M3C1C8093916, which has been assigned a new number at IRIS server, RS-2022-NR119739], the Fundamental Research Program of the Korea Institute of Materials Science (KIMS) [PNKA420] and the Technology Innovation Program funded by the Ministry of Trade, Industry & Energy (MOTIE) [Grant No. 20014562]. This work was also supported by a cooperative program of the Collaborative Research and Development Center for Advanced Materials (CRDAM) and the ICC-IMR program at the Institute for Materials Research (IMR), Tohoku University.

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