Electrochemical Performance and Stress Distribution of Sb/Sb₂O₃ Nanoparticles as Anode Materials for Sodium-Ion Batteries

Abstract

We synthesize Sb/Sb₂O₃ nanoparticles by the oxidation of Sb nanoparticles at 100, 200, and 300 °C. The half sodium-ion batteries with Sb/Sb₂O₃-200 exhibit the optimal performance with a charge capacity of 540 mAh g⁻¹ after 100 cycles at 0.1 A g⁻¹, maintaining up to six times more capacity than pure Sb, and superior rate performance with 95.7% retention after cycling at varied current densities. One reason for this is that Sb/Sb₂O₃-200 is at exactly the optimum ratio of Sb₂O₃:Sb and the particle size of Sb/Sb₂O₃ to ensure both high capacity for Na⁺ and small stress during sodiation/desodiation, which is confirmed by the diffusion–stress coupled results. It indicates that increasing the ratio of Sb₂O₃:Sb causes a decrease of Mises equivalent stress, radial stress, and tangential stress in the range of 1:1–3.5:1, and an increase in the range of 3.5:1–4:1. These stresses decrease with a particle radius in the range of 30–50 nm and increase with a particle radius in the range of 50–70 nm. Additionally, another reason is related to the formation of cycling-induced coral-like Sb, which can promote Na⁺ diffusion, relieve cycling-induced volume changes, and provide exceptional Na⁺ storage.

1. Introduction

As high-efficiency energy storage facilities, lithium-ion batteries (LIBs) have been diffusely applied in luggable electronic products, electric vehicles, and aerospace and military electronic equipment [1,2], and their application field is increasing with the improvement of LIBs performance. However, due to the limited lithium resources on earth, there is a need to exploit new energy-storage facilities and systems to replace the LIBs. Sodium-ion batteries (SIBs) are a suitable candidate due to the sufficient abundance and the low cost of sodium (Na), as well as their having similar capabilities to lithium (Li) [3]. Meanwhile, LIBs can accelerate and enhance the research of SIBs because they have almost the same battery assembly and operation mechanism [4]. Unfortunately, the Na metal is not an appropriate anode material for SIBs owing to the safety problems caused by the Na dendritic during operation [5]. Moreover, the commercial graphite anode in LIBs is not suitable for SIBs because the interlayer spacing of graphite is insufficient to allow the insertion of Na⁺ with larger radius [6]. Therefore, it is significant to explore appropriate anode materials for SIBs with high specific capacity, low reversible capacity loss, and long cycle life [7].

To date, many materials have been studied for SIBs including carbon-based materials [8], pure metals (Sn, Sb) [5,9], alloys (SnSb, Bi_xSb_y) [4,10], metal oxides (TiO₂, MoO₃, SnO₂) [11,12,13], nonmetallic elements (C, P) [14,15], and organic compounds [16]. Among them, Sb is highly preferred because of its outstanding theoretical capacity (660 mAh g⁻¹), lower reaction potential (0.5–0.8 V vs. Na/Na⁺), and tiny polarization potential (~0.25 V Na/Na⁺) [17]. Nevertheless, during sodiation/desodiation, the large volume-induced stress (volume expansion by lattice size changing from Sb to Na₃Sb is about 390%) of Sb causes the appearance and propagation of cracks on the surface of electrode materials, and finally, results in the destruction of the mechanical structure and the reduction of reversibility [18]. There are five approaches that have been used to reduce the volume expansion, including preparing Sb nanomaterials [17], Sb/C composites [18], Sb alloys [19,20], Sb oxides and Sb sulfide [21,22,23], and micro- and nano-structures with special pore morphology [24,25,26].

Recently, increasing attention has been paid to Sb/Sb₂O₃ due to its excellent theoretical capacity (1103 mAh g⁻¹) and the buffering effect of Sb₂O₃ by the emergence of an amorphous Na₂O phase [27]. Some kinds of Sb/Sb₂O₃ nanoparticles, such as coral-like, morula-like, and 3D porous Sb/Sb₂O₃ are synthesized [28,29,30], and the corresponding Na⁺ storage performance was enhanced. The first outstanding work involving Sb/Sb₂O₃ material in SIBs came from Wang’s team [21]. They used the carbon sheet network (CSN) as a base to settle Sb/Sb₂O₃ nanoparticles, which was followed by the outgrowth of graphene upon the composite. The Sb/Sb₂O₃@graphene-CSN presented a capacity of ~221 mAh g⁻¹ at 5 A g⁻¹ over 0.01–2.0 V. Hu et al. [28] reported the coral-like Sb₂O₃@Sb obtained by etching from Sb₅Al₉₅ and oxidization in air, and the composites exhibited the enhanced charge capacity of 526.2 mAh g⁻¹ after 150 cycles at 1 A g⁻¹ and the superior rate performance with the charge capacity of 497.3 mAh g⁻¹ at 3 A g⁻¹. Hong and his coworkers synthesized morula-like Sb/Sb₂O₃ composites [29], and the Sb/Sb₂O₃ showed the outstanding cycle performance after 100 cycles with 91.8% capacity preservation, and the remarkable rate capability of 212 mAh g⁻¹ at 3.3 A g⁻¹. Nam and Kwon reported that three-dimensional porous Sb/Sb₂O₃ anode materials are successfully fabricated using a constant potential electrodeposition of Sb₂O₃ on a polypyrrole nanowire network, which exhibits excellent cycle performance with 512.01 mAh g⁻¹ over 100 cycles at the current density of 66 mA g⁻¹ [30]. In addition, Qian and Yang et al. obtained the stomatal Sb/Sb₂O₃ nanocomposite [31], which still showed a reversible capacity of 540 mAh g⁻¹ at 0.66 A g⁻¹ after 180 cycles in the voltage window from 0.02 to 1.5 V. In addition, they found that the voltage window plays an important role on the charge capacity of Sb/Sb₂O₃ nanocomposite. The consequences also indicated that the transformation reaction between Sb and Sb₂O₃ occurring in the discharge/charge voltage window of 0.02 to 2.5 V will cause a significant change in volume and distinct framework strain/stress of the electrode, degenerating the cycle stability. All of the above-mentioned reports indicate that the Sb₂O₃ in Sb/Sb₂O₃ composites can buffer the volume change and enhance the cycling stability. However, the detailed mechanism of how Sb₂O₃ improves the capacity and stability of Sb is still not clear. Meanwhile, the effect and its mechanism of the composition ratio of Sb₂O₃:Sb in Sb/Sb₂O₃ and the particle size of Sb/Sb₂O₃ on the capacity and stability have not been demonstrated.

From the numerical simulation studies on Si (or Sn)-based LIBs, it is believed that the electrochemical cycling-induced stress will affect the mechanical stability of the active materials/electrode, and the thermodynamics process of the electrochemical reaction, especially for the alloying/dealloying voltage, and finally, lead to the electrochemical performance changes of electrode materials [32,33,34]. For example, Zhang et al. [35] studied the generation and evolution of diffusion-induced stress of spherical and ellipsoidal particles and found that a larger aspect ratio helps for reducing the diffusion-induced stress in particles. The results by Zhu et al. [36] indicated that the dislocation and the wall thickness of hollow particles have an important effect on the diffusion-induced stress. Cheng et al. [37] explored the influence of surface tension on diffusion-induced stress in spherical nanoparticles and believed that the stress state can be changed by adjusting the size of nanoparticles. These results suggest that the extent of the electrochemical performance change is associated with the stress state of electrode materials, which is almost reported in SIBs. Because of the similar principle of SIBs as LIBs, therefore, it is of importance to investigate the strain-induced stress distribution of Sb/Sb₂O₃ with different ratios of Sb₂O₃:Sb and particle sizes to understand how Sb₂O₃ changes the electrochemical performance of Sb/Sb₂O₃-based SIBs.

Accordingly, we synthesize the Sb/Sb₂O₃ nanoparticles with a different composition ratio of Sb₂O₃:Sb by the oxidation of Sb nanoparticles at different temperatures (100, 200, and 300 °C), and investigate the detailed effect of Sb₂O₃ on the electrochemical performance of half SIBs with Sb/Sb₂O₃ as the anode’s active materials by the experiential method. The Sb/Sb₂O₃-based batteries exhibit superior reversible performance, maintaining up to four-to-six times more capacity than the pure Sb after 100 cycles at 0.1 A g⁻¹. Moreover, the half SIBs with the optimized Sb/Sb₂O₃-200 nanoparticles exhibit a superior rate performance with 95.7% retention after cycling at varied current densities, and finally, they show good capacity recovery back to 0.1 A g⁻¹. Based on this, we establish a diffusion–stress coupled model to analyze the effect of the ratio of Sb₂O₃:Sb and the particle size of Sb/Sb₂O₃ on the Na⁺ concentration and stress distribution variation during the sodiation process, in order to clarify how they influence the capacity and stability of Sb/Sb₂O₃-based SIBs, which can provide the perspective and guidance for the structure design of Sb/Sb₂O₃ composites.

2. Experimental

The Sb/Sb₂O₃ nanoparticles are prepared by oxidation of Sb nanoparticles in the air at 100, 200, and 300 °C, marked as Sb/Sb₂O₃-100, Sb/Sb₂O₃-200, Sb/Sb₂O₃-300, respectively, and the as-obtained Sb powder before oxidation is marked as BA-Sb, as illustrated in Figure S1 [38,39]. The detailed experimental methods and instrument parameters of characterization tests are described in the Supporting Information. The details of the electrode fabrication, assemble process of the half-SIBs, and electrochemical test parameters are provided in the Supporting Information.

3. Calculations Stress Analysis during Sodiation Process

A spherical particle model is established using COMSOL Multiphysics software to study the diffusion-induced stress of Sb/Sb₂O₃ composites during the sodiation process.

Figure 1 shows the diffusion of sodium-ion in a hollow spherical particle electrode, which can be used as a reference for stress direction modeling. ${\sigma }_{rr}$ and ${\sigma }_{\theta \theta }$ are radial stress and tangential stress, respectively. ${\epsilon }_{rr}$ are ${\epsilon }_{\theta \theta }$ represent corresponding radial strain and tangential strain; u is displacement. Table S1 lists the main parameters used in simulation [32,33,34].

The concentration of Na⁺ satisfies Fick’s second law of mass conservation, which can be defined as [35]:

$$\partial c/\partial t+\nabla ·J=0$$

(1)

The diffusion flux $J$ is expressed as:

$$J=-Mc\nabla \mu$$

(2)

where M is the mobility of sodium in Sb-Sb₂O₃ solid particles, μ is the chemical potential of sodium active particles, c is the amount related to sodium-ion concentration and surrounding hydrostatic stress.

For chemical potential μ, adding hydrostatic stress term to chemical potential is the reflection of stress on the diffusion process, and the chemical potential gradient is the driving force of sodium ion movement. Based on the assumption of the tiny elastic deformation, the mechanical properties depend on the sodium fraction. Therefore, the chemical potential expression is transformed into:

$$\mu ={\mu }_0+RTlnX-\Omega {\sigma }_h$$

(3)

of which, μ₀ is the chemical potential in the absence of stress, T is the absolute temperature, R stands for gas constant, X is the mole fraction of sodium ions, Ω is the sodium activated partial molar volume of the particles, σ_h is the hydrostatic pressure of the particles, and σ_ij is the stress tensor. Additionally, σ_h is defined as: ${\sigma }_h={\sigma }_{11}+{\sigma }_{22}+{\sigma }_{33}/3$.

Assuming that the temperature is uniform, substituting Equation (3) back into Equations (1) and (2), the following equations can be obtained [35]:

$$\nabla RTlnX=RT·\nabla X/X=RT·\nabla c/c$$

(4)

$$\partial c/\partial t=D\left({\nabla }^{2}c-\Omega ·\nabla c·\nabla {\sigma }_h/RT-\Omega c·{\nabla }^2{\sigma }_h/RT\right)$$

(5)

where D = MRT, and it is the diffusion coefficient of sodium ion in Sb-Sb₂O₃ nanoparticles. After the expression of the concentration of Na⁺ in Sb-Sb₂O₃ nanoparticles, we need to add constraints to solve the equation. Flux and concentration are 0, and the following expression can be obtained [35]:

$$r=0: \partial c_1/\partial r=0$$

$$r=b: J_2=i_n/F$$

(6)

where i_n represents the current density and F is the Faraday constant.

For the spherical structure, the stress tensor contains two independent components of radial stress σ_rr and tangential stress σ_θθ, and the static equilibrium equation of the sphere is [36,37]:

$${d\sigma }_{rr}/dr+2\left({\sigma }_{rr}-{\sigma }_{\theta \theta }\right)/r=0$$

(7)

Due to the symmetry of sphere, the strain-displacement relation of infinitesimal deformation in the spherical coordinate system without considering the dislocation effect can be expressed as follows:

$${\epsilon }_{rr}=du/dr {\epsilon }_{\theta \theta }=u/r$$

(8)

The main body of Sb/Sb₂O₃ particles is assumed to be an isotropic linear elastic solid and the deformation is quasi-static. The stress–strain relationship of radial and tangential components can be expressed in spherical coordinates as [35,37,40]:

$${\sigma }_{rr}=\left[\left(1-v\right){\epsilon }_{rr}+2v{\epsilon }_{\theta \theta }-\left(1+v\right)·\Omega \tilde{c}/3\right]·E/\left(1+v\right)\left(1-2v\right)$$

$${\sigma }_{\theta \theta }{=[v\epsilon }_{rr}{+\epsilon }_{\theta \theta }-(1+v)·\Omega \tilde{c}/3]·E/(1+v)(1-2v)$$

(9)

where v is Poisson’s ratio and E is Young’s modulus; $\tilde{c}=c-c_0$, and it indicates the difference in concentration of Na⁺ in the Sb/Sb₂O₃ environment, which is between the current state of concentration c and the initial stress-free state c₀.

Equations (7) and (8) can be substituted into Equation (9), and Equation (10) can be obtained:

$$d^{2}u/{dr}^2+2/r·du/dr-2u/r=(1+v)/(1-v)·\Omega /3·d\tilde{c}/dr$$

(10)

The integral of this equation yields a general solution of u, from which the stress appears. The stress at the center of the sphere is finite (r = 0), and the radial stress on the particle surface is 0, that is, its boundary condition is:

$$u_1\left(r=0\right)=0$$

$${\sigma }_{rr,2}\left(r=b\right)=0$$

(11)

According to the above formula, the radial stress on the external and inner region of Sb nanoparticles can be obtained:

$${\sigma }_{rr,1}=2E_1{\Omega }_1·\left({{\displaystyle \int }}_0^a{\tilde{c}}_1{r}^{2}dr/a^3-{{\displaystyle \int }}_0^r{\tilde{c}}_1{r}^{2}dr/r^3\right)/3\left(1-v_1\right)+{\sigma }_{rr}^{cs}$$

$${\sigma }_{rr,1}=2E_1{\Omega }_1·\left({{\displaystyle \int }}_0^a{\tilde{c}}_1{r}^{2}dr/a^3-{{\displaystyle \int }}_0^r{\tilde{c}}_1{r}^{2}dr/r^3\right)/3\left(1-v_1\right)+{\sigma }_{rr}^{cs}$$

$$u_1=r(1-2v_1){\sigma }_{rr}^{cs}/E_1+r{\Omega }_1/3·[2\left(1-2v_1\right)/\left(1-v_1\right)·{{\displaystyle \int }}_0^a{\tilde{c}}_1{r}^{2}dr/a^3+\left(1+v_1\right)/\left(1-v_1\right)·{{\displaystyle \int }}_0^r{\tilde{c}}_1{r}^{2}dr/r^3]$$

(12)

$${\sigma }_{rr,2}=2E_2{\Omega }_2/3\left(1-v_2\right)·\left(\left(1-{\left(a/r\right)}^3\right)·{{\displaystyle \int }}_a^b{\tilde{c}}_2{r}^{2}dr/(b^3-a^3)-{{\displaystyle \int }}_a^r{\tilde{c}}_2{r}^{2}dr/r^3\right)+a^3/(b^3-a^3)·\left[{\left(b/r\right)}^3-1\right]·{\sigma }_{rr}^{cs}$$

$${\sigma }_{\theta \theta ,2}=E_2{\Omega }_2/3\left(1-v_2\right)·\left(\left(2+{\left(a/r\right)}^3\right)·{{\displaystyle \int }}_a^b{\tilde{c}}_2{r}^{2}dr/(b^3-a^3)+{{\displaystyle \int }}_a^r{\tilde{c}}_2{r}^{2}dr/r^3\right)-a^3/(b^3-a^3)·\left[{\left(b/r\right)}^3/2+1\right]·{\sigma }_{rr}^{cs}$$

$$\begin{gathered} u_2=-r{a}^3{\sigma }_{rr}^{cs}/\left[\left(b^3-a^3\right)E_2\right]·\left[\left(1-2v_2\right)+{\left(b/r\right)}^3/2·\left(1+v_2\right)\right]+r{\Omega }_2/3 \\ ·\left[\left(2\left(1-2v_2\right)/\left(1-v_2\right)+{\left(a/r\right)}^3·\left(1+v_2\right)/\left(1-v_2\right)\right)·{{\displaystyle \int }}_a^b{\tilde{c}}_2{r}^{2}dr/(b^3-a^3\right)+\left(1+v_2\right)/ \\ \left(1-v_2\right)·{{\displaystyle \int }}_a^r{\tilde{c}}_2{r}^{2}dr/r^3] \end{gathered}$$

(13)

4. Results and Discussion

4.1. Morphology, Structures, and Electrochemical Analysis

Figure 2a shows the Raman spectra of Sb/Sb₂O₃-100, Sb/Sb₂O₃-200, Sb/Sb₂O₃-300 nanoparticles. From Figure 2a, the coexistence of Sb₂O₃ with Sb can be observed, in which the peaks at 192 and 257 cm⁻¹ originate from Sb₂O₃, and the peaks at 115 and 150 cm⁻¹ derive from Sb [27,29]. Comparing these three curves of Sb/Sb₂O₃-100, Sb/Sb₂O₃-200, and Sb/Sb₂O₃-300, the main peaks of Sb are concurrent and conspicuous, but the main peaks of Sb₂O₃ are more conspicuous only in Sb/Sb₂O₃-300, which indicates the Sb₂O₃ content accrues with increasing in oxidation temperature. This result is further confirmed by the X-ray diffraction (XRD) patterns (Figure 2b). In Figure 2b, there exist the diffraction peak differences for Sb/Sb₂O₃-100, Sb/Sb₂O₃-200, Sb/Sb₂O₃-300, and pure Sb before oxidation (BA-Sb). It can be found that the diffraction peaks of BA-Sb correspond well to the Sb: 85-1322 (JCPDS card, Jade 6, Materials Data, Inc., Livermore, CA, USA) with the hexagonal crystal system, R-3m space group. The prominent diffraction peaks of Sb/Sb₂O₃ not only coincide with Sb, but also coincide with Sb₂O₃: 42-1466 (JCPDS card, Jade 6, Materials Data, Inc.), corresponding to the cubic system, Fd-3m space group. Some small peaks at 25.47°, 27.67°, 32.17°, 35.15°, 54.51°, and 57.19° related to the Sb₂O₃ phase are only able to be found for the Sb/Sb₂O₃-300, which indicates that the content of Sb₂O₃ increases with the rise of oxidation temperature.

Figure 3 shows the high-resolution X-ray photoelectron spectroscopy (XPS) spectra of Sb of the Sb/Sb₂O₃ nanoparticles. It can be seen from the figure that the positions of the main fitting peaks of the samples are basically the same, while the Sb/Sb₂O₃-200 shows the highest intensity among them. The Sb 3d spectrum exhibits the characteristic peaks of Sb⁰ and Sb³⁺. It can be seen that the peaks appearing at binding energies of 529.2 and 538.5 eV correspond to the 3d_5/2 and 3d_3/2 of Sb³⁺, which is in line with the existence of the Sb₂O₃. Two peaks located at 527.0 and 536.4 eV correspond to 3d_5/2 and 3d_3/2 of Sb⁰, respectively, which can be attributed to metallic Sb [27,28]. In addition, the 3d_5/2 peak of Sb³⁺ overlaps with the O 1s peak at 529.2 eV, well in agreement with what was previously reported [28,29]. Meanwhile, according to the fitting peak of Sb element, the content ratio of Sb₂O₃ and Sb in the Sb/Sb₂O₃-100, Sb/Sb₂O₃-200, and Sb/Sb₂O₃-300 are 3.2:1, 3.5:1, and 4:1, respectively. These results confirm the coexistence of Sb and Sb₂O₃ in the nanoparticles, as observed in the aforementioned XRD and Raman measurements.

Figure 4a is the N₂ adsorption–desorption isotherms of the Sb/Sb₂O₃ nanoparticles. It can be seen that there are apparent sorption hystereses and type IV isotherms for all curves, indicating the mesoporous structure of Sb/Sb₂O₃ nanoparticles [31,41]. The specific surface area of Sb/Sb₂O₃-100, Sb/Sb₂O₃-200, and Sb/Sb₂O₃-300 is 126.8, 132.4, and 74.8 m² g⁻¹ by the BET (Brunauere–Emmette–Teller) method, respectively, indicating the large specific surface area of Sb/Sb₂O₃-200. Combined with pore width distribution data (Figure 4b), the pore size is mainly in the range of 4.5–15 nm for all Sb/Sb₂O₃ nanoparticles, and the pores with the width concentrated at ~20 nm can be only observed for Sb/Sb₂O₃-100 and Sb/Sb₂O₃-200. In addition, there exists a small amount of pores in the range 35–42 nm for Sb/Sb₂O₃-200. A multi-level pore structure of Sb/Sb₂O₃-200 is suggested, which is a benefit for facilitating electrolyte diffusion and ion transportation.

Figure 5a–c show the field emission scanning electron microscope (FESEM) images of Sb/Sb₂O₃-100, Sb/Sb₂O₃-200, and Sb/Sb₂O₃-300. It is noted that the size of the Sb/Sb₂O₃ nanoparticles increases obviously with the oxidation temperature. In addition, aggregation leads to the further formation of cavities between adjacent nanoparticles, producing distinct porous structures [28,29]. The characteristics also can be observed in the transmission electron microscope (TEM) images (Figure 5d–f). From the high-resolution TEM images of Sb/Sb₂O₃ nanoparticles, there is a well resolved (0 1 2) crystal plane of Sb from the lattice fringe width of 0.312 nm for Sb/Sb₂O₃-100, Sb/Sb₂O₃-200, and Sb/Sb₂O₃-300 (Figure 5g). In addition, the lattice fringe width of 0.228 nm correlating to the (4 2 2) crystal plane of Sb₂O₃ can be only found for Sb/Sb₂O₃-200 and Sb/Sb₂O₃-300 (Figure 5h,i), which may be associated with the high content of Sb₂O₃ in Sb/Sb₂O₃-200 and Sb/Sb₂O₃-300. The coexistence of the bright spot and halo in the SEAD image in Figure 5j–l indicates the existence of both crystal and amorphous phase in the Sb/Sb₂O₃ nanoparticles [22,23]. The obvious diffraction ring with the diameter of 0.312 nm for Sb/Sb₂O₃-100 (Figure 5j) is in agreement with the (0 1 2) crystal plane of Sb, and the main diffraction rings with the diameters of 0.310, 0.377, and 0.229 nm for Sb/Sb₂O₃-200 (Figure 5k), which agree well with the (0 1 2) and (0 0 3) crystal plane of Sb and the (4 2 2) crystal plane of Sb₂O₃, respectively. For Sb/Sb₂O₃-300 (Figure 5l), the diameters of the main diffraction rings are 0.312, 0.228, and 0.643 nm, corresponding to the (0 1 2) crystal plane of Sb, and the (4 2 2) and (1 1 1) crystal plane of Sb₂O₃, respectively. The results are consistent with the results of XRD. Moreover, it can be found that the amorphous Sb₂O₃ in Figure 5l becomes more and more obvious with the increase of oxidation temperature, suggesting an increase of Sb₂O₃ content in Sb/Sb₂O₃ with the oxidation temperature. In addition, Sb and O are evenly distributed in the Sb/Sb₂O₃-200 from the EDX mapping in Figure 5m–o.

CV curves of Sb/Sb₂O₃-200 are gauged at 0.1 mV s⁻¹ at the voltage window of 0.01–2.0 V. In Figure 6a, the weak and narrow peak at 0.92 V is the initial cathodic scan, because of the reduction of Sb₂O₃ to Sb. One sharp and broad peak over 0.2–0.5 V is linked with the interpolation of Na into Sb and the becoming of the solid–electrolyte interphase (SEI) film [28,42]. The premier anodic scan shows the uninterrupted oxidation about the Na₃Sb alloy, containing the insertion of Na⁺ (0.94–1.11 V), and the transformation from Sb to oxides (1.3–2.0 V) [31]. It produces an extremely minimal current and broad extents in the peak range of 1.3–2.0 V because of the low content of Sb₂O₃ in the composites and the partial invertibility of this oxidation process. In the next cycles, the cathodic peak at ~1.0 V remains, implying the invertible transformation between Sb₂O₃ and Sb. This result has also been obtained in previous research [29,30]. Meanwhile, the two peaks at 0.67 and 0.41 V show the gradual decrease of Sb to Na_xSb and Na₃Sb [28,43]. This transfer indicates favorable kinetics within the composites, and compared with the first cycle, the electrode polarization is reduced. The cathodic and anodic peaks are stable after the first cycle, showing the satisfying electrochemical stability. Figure 6b reveals the discharge–charge curves of Sb/Sb₂O₃-200 over 0.01–2.0 V. In the first discharge cycle, the reaction platform firstly appeared at ~0.8 V and disappeared in the succeeding sweeping, that can be attributed to the establishment of SEI film. Two platforms appeared successively at 0.4 and 0.25 V, representing the gradual alloying process of Sb with Na [28]. In the charge sweeping, two reaction platforms appeared near 1.0 and 0.9 V, representing the two-step dealloying process from Na₃Sb to Sb. This result agrees with the data of the CV curves. The Coulombic efficiency of the initial cycle is 67.5%, and the capacity decline in this case is associated with the disintegration of electrolytes, the establishment of SEI film, and the partially invertible redox reaction between Sb and Sb₂O₃. In the second cycle, the Coulombic efficiency reaches up to 98.0% indicating the electrode/electrolyte interface becoming stable at charging/discharging process. Meanwhile, the results show that more Na⁺ can be inserted at a higher voltage, due mainly to the reduction of size and restructuring of the active particles caused by the conversion and alloy reactions. The CV curves and discharge–charge curves of Sb/Sb₂O₃-100 and Sb/Sb₂O₃-300 are shown in Figure S2 in the Supporting Information. It can clearly be seen that although both the cathodic/anodic peaks and the charge–discharge platform are basically the same as the Sb/Sb₂O₃-200, the electrochemical behavior is not up to expectations.

The cycling and rate performance of the cells with Sb nanoparticles and Sb/Sb₂O₃ nanoparticles are given in Figure 6c,d. The Sb nanoparticles before oxidation (BA-Sb) were employed as the control group to manifest the performance of Sb/Sb₂O₃ nanoparticles precisely. All the cells with the Sb/Sb₂O₃-100, Sb/Sb₂O₃-200, and Sb/Sb₂O₃-300 nanoparticles present a superior cycling stability compared to the BA-Sb, which benefited from the buffering effect of the Sb₂O₃ in Sb/Sb₂O₃ nanoparticles. In addition, at 0.1 A g⁻¹ after 100 cycles, the reversible capacity of the half SIBs with the Sb/Sb₂O₃-200 (540 mAh g⁻¹) exhibits a higher invertible capacity than that of the Sb/Sb₂O₃-100 (400 mAh g⁻¹) and Sb/Sb₂O₃-300 (365 mAh g⁻¹). From Figure 6d, at 0.1, 0.2, 0.4, 0.8, 1.6, and 3.2 A g⁻¹, the reversible capacity of the cell with Sb/Sb₂O₃-200 is 628.8, 598.8, 562.7, 482.4, 432.2, and 317.1 mAh g⁻¹, respectively. When the current density is returned from high to low (at 0.1 A g⁻¹), its reversible capacity can be recovered to 601.9 mAh g⁻¹, which corresponds to 95.7% of the prime capacity, demonstrating an excellent rate performance. This superior stability of Sb/Sb₂O₃-200 can be assigned to the adequate ratio of Sb/Sb₂O₃ in the Sb/Sb₂O₃-200, in which, Sb can provide a high capacity for sodiation while Sb₂O₃ acts as a buffer matrix to accommodate the extremely volume expansion without cracking. Interestingly, for the BA-Sb, which was used as a control group, it exhibits a higher charge capacity than Sb/Sb₂O₃-300 in the initial 83 cycles, and the charge capacity of BA-Sb degrades sharply upon cycling after 83 cycles. Finally, the charge capacity is 90 mAh g⁻¹ after 100 cycles lower than that (365 mAh g⁻¹) of Sb/Sb₂O₃-300 in Figure 6c, which is associated with the large stress of Sb during cycling. For the rate performance shown in Figure 6d, the better performance of Sb is due to the small number of charge–discharge cycles, but its rate performance is not stable. So, in terms of long-term cycle stability, the Sb nanoparticles shows a poorer stability than Sb/Sb₂O₃-300, and a lower charge capacity than Sb/Sb₂O₃-300 after 83 cycles.

For comparison,

Table 1. Comparison of electrochemical performance of electrodes made from Sb/Sb₂O₃ composites.

Electrode Materials	Key Improvements	Electrolyte/ Concentration	Electrode Size (Mass Loading of Active Material)	Cycling Performance (mAh g−1)	Capacity Retention Ratio	Ref.
Sb/Sb2O3 nanoparticles	Sb alloys & Sb oxides & special morphology nanostructure	1 M NaClO4 + PC a + 3%FEC b	Copper foil diameters of 12 mm (1.0–1.2 mg)	540 at 100 mA g−1 after 100 cycles	98.0%	This work
Sb/Sb2O3-polypyrone electrode	3D porous Sb/Sb2O3 & fabricated with a polypyrrole nanowire network	1 M NaClO4 +2% FEC b	A sheet of nodular Cu (0.67 mg cm−2)	512.01 at 66 mA g−1 after 100 cycles	99%	[30]
Sb2O3/Sb@ graphene-CSN electrode	Sb2O3/Sb Nanoparticles & graphene shell nanostructure & anchored on carbon sheet networks	1 M NaClO4 + EC c + DMC d	Copper foil with 0.97 mg cm−2 (1.5 mg)	525.4 at 100 mA g−1 after 100 cycles	98%	[21]
Sb and Sb2O3 particles in waste-tire derived carbon	A conductive network of waste tire derived carbon & Sb composites	1 M NaPF6 + EC c + PC a	Cu current collector with the size of 14 mm diameter (3.6 mg)	207 at 37 mA g−1 after 100 cycles	88%	[44]
Antimony-based alloy/oxides nanosheets	Sb-based alloy/oxides & nanosheet structure	1 M NaClO4 + PC a + EC c + 2% FEC b	Cu foil (1.4–1.7 mg cm−2)	311 at 100 mA g−1 after 120 cycles	89%	[45]
Porous Sb/Sb2O3 nanocomposite	Porous nano-structure & Sb/Sb2O3 composites	1.0 M NaClO4+EC c + DEC e+10% FEC b	Copper foil diameters of 12 mm (0.9–1.2 mg cm−2)	481 at 660 mA g−1 after 180 cycles	~92.8%	[31]
Coral-like nanostructured Sb2O3@Sb	Mild oxidization in air & etching of element & coral-like nanostructure	1 M NaPF6 + EC c + DEC d + 5% FEC b	Cu foil (0.7–0.9 mg cm−2)	574.8 at 100 mA g−1 after 150 cycles	99.0%	[28]
Sb/Sb2O3 composites	The electrodeposition of Sb & the chemical deposition of Sb2O3 & morula-like Sb/Sb2O3 particles	1 M NaClO4 + PC a + 0.5% FEC b	The nodule-type Cu foil (0.86 mg cm−2, thickness of 1.34 μm)	615 at 66 mA g−1 after 100 cycles	97.56%	[29]

^a propylene carbonate. ^b fluoroethylene carbonate. ^c carbonate. ^d dimethyl carbonate. ^e diethyl carbonate.

lists the electrochemical performance of some literature about the Sb/Sb₂O₃ electrodes for SIBs, further demonstrating that the as-obtained Sb/Sb₂O₃-200 electrode materials in this work exhibit better cycling and rate performance than most of those reported in the literature.

Figure 7a displays the CV curves of the Sb/Sb₂O₃-200 cell from 0.1–1.0 mV s⁻¹. One anodic peak (Peak 1) and two cathodic peaks (Peak 2 and Peak 3) are clearly shown in these curves. The b values of all cathodic and anodic peaks calculated by the slope of log (peak current) versus log (scan rates) are shown in Figure 7b. According to existing research results [46], the charge exchange system mainly consists of three parts: (a) for b = 0.5, the diffusion-control behavior produced in the process of Na⁺ interpolation; (b) for b = 1, the facial atoms transportation caused the Faraday contribution; and (c) the non-Faradaic part of the bilayer effect because of the surface-control behavior. The b values are 0.6, 0.66, and 0.75 of peak 1, 2, and 3, respectively, demonstrating that the electrochemical reaction is primarily diffusion-controlled behavior [46].

To study the influence of Sb₂O₃ on the electronic conductivity and diffusion of Na⁺, the electrochemical impedance spectroscopy (EIS) is tested and displayed in Figure 7c. The impedance spectra are constitutive of a semicircle with a slanted line. Generally speaking, the high frequency semicircle is in connection with R_s and represents the impedance of the SEI film, while the middle frequency semicircle refers to the charge transfer impedance (R_ct). Furthermore, the slanted line represents the Warburg impedance (Z_w), which can confirm the diffusion rate of Na⁺ in the electrode matrix. According to Equation (14), the diffusion coefficient of Na⁺ ($D_{N{a}^{+}}$) can be acquired, which has an essential influence on the electrochemical performance [47].

$$D_{N{a}^{+}}=0.5R^2{T}^2/\left(A^2{n}^4{F}^4{C}^2{\sigma }^2\right)$$

(14)

$$Zre=Rs+Rct+Zw+\sigma {\omega }^{-1/2}$$

(15)

where R, T, F, and n are on behalf of the gas constant (8.314 J mol⁻¹K⁻¹), the absolute temperature (298 K), the Faraday constant (96,485 C mol⁻¹), and the number of electrons transferred. A represents the effective contract area (1.13 cm⁻²), and C refers to the bulk concentration of Na⁺ [38]. The σ is calculated from the slope of Zre-${\omega }^{-1/2}$ according to Equation (15), and σ values of Sb/Sb₂O₃-100, 200, and 300 are shown in Figure 7d. From Equation (14), the $D_{N{a}^{+}}$ of the Sb/Sb₂O₃-100, 200, and 300 are 3.34 × 10⁻²⁴, 4.65 × 10⁻²⁴, and 5.34 × 10⁻²⁵ cm² s⁻¹, respectively, indicating the faster diffusion rate of Na⁺ in Sb/Sb₂O₃-200 than Sb/Sb₂O₃-100 and Sb/Sb₂O₃-300.

To clarify the superior performance of Sb/Sb₂O₃-200 over Sb/Sb₂O₃-100 and Sb/Sb₂O₃-300, the morphological changes of Sb/Sb₂O₃ nanoparticles after cycling are characterized by ex situ SEM, as shown in Figure 8a–c. Comparing with Figure 5a–c, for Sb/Sb₂O₃-100 and Sb/Sb₂O₃-300, the initial “particle shape” is almost found after 100 cycles, and obvious volume expansion is observed after 100 cycles from before cycling, which is related to the irreversible dealloying of sodium ions in Sb. The cycling caused the pulverization and structure deterioration of Sb/Sb₂O₃ nanoparticles, finally resulting in the formation of the irregular and porous structure [27,30]. Additionally, the particle adhesion and fragmentation of Sb/Sb₂O₃-300 is more obvious than that of Sb/Sb₂O₃-100 after 100 cycles. It is noted that coral-like particles exist for Sb/Sb₂O₃-200 after cycling, which means the cycling induces a morphologic transformation from the nanosphere to the coral-like structure. This coral-like structure can favor electrolyte accessibility for fast Na⁺ diffusion, provides sites for more Na⁺ storage, buffers the cycling-induced volume changes, and finally, contributed to the superior performance of Sb/Sb₂O₃-200.

Further, we investigate the phase composition of Sb/Sb₂O₃ nanoparticles after cycling by XPS and XRD measurements. From the XPS spectra in Figure 8d, all peaks related to the Sb³⁺ and Sb⁰ can be clearly observed for Sb/Sb₂O₃-100_, Sb/Sb₂O₃-200, and Sb/Sb₂O₃-300. The relative weak intensity of Sb³⁺ peaks is related to the elimination of the surface oxide layer after ion etching [29]. Figure 8e shows the XRD patterns of Sb/Sb₂O₃ after cycling. For Sb/Sb₂O₃-100 and Sb/Sb₂O₃-200, all the diffraction peaks correspond to the hexagonal phase of Sb without Sb₂O₃. It is suggested that the reversible transformation between Sb and Na₃Sb occurred during the sodiation/desodiation process [30]. In addition, it is worth noting that there still exists the peak of Sb₂O₃ (222) at 27.67° for Sb/Sb₂O₃-300, which means the Sb₂O₃ is not fully converted to Sb and Na₂O, and the remaining inactive Sb₂O₃ may result in the unsatisfactory performance of the Sb/Sb₂O₃-300 electrode [29,30].

4.2. Stress Analysis

In order to explain the detailed mechanism of how Sb₂O₃ improves the capacity and stability of Sb, we establish a diffusion-stress coupled model to analyze the Na⁺ concentration and stress distribution variation with the composition ratio of Sb₂O₃:Sb and the particle size of Sb/Sb₂O₃ during the Na⁺ insertion process. Due to the frequent charge/discharge process of SIBs, the embedding and removing of Na⁺ will cause the Sb-based electrode materials to expand and contract substantially, finally leading to fracture, crushing, and failure of the electrode. The process of Na⁺ removal from cathode/anode, transportation by electrolyte, and embedment can be regarded as a solute diffusion process. As a contrast, the insertion/removal process of Na⁺ (electrochemical process) can cause the change of material lattice, which induces the generation of stress, and the stress can further affect the Na⁺ diffusion process. That is, the evolution of the stress field is coupled with the diffusion process of the concentration. According to this characteristic, the radial variation trend of the concentration and stress field of the Sb/Sb₂O₃ material are analyzed using the physical and chemical parameters.

Figure 9a–c show the radial distribution of (I) concentration of Na⁺, (II) Von Mises stress, (III) radial stress, and (IV) tangential stress with a radius of the Sb/Sb₂O₃ spherical model. Figure 9a presents the variation trend at different charging time from 0 to 3000 s with the composition ratio of 1:1 of Sb₂O₃:Sb. From Figure 9a, on the whole, the concentration and stress field of the Sb/Sb₂O₃ spherical model increase with the charging time, which is associated with the insertion of a large amount of Na⁺ into Sb/Sb₂O₃ electrode materials, in line with the working principle of SIBs. In Figure 9a(I), the radial distribution of Na⁺ concentration in Sb/Sb₂O₃ varies with the radius of the Sb/Sb₂O₃ spherical model at different charging time. As can be seen, the concentration gradient of Na⁺ in the radius direction is close to 0 during the charging process. In addition, the characteristic time of diffusion, respectively, 0.0048 s and 0.0179 s in Sb and Sb₂O₃, can be obtained by the diffusion coefficient D₀ in Table S1 [36,37], indicating that the embedding of Na⁺ is a very rapid process. This is due to the appropriate nanoscale size of Sb/Sb₂O₃ particles, suggesting that the material has an excellent quick-charging performance. In Figure 9a(II) and (IV), the variation trends of Von Mises equivalent stress and tangential stress are basically the same. Both the Mises equivalent stress and tangential stress reach the maximum at the interface between Sb and Sb₂O₃ and gradually decrease in the region of Sb₂O₃. From Figure 9a(III), the radial stress increases near the edge of the model kernel and decreases obviously in the outer layer, which is determined by the boundary condition that the normal stress is 0 on the surface of Sb₂O₃. With the increase of charge time, the volume expansion of the structure increases gradually, but the Sb expansion is constrained by the Sb₂O₃ matrix. These results indicate that the mutation on the interface between Sb and Sb₂O₃ is easy to cause the failure of the interface bond.

Figure 9b shows the variation trend of stresses with the different ratio of the participating component of Sb₂O₃ and Sb at the charging time of 3000 s. As can be seen from the figures, for pure Sb nanoparticles (the composition ratio of Sb₂O₃:Sb is 0:1), the change trend of the Von Mises equivalent stress, the radial stress, and the tangential stress particle force is obviously different from those of Sb/Sb₂O₃ with a different ratio of Sb₂O₃:Sb. It is observed that there exists a large decrease of Von Mises equivalent stress, radial stress, and tangential stress of Sb/Sb₂O₃ nanoparticles compared with those of Sb nanoparticles, which indicates that Sb₂O₃ can effectively reduce the internal stress of the particles and reduce the structural collapse during cycling. This can be deemed as the root of the enhanced cyclicity of Sb/Sb₂O₃ anode materials over Sb nanoparticles. For Sb/Sb₂O₃ nanoparticles, it is found that increasing the composition ratio of Sb₂O₃:Sb in Sb/Sb₂O₃ will lead to a decrease of Mises equivalent stress, radial stress, and tangential stress in the ratio range 1:1–3.5:1 and cause a stress increase in the ratio range of 3.5:1 to 4:1. Meanwhile, the maximum Mises equivalent stress and tangential stress occurred at the interface between Sb and Sb₂O₃, indicating that it is prone to break at the interface. The results suggest that there is an optimum content of Sb₂O₃ in Sb/Sb₂O₃ nanoparticles, which will induce a small stress of the particles, finally enhancing the cyclic stability of SIBs. More involvement of Sb₂O₃ will increase the internal force, deteriorating the cycling performance of Sb/Sb₂O₃ nanoparticles.

Figure 9c shows the variation trend of stresses with the particle radius from 30 to 70 nm at the charging time 3000 s of Sb/Sb₂O₃ (the component ratio of 1:1 of Sb₂O₃: Sb). As observed, the Mises equivalent stress, radial stress, and tangential stress show a decrease with the particle radius in the range of 30–50 nm of Sb/Sb₂O₃ nanoparticles, and an increase with a particle radius in the range 50–70 nm This indicates that the appropriate size of particles can induce a small strain-induced stress during the sodiation process, which is a benefit for improving the cycling stability and capacity of Sb/Sb₂O₃ anode materials. The results obtained from Figure 9b and c can be used to explain the superior stability of Sb/Sb₂O₃-200 obtained by experiments, which is because Sb/Sb₂O₃-200 is at exactly the optimum composition ratio of Sb₂O₃:Sb in Sb/Sb₂O₃ and the particle size, which can ensure both a high capacity for Na⁺ and induce small strain-induced stress during sodiation/desodiation.

5. Conclusions

In summary, Sb/Sb₂O₃ nanoparticles are synthesized by two-steps oxidation of Sb nanoparticles in air at different temperatures (100, 200, and 300 °C). The electrochemical performance of SIBs with Sb/Sb₂O₃ as the anode’s active materials has been investigated. A diffusion-stress coupled model, too, is employed to clarify how they influence the capacity and stability of SIBs. The results are summarized as follows:

• The half SIBs with the optimized Sb/Sb₂O₃-200 nanoparticles exhibit superior reversible performance, maintaining up to six times more capacity (540 mAh g⁻¹) than the pure Sb (90 mAh g⁻¹) after 100 cycles at 0.1 A g⁻¹, and a superior rate performance with 95.7% retention after cycling at the varied current densities. One reason for this is that the oxidation temperature affects the content of Sb₂O₃ in Sb/Sb₂O₃ nanoparticle and the particle size of Sb/Sb₂O₃, and Sb/Sb₂O₃-200 is at exactly the optimum composition ratio of Sb₂O₃:Sb in Sb/Sb₂O₃ and the particle size to ensure both a high capacity for Na⁺ and small strain-induced stress during sodiation/desodiation, which is supported by the diffusion-stress coupled results.
• The results of the diffusion-stress coupled model indicate that increasing the composition ratio of Sb₂O₃:Sb in Sb/Sb₂O₃ will lead to a decrease of Mises equivalent stress, radial stress, and tangential stress in the ratio range 1:1–3.5:1 and cause a stress increase in the ratio range 3.5:1–4:1. The Mises equivalent stress, radial stress, and tangential stress show a decrease with the particle radius in the range 30–50 nm of Sb/Sb₂O₃ nanoparticles, and an increase with a particle radius in the range 50–70 nm.
• The superior performance of Sb/Sb₂O₃-200 is also related to the formation of cycling-induced coral-like structure Sb particles, which can promote Na⁺ diffusion, relieve cycling-induced volume changes, and provide exceptional Na⁺ storage. This morphology transformation is associated with the state of stress of active materials.

This study provides the perspective for understanding how Sb₂O₃ influences the stability of Sb/Sb₂O₃-based SIBs and the structure design of Sb/Sb₂O₃ anode materials.