Quantifying vanadium-vacancy clusters in V2O3 towards ultra-long cycling aqueous zinc-ion battery

Defect engineering has been attracted widespread attention for promoting the stability of the electrodes. However, accurately quantifying and defining the effect of defects is extremely difficult. Here, the Rietveld analysis with combined neutron powder diffraction (NPD) and X-ray powder diffraction (XRD) patterns reveal vanadium defect (Vd) clusters in the V2O3 lattice up to 5.7% in aqueous zinc-ion batteries (ZIBs), further confirmed by positron annihilation spectroscopy (PAS) and synchrotron-based X-ray analysis. Benefitting from the Vd clusters, the V2O3 cathode achieves excellent cycle life with 81% capacity retention at 5.0 A g after 30,000 cycles that is the most superb stable cathode for aqueous ZIBs at this current density. Besides, the density functional theory (DFT) calculations strongly indicate that the Vd clusters not only provide permanent sites for Zn anchormen to enhance the integrity of V2O3 after the first discharging process, but also make Zn de/intercalation in complex oxide, contributing collectively and effectively reducing the strong electrostatic interaction between host multivalent ions, resulting in the remarkable storage performance of Zn. This work highlights accurately quantifying and identifying the significant effect of defects for designing cathodes with ultra-long cycle life in future intelligent devices.


Introduction
With the increase of energy crisis and environmental pollution problems, it is essential to develop green and clean energy storage devices. As a bellwether in the field of energy storage, lithium-ion batteries (LIBs) are a key technique in advanced power technologies 1,2 . However, emerging worries are their limited lithium resources and security issues towards future large-scale applications [3][4][5][6] . Encouragingly, rechargeable aqueous ZIBs have emerged as the most promising complements to LIBs regarding high specific capacity (819 mA h g -1 ), low cost, abundant resources, and environment friendly [7][8][9] . It has been demonstrated that aqueous ZIBs have been applied in miniaturized electronic devices, such as epidermis, implantable and wearable sensors [10][11][12] , indicating that aqueous ZIBs have great commercial potential. But great upgrading is needed to put it into a widespread application. The most compelling issue is to seek long-cycling cathodes for aqueous ZIBs due to serious consequences of stability penalty caused by the aqueous system and bigger ionic radius of Zn 2+ . Defect engineering has been regarded as an availability approach for promoting the stability of electrodes, where the strong electrostatic interaction between the host and multivalent ions with a greater charge can be efficiently reduced, accelerate the reaction kinetics and facilitate the reversible storage of Zn ions [13][14][15][16] . Particularly, the research of defects in oxide electrodes most used for ZIBs is required due to the complex composition and the dynamic process during the working process. Accurately quantification of material defects is essential to determine the metal vacancies and oxygen vacancies at the same time. However, it is extremely hard to simultaneously determine the concentration of two vacancies. For example, light oxygen is difficult to be detected by XRD owing to its small atomic radius, compared with most metal elements. Consequently, the joint application of multiple spectroscopy is essential to accurately quantify defects.
In this work, we have quantified for the first time in aqueous ZIBs that V2O3 (Vd-V2O3) electrode contains 5.7% Vd clusters by Rietveld analysis with combined XRD and NPD patterns. It is the V2O3 cathode containing Vd clusters that delivers ultra-long cycling stability (81% retention after 30,000 cycles at a current density of 5 A g -1 ), which is the longest cycling stability for the aqueous ZIBs cathode to date. Accurately quantifying and identifying the effect of defects provides a new path for the design of cathodes with long stability for energy storage devices.

Structure and morphology characterization of Vd-V2O3
The Vd-V2O3 cathode was designed by a hydrothermal method and an ensuing annealing process (see Supplementary Information for details). Scanning electron microscopy (SEM, Supplementary Fig. 1) and Transmission electron microscope (TEM, Supplementary Fig. 2a) images show that the Vd-V2O3 is a uniform flower-like hierarchical structure assembled by thin nanosheets with a size of around 100-200 nm.
In the high-resolution TEM (Supplementary Fig. 2b) image of the flower-liked Vd-V2O3, a lattice fringe with a layer spacing of d = 0.27 nm was found, corresponding to the (104) lattice plane. The surface area and pore size were detected by BET (Brunauer-Emmett-Teller) characterization, the Vd-V2O3 has a high surface area of 60.34 m 2 g -1 and a large pore size of about 22 nm (Supplementary Fig. 3). A large surface area can provide sufficient contact between the electrode and electrolyte and shorten the Zn 2+ diffusion path time. The mesoporous structure is advantageous to the insertion and extraction of Zn 2+ , which can effectively improve the cycle life of the battery.
For detailed structure information, X-ray absorption fine structure (XAFS) was performed to investigate the local fine structure of Vd-V2O3. As illustrated in the XANES spectra of V K-edge ( Fig. 1a inset), the absorption edge of the Vd-V2O3 is found to shift toward higher energy (Site B) compared with commercial V2O3 (c-V2O3), stating clearly that Vd-V2O3 possesses a higher average valence state. The highresolution XPS of V 2p further shows that despite the valence states of V in Vd-V2O3 and c-V2O3 are +3 and +4 coexistence (Supplementary Fig. 4), the content of V 4+ is larger (Supplementary Table 1). The identical result can be gotten from electron paramagnetic resonance (EPR) spectroscopy, where the EPR signal of tetravalent vanadium has a stronger response strength 17,18 (Supplementary Fig. 5). It has been reported that the surface of V2O3 is vulnerable to be oxidized to V 4+ , which explains the existence of V 4+ in c-V2O3 19,20 . But the situation in Vd-V2O3 is different, the surface of Vd-V2O3 is proved to be uniformly coated with carbon ( Supplementary Figs. 6 and 7).
Thermogravimetric analysis (TGA) shows that the carbon content is 19.36% ( Supplementary Fig. 8). Surface coated with the carbon of Vd-V2O3 is believed to be not easily oxidized, so the higher content of V 4+ in Vd-V2O3 may attribute to the existence of vanadium vacancies, which leads to a valence increase of V. The pre-edge peak in the XANES of V K-edge corresponds to the electronic transition from 1s to 3d 21 , which can promulgate the local structure symmetry. As shown in Fig. 1a inset (Site A), the increase of pre-edge peak intensity attributes to the decrease of local symmetry of Vd-V2O3. That is suggested that the structure of Vd-V2O3 is distorted around V atoms, owing to the absence of surrounding atoms. To further obtain the accurate coordination numbers (CN), the corresponding Fourier transformed EXAFS is fitted that is shown in Supplementary Fig. 9 and the detailed fitting results can be found in Supplementary Table 2. The results demonstrate that the CN of the V-V in Vd-V2O3 is significantly lower than that in c-V2O3 (2.2 vs. 4), which exhibits that there are vanadium vacancies in Vd-V2O3.
In order to further corroborate the defect situation in Vd-V2O3, we used PAS to explore the defect type and concentration of the material 22 . Table 1 shows the positron annihilation lifetime data of Vd-V2O3 and c-V2O3. There are three life components (τ1, τ2, and τ3), among which τ1, τ2, and τ3 correspond to defect-free bulk region and the tiny vacancies, vacancy clusters, and interfaces (free space between nanograins) in the material, respectively 23,24 . Due to the microscopic sizes of both Vd-V2O3 and c-V2O3 are above 500 nm (Supplementary Figs. 1 and 10), there exist considerable amount of vacancy clusters in both samples. It is noteworthy that the intensity I2 of τ2 for Vd-V2O3 is 78.01%, which is much higher than that of c-V2O3, indicating that the concentration of vacancy clusters in Vd-V2O3 is much higher than that in c-V2O3. The PALS results provide reliable and valuable proof of the coexistence of vanadium vacancies with a relatively high concentration in Vd-V2O3, and the phenomenon of defect aggregation may occur, also revealed by DFT.
For accurately determine the type and concentration of defects, we combined NPD and XRD techniques. In the Vd-V2O3 cathode, the neutron scattering amplitude of V element is just -0.3438cm -12 and the atomic radius of light oxygen element is about 0.66Å. As a result, the scattering factor of the vanadium element in the Vd-V2O3 cathode is too small to be detected by NPD, while the light oxygen element is hard to be probed by XRD. Therefore, Rietveld analysis with combined XRD and NPD patterns was conducted to reveal the crystal structure information (Fig. 1c). The refinement results Table 3) and show that, the Vd-V2O3 has a typical corundum-type hexagonal structure (Space group: R -3 c) with lattice parameters to be a=b=4.9473 (1) Å, c=13.9990(5) Å. The V and O atoms occupy the 12c (0, 0, 0.15437(6)) and 18e (0.3145(3), 0, 0.25) crystallographic positions, respectively. Moreover, the occupancy rate of vanadium atoms at 12c sites is about 94.3(1) %, while no oxygen vacancy was detected at 18e sites (Fig. 1b). In general, we have demonstrated the presence of coordinately unsaturated atoms of V in Vd-V2O3 and the vacancy occupancy rate of vanadium is 5.7%, and the vanadium vacancies exist in the form of vacancy clusters.

Electrochemistry
To investigate the Zn 2+ storage performance of the Vd-V2O3 cathode, the 2032 type coin-cells were assembled using a zinc foil anode, a 3 M Zn(CF3SO3)2 electrolyte ( Supplementary Figs. 11 and 12), and a filter paper separator. As shown in Supplementary Fig. 13, the cyclic voltammetry (CV) curves of the Vd-V2O3 electrode are carried out at a scan rate of 0.1 mV s -1 within a voltage window of 0.1-1.3 V (vs Zn/Zn 2+ ). Two pairs of redox peaks located at 1.09/0.78 V and 0.93/0.53 V are observed, which attributes to a two-step (de)intercalation process of Zn 2+ . The rate performance for Vd-V2O3 at current densities from 0.1 to 4.0 A g -1 is presented in Fig. 2a and a specific capacity of 163 mA h g -1 is restored which ulteriorly illustrates the high electrochemical reversibility of the Vd-V2O3 electrode. The capacity retention reaches 70.4% when the current densities increase from 0.1 to 1.0 A g -1 , exhibiting excellent rate capability. It is ecstatic that the Vd-V2O3 electrode delivers ultra-long cycling stability with a capacity retention rate of 98% after 10,000 cycles, 90% after 20,000 cycles, and 81% after 30,000 cycles at a current density of 5 A g -1 (Fig. 2b). To the best of our knowledge, the cycling stability of 30,000 cycles is the longest cycle lifetime for reported ZIBs at this current density. As shown in Fig. 2c, the life span of Vd-V2O3 is superior to most of the other aqueous ZIBs (Supplementary Table 4) recently reported in pieces of literature [25][26][27][28][29][30] . These results certainly highlight the great potentials of Vd-V2O3 cathode-based Zn batteries in the field of smart energy storage devices. The longevity of this Vd-V2O3 cathode comes ultimately from abundant vacancy clusters that attenuate the strong electrostatic interaction between Zn 2+ and the Vd-V2O3 host. Supplementary Fig. 15, the c-V2O3 cathode, without vacancies, demonstrates inferior both rate and stability electrochemical performance for aqueous ZIBs, which strongly confirms the positive effects of vacancies in Vd-V2O3 cathode.

As shown in
To further understand the greatly enhanced Zn 2+ storage performance, the electrochemical kinetics of the Vd-V2O3 electrode was investigated. As shown in Fig.   2d, CV measurements are carried out at different scan rates. With the increase of scan rates from 0.1 to 1.0 mV s -1 , the CV curves show a similar shape and the reduction and oxidation peaks are well preserved. Regularly, the peak currents (i) and their corresponding sweep rates (v) obey a power-law relationship that is described by  (Fig. 2e). It is suggested that the Zn 2+ storage behavior of Vd-V2O3 is controlled collectively by ionic diffusion and capacitive, which leads to fast Zn 2+ diffusion kinetics enabling the high-rate performance. In order to further quantify the contribution of diffusion-controlled and capacitive-controlled at a specific scan rate, equation (1) is divided into two halves to form formula (2): i (V) = k 1 ν + k 2 ν 1/2 (2) According to the above equation, the current (i) at a specific potential (V) can be divided into a capacitance limiting effect (k1v) and a diffusion control effect (k2v 1/2 ). As shown in Supplementary Fig. 16, the capacitance contribution (corresponding to the purple region) is 82.5% of the overall contribution at scan rate 0.8 mV s -1 . With the increases of scan rates from 0.1 to 1 mV s -1 , the capacitance contribution rates increase from 66.3% to 86.4% (Fig. 2f). This suggests a substantially greater proportion of capacitivedominated process, which directly contributes to excellent rate performance due to the fast kinetics of Zn 2+ . Galvanostatic intermittent titration technique (GITT) is performed to analyze the diffusion coefficient of Zn 2+ in the Vd-V2O3 electrode ( Supplementary   Fig. 17). The result shows that the diffusion coefficient of Zn 2+ in the Vd-V2O3 electrode is between 10 -7 -10 -8 cm 2 s -1 , which stays ahead of the other existing electrodes 6,31,32 .

Zinc-ion storage mechanism of Vd-V2O3
DFT calculations were conducted to explore the veritable function of Vd-V2O3 for Zn 2+ storage. To investigate the distribution of vanadium vacancies, based on the XRD and NPD Rietveld analysis results, diverse vanadium vacancy models at the concentration of 6.25%, in good agreement with experiments were constructed as shown in Supplementary Fig. 18. A lower formation enthalpy represents a more stable phase.
Structure 1 possesses the smallest formation enthalpy, illustrating the short aggregation of Vd clusters which is consistent with Table 1. Then, the p-V2O3 and Vd-V2O3 were implemented to disclose the insertion of Zn 2+ . The frustrated insertion of Zn 2+ into p-V2O3 was observed due to the enormously positive Gibbs free energy (2.69 eV) 33 , illustrating no capacity or an extremely tiny capacity (Fig. 3a), consistent with the badly Zn 2+ storage performance of c-V2O3 (Supplementary Fig. 15). What's more, the direct insertion of Zn 2+ into p-V2O3 may cause the destruction of the structure, leading to bad stability. However, for Vd-V2O3, vanadium vacancies will accept the insertion of Zn 2+ and provide high capacity than c-V2O3. Intriguingly, the distinguishing Gibbs free energies demonstrate the process of insertion of Zn 2+ into Vd-V2O3 is different. Firstly, the vanadium defect is occupied with Zn 2+ and a large number of heat was released (-1.34 eV) due to the strong electrostatic, improving the integrities and stabilities of Vd-V2O3. Nevertheless, due to this strong electrostatic interaction, the extraction of this kind Zn 2+ is unbearable, demonstrating the self-anchoring action of Zn 2+ in the lattice.
Secondly, the feasible and sustainable insertion of Zn 2+ into Vd-V2O3 is observed, affording the capacity and voltage (Fig. 3a). This phenomenon unravels the residual of Zn in Vd-V2O3. Consequently, the dual-effect of vanadium vacancies in Vd-V2O3 is specified in Fig. 3b. When Zn 2+ initially entries into the Vd-V2O3 electrode that has many vanadium vacancies, part of Zn 2+ will be riveted on vanadium vacancies and caged inside during the whole time. In other words, the eventual structure is a Zn doped Vd-V2O3 after the first discharging self-optimized process, in which the Zn 2+ will reversibly insert or leave in the subsequent cycles.
Based on the above analysis, a series of characterizations were conducted to demonstrate the Zn 2+ storage mechanism of the Vd-V2O3 cathode and effect of vanadium vacancies. It can be seen from Figs. 4a and 4b that the characteristic (104) and (110) peaks move to a lower 2θ degree during the discharging process and return to the original position in the subsequent charge process. These reversible movements originate from the expansion and contraction of the lattice of Vd-V2O3 with the de/intercalation of Zn 2+ . Besides, no other diffraction peaks were detected, indicating no phase transformations in the Vd-V2O3 electrodes during the charge/discharge process.
The stability of Vd-V2O3 was further incarnated in the unchanged XRD curves after 500 cycles (Supplementary Fig. 19). It is noteworthy that the morphology of the Vd-V2O3  Fig. 23b) where the peak of V 4+ becomes dominant upon charging while releasing a sign of a let-up upon discharging. Given the local environment of vacancy, the local chemical and electronic environment of intercalated Zn 2+ was investigated by Zn K-edge XAFS. Since the surrounding local environment of Zn 2+ is the same during charging and discharging, the K-edge XAFS of Zn is changeless ( Fig.   4e and Supplementary Fig. 26).

Conclusion
In summary, we have quantified 5

Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.