Mechanistic investigation of ion migration in Na₃V₂(PO₄)₂F₃ hybrid-ion batteries

Abstract

The ion-migration mechanism of Na₃V₂(PO₄)₂F₃ is investigated in Na₃V₂(PO₄)₂F₃–Li hybrid-ion batteries for the first time through a combined computational and experimental study. There are two Na sites namely Na(1) and Na(2) in Na₃V₂(PO₄)₂F₃, and the Na ions at Na(2) sites with 0.5 occupation likely extract earlier to form Na₂V₂(PO₄)₂F₃. The structural reorganisation is suggested to make a stable configuration of the remaining ions at the centre of Na(1) sites. After the extraction of the second Na ion, the last ion prefers to change occupation from 1 to 0.5 to occupy two Na(2) sites. The insertion of predominant Li ions also should undergo structural reorganization when the first Li ion inserts into the centre of Na(1) site theoretically forming NaLiV₂(PO₄)₂F₃, and the second ion inserts into two Na(2) sites to form NaLi₂V₂(PO₄)₂F₃. More than a 0.3 Li ion insertion would take place in the applied voltage range by increasing the number of sites occupied rather than occupy the vacancy in triangular prismatic sites. An improved solution-based carbothermal reduction methodology makes Na₃V₂(PO₄)₂F₃ exhibit excellent C-rate and cycling performances, of which the Li-inserted voltage is evaluated by first principles calculations.

---

1. Introduction

Rechargeable lithium-ion batteries (LIBs) have been the most important and widely used energy storage systems for an extensive range of applications, from small electronic devices, such as mobile phones and notebook computers, to the increasing numbers of electric vehicles and large-scale energy storage equipment, as a result of their high stored energy densities, both volumetric and gravimetric.^1–3 However, the safety, energy density, rate capability and service life issues of LIBs limit their further employment.⁴ In addition, the lithium resource in the earth's crust only makes up 0.0065% resulting in a high cost for LIBs, and these would become potential problems in terms of the long-term and large-scale applications of LIBs.⁵ Thus, it is not only desirable but also necessary to develop alternative storage devices, and intense interest in the use of sodium-ion batteries particularly for large-scale energy storage has recently been rekindled,⁵ while one technological crux for the advancement is the improvement of high-performance cathode materials.⁶ Layered NaMO₂ (M = Ni, Mn, Cr, Co, V, etc.) compounds have attracted significant attention and potentially are a promising cathode system for Na-ion batteries due to their high capacity, low material cost and safety.⁷

Meanwhile, the phosphate polyanion framework materials are also being investigated as favourable replacements for sodium metal oxides due to their higher energy storage capacities combined with electrochemical stability,^8,9 such as NaTi₂(PO₄)₃¹⁰ and Na₃M₂(PO4)₃ (M = Ti, Fe, V).^5,11–19 The structural polyanion is constructed by a rigid [PO4]³⁻ network which helps to stabilize the crystal structure of the material, from which the oxygen atoms are fixed in the [PO₄]³⁻ structure to limit the likelihood of oxygen liberation and lead to good thermal stability.²⁰ Moreover, the charge–discharge potentials of the materials would be favoured to rise as a consequence of the inductive effect originated from the incorporation of [PO₄]³⁻ groups.²¹ Since then, NASICON (Na superior conductor)-structured compounds have been explored mostly in hybrid-ion batteries or sodium-ion batteries attributed to the feature of a highly covalent three-dimensional framework that generates large interstitial spaces for ions to diffuse.^22,23 The high redox potentials and good ion transport could contribute to remarkable electrochemical and thermal stability in comparison with sodium metal oxides and are capable to be utilised in the fabrication of high-energy batteries. Furthermore, the working potentials for these fluorophosphates polyanion frameworks could be enhanced when the fluorine participates in the structural construction with transient metal-based phosphate, which should be attributed to a larger ionicity of the M–F (M = transient metal) bond than that of the M–O.^24,25 Consequently, sodium vanadium fluorophosphates, Na₃V₂(PO₄)₂F₃ have received attention because of the promising properties and ease of fabrication.^26–28

Na₃V₂(PO₄)₂F₃ was first prepared by Meins et al. with a tetragonal crystal structure in a space group of P4₂/mnm.²⁹ Gover et al. reported a specific capacity of 120 mA h g⁻¹ at an average discharge voltage of 4.1 V vs. Li⁺/Li for Na₃V₂(PO₄)₂F₃ and they also suggested that the voltage excursion to 5 V vs. Li⁺/Li would result in successful extraction of three Na ions from the fluorophosphates phase although this process was likely accompanied by some concurrent structural degradation.³⁰ Barker et al. described the first details of a hybrid-ion battery concept where a non-lithium containing Na₃V₂(PO₄)₂F₃ cathode was used in conjunction with a conventional graphite anode material.³¹ Jiang et al. prepared Na₃V₂(PO₄)₂F₃ by a simple sol–gel process with a reversible discharge capacity of 117 mA h g⁻¹ which exhibited a good capacity retention.³² Recently, Shakoor et al. have investigated Na₃V₂(PO₄)₂F₃ as a promising cathode material in a sodium-ion battery, which presented an average voltage of ∼3.95 V vs. Na⁺/Na²⁶ and a specific capacity of 120 mA h g⁻¹ at 0.05 C rate.²⁶ According to these few studies available up to now, Na₃V₂(PO₄)₂F₃ is capable to be considered as potential cathode material for the fabrication of high-energy batteries ascribed to the exhibited high discharge voltage and capacity. Referred to the reported concept of hybrid-ion battery,^31,33,34 a Na₃V₂(PO₄)₂F₃–LiPF₆–Li hybrid-ion system composed of traditional lithium-based non-aqueous electrolyte and metallic lithium anode would be favoured for the investigation of its electrochemical properties in order to develop the theoretical research of Na₃V₂(PO₄)₂F₃ and provide directions to construct high-energy secondary batteries.

In this work, Na₃V₂(PO₄)₂F₃ was synthesized by an improved solution-based carbothermal reduction (S-CTR) methodology. Moreover, the mechanism exploration of ion migration in the Na₃V₂(PO₄)₂F₃ hybrid-ion system provides insight to assists in understanding its promising properties with a specific capacity of 147 mA h g⁻¹ and an average discharge voltage around 4 V, which were elucidated by first principles calculations.

2. Methods

Stoichiometric amounts of Na₂CO₃, NH₄H₂PO₄, NaF and V₂O₅ were adequately dissolved into 50 mL distilled water and dried under 50 °C by forced-air drying. Acetylene black powders were then mixed in the above mentioned precursor and ground to a uniformly particle distribution at 5 wt% to the total mass of the reagents where the latter is the conductive agent. All the reagents used here are analytical grade and used without any purification. Afterwards, the ground powders were preheated at 350 °C in flow argon for 4 h, and reground when it cooled to room temperature. Then, the obtained powders were re-fired at 650 °C in argon atmosphere for 8 h to generate Na₃V₂(PO₄)₂F₃–C composite materials.

The crystallographic structure of the as prepared material was studied by X-ray powder diffraction (XRD) using a Bruker D8 diffractometer with monochromatic Cu Kα radiation (λ = 1.5406 Å), and the diffraction data was recorded in the 2θ range of 10–60° with a scan rate of 8° per min. The infrared (IR) spectra was obtained using an FT-IR Spectrometer (Jasco, FT/IR-4100, Japan) under transmission mode based on the KBr pellet method in the range of 500–2000 cm⁻¹. The particle morphology of the composite was investigated by a FEI Quanta 200 scanning electron microscopy (SEM) and JEOL 2010F transmission electron microscopy (TEM). The thermogravimetric analysis (TG) of the samples was carried on a Diamond TG thermo-analyzer.

The cathode electrode was fabricated with the active material, acetylene black, and binder (polyvinylidene fluoride, PVDF) in a weight ratio of 8 : 1 : 1 by using NMP as solvent and an aluminium foil as current collector (∼4.5 mg cm⁻²), followed by drying in vacuum at 110 °C for 24 h. The R2016 coin cell was assembled in an argon-filled glove box using metallic lithium as the anode with a Celgard 2500 membrane as separator. The electrolyte was 1 M LiPF₆ dissolved in a mixture of ethylene carbonate (EC), dimethyl carbonate (DMC), diethyl carbonate (DEC) (v/v/v, 1/1/1). Cyclic voltammetry (CV) and galvanostatic charge–discharge cycling tests via CC–CV (constant current–constant voltage) protocol were carried out in a setting voltage range by using an electrochemical workstation (CHI660C) and a CT2001A LAND battery tester, respectively. Electrochemical impedance spectroscopy (EIS) was studied using a Modulab (Solartron Analytical) with the amplitude of 5 mV in the frequency range from 1 MHz to 10 mHz. All electrochemical tests were carried out at room temperature (22 °C).

All calculations on Na₃V₂(PO₄)₂F₃ were performed with the spin-polarized generalized gradient approximation (GGA) using the Perdew–Burke–Ernzerhof (PBE) exchange–correlation parameterization to density functional theory (DFT) using CASTEP program. A plane-wave basis with a kinetic energy cutoff of 330 eV was used, and size of standard grid was 1.5. BFGS optimization method was used and the geometry optimization parameters of total energy convergence, max ionic force, max ionic displacement and max stress component tolerance were 0.2 × 10⁻⁴ eV per atom, 0.5 × 10⁻¹ eV Å⁻¹, 0.2 × 10⁻² Å and 0.1 GPa respectively. The electronic convergence thresholds parameters of total energy were 0.2 × 10⁻⁵ eV and 0.5638 × 10⁻⁶ eV.

3. Results and discussion

Fig. 1 shows the XRD patterns of the as-prepared material and the fitted Rietveld refinement patterns with the corresponding Bragg positions. All the diffraction peaks can be indexed to a tetragonal structure with a space group of P4₂/mnm, which are consistent with previous reports.^28–30,35 The refined unit cell lattice parameters are a = b = 9.05 Å, c = 10.679 Å, V = 874.64 ų for Na₃V₂(PO₄)₂F₃ and the observed crystallographic planes (hkl) are suggested to be denoted when the simulated results of DFT calculation on Na₃V₂(PO₄)₂F₃ model have been referred. Additionally there are no observed traces of carbon in the XRD patterns which could indicate that the residual carbon in the as-prepared material is in an amorphous state.^32,33

Fig. 1 XRD patterns of Na₃V₂(PO₄)₂F₃.

The crystal structure of Na₃V₂(PO₄)₂F₃ has been characterized with a three-dimensional (3D) NASICON framework as shown in Fig. 2(a), which are the graphical representations of the fluorophosphates structure. This framework structure can be best described in terms of [V₂O₈F₃] bi-octahedral and [PO₄] tetrahedral units. The [V₂O₈F₃] bi-octahedra is bridged by one fluorine atom with two [VO₄F₂] octahedra united, and the oxygen atoms are all interconnected through the [PO₄] units. This arrangement results in the formation of channels along x and y directions with sodium ions statistically distributed in the resultant network of the NASICON structure, from which the presence of channels in this 3D NASICON-type structure is expected to be capable to facilitate ion diffusion.³³ As suggested by Shakoor et al.,²⁶ there are two kinds of sites, namely a triangular prismatic site surrounded by two F ions and four O ions, and an augmented triangular prismatic site attached to the F apex-square pyramid. Furthermore, Shakoor et al.²⁶ have found that the calculated site energy of the augmented triangular prismatic site was 56 meV lower than that of a triangular prismatic site in the desodiated phase, NaV₂(PO₄)₂F₃, and three augmented triangular prismatic sites are occupied out of 8 available Na sites according to the DFT results. However, the refined Na configuration among four augmented triangular prismatic sites is that two sites are fully occupied namely Na(1) sites and two are half occupied namely Na(2) sites by Na ions in Na₃V₂(PO₄)₂F₃ as presented in Fig. 2(b). This is because when the Na ions in Na(1) sites have slightly shifted off the centers of augmented prismatic sites attributed to the Na–Na repulsion, the two neighbouring Na(2) sites cannot be simultaneously occupied due to the large electrostatic repulsions not only from the Na ions in Na(2) sites but also from the Na ions in Na(1) sites, which could repulse the ion in Na(2) sites to shift more to the opposite. Therefore, the two kinds of tunnelling sites of Na(1) and Na(2) in Na₃V₂(PO₄)₂F₃ could accommodate up to three alkali ions which would be responsible for the electrochemical performances and as a consequence, the mechanism of ion migration in a hybrid-ion system would be considered to be vital and interesting to investigate the promising properties of Na₃V₂(PO₄)₂F₃ cathode material.

Fig. 2 (a) Scheme representation of the structure of Na₃V₂(PO₄)₂F₃. (b) The stable configuration of Na ions in Na₃V₂(PO₄)₂F₃ projected along z axis.

Fig. 3 shows the SEM image of as-prepared Na₃V₂(PO₄)₂F₃ material and these particles have presented irregular shapes with size distribution less than 1 μm, which may be attributed to the mechanochemical activation before sintering,¹⁸ while to the best of our knowledge, there are very few literatures reports that have published the morphology of Na₃V₂(PO₄)₂F₃. Moreover, some “fluffy” structures exist in the dark region which can be identified as the residual carbon in the sample. For future investigation of the particle surface structure, TEM was utilised and the dark particles shown in Fig. 4(a and b) are embedded in a light grey network of carbon. Observed from the TEM image in Fig. 4(a), layers of carbon seem to cover the particles asymmetrically and the coated carbon in Fig. 4(b) also seems not to be uniform, which could be ascribed to the utilised carbon source of water-fast acetylene black and inadequate grinding. Meanwhile, the diffraction rings in Fig. 4(c) illustrate an amorphous characteristic of the coated carbon consistent with the conclusion from XRD analysis, and the rings in Fig. 4(d) represent crystalline particles. In addition, TG test was employed to estimate the carbon content in the as-prepared Na₃V₂(PO₄)₂F₃–C composite, and a content value of 9.2% could be obtained. As known residual carbon in the sample would be of great significance to improve the electronic conductivity of the particles, which is beneficial for the electrochemical properties of Na₃V₂(PO₄)₂F₃ electrode material and to some extent, is able to prevent the growth of particles in the synthetic process at high temperatures.

Fig. 3 SEM image of as-prepared Na₃V₂(PO₄)₂F₃.

Fig. 4 (a, b) TEM images of Na₃V₂(PO₄)₂F₃ and (c, d) the corresponding diffraction rings.

The CV curve of the first cycle in a voltage range of 2.5 to 4.6 V vs. Li⁺/Li for the Na₃V₂(PO₄)₂F₃–C composite at a scan rate of 0.1 mV s⁻¹ is displayed in Fig. 5. Two couples of sharp redox peaks can be observed, of which the two oxidation peaks located at 3.98 and 4.34 V signify the deinsertion of sodium ions and the reduction peaks at 3.62 and 4.11 V would contribute to the insertion of Na⁺–Li⁺ hybrid ions. When fully charged to 4.6 V vs. Li⁺/Li, a cathode composition approximating to NaV₂(PO₄)₂F₃ is produced, a condition in which all the vanadium has been oxidized to V⁴⁺.³⁰ Reasonably, these redox peaks associated with V⁴⁺/V³⁺ redox couple in this compound should correspond to the electrochemical behaviours of two alkali ions per Na₃V₂(PO₄)₂F₃ unit. Notably, the electrochemical activity of Na_xV₂(PO₄)₂F₃ at 1 ≤ x ≤ 3 has been demonstrated to be mainly attributed to V⁴⁺/V³⁺ redox reaction according to the results of net spin moment integrated as a function of the distance from the ion core.²⁶

Fig. 5 CV curve in a voltage range of 2.5 to 4.6 V vs. Li⁺/Li for the Na₃V₂(PO₄)₂F₃–C composite at a scan rate of 0.1 mV s⁻¹.

To explore the storage capacity of Na₃V₂(PO₄)₂F₃ hybrid-ion battery, galvanostatic charge–discharge at different current densities in a voltage range of 1.6–4.6 V vs. Li⁺/Li has been carried out. As shown in Fig. 6(a), the hybrid-ion batteries are capable of delivering initial discharge capacities of 146.5, 125.3, 121.9, 116.5 and 111 mA h g⁻¹ at 0.09, 0.18, 0.45, 0.91 and 1.82 C rates, respectively. Also, the profiles have presented two discharge plateaus of about 3.8 and 4.2 V corresponding to the two couples of peaks in CV curves. The average voltage of nearly 4 V could be thought to be one of the highest among cathode materials with the same redox coupe V⁴⁺/V³⁺. With V⁴⁺/V³⁺ redox couple in lithium cells, the average voltage of NASICON-type Li_2−xNaV₂(PO₄)₃ is about 3.8 V¹⁸ and for vanadium oxides such as V₂O₅ and LiV₃O₈ (vs. Li⁺/Li), where it ranges from 2.7 V to 3.5 V.³⁶Fig. 6(b) shows that the capacity can retain 107 mA h g⁻¹ at 1.82 C with a high coulombic efficiency of 98.2% for the 101th cycle. The excellent C-rate and cycling performances of Na₃V₂(PO₄)₂F₃ mainly ascribe to the small volume variation (1.79%) upon cycling²⁶ and the predominant Li⁺ ions migration substituting Na⁺ ions which has been confirmed by Inductively Coupled Plasma (ICP) analysis.³² While the fluctuations of the coulombic efficiencies for the preliminary cycles are suggested to be attributed to an activation process for the electrodes during the electrochemical reactions, the degradation of the current efficiency and cyclic capacity could potentially be attributed to the failure of SEI (solid electrolyte interface) layer.^37,38

Fig. 6 (a) Charge–discharge profiles for the Na₃V₂(PO₄)₂F₃–C sample at different current densities in a voltage range of 1.6–4.6 V vs. Li⁺/Li. (b) The corresponding rate and cycling performances.

First principles calculations were performed to investigate the average discharge voltage (V) of NaLi_xV₂(PO₄)₂F₃ in a lithium ion battery at 1 ≤ x ≤ 2 assuming that the inserted ions were all Li⁺ ions. The average value can be simply determined by adopting the eqn (1) according to the reported theories:^25,39,40

V = −[E(Na₃V₂(PO₄)₂F₃) − E(NaV₂(PO₄)₂F₃) − 2E(Li)]/2F (1)

where E(Li) is the energy of elemental lithium in a bcc crystal structure and F is the Faraday constant.^32,33 The calculated average voltage is around 4.11 V vs. Li⁺/Li between x = 2 and x = 1 and is comparable to the experimental results. Therefore, it is suggested that Na₃V₂(PO₄)₂F₃ is capable to be used as a promising cathode to fabricate high-energy battery (both high capacity and high voltage).

To further explore the ion migration mechanism of Na₃V₂(PO₄)₂F₃ in the hybrid-ion battery, the electrochemical voltage-composition curve for the cell at a current density of 0.09 C in the voltage range of 1.6–4.6 V vs. Li⁺/Li during the first cycle is depicted in Fig. 7. Here the first calculated cycle in the figure is composed by a first discharging curve and a following charging profile. Two distinct voltage plateaus are related to the extraction/insertion of two alkali ions in charge–discharge processes because of the existence of two different environments for ions. Although three Na ions are present at crystallographically equivalent sites in Na₃V₂(PO₄)₂F₃ (Fig. 2b), the Na ions at Na(2) sites are less stable than those at Na(1) sites because Na ions at Na(2) sites are far shifted from the stable position.²⁶ Therefore, the alkali ions at Na(2) sites would have higher chemical potential than those at Na(1) sites, and thus, the ions at Na(2) sites would be extracted at an earlier state of charge and insert at later stage of discharge.²⁶ In the charging stage as illustrated in Fig. 8, the extraction of Na⁺ ions mainly begins from 3.7 V vs. Li⁺/Li and the extraction of the second ion could not be completed until 4.6 V as suggested by Gover et al.³⁰ While the charging section below 3.7 V is equal to the extraction of 0.3 Na⁺ ion which activates the electrode and overcomes the energy consumption originated from internal impedance of the battery. After the first ion extraction from Na(2) sites, it is expected that leaving Na ions will be reorganized to a stable configuration in Na₂V₂(PO₄)₂F₃ (shown in Fig. 8a), due to the short Na–Na distances between the ions occupying at the centres of Na(1) sites. Thus, the second Na⁺ ion would be extracted at a higher potential, leading to a second plateau observed at a higher voltage. The extraction of the second ion might have two kinds of sites, one of which is that each ion at Na(1) site will change the ion occupation from 1 to 0.5 producing a configuration as depicted in Fig. 8(b). The other site is that one Na ion at Na(1) sites per unit with 1 occupation would be completely extracted while another one is left to produce an unstable arrangement in Fig. 8(c). It is speculated that only one ion with 1 occupation in NaV₂(PO₄)₂F₃ is not stable and easy to reorganize, because of the strongly vacant environments surrounding the Na sites.

Fig. 7 The electrochemical voltage-composition curve for the cell of Na₃V₂(PO₄)F₃/Li at a constant current density of 0.09 C in the voltage range of 1.6–4.6 V vs. Li⁺/Li during the first cycle.

Fig. 8 Schematic representation of the refined structures of (a) Na₂V₂(PO₄)F₃, (b) NaV₂(PO₄)F₃ with 0.5 occupation Na ion, (c) NaV₂(PO₄)F₃ with 1 occupation Na ion during Na-ion extraction, and (d) NaLiV₂(PO₄)F₃, (e) NaLi₂V₂(PO₄)F₃, (f) NaLi₂.₃V₂(PO₄)F₃ in Li-ion insertion.

For the ion insertion procedure, the migrated ions should be predominant Li⁺ ions as we previously reported,¹⁹ on account of the enrichment of Li⁺ resource and the irreversibility for Na⁺ ions such as the larger ionic radius. Similarly, the insertion prefers to be divided into two steps with two discharge plateaus as exhibited in Fig. 7. Assuming the intercalated ions are pure Li⁺ ions, when the first one inserts into a unit, NaV₂(PO₄)₂F₃, the Na and Li ions would have 1 occupation at each Na(1) site after structural reorganization in the intermediate phase, NaLiV₂(PO₄)₂F₃, as shown in Fig. 8(d). Straight after the insertion and stabilization of the first ion corresponding to a high voltage plateau, the lower discharge plateau should be responsible for the intercalation of the second Li⁺ ion to make it at two Na(2) sites with an ion occupation of 0.5. Fig. 8(e) presents the equivalently formed phase, NaLi₂V₂(PO₄)₂F₃. It is factual that the Li⁺ ions could continue to insert into NaLi₂V₂(PO₄)₂F₃ if the discharge cut-off voltage has passed ∼2.2 V for which a potential corresponds to the completed insertion of two Li⁺ ions. Referring to the results presented in Fig. 7, it is also suggested that the excess inserted ions would exist in NaLi_2.3V₂(PO₄)₂F₃ by increasing the number of site occupation rather than occupy the vacancy in triangular prismatic sites, as demonstrated in Fig. 8(f). This is because the occupation in vacancy needs more energy to satisfy the site energy and get over the strong Na–Na or Li–Li repulsion.²⁶ A theoretical value of 159 mA h g⁻¹ for NaLi_2.3V₂(PO₄)₂F₃ might be generated provided that the inserted 2.3 ions in NaV₂(PO₄)₂F₃ are total Li, by employing Faraday's Law (C = 26.8n/M A h g⁻¹, where C is the theoretical capacity of the active material, n is the number of electrons in reaction and M is the relative molecular mass). However, the large capacity seems difficult to be achieved in our experiments as the insertion mixed with heavier Na⁺ ions is a possibly main reason in addition to other irreversible factors.

The EIS experiment was performed on the battery charged to 3.2 V vs. Li⁺/Li after 5 charge–discharge cycles, which is used to investigate the electrochemical kinetics of Na₃V₂(PO₄)₂F₃ in a hybrid-ion system. The corresponding Nyquist plots are displayed in Fig. 9(a), from which the small intercept at the Z_re axis signifies the internal resistance of the battery, and the semi-circle in the high frequency region is related to the resistance of SEI film while in the middle frequency region is due to the charge transfer resistance.³² While for the low frequency region, this sloping line could be attributed to the diffusion of ions into the electrode bulk, namely Warburg impedance, where the ions in the 5th cycle would be hybrid with Na⁺ and Li⁺ ions. Furthermore, the diffusion coefficient of ion, D, can be obtained from an analysis of the Warburg impendence, which could be expressed in eqn (2):⁴¹

D = 0.5 R²T²/S²n⁴F⁴C²σ² (2)

where D is the diffusion constant, R the gas constant, T the absolute temperature (performed at room temperature), S the effective contact area between electrode and electrolyte (S = 0.79 cm²), n the number of electrons in reaction when charged to 3.2 V, F the Faraday constant and C the concentration of alkali ions in the cathode calculated based on the crystallographic cell parameter of Na₃V₂(PO₄)₂F₃. While, σ is the Warburg factor which obeys the following relationship:³⁶

Z_re = R + σω^−1/2 (3)

where ω is the angular frequency and Z_re is the real impendence. σ could be thus obtained from the liner relationship of the real impedance as a function of the inverse square root of angular frequency in the Warburg region, as shown in Fig. 9(b). Thereby, the chemical diffusion coefficient (D) is calculated as 1.26 × 10⁻¹⁰ cm² s⁻¹, of which the diffused value is comparable to the reported literatures for Na₃V₂(PO₄)₂F₃ in lithium-ion battery (0.27–7.6 × 10⁻¹⁰ cm² s⁻¹).^42,43 Herein, the predominant Li⁺ ions migration during the cycle would be of great importance to the result because the smaller ionic radius and mass for Li⁺ ions could allow them to be facilely transported with higher mobility. Moreover, the magnitude of the D in this work for Na₃V₂(PO₄)₂F₃ hybrid-ion battery is much higher than that in LiFePO₄ measured by Prosini et al. (10⁻¹⁶ to 10⁻¹⁴ cm² s⁻¹)⁴⁴ and Franger et al. (10⁻¹⁴ to 10⁻¹³ cm² s⁻¹),⁴⁵ which should be attributed to the NASICON-type structure allowing ions transport in a 3D framework, indicating that Na₃V₂(PO₄)₂F₃ is a promising cathode superior to LiFePO₄ in achieving high rate capability.⁴⁶

Fig. 9 (a) Nyquist plots of the hybrid-ion battery charged to 3.2 V vs. Li⁺/Li for the 5th cycle. (b) Corresponding relationship of the real impedance part Z_re as a function of the inverse square root of angular frequency ω^−1/2 in the Warburg region.

4. Conclusion

Na₃V₂(PO₄)₂F₃ as a promising cathode material was prepared by an improved S-CTR method to fabricate a hybrid-ion battery in conjunction with lithium-based electrolyte and anode. The combined first principles calculations and experimental study were used to elucidate the ion-migration mechanism and the electrochemical behaviour of Na₃V₂(PO₄)₂F₃ in Na₃V₂(PO₄)₂F₃–Li hybrid-ion batteries. It was reasonable that the reversible insertion/extraction of ions into/from Na₃V₂(PO₄)₂F₃ occurred via phase reaction was associated with the two kinds of Na sites namely Na(1) and Na(2) and the structural reorganization. Na₃V₂(PO₄)₂F₃–C composite synthesized by the facile method could obtain a specific capacity of 147 mA h g⁻¹ with excellent C-rate and cycling performances. Moreover, the high diffused coefficient of 1.26 × 10⁻¹⁰ cm² s⁻¹ was found to improve to achieve the high-rate capability. The high discharge plateau of nearly 4 V vs. Li⁺/Li which has been evaluated by the computational calculations, demonstrated that it was potential to be used as cathode material for the fabrication of high-energy batteries.

Acknowledgements

Financial supports from the NNSF of China (No. 21473258), Program for the New Century Excellent Talents in University (No. NCET-11-0513), Funds for Distinguished Young Scientists of Hunan Province, China (No. 13JJ1004), Fundamental Research Funds for Central South University (No. 2013zzts159, 2012zzts059) and Innovation and Entrepreneurship Training Program of China for University Students are greatly appreciated.

References

1. M. Armand and J. M. Tarascon, Nature, 2008, 451, 652.
2. J. B. Goodenough and Y. Kim, Chem. Mater., 2009, 22, 587.
3. C.-X. Zu and H. Li, Energy Environ. Sci., 2011, 4, 2614.
4. Z. Chen, C. Dai, G. Wu, M. Nelson, X. Hu, R. Zhang, J. Liu and J. Xia, Electrochim. Acta, 2010, 55, 8595.
5. Z. Jian, W. Han, X. Lu, H. Yang, Y.-S. Hu, J. Zhou, Z. Zhou, J. Li, W. Chen, D. Chen and L. Chen, Adv. Energy Mater., 2013, 3, 156.
6. N.-S. Choi, Z. Chen, S. A. Freunberger, X. Ji, Y.-K. Sun, K. Amine, G. Yushin, L. F. Nazar, J. Cho and P. G. Bruce, Angew. Chem., Int. Ed., 2012, 51, 9994.
7. V. Palomares, M. Casas-Cabanas, E. Castillo-Martinez, M. H. Han and T. Rojo, Energy Environ. Sci., 2013, 6, 2312.
8. N. Yabuuchi, M. Kajiyama, J. Iwatate, H. Nishikawa, S. Hitomi, R. Okuyama, R. Usui, Y. Yamada and S. Komaba, Nat. Mater., 2012, 11, 512.
9. B. L. Ellis, W. R. M. Makahnouk, Y. Makimura, K. Toghill and L. F. Nazar, Nat. Mater., 2007, 6, 749.
10. S. I. Park, I. Gocheva, S. Okada and J.-i. Yamaki, J. Electrochem. Soc., 2011, 158, A1067.
11. H. Kabbour, D. Coillot, M. Colmont, C. Masquelier and O. Mentre, J. Am. Chem. Soc., 2011, 133, 11900.
12. J. Kang, S. Baek, V. Mathew, J. Gim, J. Song, H. Park, E. Chae, A. K. Rai and J. Kim, J. Mater. Chem., 2012, 22, 20857.
13. K. Saravanan, C. W. Mason, A. Rudola, K. H. Wong and P. Balaya, Adv. Energy Mater., 2013, 3, 444.
14. W. Song, Z. P. Wu, J. Chen, K. Huangfu, X. Wang, Y. Huang and X. Ji, Phys. Chem. Chem. Phys., 2014, 16, 17681.
15. W. Song, X. Ji, Y. Yao, H. Zhu, Q. Chen, Q. Sun and C. E. Banks, Phys. Chem. Chem. Phys., 2014, 16, 3055.
16. W. Song, X. Ji, Z. Wu, Y. Zhu, Y. Yao, K. Huangfu, Q. Chen and C. E. Banks, ChemElectroChem, 2014, 1, 871.
17. W. Song, X. Ji, Z. Wu, Y. Zhu, Y. Yang, J. Chen, M. Jing, F. Li and C. E. Banks, J. Mater. Chem. A, 2014, 2, 5358.
18. K. Du, H. Guo, G. Hu, Z. Peng and Y. Cao, J. Power Sources, 2013, 223, 284.
19. W. Song, X. Ji, C. Pan, Y. Zhu, Q. Chen and C. E. Banks, Phys. Chem. Chem. Phys., 2013, 15, 14357.
20. T. Jiang, Y. J. Wei, W. C. Pan, Z. Li, X. Ming, G. Chen and C. Z. Wang, J. Alloys Compd., 2009, 488, L26.
21. C. Masquelier, A. K. Padhi, K. S. Nanjundaswamy and J. B. Goodenough, J. Solid State Chem., 1998, 135, 228.
22. J. Gopalakrishnan and K. K. Rangan, Chem. Mater., 1992, 4, 745.
23. B. L. Cushing and J. B. Goodenough, J. Solid State Chem., 2001, 162, 176.
24. N. Recham, J. N. Chotard, J. C. Jumas, L. Laffont, M. Armand and J. M. Tarascon, Chem. Mater., 2010, 22, 1142.
25. W. Song, X. Ji, Z. Wu, Y. Zhu, Y. Yao, K. Huangfu, Q. Chen and C. E. Banks, J. Mater. Chem. A, 2014, 2, 2571.
26. R. A. Shakoor, D.-H. Seo, H. Kim, Y.-U. Park, J. Kim, S.-W. Kim, H. Gwon, S. Lee and K. Kang, J. Mater. Chem., 2012, 22, 20535.
27. W. Song, Z. Wu, J. Chen, Q. Lan, Y. Zhu, Y. Yang, C. Pan, H. Hou, M. Jing and X. Ji, Electrochim. Acta, 2014, 146, 142.
28. W. Song, Z. Wu, J. Chen, Y. Zhu, H. Hou, Q. Lan and X. Ji, Langmuir, 2014, 30, 12438.
29. J. M. Le Meins, M. P. Crosnier-Lopez, A. Hemon-Ribaud and G. Courbion, J. Solid State Chem., 1999, 148, 260.
30. R. K. B. Gover, A. Bryan, P. Burns and J. Barker, Solid State Ionics, 2006, 177, 1495.
31. J. Barker, R. K. B. Gover, P. Burns and A. J. Bryan, Electrochem. Solid-State Lett., 2006, 9, A190.
32. T. Jiang, G. Chen, A. Li, C. Z. Wang and Y. J. Wei, J. Alloys Compd., 2009, 478, 604.
33. W. Song and S. Liu, Solid State Sci., 2013, 15, 1.
34. W. Song, X. Ji, Z. Wu, Y. Zhu, F. Li, Y. Yao and C. E. Banks, RSC Adv., 2014, 4, 11375.
35. W. Song, X. Ji, Z. Wu, Y. Yang, Z. Zhou, F. Li, Q. Chen and C. E. Banks, J. Power Sources, 2014, 256, 258.
36. A. K. Padhi, K. S. Nanjundaswamy and J. B. Goodenough, J. Electrochem. Soc., 1997, 144, 1188.
37. M. Winter, Zeitschrift für Physikalische Chemie International journal of research in physical chemistry and chemical physics, 2009, vol. 223, p. 1395.
38. M. Nie, D. Chalasani, D. P. Abraham, Y. Chen, A. Bose and B. L. Lucht, J. Phys. Chem. C, 2013, 117, 1257.
39. M. Ramzan, S. Lebègue and R. Ahuja, Appl. Phys. Lett., 2009, 94, 151904.
40. G. Ceder, M. K. Aydinol and A. F. Kohan, Comput. Mater. Sci., 1997, 8, 161.
41. X. Liao, Z. Ma, Q. Gong, Y. He, L. Pei and L. Zeng, Electrochem. Commun., 2008, 10, 691.
42. J. Barker, R. K. B. Gover, P. Burns and A. J. Bryan, J. Electrochem. Soc., 2007, 154, A882.
43. M. Y. Saidi, J. Barker, H. Huang, J. L. Swoyer and G. Adamson, J. Power Sources, 2003, 119, 266.
44. P. P. Prosini, M. Lisi, D. Zane and M. Pasquali, Solid State Ionics, 2002, 148, 45.
45. S. Franger, F. Le Cras, C. Bourbon and H. Rouault, Electrochem. Solid-State Lett., 2002, 5, A231.
46. X. H. Rui, N. Ding, J. Liu, C. Li and C. H. Chen, Electrochim. Acta, 2010, 55, 2384.

---