Journal of Solid State Electrochemistry https://doi.org/10.1007/s10008-017-3850-6
Electrochemical properties and first-principle analysis of Nax[MyMn1−y]O2 (M = Fe, Ni) cathode Debasis Nayak 1 & Tanmay Sarkar 2,3 & N. Vijay Prakash Chaudhary 4 & Mridula Dixit Bharadwaj 2 & Sudipto Ghosh 1 & Venimadhav Adyam 4 Received: 2 June 2017 / Revised: 29 October 2017 / Accepted: 27 November 2017 # Springer-Verlag GmbH Germany, part of Springer Nature 2017
Abstract Sodium-ion batteries are the commercially and environmentally viable next-generation candidates for automobiles. Structural and electrochemical aspects are greater concerns towards the development of a stable cathode material. Selecting transition metals and their composition greatly influences charge order, superstructures, and different voltage plateaus. This, in turn, influences transport properties and cyclic performance. This article aims to study the electrochemical performance, diffusivity, and structural stability of Nax[MyMn1−y]O2 (M = Fe, Ni) as cathode. Both experimental and DFT-based calculations apprehend the voltage plateaus due to redox reactions. The rate of cycling and the initial structure also influence the cycle life. The diffusion coefficient of P2-type Na0.67Fe0.5Mn0.5O2 for Mn3+/4+ redox reactions is more than that of the O3-type NaFe0.5Mn0.5O2 while it is less for Fe3+/4+ redox reactions, because of structural transition. The diffusion coefficient of NaNi0.5Mn0.5O2 is less for Ni2+/4+ redox reaction and is up to the order of 10−11 cm2 s−1.
Introduction Recently, secondary sodium-ion batteries (SIBs) have drawn the attention of researchers due to lower cost of sodium as compared to that of lithium. Due to their cost-effectiveness, SIBs are the potential alternative to lithium-ion batteries (LIBs) for a broad range of applications. Commercial production of SIBs has also begun . Sodium has a higher molecular weight (about three times) and bigger size compared to lithium. Because of this, insertion–extraction of sodium ion
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10008-017-3850-6) contains supplementary material, which is available to authorized users. * Debasis Nayak [email protected]
Department of Metallurgical and Materials Engineering, Indian Institute of Technology, Kharagpur 721302, India
Center for Study of Science, Technology and Policy, Bangalore 560094, India
Central Electro Chemical Research Institute, Chennai 630003, India
Cryogenic Engineering Centre, Indian Institute of Technology, Kharagpur 721302, India
into both cathode and anode is relatively difficult. Attempts have been made to address the difficulty of insertion–extraction at the anode by using binder-free and free-standing carbon nanofibers synthesized by electrospun technique . Also, it has been suggested that the quasi-metallic property of sodium ion is not manifested in the presence of closed nanopores of hard carbon . Although the corrosive behavior of carbon due to insufficient passivation has led researchers to explore sodium metal as anode material , the attempt did not succeed due to the problem of dendrite formation [4, 5] and carbon-based anodes are in use as anode materials for SIBs [6–8]. A number of studies have been carried out to search appropriate cathode materials for SIBs [5, 9, 10]. The search has led researchers to study the electrochemical performance of layered sodium transition metal oxides NaxMO2 (M = Mn, Co, Cr, Fe, and V) [11–14] and Nax[M1xM2(1−x)]O2 (M1 and M2 are different transition metals) [10, 15–17]. Transition metal oxide-based structures remain stable over a number of charge– discharge cycles. In addition, transition metals’ being abundant on earth makes these cathode materials cost-effective. Layered sodium transition metal oxides can be classified into O3, P2, and P3 types . O3 refers to three layered structures having sodium in octahedral sites,  and P2 (two-layered) and P3(three-layered) refer to structures having sodium in the prismatic sites. It has been seen that for the
J Solid State Electrochem
layered sodium transition metal oxides, the P2 type usually exhibits more capacity than the O3-type structures . The five 3d bands of transition metal ions are split into the three low-energy bands (t2g) and two high-energy bands (eg) under the influence of crystal field. In the case of Mn-based oxides, it is well-known that Mn 3+ has four up-spin electrons ((t2g)3(eg)1) that show the Jahn–Teller effect during the sodium ion insertion, thereby transforming from P2 to O2, OP4, or between P3 and O3 polytypes [20, 21]. Thus, other metallic ions, like Fe, Co, and Ni, are introduced to alleviate this problem. The change in the oxidation state of these elements completely or partially suppresses the Jahn–Teller distortion.  In situ XRD study of Na2/3[Fe1/2Mn1/2]O2 reveals that during insertion and extraction of sodium, the material undergoes P2–OP4 reversible structural transitions . OP4 is an alternate stacking of octahedral (O2) and prismatic (P2) layers along the c-axis occurring due to partial layer shearing. DFT-based calculation also suggests the transition of oxygen framework from the P2 to the O2 phase is energetically favorable in P2-type Nax[Ni1/3Mn2/3]O2 upon discharging . Various studies have been conducted to synthesize and characterize electrochemical properties of different P2-type layered sodium transition metal oxides. Several combinations of transition metals have been taken into consideration [16, 22, 25–27]. The proper stoichiometric combination of sodium transition metal oxides can lead to achieving stable structure over a number of cycles  and also can provide higher diffusion coefficient (DNa) [18, 28]. Lee et al.  showed that layered P2 Nax[Ni1/3Mn2/3]O2 exhibits higher diffusion of Na ion than O3-structured Li-ion battery, provided transformation of the oxygen framework from the P2 to the O2 phase is checked. The diffusion coefficient (DNa) of layered P2 Na x [Ni 1/3 Mn 2/3 ]O 2 is up to the order of 10 −9 to 10−10 cm2 s−1. Similarly P2-type NaCoO2 thin film shows higher DNa value of Na+ ion (≈ 0.5–1.5 × 10−10 cm2 s−1)  as compared to the DLi value of Li+ ion (1 × 10−10 cm2 s−1) in layered thin-film O3-type LiCoO2 . Despite showing higher diffusion coefficient and coulombic efficiency, NaCoO2 has a disadvantage of lower operating potential (up to 3.5 V) and low specific capacity even at a slow rate of discharge (70.4 mAh g −1 , 0.08-C rate) [29, 31]. Na[Ni1/3Fe1/3Mn1/3]O2 as a cathode material maintains its layered structure and crystallinity over 150 cycles opposite to carbon as an anode. This also yields a discharge capacity of 100 mAh g−1 with a 0.5-C rate . Huang et al.  found that Na3FePO4CO3 shows good crystalline structure even at a current density of 200 mA g−1, exhibiting a specific discharge capacity of 58 mAh g−1. In this present work, we report the electrochemical performance of NaFe 0. 5 Mn 0. 5 O 2 , Na 0. 67 Fe 0.5 Mn 0.5 O 2 and NaNi0.5Mn0.5O2 as cathode materials. Density functional theory-based computations were carried out for explaining
the effect of altered sodium content and the presence of different transition metals in the Nax[M1xM2(1−x)]O2 framework on electrochemical performance.
Experimental Material synthesis All the three cathode materials were prepared using solid-state methods. The methods are as follows. 1. NaFe0.5Mn0.5O2: Stoichiometric amounts of Na2CO3 (> 99%, Sigma-Aldrich), Fe2O3 (> 99.98%, Sigma-Aldrich), and Mn2O3 (> 99%, Sigma-Aldrich) powders were mixed thoroughly using a mortar and pestle for ~ 2 h. Subsequently, the mixture was pressed into pellets, and the pellets were annealed at 700 °C and under the normal atmospheric condition for 36 h. The chemical reaction is Na2CO3 + 1/2Fe2O3 + 1/2Mn2O3 = 2NaFe0.5Mn0.5O2 + CO2. 2. Na0.67Fe0.5Mn0.5O2: Stoichiometric amounts of highpurity Na2CO3, Fe2O3, and Mn2O3 were mixed thoroughly using a mortar and pestle for ~ 2 h. The mixture was dried in an over overnight, and the dried mixture was ground using a mortar and pestle. Finally, the powder mixture was pressed into pellets, and the pellets were annealed at 900 °C and under the normal atmospheric condition for 12 h. The chemical reaction is 2/3Na2CO3 + 1/2Fe2O3 + 1/2Mn2O3 = 2Na0.67Fe0.5Mn0.5O2 + 2/3CO2. 3. NaNi0.5Mn0.5O2: Stoichiometric amounts of Na2CO3, Ni(OH)2, and Mn2O3 were wet ball-milled for 24 h using acetone as the wet medium. After the milling, the mixture was dried, and the dried mixture was ground using a mortar and pestle. Subsequently, the powder mixture was pressed into pellets, and the pellets were annealed at 900 °C and under the normal atmospheric condition for 24 h. Finally, the pellets were rapidly cooled to room temperature by placing the pellets on a copper plate. The chemical reaction is Na 2 CO 3 + Ni(OH) 2 + 1/ 2Mn2O3 = 2NaNi0.5Mn0.5O2 + CO2 + H2O.
Sample characterization Structural characterization of the samples was performed with X-ray diffraction (XRD, Bruker D8 Advance X-ray diffractometer, Cu Kα) at room temperature. The surface morphology of the films was examined using a field emission scanning electron microscope (FE-SEM, ZEISS EVO 60) and an inlens detector for secondary electrons, coupled with a XMAX EDX probe (Oxford Instruments) for energydispersive spectroscopy (EDS) and chemical mapping.
J Solid State Electrochem
Electrochemistry Cathodes consisting of active material, acetylene black, and polyvinylidene fluoride in the weight ratio of 8:1:1 were prepared by preparing a slurry using N-methyl-2-pyrrolidone followed by coating the slurry onto Al foil and drying at 120 °C for 2 h. Subsequently, coatings were roll-pressed to 80 μm. The individual cathode performances were measured in CR-2032 coin cells with Na metal as the counter electrode and glass fiber as the separator. One molar NaClO4 dissolved in ethylene carbonate with diethylene carbonate (1:1 volume ratio) was used as the electrolyte. Each cell was cycled in the voltage range of 2.0–4.3 V.
Na0.67Fe0.5Mn0.5O2 shows hexagonal symmetry with P63/ mmc space group. It is isostructural with P2-type NaxCoO2 (monoclinic). The presence of impurities is not evident from any of the three XRD patterns. Their corresponding lattice parameters are ahex = 2.4610 Å and chex = 15.7139 Å for NaFe 0.5 Mn 0.5O 2 , a = 2.4244 Å and c = 11.2818 Å for Na0.67Fe0.5Mn0.5O2, and a = 2.5907 Å and c = 16.7092 Å for NaNi0.5Mn0.5O2. Surface topography of the samples was analyzed using a scanning electron microscope (ZEISS, EVO 60). For all the three compositions, the average particle sizes vary from submicron to several microns (Fig. 1). The EDX data (Fig. S1) for all the samples suggests that the ratio of the metal ions obtained for Na/Fe/Mn has desirable stoichiometry.
Results and discussion
Figure 2 shows a variation in the voltage of cells having NaFe0.5Mn0.5O2, Na0.67Fe0.5Mn0.5O2, and NaNi0.5Mn0.5O2 as cathode materials under different conditions of discharge rate. All the samples give higher discharge capacity corresponding to a voltage window of 4.3–2.0 V for lower discharge rate. Full discharge capacity is obtained by charging the cells at a constant current up to a voltage of 4.3 V followed
The powder XRD patterns are shown in Fig. 1. The phases obtained matched correctly with the corresponding reported phases . NaFe0.5Mn0.5O2 and NaNi0.5Mn0.5O2 have rhombohedral symmetries and have R3m space group. They are isostructural with O3-type α-NaFeO2(hexagonal).
Fig. 1 XRD and SEM of NaNi0.5Mn0.5O2, NaFe0.5Mn0.5O2, and Na0.67Fe0.5Mn0.5O2. SEM scale is 5 μm
J Solid State Electrochem
Fig. 2 Discharge curve of cells having a NaFe0.5Mn0.5O2, b Na0.67Fe0.5Mn0.5O2, and c NaNi0.5Mn0.5O2 as cathode materials at different discharge rates and the d corresponding charge capacities at C/20 rate
by charging at constant voltage and discharging at a constant current corresponding to a current density of 13 mA g−1 (C/20), down to a voltage of 2.0 V. This procedure of cycling is commonly referred to CCCV-CC. NaFe 0.5 Mn 0.5 O 2 , Na0.67Fe0.5Mn0.5O2, and NaNi0.5Mn0.5O2 have shown maximum discharge capacity of ∼ 156, ∼ 182, and ∼ 157 mAh g−1 at a discharge rate of 0.05 C or C/20. Previous experimental findings suggest that NaNi0.5Mn0.5O2 can give up to ∼ 185 mAh g−1 (2.2–4.5 V) when discharged at a 0.02-C (C/50) rate . In the present study, the discharge capacity decreases to ∼ 162 and ∼ 153 for discharge rates of 0.01 and 1 C. The cyclic performance of NaFe 0 . 5 Mn 0 .5 O 2 and Na0.67Fe0.5Mn0.5O2 at different rates is shown in Fig. 3. The cyclic performances of the cells were obtained by charging at constant current (CC) mode and at a charging rate of 0.1 C until it gets charged up to 4.3 V. At a discharge rate of 0.1 C (up to 2.0 V), NaFe0.5Mn0.5O2 and Na0.67Fe0.5Mn0.5O2 were cycled up to 50 and 100 cycles. An increase in capacity after few cycles is observed in NaFe0.5Mn0.5O2. This could be due to particle pulverization also observed in a similar class of material by .
Cycling performance of NaNi0.5Mn0.5O2 was comparatively poor and could only be cycled up to 8 cycles at both C/10 and C/20 rates. The poor cycle life of NaNi0.5Mn0.5O2 is due to Ni4+–O bonds possessing high covalence and low-lying LUMO; thereby, Ni4+ reduces with oxygen or electrolyte species hampering the cathode-stable structure .
Cyclic voltammetry NaFe0.5Mn0.5O2, Na0.67Fe0.5Mn0.5O2, and NaNi0.5Mn0.5O2 exhibited open-circuit voltages (OCVs) of 2.34, 2.48, and 1.94 V, respectively, for as-assembled samples. Hence, OCV greatly depends on structure rather than sodium concentration. Two NaFe0.5Mn0.5O2 redox peaks at 3.31/3.21 and 3.69/ 3.50 V, corresponding to redox reactions of Mn3+/Mn4+ and Fe3+/Fe4+, respectively, were observed. Similar peaks were also observed at 3.36/3.20 and 3.73/3.49 V for Na0.67Fe0.5Mn0.5O2. Similar phenomena have been represented by Komaba et al. . In the case of NaNi0.5Mn0.5O2, it was a single redox peak at 3.72/3.51 V corresponding to Ni2+/Ni4+
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Fig. 3 Cycle performance of a NaFe0.5Mn0.5O2 at C/20 rate and of b Na0.67Fe0.5Mn0.5O2 at C/10 rate and C/20 rate
Fig. 4 a CV curves of NaFe0.5Mn0.5O2, Na0.67Fe0.5Mn0.5O2, and NaNi0.5Mn0.5O2 and b the corresponding relationship between the square root of the scan rate v1/2 and peak current ip
J Solid State Electrochem
Fig. 5 Nyquist plots and equivalent circuit diagrams for Na0.67Fe0.5Mn0.5O2, NaFe0.5Mn0.5O2, and NaNi0.5Mn0.5O2 after a 5 cycles and b max cycle
transition. The redox couples can be observed as plateaus in charge–discharge cycle under constant current (Fig. 2b) corresponding to phase changes for Na0.67Fe0.5Mn0.5O2. For faster rates, charge–discharge rates are similar to Singh et al. , where the structural transition was found to be from P2-OP4, while for slower discharge rates, as shown in Figs. 3b and 4b, two plateaus were observed in charging and discharging curves of Na0.67Fe0.5Mn0.5O2. The plateaus are at 3.3–3.4 and 3.7–3.8 V, and this can be attributed to the phase transition of Na0.67Fe0.5Mn0.5O2 from P2 to OP4 which is intermediate between the P2 and O2 layer stackings [18, 22, 23, 36]. Since OP4 is more structurally stable and reversible than the P2 and O2 layer stackings, C/10-rate cycling shows more number of cycles than C/20 rate. The two plateaus are observed due to the redox reaction of Mn3+/4+ and Fe3+/4+. The plateaus diminish for charge and discharge rates higher than C/10. This may be due to the polarization of the electrodes. This suggests that phase transition in the electrode is highly dependent on the rate of charging and discharging. The high rate of charging and discharging bypasses reversible phase transition from P2 to OP4 [26, 36]. This is analogous to the cycling of LiFePO4 at a high rate leading to a continuous change in phase, thereby avoiding major
Table 1 Impedance parameters obtained from EIS after fitting in the equivalent circuits of the cells
structural rearrangement in the form of a metastable phase . The cyclic voltammogram (CV) of NaNi0.5Mn0.5O2 has not shown a clear picture of sodium extraction and insertion peaks. Contrastingly, in the NaNi0.5Mn0.5O2 cell, only one redox couple is seen at 3.72/3.51 V. Here, Ni and Mn are present in 2+ and 4+ states, and only Ni can show the redox reaction of Ni2+/Ni4+ while Mn remains inactive . The polarization increases with cycling scan for NaFe0.5Mn0.5O2 and Na0.67Fe0.5Mn0.5O2, while it decreases slightly for NaNi0.5Mn0.5O2. The CV measurement is an important characterization of the cell and can reveal the Na-ion diffusion. Cyclic voltammogram curves of the cells were done at scan rates of 0.01, 0.02, 0.05, 0.08, and 0.1 mV s−1. The Na+ diffusion coefficients of the cathodes opposite to sodium metal as an anode are calculated according to the Randles– Sevcik equation. 
F ip ¼ 0:4463 RT
n3=2 ADNa 1=2 Cν 1=2
where ip, n, A, C, and ν are the peak current (A), the number of exchanged electrons, the surface area (cm2),
W (S s1/2)
Diffusion coefficient (DNa)(cm2 s−1)
5 Max 5 Max 5 Max
93.13 222.1 29.63 104.9 32.17 90.34
451 1.17E − 4 432.1 621.6 628.6 8353
183.3 440.7 816.1 2994 3471 6847
1.49E − 3 4.05E − 4 4.4E − 4 1.82E − 4 6.78E − 4 1.14E − 4
3.65 × 10−14 2.7 × 10−15 2.93 × 10−14 5.03 × 10−15 3.53 × 10−15 1.3 × 10−16
J Solid State Electrochem
Fig. 6 a Formation energy and b computational voltage profiles for sodium intercalation in NaFe0.5Mn0.5O2 and NaNi0.5Mn0.5O2
the concentration of sodium inserted in Nax[MyMn1-y]O2 (M = Fe, Ni) (mol cm−3), and the sweep rate (mV s−1). DNa is the diffusion coefficient (cm2 s−1) measured by CV. The cathodic and anodic diffusion constants of Mn3+/Mn4+ in the NaFe0.5Mn0.5O2 system are calculated to be 6.5 × 10−10 and 5.44 × 10−10 cm2 s−1 and those for Fe3+/Fe4+ to be 1.42 × 10−10 and 1.91 × 10−10 cm2 s−1, respectively. Similarly, for Na0.67Fe0.5Mn0.5O2, cathodic and anodic diffusion constants of Mn3+/Mn4+ are 7.17 × 10−10 and 4.07 × 10−10 cm2 s−1 and those of Fe3+/Fe4+ are 1.026 × 10−11 and 1.359 × 10−10 cm2 s−1. Again, for NaNi0.5Mn0.5O2, cathodic and anodic diffusion constants of Ni 2 + /Ni 4 + are 2.11 × 10 − 11 and 1.19 × 10−11 cm2 s−1. All the electrodes have an impressive diffusion coefficient (up to and above an order of 10−12 cm2 s−1). The diffusion coefficient values for NaFe 0.5 Mn 0.5 O 2 and Na 0.67 Fe 0.5 Mn 0.5 O 2 are more than that of the P2-type NaCoO2 and LiCoO2 thin films . The faster diffusion of Na+ ions than that of Li+ ions in the oxide framework is because of longer alkali–oxygen bonding, resulting in weaker electrostatic interaction . Again, solvation of Na+ ion is weaker than that of Li+ ion in carbonate-based solution . These conditions are favorable to provide a low-diffusion barrier for Na+ ions.
Thus, electro-impedance spectroscopy (EIS) can be used to describe the cause of limited cyclability of the batteries. Figure 5 shows Nyquist plots of NaFe0.5Mn0.5O2, Na0.67Fe0.5Mn0.5O2, and NaNi0.5Mn0.5O2 after 5 cycles and those undergoing a maximum number of cycles for the C/20 rate. The corresponding values of circuit elements are presented in Table 1, signifying the cause of a limited number of cycles of all the cells. The behavior of these insulating layers satisfies a series combination of constant-phase element (Q) and a resistor as a circuit element. Semicircle in higher-frequency region is related to solid-electrolyte interface (SEI) film (RSEI), and in the medium frequency range, it is related to charge transfer resistance (Rct) while the inclined line at the low-frequency region is the Warburg impedance(W), which is associated with the diffusion of Na+ ions. An additional term in the circuit, Req, is associated with the electrolyte resistance, while QSEI and Qct are constantphase elements. In Na 0.67 Fe 0.5 Mn 0.5 O 2 , we see two semicircles indicating the formation of SEI in the higher-frequency region with resistance, Rf, of 1860 Ω.
Table 2 Lattice parameter of NaxFe0.5Mn0.5O2 for various sodium compositions
Table 3 Lattice parameter of NaxNi0.5Mn0.5O2 for various sodium compositions
0 0.33 0.67 1
Lattice parameter (Å) a
2.96 3.01 3.06 3.04
2.95 3.00 3.02 3.02
15.59 15.79 15.90 16.17
117.57 123.08 126.81 128.75
0 0.33 0.67 1
Lattice parameter (Å) a
2.86 2.94 3.00 3.04
2.86 2.93 2.98 3.03
14.99 15.24 15.48 16.02
106.27 112.80 118.91 126.95
J Solid State Electrochem Table 4
Oxidation state from the Bader analysis
x in NaxFe0.5Mn0.5O2
Oxidation state from the Bader analysis O
− 1.08 − 0.99
The Na+ diffusion coefficient (DNa+) can be calculated from the following equation: DNaþ ¼ R2 T 2 = 2A2 n4 F 4 C 2 σ2
In this equation, R is the ideal gas constant, T is the absolute temperature, A is the area of the surface of electrode, n is the number of the electrons participating in the reaction, F is the Faraday constant, C is the molar concentration of Na+, and σ is the Warburg coefficient, which can be calculated from the Cole–Cole plot. The value of DNa+ is found to be ~ 5.03 × 10−15, 2.7 × 10−15, and 1.3 × 10−16 cm2 s−1 for Na0.67Ni0.5Mn0.5O2, NaFe0.5Mn0.5O2, and NaNi0.5Mn0.5O2, respectively, after maximum number cycles. The low diffusivity is expected as the EIS was carried after a large number of cycles due to several irreversible factors . The circuit parameters and diffusion coefficients after 5 cycles and the maximum number of cycles are shown in Table 1.
DFT In DFT calculations, we have taken initial crystallographic structure as the O3 type of NaFeO2, where Ni/Mn and Fe/ Mn are in a zigzag arrangement in the structure of NaxNi0.5Mn0.5O2 and NaxFe0.5Mn0.5O2, respectively. We have taken supercells of 2 × 3 × 1 in all the calculations. All structures were fully relaxed in order to achieve the lowest total
Oxidation state from the Bader analysis
x in NaxNi0.5Mn0.5O2
1 0.67 0.33 0
Oxidation state from the Bader analysis O
− 1.07 − 0.97 − 0.87 − 0.77
1.11 1.18 1.25 1.30
1.72 1.73 1.76 1.76
energy configurations. All calculations were performed with the projector-augmented wave (PAW) method as implemented in the Vienna Ab initio Simulation Package (VASP)  with GGA  as an exchange-correlation energy functional. For electron correlation in d orbitals, Hubbard on-site repulsion terms, U (GGA + U), of 5.9, 5.0, and 5.3 eV for Ni-3d, Mn3d, and Fe-3d, respectively, were used. We used an energy cutoff of 500 eVon the plane wave basis set and k-mesh grids of 7 × 7 × 1 for sampling Brillouin zone integration. The k points are used to ensure the total energy convergence and pressure less than 0.01 eV Å−1 and 0.01 kbar, respectively. We have estimated the voltage of the cell (Vcell) using the following approximation relationship.
V cell ¼
−ΔG −ΔE ≈ ¼ −ðE sodiated −E desodiated −Esodium Þ nF nF
where n is the number of moles of electrons transferred, F is the Faraday constant, ΔG is the change of Gibb free-energy change per mole, ΔE is the change of total energy of the overall reaction per mole, and E sodiated, Edesodiated, and Esodium are the energies per formula unit of sodiated structure, desodiated structure, and sodium atom, respectively. The total energy of NaxFe0.5Mn0.5O2 and NaxNi0.5Mn0.5O2 for different sodium configurations (x = 0, 0.33, 0.67, and 1) are calculated. The potential steps enumerated for the above configurations (Fig. 6) match with redox peak potentials obtained from CV. It is assumed that the Na+ deintercalation did not change the layered structure. The optimized structural parameters are summarized in Tables 2 and 3. The convex hull method has been used to analyze the phase stability for different concentration of NaxFe0.5Mn0.5O2 and NaxNi0.5Mn0.5O2 . Figure 6a shows the convex hull plot of both the compounds, which has the formation energy of most stable configurations. It is found that composition of NaxFe0.5Mn0.5O2 at x = 0.67 and 0.33 falls in the curvature of the convex hull plot; as a result, we observed multiple voltage steps (Fig. 6b). For NaxNi0.5Mn0.5O2, compositions at x = 0.67 and 0.33 stay above the convex hull leading to a single voltage step. The DFT-based calculation shows that with a decrease in Na content in NaxFe0.5Mn0.5O2, the voltage increases (referenced to pure Na metal Na/Na+, Fig. 6b) whereas the average potential needed to extract Na ion from NaxNi0.5Mn0.5O2 is ~ 3.5 V. This trend in constant average potential upon sodium extraction shares similarity with findings of Goodenough et al.  for Na2FeMn(CN)6-based system. We have calculated the effective charge (see Tables 4 and 5) of an atom by taking the difference between valence electrons and the Bader charge of the atom . In NaxFe0.5Mn0.5O2, the calculated effective charge of Fe is ~ + 1.7e for all the compositions, and it has changed for Mn
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Fig. 7 Partial density of states. a Na1−xFe0.5Mn0.5O2. b Na1−xFe0.5Mn0.5O2 for x = 0, 0.33, 0.67, and 1
from ~ + 1.5e to ~ + 1.8e for x = 1 and x = 0, respectively. This suggests that Fe is mostly redox-inactive and Mn is redoxactive in the charge transfer process. For NaxNi0.5Mn0.5O2, Mn effective charge remains the same (~ + 1.7e) and Ni changed from ~ + 1.1e to + 1.3e for x = 1 to x = 0, which suggests that Ni is redox-active (Fig. 7). Figure 8 shows the diagrammatic images of NaMO2 for different desodiated conditions. The simulated XRD pattern of NaxFe0.5Mn0.5O2 and NaxNi0.5Mn0.5O2 (x = 0, 0.33, 0.67, 1) is shown in Fig. S2. For x = 1, the simulated XRD pattern of O3-type NaxFe0.5Mn0.5O2 and NaxNi0.5Mn0.5O2 matches with the experimental results. The transition in the Bader charge suggests the first and second peaks of the CV of both NaFe 0.5 Mn 0.5 O 2 and Na0.67Fe0.5Mn0.5O2 are associated with a change in oxidation state of Mn (Table 4). Similarly, the first and second peaks of the CV of NaNi0.5Mn0.5O2 are associated with a change in oxidation state of Ni (Table 5). Comparing Fermi energies, the voltages are consistent with the shift in the Fermi energy levels of Nax[MyMn1−y]O2 (M = Fe, Ni; x = 0, 0.33, 0.67, and 1; and y = 0.5).
NaFe 0.5 Mn 0.5 O 2 (156 mAh g −1 ) and NaNi 0.5 Mn 0.5 O 2 (157 mAh g−1). The cyclic performance of NaNi0.5Mn0.5O2 was indigent. The diffusion coefficient of sodium depends upon the structure and the transition metal taking part in the redox reaction. All the cathode materials show an impressive diffusion coefficient value up to the orders of 10−10 and 10−11 cm2 s−1. Diffusion coefficient value depends on the transition taking part in a redox reaction. The potential steps calculated from the Gibbs free energy of formation are in good agreement with the experimentally obtained values. For P2-type Na0.67Fe0.5Mn0.5O2, two plateaus are observed during cycling corresponding to Na+/vacancy ordering. These two plateaus diminish due to a faster rate of cycling, thereby bypassing the intermediate-phase transformation. Thus, the structural stability is greatly influenced by the rate of cycling.
Conclusions In this present study, we have investigated the electrochemical performance and diffusion coefficient of NaFe0.5Mn0.5O2, Na0.67Fe0.5Mn0.5O2, and NaNi0.5Mn0.5O2 made by solid-state synthesis. Na0.67Fe0.5Mn0.5O2 shows the maximum reversible capacity of 182 mAh g−1 at C/20-rate discharge (2.0–4.3 V) when fully charged (at CCCV mode), followed by
Fig. 8 a, b Diagrammatic presentation of the O3-type structures of NaM10.5M20.5O2 (M1 = Mn, M2 = Ni/Fe).
J Solid State Electrochem
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