Synchrotron-Radiation X-Ray Investigation of Li + / Na + Intercalation into Prussian Blue Analogues

Prussian blue analogies (PBAs) are promising cathode materials for lithium ion (LIB) and sodium ion (SIB) secondary batteries, reflecting their covalent and nanoporous host structure. With use of synchrotron-radiation (SR) X-ray source, we investigated the structural and electronic responses of the host framework of PBAs against Li and Na intercalation by means of the X-ray powder diffraction (XRD) andX-ray absorption spectroscopy (XAS).The structural investigation reveals a robust nature of the host framework against Li and Na intercalation, which is advantageous for the stability and lifetime of the batteries.The spectroscopic investigation identifies the redox processes in respective plateaus in the discharge curves. We further compare these characteristics with those of the conventional cathode materials, such as, LiCoO 2 , LiFePO 4 , and LiMn 2 O 4 .


Introduction
1.1.Brief History of Lithium Ion Secondary Battery.Lithium is the most base and lightest metal element.Therefore, "lithium metal secondary battery, " whose anode is Li metal, is expected to exhibit the highest energy density [=(voltage versus Li) (capacity/mass)].The development of "lithium metal secondary battery" started from the 70s.In 1986, a Canadian company commercialized a Li/MoS 2 cell, which exhibits an average working voltage of 3 V.The production, however, stoped due to firings and explosions of the cell.After that, the researchers tried to explore the safer anode materials and finally found that graphite (C 6 ) exhibits the Li + intercalation/deintercalation between the C 6 sheets.In addition, LiCoO 2 with layered rocksalt structure is found to exhibit the Li + intercalation/deintercalation between the CoO 2 layers.In 1991, Sony cooperation firstly commercialized a C 6 /LiCoO 2 cell, which exhibits an average operating voltage of 3.9 V.The cell is called "lithium ion secondary battery" (LIB), because the cell does not use dangerous Li metal.Today, the high volume and gravimetric energy density of LIBs have realized mobile electrics, such as smart phone and mobile computer.However, cost, safety, stored energy density, charge/discharge rate, and service life are still issues that force the development of LIBs for the potential mass market of electric vehicle [1,2].
Here, let us survey electrochemical and structural/electronic properties the the conventionally used cathode materials for LIBs.LiCoO 2 with layered rock-salt structure is the most prototypical cathode material for LIBs, which exhibits an average working voltage of 3.9 V against Li.The material consists of covalently bonded CoO 2 layers and Li + , which is accommodated between the layers.The ideal capacity, LCoO 2 → CoO 2 + Li, is 274 mAh/g, which is realized with the charge voltage of 4.7 V.The Li + deintercalation, however, causes successive structural phase transitions due to the Li + ordering and eventually produces CoO 2 with CdI 2 structure.So, in the actual use of the cell, the cutoff voltage is set to be below 4 V.The C 6 /LiCoO 2 cell exhibits a practical capacity of 150 mAh/g.LiFePO 4 with ordered-olivine structure exhibits an average working voltage of 3.5 V against Li.The material consists of one-dimensional (1D) framework made by covalently connected PO 4 tetrahedron and FeO 6 octahedron and Li + , which is accommodated in the tube-type interstitial sites.The ideal capacity, LiFePO 4 → FePO 4 + Li, is 170 mAh/g.The Li deintercalation, however, causes phase separation into Advances in Materials Science and Engineering LiFePO 4 and FePO 4 .In addition, LiFePO 4 is an insulator with low electron conductivity ( < 10 −8 Ω cm), which is disadvantageous for the high charge/discharge rate.Fortunately, a carbon-coating procedure mysteriously improves the rate properties of LiFePO 4 .LiMn 2 O 4 with spinel structure exhibits an average working voltage of 4 V against Li.In this material, Li + does not occupy the interstitial sites, but three-dimensionally connects the MnO 6 octahedra.The ideal capacity, LiMn 2 O 4 → Mn 2 O 4 + Li, is 285 mAh/g.-MnO 2 , however, is produced at low Li concentration region.The C 6 / LiMn 2 O 4 • cell exhibits practical capacity of 140 mAh/g.

Sodium Ion Secondary
Battery.Sodium ion secondary battery (SIB) is a promising candidate for the next-generation battery beyond the lithium ion secondary battery (LIB) with safe, environmentally friendly, and low-cost characteristics.The SIB device stores the electric energy utilizing intercalation/deintercalation process of abundant Na + (Clark number = 2.63), instead of rare Li + (0.006), within the cathode and anode materials.In this sense, the SIB is suitable for a large-scale battery for stable use of the solar and wind energies.Among a variety of cathode materials for SIB [3,4], Na  MO 2 (M is transition metal element) with layered structure exhibits promising electrochemical properties as well as rich structural properties.In particular, the replacement of Na + for Li + significantly expands the choice of the transition metals.For example, NaCrO 2 [5] with -NaFeO 2 structure exhibits a capacity of 120 mAh/g and an average operating voltage of 3.0 V with a good cyclability in SIB, while isostructural LiCrO 2 exhibits poor capacity and cyclability in LIB.Na 0.6 MnO 2 [6] with P2-type structure exhibits a capacity of 140 mAh/g and an average operating voltage of 2.5 V. Recently, a coin-type full SIB cell with hard carbon/NaNi 0.5 Mn 0.5 O 2 configuration is demonstrated to exhibit a high capacity more than 200 mAh/g (anode basis) and an average operating voltage of 3 V with a good cyclability [7].This demonstration opens the view to commercial utilization of SIBs and hence significantly stimulates investigation and exploration of cathode materials for SIBs.[9][10][11][12], SIB properties [13][14][15], and electrochromism [16,17].Interestingly, the size of the nanopores can be controlled by the substitution of M: the lattice constant (a) linearly increases with the ionic size ( M ) of M as a (nm) = 0.891 + 2 M (nm) in (Cs, Rb)   II [Fe III (CN) 6 ]  ( = Co, Fe, Ni, Cu, Zn, Mn, and Cd) [8].Historically, the alkali cation intercalation was interpreted in terms of the hydrated radius ( H ) [22][23][24], rather than the ionic radius ( A ) of bare alkali cation.Actually, Tieke's group [23,24] reported that the selfassembled films of PBAs are permeable to smaller hydrated ions such as Cs + ( H = 0.119 nm) and K + ( H = 0.125 nm), whereas they block bigger hydrated ions such as Na + ( H = 0.184 nm).These films, however, consist of microcrystals with considerable [Fe(CN) 6 ] vacancies (y ∼ 0.67).On the other hand, Moritomo et al. [25] electrochemically synthesized a thin film of crystalline Na 0.76 Co[Fe(CN) 6 ] 0.90 2.9H 2 O ( = 0.9) with fewer vacancies.They observed that the intercalation of Na + ( A = 0.118 nm) is much faster than those of K + ( A = 0.151 nm) and Rb + ( A = 0.161 nm).This observation suggests that the intrinsic alkali cation intercalation should be interpreted in terms of  A : Li + ( A = 0.092 nm), Na + (0.118 nm), K + (0.151 nm), Rb + (0.161 nm), and Cs + (0.174 nm).They further demonstrated that the intercalation behavior is qualitatively explained by the cation potentials based on the ab initio calculation.32).They reported that the thin-film electrode exhibits a high capacity of 128 mAh/g and an average operating voltage of 3.6 V against Li with a good cyclability.Recently, Goodenough's group [13] reported Na + intercalation behaviors in a K-M-Fe(CN) 6 system ( = Mn, Fe, Co, No, Cu, and Zn).However, their coulomb efficiency (=60% for  = Fe), that is, the ratio of discharge capacity and charge capacity, is very low.The low efficiency suggests an irreversible redox process in addition to the reversible Na + intercalation/deintercalation process.Matsuda et al. [14] investigated electrochemical properties of film electrode of Na 1. 32 Mn II [Fe II (CN) 6 ] 0.83 3.5H 2 O and reported a high capacity of 109 mAh/g and an average operating voltage of 3.4 V against Na with a good cyclability.In addition, Takachi et al. [15] reported that Na 1.60 Co II [Fe II (CN) 6 ] 0.90 2.9H 2 O film electrode exhibits a high capacity of 135 mAh/g and an average operating voltage of 3.6 V against Na with a good cyclability.
In this paper, with use of synchrotron-radiation (SR) X-ray source, we investigated the structural and electronic responses of the host framework of PBA against Li + and Na + intercalation by means of the X-ray powder diffraction (XRD) and X-ray absorption spectroscopy (XAS).The structural investigation reveals a robust nature of the host framework against Li + and Na + intercalation, which is advantageous for the stability and lifetime of the batteries.The spectroscopic investigation identifies the redox processes in respective plateaus in the discharge curves.We further compare these    1.Typical thickness of the films is ca. 1 m, which was measured with a profilometer (Dektak3030).The mass of each film was measured with a conventional electronic weighing machine after the film was carefully removed from the ITO glass with a microspatula.
The Li compounds were synthesized by electrochemical substitution of Li + for Na + within a beaker-type cell against Li.The electrolyte was ethylene carbonate (EC)/ diethyl carbonate (DEC) solution containing 1 mol/L LiClO 4 .The charge/discharge current was ca. 5 A/cm 2 , and the cutoff voltage was from 2.0 to 4.2 V.The active area of the film was about 2.0 cm 2 .We obtained Li-substituted films: Li

Electrochemical Measurement.
The discharge/charge measurement was performed in a beaker-type cell.For the Li + intercalation/deintercalation process, the PBA films and the Li metal were used as the cathode and anode, respectively.The active area of the film was about 2.0 cm 2 .The electrolyte was EC/DEC solution containing 1 mol/L LiClO 4 .The cutoff voltage was from 2.0 to 4.2 V.For the Na + intercalation/deintercalation process, the PBA films and the Na metal were used as the cathode and anode, respectively.The active area of the film was about 2.0 cm 2 .The electrolyte was propylene carbonate (PC) solution containing 1 mol/L NaClO 4 .The cut-off voltage was from 2.0 to 4.2 V.
For the ex situ XRD and XAS experiments, the Li/Na concentration () of the PBA film was controlled by the charge/discharge process in a beaker-type cell.The discharge capacities of the respective PBA films are close to the ideal values.Therefore, the magnitude of Li concentration () is determined by the current with assuming nominal chemical compositions in the charge and discharge states.Similarly, the magnitude of Na concentration () is determined by the current with assuming nominal chemical compositions in the charge and discharge states.In Table 2, abbreviation, chemical compositions, and Li/Na concentration () in the discharge and charge states are summarized.

X-Ray Powder Diffraction Measurement.
The ex situ XRD measurements were performed at the BL02B2 beamline [27] of SPring-8 and 8A beamline of the Photon Factory, KEK.The films were carefully removed from the ITO glass with a microspatula in air atmosphere.The fine powder samples were filled and sealed in a 0.3 mm  glass capillary.In the entire x-region, the films were stable in air for at least 1 h.The capillary was placed on a Debye-Scherrer camera.The powder diffraction patterns were detected with an imaging plate (IP) at 300 K.The exposure time was 5 min.The wavelength of the X-ray was calibrated by the lattice constant of standard CeO 2 powders ( = 5.41111 A).Thus obtained power diffraction patterns are analyzed by the Rietveld method (Rietan-FP program [28]).

X-Ray Absorption Measurement.
The ex situ XAS measurements were performed at beamline 7C of the Photon Factory, KEK.The XAS spectra were measured in a fluorescent yield mode with a Lytle detector at 300 K.The X-ray was monochromatized with a Si(111) double-crystal monochromator.At the XAS measurement for respective elements, for example, Mn, Fe, Co, and Ni, the monochromator was calibrated by the K-edge of the respective metal foils.The PBA films were sealed in plastic to avoid air exposure.The background subtraction, normalization, and component decomposition were performed with ATHENA program [29].The valence states of the constituent transition metals, that is, Mn, Fe, Co, Ni, and Cd, are determined by the XAS spectra around the Mn K-, Fe K-, Co K-, Ni K-, and Cd L I -edges.
In the X-ray fluorescence measurements, we should be careful to the two types of the self-absorption effects.One is the absorption of the fluoresced X-rays and the other one is that of the incident X-ray.In Table 3, the penetration depths () for ideal Na 2 Mn[Fe(CN) 6 ] and Na 2 Co[Fe(CN) 6 ] are listed at the fluorescence and absorption energies of the Mn, Fe, and Co K-edges.The  values are much bigger than the thickness (∼1 m) of the film.In this condition, the absorbed photon (= 1 −  −d ;  is the absorption coefficient) by the film is proportional to .
Figure 3 shows the XRD patterns of powered LFM83 against Li concentration ().All the reflections can be indexed with the face-centered cubic setting, as shown in parentheses.No structural phase transition nor phase separation is observed in the entire -region.The lattice constants (a) are refined by Rietveld analysis with the face-centered cubic (Fm3m:  = 4) model.
Figure 4(a) shows the XAS spectra of LMF83 films around the Fe K-edge against .The peak energy at  = 1.32 coincides with that of low-spin (LS) Fe 2+ [30].The blue-shift with decrease in  indicates partial formation of LS Fe 3+ .The peak Figure 2: OCV discharge curves of LMF83 film against Li measured at 0.05 C. For convenience of explanation, we define plateaus I and II (cited from [18]).
energy at  = 0.00 coincides with that of LS Fe 3+ [30].In other words, all the Fe sites are oxidized in the charge state.The electronic configuration at  = 0.00 becomes Mn  Thus obtained lattice constant (a), Mn valence, and the Co valence are plotted in Figure 5.In the plateau I (0.0 <  < 0.4), the Mn valence decreases while the Fe valence remains trivalent.In the plateau II (0.4 < 1.32), the Fe valence decreases while Mn valence remains divalent.These observations clearly indicate that the plateaus I and II are ascribed to the reduction processes of Mn 3+ and Fe 3+ , respectively.Surprisingly, LMF83 remains single cubic phase without structural phase transition nor phase separation in the entire -region.In the plateau I, the lattice constant steeply increases from 10.40 A at  = 0.00 to ∼10.58A at  ∼ 0.4.The expansion is ascribed to the bigger ionic radius (=0.83 A) of high-spin (HS) Mn 2+ than that (=0.65 A) of HS Mn 3+ .On the other hand, the lattice constant slightly decreases with increasing in  in the plateau II.The decrease In manganese PBA, Li x Mn[Fe(CN) 6 ] y , both the transition metals, that is, Mn and Fe, take part in the redox process.Then, the capacity is expected to increase with sum of the transition metal concentration (1 + ).Strictly speaking, however, the capacity increases with the initial Li concentration ( 0 ), because  0 (=4 − 2) is lower than 1 +  in the entire -region (0 <  < 1). Figure 6 shows the OCV discharge curves of manganese PBA films against Li: LMF83 ( = 0.83), LMF87 ( = 0.87), and LMF93 ( = 0.93).As expected, the capacity increases with : 115 mAh/g for LMF83, 130 mAh/g for LMF87, and 143 mAh/g for LMF93.These values are comparable to the ideal values, 110 mAh/g for LMF83, 134 mAh/g for LMF87, and 153 mAh/g for LMF93.
Similarly to the case of the LMF83 film, LMF87 and LNF93 films exhibit two plateaus at 3.8 (plateau I) and 3.5 V (plateau II).Then, the plateaus I and II are reasonably ascribed to the reduction process of Mn 3+ and Fe 3+ , respectively.This Advances in Materials Science and Engineering   Advances in Materials Science and Engineering Figure 9: OCV discharge curves of LCF90 film against Li measured at 0.8 C. For convenience of explanation, we define plateaus I, II, and III (cited from [20]).
assignments are confirmed by the infrared absorption (IR) spectroscopy around the CN stretching mode region [18].
Figure 7 shows the XRD patterns of (a) LMF83 and (b) LMF93 against .Similarly to the case of LMF83, the XRD patterns of LMF87 and LMF93 in the high -region can be indexed with the face-centered cubic setting.In the low region, however, two phase features are observed.The extra reflections are indexed with the face-centered cubic (Fm3m:  = 4) setting in LMF87, while they are indexed with the tetragonal (I4m2:  = 2) setting in LMF93.The lattice constants are refined by the Rietveld analysis with the singleand two-phase models.
Figures 8(a   The most probable origin of the phase separation in the Li intercalation system is the spontaneous phase separation into the Li-rich and Li-poor regions.Actually, Li x FePO 4 exhibits a phase separation into LiFePO 4 and FePO 4 in most of the region [32].In the present manganese PBA, the coexistence of bigger Mn 2+ and smaller Mn 3+ may cause the local strain in the low -region.In this situation, the system tends to exhibit a spontaneous phase separation into the Li-rich (Mn 2+ -rich) and Li-poor (Mn 3+ -rich) regions to release the local strain.In this scenario, the second phase corresponds to the Li-poor region.In LMF93 with fewer [Fe(CN) 6 ] vacancies, the cooperative JT distortion due to Mn 3+ causes the tetragonal distortion.More detailed discussions are described elsewhere [18].

Cobalt PBA.
Figure 9 shows the OCV discharge curve of NCF90 film against Li measured at 0.8 C. The discharge curve shows plateau features.We tentatively divided the discharge curve into three plateaus, that is, plateaus I, II, and III.The observed capacity (=139 mAh/g) is comparable to the ideal value (=138 mAh/g).
Figure 10 shows the XRD patterns of powered LCF90 against .All the reflections can be indexed with the facecentered cubic setting, as shown in parentheses.At  = 1.2, two-phase feature is observed.In addition, the reflections discontinuously shift to the lower angle side between  = 1.0 and 1.2.These indicate a first-order structural transition induced by Li + intercalation.The lattice constants (a) are refined by Rietveld analysis with the face-centered cubic (Fm3m:  = 4) model.
Figure 11(a) shows the XAS spectra of LCF90 films around the Co K-edge against .The XAS spectrum at  = 0.0 coincides with that of LS Co 3+ , while the spectrum at 1.6 coincides with that of HS Co 2+ [30].The electronic configuration at  = 0.00 becomes Co 3+ -Fe 2.78+ if we assume the charge neutrality: Li  (1.6), where  is an adjustable parameter.The average Co valence is expressed as  + 2. Note that (0.6)[ (1.4)] is essentially identical to (0.0) [ (1.6)].In other words, Co is divalent in 0.0 <  < 0.6 while it is trivalent in 1.4 <  < 1.6.Figure 4(b) shows the XAS spectra of LCF90 films around the Fe K-edge against .The peak energy at  = 1.6 coincides with that of LS Fe 2+ [30].The blue-shift with decrease in  indicates partial formation of LS Fe 3+ .The average Fe valence ( Fe ) is determined by the peak energy () as  Fe = −6569.0+ 0.92204.It is, however, difficult to extract any effective information on the Fe valence due to the big error bars.
Thus obtained lattice constant (a), Co valence, and the Fe valence are plotted in Figure 12.The Co valence remains trivalent in plateau I (0.0 <  < 0.7), while it remains divalent in plateau III (1.1 <  < 1.6).On the other hand, the Co valance steeply decreases with  in plateau II (0.7 <  < 1.1).These observations suggest that the plateaus I, II, and III are ascribed to the reduction processes of Fe 3+ , Co 3+ , and Fe 3+ , respectively.Around the boundary between plateaus II and III, a first-order structural phase transition takes place and the lattice constant discontinuously increases from 10.0 A to 10.2 A.
The most probable scenario for the structural phase transition is a cooperative charge-transfer from Fe 2+ to Co 3+ or the variation of the electronic configuration from Fe   Values in parentheses represent indexes in the face-centered cubic setting (cited from [21]).
[33] exhibits a thermally induced structural phase transition due to the cooperative charge-transfer.This scenario well explains the abrupt reduction of the Co valence from 2.5 at  = 1.2 to 2.0 at 1.4.According to the scenario, the discontinuous increase in the lattice constant is ascribed to the bigger ionic radius (=0.75 A) of HS Co 2+ than that (=0.55 A) of LS Co 3+ .More detailed discussions are described elsewhere [20].

Other PBAs.
Figure 13 shows the OCV discharge curves of PBA films against Li: (a) LNF68, (b) LCF71, and (c) LCdF96.The observed capacities, 69 mAh/g for LNN68, 70 mAh/g for LCF71, and 58 mAh/g for LCdF96, are comparable to the ideal values, 64 mAh/g for LNF68, 72 mAh/g for LCF71, and 64 mAh/g for LCdF96.The ideal values are calculated with assuming that only Fe takes part in the redox process.
Figure 14 shows the XRD patterns of powered (a) LNF68 and (b) LCF71 against .All the reflections can be indexed with the face-centered cubic setting, as shown in parentheses.The lattice constants (a) are refined by Rietveld analysis with the face-centered cubic (Fm3m:  = 4) model.Unfortunately, the powdered LCdF96 films are seriously unstable in air, and many impurity reflections are observed in the XRD pattern.
Figures 15(a) and 15(b) shows the XAS spectra of LNF68 films.The Fe K-edge spectrum exhibits red-shift with increase in  while the Ni K-edge spectra are essentially unchanged.This indicates that the reduction site is Fe in LNF68.Figures 15(c) and 15(d) show the XAS spectra of LCF71 films.Similarly to the case of LNF68, the Fe K-edge spectrum exhibits red-shift with increase in  while the Co K-edge spectra are essentially unchanged.This indicates that the reduction site is Fe in LCF71.Figures 15(e) and 15(f) show the XAS spectra of LCdF96 films.Similarly to the case of LNF68, the Fe K-edge spectrum exhibits red-shift with increase in  while the Cd L I -edge spectra are essentially unchanged.This indicates that the reduction site is Fe in LCdF96.

Na + Intercalation
4.1.Manganese PBA. Figure 16 shows the OCV discharge curve of NMF83 film against Na measured at 0.6 C. The discharge curve shows two plateaus at 3.6 (plateau I) and 3.3 V (plateau II).The discharge voltages are slightly (∼0.2V) lower than those of LMF83.This is because the redox voltage (=−3.71Vversus SHE) of Na/Na + is higher than that (=−3.04V versus SHE) of Li/Li + .The observed capacity (=130 mAh/g) is comparable to the ideal value (=103 mAh/g).The overall feature of the OCV discharge curve resembles that of LMF83 even though the curve is rather blurred in NMF83.This suggests that the plateaus I and II can be ascribed to the reduction processes of Mn 3+ and Fe 3+ , respectively.This assignments are confirmed by the IR spectroscopy around the CN stretching mode region [34].
Figure 17 show the XRD patterns of powered NFM83 against Na concentration ().All the reflections can be indexed with the face-centered cubic setting, as shown in parentheses.No structural phase transition nor phase separation is observed in the entire -region.The lattice constants (a) are refined by Rietveld analysis with the face-centered cubic (Fm3m:  = 4) model.
Thus obtained lattice constant (a) is plotted in Figure 18.In the plateau I, the lattice constant steeply increases from 10.40 A at  = 0.00 to ∼10.58A at  ∼ 0.3.The expansion is ascribed to the bigger ionic radius (=0.83 A) of HS Mn 2+ than that (=0.65 A) of HS Mn 3+ .On the other hand, the lattice constant remains nearly constant in the plateau II.The overall feature of structural response of the host framework against Na + intercalation is nearly the same as that against Li + intercalation (see Figure 18(c)).This suggests that the guesthost interaction is rather weak in the PBA system, and the structural response of the host framework is governed by the ionic radius of the constituent M. 4.2.Cobalt PBA. Figure 19 shows the OCV discharge curve of NCF90 film against Na measured at 0.6 C. The discharge curve shows two plateaus at 3.8 (plateau I) and 3.4 V (plateau II).The discharge voltage in plateau I is slightly (∼0.2 V) lower than that of LMF83.This is because the redox voltage of Na/Na + is higher than that of Li/Li + .The observed capacity (=133 mAh/g) is comparable to the ideal value (=127 mAh/g).The IR spectroscopy around the CN stretching mode and Figure 16: OCV discharge curves of NMF83 film against Na measured at 0.6 C. For convenience of explanation, we define plateaus I and II (cited from [14]).
XAS around the Fe K-and Co K-edges reveal that the plateaus I and II are ascribed to the reduction processes of Fe 3+ and Co 3+ , respectively [34].
Figure 20 shows the XRD patterns of powered NCF90 against .All the reflections can be indexed with the facecentered cubic setting, as shown in parentheses.No structural phase transition nor phase separation is observed in the entire -region, making a sharp contrast with LCF90 (Figure 21(c)).The lattice constants (a) are refined by Rietveld analysis with the face-centered cubic (Fm3m:  = 4) model.
Thus obtained lattice constant (a) is plotted in Figure 21.In plateau I, the lattice constant remains nearly constant.In plateau II, a gradually increases from 9.96 A at  ∼ 0.6 to ∼10.16A at  ∼ 1.6.The expansion is ascribed to the bigger ionic radius (=0.75 A) of HS Co 2+ than that (=0.45 A) of LS Co 3+ .NCF90 exhibits no structural phase transition nor phase separation, which is advantageous for the stability and lifetime of the batteries.The disappearance of the structural phase transition in NCF90 is perhaps because the lattice constants of NCF90 in low-x-region are slightly (∼0.02A) bigger than those of LCF90.In Table 4, we summarise the experimental and calculated capacities of PBA films together with the structural responses.Except for LMF87, LMF93, and LCF90, the host framework exhibits no structural phase transition nor phase separation in the entire -region.In other words, they are robust against Li + and Na + intercalation.Surprisingly, in LMF83, LMF87, LMF93, LCF90, NMF83, and NCF90, the framework is stable  Figure 19: OCV discharge curves of NCF90 film against Na measured at 0.6 C. For convenience of explanation, we define plateaus I and II (cited from [15]).

Characteristics of PBA
even if all the alkali cations are removed.These features are advantageous for practical use of the materials in LIBs and SIBs.The robust nature of the host framework of the PBA system is probably ascribed to (1) the rigid 3D network and (2) the strong covalent nature of M-NC-Fe bonding.

Fat Plateau without Phase Separation.
In conventional cathode materials, the plateau structure is ascribed to the phase separation.In other words, the voltage is pinned at the voltage of the decreasing phase, whose composition is unchanged against the charge/discharge process.For example, in LiFePO 4 , the Li + deintercalation causes phase separation into LiFePO 4 and FePO 4 [32].The flat working voltage of 3.5 V is determined by LiFePO 4 .
The OCV discharge curves of PBA films exhibit flat plateaus, for example, the 3.8 and 3.5 V plateaus in LMF83 and the 3.8 and 3.4 V plateaus in NCF90.Importantly, our spectroscopic investigation reveals that these flat plateaus cannot be ascribed to the phase separation.The flat plateaus, which are advantageous for the practical use of the materials in LIBs and SIBs, are intrinsic nature of the host framework.The flat plateaus are reasonably ascribed to the weak interaction (J) between the guest Li + /Na + .The weak-J is originated in (1) the longer inter-ion distance (∼5 A) as well as (2) the separation of the ions by the square window of the framework.

Summary
The SR XRD and XAS reveal the following characteristic features of PBA against Li + /Na + intercalation/deintercalation.
(2) Discharge curve exhibits intrinsic flat plateaus, which cannot be ascribed to the phase separation.
The robust nature of the host framework is probably ascribed to (1) the rigid 3D network and (2) the strong covalent nature of M-NC-Fe bonding.The intrinsic flat plateaus are reasonably ascribed to the weak-J between the guest Li + /Na + .The weak-J is originated in (1) the longer interion distance (∼5 A) as well as (2) the separation of the ions by the square window of the framework.

Figure 1 :
Figure 1: Schematic structures of PBA, A x M[Fe(CN) 6 ] y zH 2 O (A and M are alkali metal and transition metal, resp.) in charge (a) and discharge (b) states.Transition metal and iron (small spheres) are alternatively bridged by the cyano groups (sticks).Big spheres represent the guest alkali cations.Water molecules are omitted for simplicity.

Figure 4 (
b) shows the XAS spectra of LMF83 films around the Mn K-edge against .In the low -region, a shoulder structure appears around 6553 eV.The absorption is ascribed to Mn 3+ state.The Mn valence ( Mn ) is estimated from the relative intensity (I) at 6553 eV as  Mn = 2 + 0.49 * [I() − I(0.00)]/[I(1.32)− I(0.00)].

Figure 3 :
Figure 3: XRD pattern of powered LMF83 against Li concentration ().Values in parentheses represent indexes in the face-centered cubic setting (cited from [19]).
) and 8(b) show the lattice constants against x.In plateau II, where the Fe sites are selectively reduced with

Figure 10 :
Figure 10: XRD pattern of powered LCF90 against .Values in parentheses represent indexes in the face-centered cubic setting (cited from[20]).

Figure 15 :
Figure 15: XAS spectra of LNF68 films against  around the (a) Fe K-and (b) Ni K-edges.XAS spectra of LCF71 films against  around the (c) Fe K-and (d) Co K-edges.XAS spectra of LCdF96 films against  around the (e) Fe K-and (f) Cd L I -edges (cited from [21]).

Table 3 :
Penetration depths () for ideal Na 2 Mn[Fe(CN) 6 ] and Na 2 Co[Fe(CN) 6 ] at the fluorescence and absorption energies of the Mn, Fe, and Co K-edges.

Table 4 :
Experimental and calculated capacities of PBA films together with the structural responses.
5.1.Robust Framework against Li+ /Na + Intercalation.In conventional cathode materials, Li + deintercalation causes the structural phase separation and/or phase separation.For example, the Li deintercalation in LiCoO 2 causes the successive structural phase transitions and eventually produces CoO 2 with CdI 2 structure.In LiMn 2 O 4 .-MnO 2 is produced at low Li concentration region.In LiFePO 4 , the Li deintercalation causes the phase separation into LiFePO 4 and FePO 4 .