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

Authors: Yutaka Moritomo; Masamitsu Takachi; Yutaro Kurihara; Tomoyuki Matsuda
Journal: Advances in Materials Science and Engineering
 (2013)

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## Abstract

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) 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 characteristics with those of the conventional cathode materials, such as, LiCoO2, LiFePO4, and LiMn2O4.


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## Body

## 1. 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/MoS2 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 (C6) exhibits the Li+ intercalation/deintercalation between the C6 sheets. In addition, LiCoO2 with layered rocksalt structure is found to exhibit the Li+ intercalation/deintercalation between the CoO2 layers. In 1991, Sony cooperation firstly commercialized a C6/LiCoO2 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. LiCoO2 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 CoO2 layers and Li+, which is accommodated between the layers. The ideal capacity, LCoO2 → CoO2 + 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 CoO2 with CdI2 structure. So, in the actual use of the cell, the cutoff voltage is set to be below 4 V. The C6/LiCoO2 cell exhibits a practical capacity of 150 mAh/g. LiFePO4 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 PO4 tetrahedron and FeO6 octahedron and Li+, which is accommodated in the tube-type interstitial sites. The ideal capacity, LiFePO4 → FePO4 + Li, is 170 mAh/g. The Li deintercalation, however, causes phase separation into LiFePO4 and FePO4. In addition, LiFePO4 is an insulator with low electron conductivity (σ<10-8Ωcm), which is disadvantageous for the high charge/discharge rate. Fortunately, a carbon-coating procedure mysteriously improves the rate properties of LiFePO4. LiMn2O4 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 MnO6 octahedra. The ideal capacity, LiMn2O4 → Mn2O4 + Li, is 285 mAh/g. γ-MnO2, however, is produced at low Li concentration region. The C6/LiMn2O4∙ cell exhibits practical capacity of 140 mAh/g.


### 1.2. 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+ (Clarknumber=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], NaxMO2 (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, NaCrO2 [5] with α-NaFeO2 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 LiCrO2 exhibits poor capacity and cyclability in LIB. Na0.6MnO2 [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/NaNi0.5Mn0.5O2 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.


### 1.3. Overview of Prussian Blue Analogues

Prussian blue analogue (PBA),AxM[Fe(CN)6]yzH2O (A and M are alkali metal and transition metal, resp.), is the oldest complex compound that the human being has synthesized. The PBAs consist of a three-dimensional (3D) cyano-bridged transition metal framework (M[Fe(CN)6]y) and guests (A+and H2O) accommodated at the cubic nanopores, as schematically shown in Figure 1. Parts of the waters (ligand water) locate at the [Fe(CN)6] vacancies and coordinate to M. The residual waters (zeolite water) and alkali cations (A+) locate in the nanopores of the host framework. Most of the PBAs exhibit face-centered cubic structure (Fm3m; Z=4) [8]. The PBAs are attracting current interest of material scientists, because they exhibit useful functionalities, such as LIB properties [9–12], SIB properties [13–15], and electrochromism [16, 17].Schematic structures of PBA,AxM[Fe(CN)6]yzH2O (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.
(a)
(b)Interestingly, the size of the nanopores can be controlled by the substitution ofM: the lattice constant (a) linearly increases with the ionic size (rM) of M as a (nm) =0.891+2rM (nm) in (Cs,Rb)xMII[FeIII(CN)6]y (M=Co, Fe, Ni, Cu, Zn, Mn, and Cd) [8]. Historically, the alkali cation intercalation was interpreted in terms of the hydrated radius (rH) [22–24], rather than the ionic radius (rA) of  bare alkali cation. Actually, Tieke’s group [23, 24] reported that the self-assembled films of PBAs are permeable to smaller hydrated ions such as Cs+ (rH=0.119 nm) and K+ (rH=0.125 nm), whereas they block bigger hydrated ions such as Na+ (rH=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 Na0.76Co[Fe(CN)6]0.902.9H2O (y=0.9) with fewer vacancies. They observed that the intercalation of Na+ (rA=0.118 nm) is much faster than those of K+ (rA=0.151 nm) and Rb+ (rA=0.161 nm). This observation suggests that the intrinsic alkali cation intercalation should be interpreted in terms of rA: Li+ (rA=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.


### 1.4. Prussian Blue Analogues as Cathode Materials

The PBAs are promising cathode materials for LIBs and SIBs. Imanishi et al. [9, 10] reported Li+ intercalation behaviors in M[Fe(CN)6]y (M = V, Mn, Fe, Ni, and Cu), even though their cyclability is far from satisfactory. The cyclability is fairly improved in K0.10MnII[FeIII(CN)6]0.704.2H2O and Rb0.61MnII[FeIII(CN)6]0.872.2H2O [11]. Matsudaet al. [12] synthesized a manganese hexacyanoferrate thin film, Li1.32MnII[FeII (CN)6]0.833.5H2O, with high Li concentration (x=1.32). 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 (M=Mn, Fe, Co, No, Cu, and Zn). However, their coulomb efficiency (=60% for M=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 Na1.32MnII[FeII(CN)6]0.833.5H2O 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 Na1.60CoII[FeII(CN)6]0.902.9H2O 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 characteristics with those of the conventional cathode materials, such as LiCoO2, LiFePO4, and LiMn2O4.


## 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/MoS2 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 (C6) exhibits the Li+ intercalation/deintercalation between the C6 sheets. In addition, LiCoO2 with layered rocksalt structure is found to exhibit the Li+ intercalation/deintercalation between the CoO2 layers. In 1991, Sony cooperation firstly commercialized a C6/LiCoO2 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. LiCoO2 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 CoO2 layers and Li+, which is accommodated between the layers. The ideal capacity, LCoO2 → CoO2 + 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 CoO2 with CdI2 structure. So, in the actual use of the cell, the cutoff voltage is set to be below 4 V. The C6/LiCoO2 cell exhibits a practical capacity of 150 mAh/g. LiFePO4 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 PO4 tetrahedron and FeO6 octahedron and Li+, which is accommodated in the tube-type interstitial sites. The ideal capacity, LiFePO4 → FePO4 + Li, is 170 mAh/g. The Li deintercalation, however, causes phase separation into LiFePO4 and FePO4. In addition, LiFePO4 is an insulator with low electron conductivity (σ<10-8Ωcm), which is disadvantageous for the high charge/discharge rate. Fortunately, a carbon-coating procedure mysteriously improves the rate properties of LiFePO4. LiMn2O4 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 MnO6 octahedra. The ideal capacity, LiMn2O4 → Mn2O4 + Li, is 285 mAh/g. γ-MnO2, however, is produced at low Li concentration region. The C6/LiMn2O4∙ cell exhibits practical capacity of 140 mAh/g.


## 1.2. 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+ (Clarknumber=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], NaxMO2 (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, NaCrO2 [5] with α-NaFeO2 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 LiCrO2 exhibits poor capacity and cyclability in LIB. Na0.6MnO2 [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/NaNi0.5Mn0.5O2 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.


## 1.3. Overview of Prussian Blue Analogues

Prussian blue analogue (PBA),AxM[Fe(CN)6]yzH2O (A and M are alkali metal and transition metal, resp.), is the oldest complex compound that the human being has synthesized. The PBAs consist of a three-dimensional (3D) cyano-bridged transition metal framework (M[Fe(CN)6]y) and guests (A+and H2O) accommodated at the cubic nanopores, as schematically shown in Figure 1. Parts of the waters (ligand water) locate at the [Fe(CN)6] vacancies and coordinate to M. The residual waters (zeolite water) and alkali cations (A+) locate in the nanopores of the host framework. Most of the PBAs exhibit face-centered cubic structure (Fm3m; Z=4) [8]. The PBAs are attracting current interest of material scientists, because they exhibit useful functionalities, such as LIB properties [9–12], SIB properties [13–15], and electrochromism [16, 17].Schematic structures of PBA,AxM[Fe(CN)6]yzH2O (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.
(a)
(b)Interestingly, the size of the nanopores can be controlled by the substitution ofM: the lattice constant (a) linearly increases with the ionic size (rM) of M as a (nm) =0.891+2rM (nm) in (Cs,Rb)xMII[FeIII(CN)6]y (M=Co, Fe, Ni, Cu, Zn, Mn, and Cd) [8]. Historically, the alkali cation intercalation was interpreted in terms of the hydrated radius (rH) [22–24], rather than the ionic radius (rA) of  bare alkali cation. Actually, Tieke’s group [23, 24] reported that the self-assembled films of PBAs are permeable to smaller hydrated ions such as Cs+ (rH=0.119 nm) and K+ (rH=0.125 nm), whereas they block bigger hydrated ions such as Na+ (rH=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 Na0.76Co[Fe(CN)6]0.902.9H2O (y=0.9) with fewer vacancies. They observed that the intercalation of Na+ (rA=0.118 nm) is much faster than those of K+ (rA=0.151 nm) and Rb+ (rA=0.161 nm). This observation suggests that the intrinsic alkali cation intercalation should be interpreted in terms of rA: Li+ (rA=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.


## 1.4. Prussian Blue Analogues as Cathode Materials

The PBAs are promising cathode materials for LIBs and SIBs. Imanishi et al. [9, 10] reported Li+ intercalation behaviors in M[Fe(CN)6]y (M = V, Mn, Fe, Ni, and Cu), even though their cyclability is far from satisfactory. The cyclability is fairly improved in K0.10MnII[FeIII(CN)6]0.704.2H2O and Rb0.61MnII[FeIII(CN)6]0.872.2H2O [11]. Matsudaet al. [12] synthesized a manganese hexacyanoferrate thin film, Li1.32MnII[FeII (CN)6]0.833.5H2O, with high Li concentration (x=1.32). 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 (M=Mn, Fe, Co, No, Cu, and Zn). However, their coulomb efficiency (=60% for M=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 Na1.32MnII[FeII(CN)6]0.833.5H2O 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 Na1.60CoII[FeII(CN)6]0.902.9H2O 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 characteristics with those of the conventional cathode materials, such as LiCoO2, LiFePO4, and LiMn2O4.


## 2. Experimental Method

### 2.1. Preparation of Films

Thin films of Na1.32Mn[Fe(CN)6]0.833.5H2O (denoted as NMF83), Na1.48Mn[Fe(CN)6]0.872.5H2O (NMF87), Na1.72Mn[Fe(CN)6]0.932.3H2O (NMF93), Na1.60Co[Fe(CN)6]0.902.9H2O (NCF90), Na0.84Co[Fe(CN)6]0.713.8H2O (NCF71), Na0.72Ni[Fe(CN)6]0.685.1H2O (NNF68), and Na1.84Cd[Fe(CN)6]0.964.8H2O (NCdF96) were electrochemically synthesized on an indium tin oxide (ITO) transparent electrode under potentiostatic conditions at −0.50 V versus a standard Ag/AgCl electrode in aqueous solutions. The electrolyte compositions of the aqueous solutions are summarized in Table 1. Typical thickness of the films is ca. 1 μm, 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.Table 1
Electrolyte compositions in the electrochemical deposition of the respective PBA films. NMF83, NMF87, NMF93, NCF90, NCF71, NNF68, and NCdF96 representNa1.24Mn[Fe(CN)6]0.813.0H2O, Na1.48Mn[Fe(CN)6]0.872.5H2O, Na1.72Mn[Fe(CN)6]0.932.3H2O, Na1.60Co[Fe(CN)6]0.902.9H2O, Na0.84Co[Fe(CN)6]0.713.8H2O, Na0.72Ni[Fe(CN)6]0.685.1H2O, and Na1.84Cd[Fe(CN)6]0.964.8H2O, respectively.
Film
Electrolytes
NMF83
1.0 mmol/L K3[Fe(CN)6]
1.5 mmol MnCl2
1 mol/L NaCl
NMF87
1.0 mmol/L K3[Fe(CN)6]
1.5 mmol MnCl2
3 mol/L NaCl
NMF93
1.0 mmol/L K3[Fe(CN)6]
1.5 mmol MnCl2
5 mol/L NaCl
NCF90
0.8 mmol/L K3[Fe(CN)6]
0.5 mmol Co(NO3)2
5 mol/L NaNO3
NCF71
0.5 mmol/L K3[Fe(CN)6]
1.25 mmol Co(NO3)2
1 mol/L NaNO3
NNF68
0.5 mmol/L K3[Fe(CN)6]
0.5 mmol Ni(NO3)2
1 mol/L NaNO3
NCdF96
1.0 mmol/L K3[Fe(CN)6]
1.5 mmol MnCl2
1 mol/L NaClThe experimental error of the mass is ca. 10%. Chemical compositions of the films were determined by the inductively coupled plasma (ICP) method and CHN organic elementary analysis (Perkin-Elmer 2400 CHN Elemental Analyzer). NMF83, NCF90, NCF71, NNF68, and NCdF96 exhibit face-centered cubic structure. The lattice constants (a) are 10.544(2) A for NMF83, 10.404(2) A for NCF90, 10.296(2) A for NCF71, 10.200(3) A for NNF68, and 10.7001(4) A for NCdF96. On the other hand, NMF87 and NMF93 exhibit trigonal distortion, reflecting the guest-host interaction [26].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 LiClO4. The charge/discharge current was ca. 5 μA/cm2, and the cutoff voltage was from 2.0 to 4.2 V. The active area of the film was about 2.0 cm2. We obtained Li-substituted films: Li1.32Mn[Fe(CN)6]0.833.5H2O (LMF83), Li1.48Mn[Fe(CN)6]0.872.5H2O (LMF87), Li1.72Mn[Fe(CN)6]0.932.3H2O (LMF93), Li1.60Co[Fe(CN)6]0.902.9H2O (LCF90), Li0.71Na0.13Co[Fe(CN)6]0.713.8H2O (LCF71), Li0.68Na0.04Ni[Fe(CN)6]0.685.1H2O (LNF68), and Li0.96 Na0.88Cd[Fe(CN)6]0.964.8H2O (LCdF96).


### 2.2. 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 cm2. The electrolyte was EC/DEC solution containing 1 mol/L LiClO4. 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 cm2. The electrolyte was propylene carbonate (PC) solution containing 1 mol/L NaClO4. The cut-off voltage was from 2.0 to 4.2 V.For theex situ XRD and XAS experiments, the Li/Na concentration (x) 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 (x) is determined by the current with assuming nominal chemical compositions in the charge and discharge states. Similarly, the magnitude of Na concentration (x) 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 (x) in the discharge and charge states are summarized.Table 2
Abbreviation, compositions, and Li/Na concentration(x) in discharge and charge states.
Film
Composition
Discharge state
Charge state
LMF83
Li
xMn[Fe(CN)6]0.833.5H2O
x
=
1.32
x
=
0.00
LMF87
Li
xMn[Fe(CN)6]0.872.5H2O
x
=
1.48
x
=
0.00
LMF93
Li
xMn[Fe(CN)6]0.932.3H2O
x
=
1.72
x
=
0.00
LCF90
Li
xCo[Fe(CN)6]0.902.9H2O
x
=
1.60
x
=
0.00
LCF71
Li
xNa0.13Co[Fe(CN)6]0.713.8H2O
x
=
0.71
x
=
0.00
LNF68
Li
xNa0.04Ni[Fe(CN)6]0.685.1H2O
x
=
0.68
x
=
0.00
LCdF96
Li
xNa0.88Cd[Fe(CN)6]0.964.8H2O
x
=
0.96
x
=
0.00
NMF83
Na
xMn[Fe(CN)6]0.833.5H2O
x
=
1.32
x
=
0.00
NCF90
Na
xCo[Fe(CN)6]0.902.9H2O
x
=
1.60
x
=
0.00


### 2.3. X-Ray Powder Diffraction Measurement

Theex situXRD 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 ϕ 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 CeO2 powders (a=5.41111 A). Thus obtained power diffraction patterns are analyzed by the Rietveld method (Rietan-FP program [28]).


### 2.4. X-Ray Absorption Measurement

Theex 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 LI-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 Table3, the penetration depths (λ) for ideal Na2Mn[Fe(CN)6] and Na2Co[Fe(CN)6] are listed at the fluorescence and absorption energies of the Mn, Fe, and Co K-edges. The λ values are much bigger than the thickness (~1 μm) of the film. In this condition, the absorbed photon (=1-e-αd; α is the absorption coefficient) by the film is proportional to α.Table 3
Penetration depths(λ) for ideal Na2Mn[Fe(CN)6] and Na2Co[Fe(CN)6] at the fluorescence and absorption energies of the Mn, Fe, and Co K-edges.
Photon energy
λ for Na2Mn[Fe(CN)6]
λ for Na2Mn[Fe(CN)6]
5900 eV
Mn fluorescence
104μm
96μm
6405 eV
Fe fluorescence
132μm
121μm
6930 eV
Co fluorescence
55μm
151μm
6539 eV
Mn K-edge
139μm
128μm
7112 eV
Fe K-edge
59μm
162μm
7709 eV
Co K-edge
41μm
38μm


## 2.1. Preparation of Films

Thin films of Na1.32Mn[Fe(CN)6]0.833.5H2O (denoted as NMF83), Na1.48Mn[Fe(CN)6]0.872.5H2O (NMF87), Na1.72Mn[Fe(CN)6]0.932.3H2O (NMF93), Na1.60Co[Fe(CN)6]0.902.9H2O (NCF90), Na0.84Co[Fe(CN)6]0.713.8H2O (NCF71), Na0.72Ni[Fe(CN)6]0.685.1H2O (NNF68), and Na1.84Cd[Fe(CN)6]0.964.8H2O (NCdF96) were electrochemically synthesized on an indium tin oxide (ITO) transparent electrode under potentiostatic conditions at −0.50 V versus a standard Ag/AgCl electrode in aqueous solutions. The electrolyte compositions of the aqueous solutions are summarized in Table 1. Typical thickness of the films is ca. 1 μm, 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.Table 1
Electrolyte compositions in the electrochemical deposition of the respective PBA films. NMF83, NMF87, NMF93, NCF90, NCF71, NNF68, and NCdF96 representNa1.24Mn[Fe(CN)6]0.813.0H2O, Na1.48Mn[Fe(CN)6]0.872.5H2O, Na1.72Mn[Fe(CN)6]0.932.3H2O, Na1.60Co[Fe(CN)6]0.902.9H2O, Na0.84Co[Fe(CN)6]0.713.8H2O, Na0.72Ni[Fe(CN)6]0.685.1H2O, and Na1.84Cd[Fe(CN)6]0.964.8H2O, respectively.
Film
Electrolytes
NMF83
1.0 mmol/L K3[Fe(CN)6]
1.5 mmol MnCl2
1 mol/L NaCl
NMF87
1.0 mmol/L K3[Fe(CN)6]
1.5 mmol MnCl2
3 mol/L NaCl
NMF93
1.0 mmol/L K3[Fe(CN)6]
1.5 mmol MnCl2
5 mol/L NaCl
NCF90
0.8 mmol/L K3[Fe(CN)6]
0.5 mmol Co(NO3)2
5 mol/L NaNO3
NCF71
0.5 mmol/L K3[Fe(CN)6]
1.25 mmol Co(NO3)2
1 mol/L NaNO3
NNF68
0.5 mmol/L K3[Fe(CN)6]
0.5 mmol Ni(NO3)2
1 mol/L NaNO3
NCdF96
1.0 mmol/L K3[Fe(CN)6]
1.5 mmol MnCl2
1 mol/L NaClThe experimental error of the mass is ca. 10%. Chemical compositions of the films were determined by the inductively coupled plasma (ICP) method and CHN organic elementary analysis (Perkin-Elmer 2400 CHN Elemental Analyzer). NMF83, NCF90, NCF71, NNF68, and NCdF96 exhibit face-centered cubic structure. The lattice constants (a) are 10.544(2) A for NMF83, 10.404(2) A for NCF90, 10.296(2) A for NCF71, 10.200(3) A for NNF68, and 10.7001(4) A for NCdF96. On the other hand, NMF87 and NMF93 exhibit trigonal distortion, reflecting the guest-host interaction [26].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 LiClO4. The charge/discharge current was ca. 5 μA/cm2, and the cutoff voltage was from 2.0 to 4.2 V. The active area of the film was about 2.0 cm2. We obtained Li-substituted films: Li1.32Mn[Fe(CN)6]0.833.5H2O (LMF83), Li1.48Mn[Fe(CN)6]0.872.5H2O (LMF87), Li1.72Mn[Fe(CN)6]0.932.3H2O (LMF93), Li1.60Co[Fe(CN)6]0.902.9H2O (LCF90), Li0.71Na0.13Co[Fe(CN)6]0.713.8H2O (LCF71), Li0.68Na0.04Ni[Fe(CN)6]0.685.1H2O (LNF68), and Li0.96 Na0.88Cd[Fe(CN)6]0.964.8H2O (LCdF96).


## 2.2. 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 cm2. The electrolyte was EC/DEC solution containing 1 mol/L LiClO4. 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 cm2. The electrolyte was propylene carbonate (PC) solution containing 1 mol/L NaClO4. The cut-off voltage was from 2.0 to 4.2 V.For theex situ XRD and XAS experiments, the Li/Na concentration (x) 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 (x) is determined by the current with assuming nominal chemical compositions in the charge and discharge states. Similarly, the magnitude of Na concentration (x) 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 (x) in the discharge and charge states are summarized.Table 2
Abbreviation, compositions, and Li/Na concentration(x) in discharge and charge states.
Film
Composition
Discharge state
Charge state
LMF83
Li
xMn[Fe(CN)6]0.833.5H2O
x
=
1.32
x
=
0.00
LMF87
Li
xMn[Fe(CN)6]0.872.5H2O
x
=
1.48
x
=
0.00
LMF93
Li
xMn[Fe(CN)6]0.932.3H2O
x
=
1.72
x
=
0.00
LCF90
Li
xCo[Fe(CN)6]0.902.9H2O
x
=
1.60
x
=
0.00
LCF71
Li
xNa0.13Co[Fe(CN)6]0.713.8H2O
x
=
0.71
x
=
0.00
LNF68
Li
xNa0.04Ni[Fe(CN)6]0.685.1H2O
x
=
0.68
x
=
0.00
LCdF96
Li
xNa0.88Cd[Fe(CN)6]0.964.8H2O
x
=
0.96
x
=
0.00
NMF83
Na
xMn[Fe(CN)6]0.833.5H2O
x
=
1.32
x
=
0.00
NCF90
Na
xCo[Fe(CN)6]0.902.9H2O
x
=
1.60
x
=
0.00


## 2.3. X-Ray Powder Diffraction Measurement

Theex situXRD 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 ϕ 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 CeO2 powders (a=5.41111 A). Thus obtained power diffraction patterns are analyzed by the Rietveld method (Rietan-FP program [28]).


## 2.4. X-Ray Absorption Measurement

Theex 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 LI-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 Table3, the penetration depths (λ) for ideal Na2Mn[Fe(CN)6] and Na2Co[Fe(CN)6] are listed at the fluorescence and absorption energies of the Mn, Fe, and Co K-edges. The λ values are much bigger than the thickness (~1 μm) of the film. In this condition, the absorbed photon (=1-e-αd; α is the absorption coefficient) by the film is proportional to α.Table 3
Penetration depths(λ) for ideal Na2Mn[Fe(CN)6] and Na2Co[Fe(CN)6] at the fluorescence and absorption energies of the Mn, Fe, and Co K-edges.
Photon energy
λ for Na2Mn[Fe(CN)6]
λ for Na2Mn[Fe(CN)6]
5900 eV
Mn fluorescence
104μm
96μm
6405 eV
Fe fluorescence
132μm
121μm
6930 eV
Co fluorescence
55μm
151μm
6539 eV
Mn K-edge
139μm
128μm
7112 eV
Fe K-edge
59μm
162μm
7709 eV
Co K-edge
41μm
38μm


## 3. Li+ Intercalation

### 3.1. Manganese PBA

Figure2 shows the open-current-voltage (OCV) discharge curve of NMF83 film against Li measured at 0.05 C. The discharge curve shows two plateaus at 3.8 (plateau I) and 3.5 V (plateau II). The observed capacity (=115 mAh/g) is comparable to the ideal value (=110 mAh/g).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]).Figure3 shows the XRD patterns of powered LFM83 against Li concentration (x). 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 x-region. The lattice constants (a) are refined by Rietveld analysis with the face-centered cubic (Fm3m: Z=4) model.Figure 3
XRD pattern of powered LMF83 against Li concentration (x). Values in parentheses represent indexes in the face-centered cubic setting (cited from [19]).Figure4(a) shows the XAS spectra of LMF83 films around the Fe K-edge against x. The peak energy at x=1.32 coincides with that of low-spin (LS) Fe2+ [30]. The blue-shift with decrease in x indicates partial formation of LS Fe3+. The peak energy at x=0.00 coincides with that of LS Fe3+ [30]. In other words, all the Fe sites are oxidized in the charge state. The electronic configuration at x=0.00 becomes Mn2.49+−Fe3+ if we assume the charge neutrality: Li1.32MnII[FeII(CN)6]0.83 → 1.6Li+ + MnII0.51MnIII0.49[FeIII(CN)6]0.83. The average Fe valence (VFe) is determined by the peak energy (E) as VFe=-6569.0+0.92204E. Figure 4(b) shows the XAS spectra of LMF83 films around the Mn K-edge against x. In the low x-region, a shoulder structure appears around 6553 eV. The absorption is ascribed to Mn3+ state. The Mn valence (VMn) is estimated from the relative intensity (I) at 6553 eV as VMn=2+0.49*[I(x)-I(0.00)]/[I(1.32)-I(0.00)].XAS spectra of LMF83 films againstx around the (a) Fe K- and (b) Mn K-edges (cited from [19]).
(a)
FeK
(b)
MnKThus obtained lattice constant (a), Mn valence, and the Co valence are plotted in Figure 5. In the plateau I (0.0<x<0.4), the Mn valence decreases while the Fe valence remains trivalent. In the plateau II (0.4x<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 Mn3+ and Fe3+, respectively. Surprisingly, LMF83 remains single cubic phase without structural phase transition nor phase separation in the entire x-region. In the plateau I, the lattice constant steeply increases from 10.40 A at x=0.00 to ~10.58 A at x~0.4. The expansion is ascribed to the bigger ionic radius (=0.83 A) of high-spin (HS) Mn2+ than that (=0.65 A) of HS Mn3+. On the other hand, the lattice constant slightly decreases with increasing in x in the plateau II. The decrease is probably due to the smaller size of [FeII(CN)6]4− than that of [FeIII(CN)6]3−. Actually, the FeII–N distance (=3.00-3.01 A) is shorter than the FeIII–N distance (=3.10 A) in RbMn[Fe(CN)6] [31].(a) Discharge curve, (b) lattice constant (a), (c) Fe valence, and (d) Mn valence of NMF83 againstx. Open (filled) marks in (b), (c), and (d) mean that the data are obtained in the charge (discharge) run (cited from [19]).
(a)
LMF83 0.05 C
(b)
(c)
(d)In manganese PBA, LixMn[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+y). Strictly speaking, however, the capacity increases with the initial Li concentration (x0), because x0 (=4y-2) is lower than 1+y in the entire y-region (0<y<1). Figure 6 shows the OCV discharge curves of manganese PBA films against Li: LMF83 (y=0.83), LMF87 (y=0.87), and LMF93 (y=0.93). As expected, the capacity increases with y: 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 Mn3+ and Fe3+, respectively. This assignments are confirmed by the infrared absorption (IR) spectroscopy around the CN stretching mode region [18].OCV discharge curves of (a) LMF83, (b) LMF87, and (c) LMF93 films against Li. For convenience of explanation, we define plateaus I and II (cited from [18]).
(a)
LMF83
(b)
LMF87
(c)
LMF93Figure7 shows the XRD patterns of (a) LMF83 and (b) LMF93 against x. Similarly to the case of LMF83, the XRD patterns of LMF87 and LMF93 in the high x-region can be indexed with the face-centered cubic setting. In the low x-region, however, two phase features are observed. The extra reflections are indexed with the face-centered cubic (Fm3m: Z=4) setting in LMF87, while they are indexed with the tetragonal (I4m2: Z=2) setting in LMF93. The lattice constants are refined by the Rietveld analysis with the single- and two-phase models.Magnified XRD patterns of (a) LMF87 and (b) LMF93 againstx. Values in the parentheses represent indexes in the face-centered-cubic setting (cited from [18]).
(a)
LMF87
(b)
LMF93Figures8(a) and 8(b) show the lattice constants against x. In plateau II, where the Fe sites are selectively reduced with x, the lattice constant remains nearly constant. In plateau I, where the Mn sites are selectively reduced with x, two-phase features are observed. In (a) LMF87, a phase separation into two cubic phases takes place below x=0.44. The volume fraction of the second phase increases as x decreases. In (b) LMF93, a phase separation into cubic and tetragonal phases takes place below x=0.26. The volume fraction of the second phase increases as x decreases.Discharge curve and lattice constant (a) of (a) LMF87 and (b) LMF93 againstx. Filled marks represent the second tetragonal phase (cited from [18]).
(a)
LMF87
(b)
LMF93The 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, LixFePO4 exhibits a phase separation into LiFePO4 and FePO4 in most of the x-region [32]. In the present manganese PBA, the coexistence of bigger Mn2+ and smaller Mn3+ may cause the local strain in the low x-region. In this situation, the system tends to exhibit a spontaneous phase separation into the Li-rich (Mn2+-rich) and Li-poor (Mn3+-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 Mn3+ causes the tetragonal distortion. More detailed discussions are described elsewhere [18].


### 3.2. Cobalt PBA

Figure9 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 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]).Figure10 shows the XRD patterns of powered LCF90 against x. All the reflections can be indexed with the face-centered cubic setting, as shown in parentheses. At x=1.2, two-phase feature is observed. In addition, the reflections discontinuously shift to the lower angle side between x=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: Z=4) model.Figure 10
XRD pattern of powered LCF90 againstx. Values in parentheses represent indexes in the face-centered cubic setting (cited from [20]).Figure11(a) shows the XAS spectra of LCF90 films around the Co K-edge against x. The XAS spectrum at x=0.0 coincides with that of LS Co3+, while the spectrum at 1.6 coincides with that of HS Co2+ [30]. The electronic configuration at x=0.00 becomes Co3+–Fe2.78+ if we assume the charge neutrality: Li1.6CoII[FeII(CN)6]0.90 → 1.6Li+ + CoIII[FeII0.33FeIII0.67(CN)6]0.90. In the intermediate x-region, the average Co valences are determined by the spectral decomposition as follows. The XAS spectra [ϕ(x)] at x are decomposed into ϕ(0.0) and ϕ(1.6) as (x)=χϕ(0.0)+(1-χ)ϕ(1.6), where χ is an adjustable parameter. The average Co valence is expressed as χ+2. Note that ϕ(0.6) [ϕ(1.4)] is essentially identical to ϕ(0.0) [ϕ(1.6)]. In other words, Co is divalent in 0.0<x<0.6 while it is trivalent in 1.4<x<1.6. Figure 4(b) shows the XAS spectra of LCF90 films around the Fe K-edge against x. The peak energy at x=1.6 coincides with that of LS Fe2+ [30]. The blue-shift with decrease in x indicates partial formation of LS Fe3+. The average Fe valence (VFe) is determined by the peak energy (E) as VFe=-6569.0+0.92204E. It is, however, difficult to extract any effective information on the Fe valence due to the big error bars.XAS spectra of LCF90 films againstx around the (a) Co K- and (b) Fe K-edges (cited from [20]).
(a)
CoK
(b)
FeKThus obtained lattice constant (a), Co valence, and the Fe valence are plotted in Figure12. The Co valence remains trivalent in plateau I (0.0<x<0.7), while it remains divalent in plateau III (1.1<x<1.6). On the other hand, the Co valance steeply decreases with x in plateau II (0.7<x<1.1). These observations suggest that the plateaus I, II, and III are ascribed to the reduction processes of Fe3+, Co3+, and Fe3+, 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.(a) Discharge curve, (b) lattice constant (a), (c) Co valence, and (d) Fe valence of NCF90 againstx. Open (filled) marks in (b), (c), and (d) mean that the data are obtained in the charge (discharge) run (cited from [20]).
(a)
LCF90
(b)
(c)
(d)The most probable scenario for the structural phase transition is a cooperative charge-transfer from Fe2+ to Co3+ or the variation of the electronic configuration from Fe2+-Co2+δ to Fe2+δ-Co3+. Actually, NaxCo[Fe(CN)6]0.713.8H2O [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 x = 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 Co2+ than that (=0.55 A) of LS Co3+. More detailed discussions are described elsewhere [20].


### 3.3. Other PBAs

Figure13 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.OCV discharge curves of (a) LNN68, (b) LCF71, and (c) LCdF96 films against Li (cited from [21]).
(a)
LNF68
(b)
LCF71
(c)
LCdF96Figure14 shows the XRD patterns of powered (a) LNF68 and (b) LCF71 against x. 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: Z=4) model. Unfortunately, the powdered LCdF96 films are seriously unstable in air, and many impurity reflections are observed in the XRD pattern.XRD pattern of powered (a) LNF68 and (b) LFC71 againstx. Values in parentheses represent indexes in the face-centered cubic setting (cited from [21]).
(a)
LNF68
(b)
LCF71Figures15(a) and 15(b) shows the XAS spectra of LNF68 films. The Fe K-edge spectrum exhibits red-shift with increase in x 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 x 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 x while the Cd LI-edge spectra are essentially unchanged. This indicates that the reduction site is Fe in LCdF96.XAS spectra of LNF68 films againstx around the (a) Fe K- and (b) Ni K-edges. XAS spectra of LCF71 films against x around the (c) Fe K- and (d) Co K-edges. XAS spectra of LCdF96 films against x around the (e) Fe K- and  (f) Cd LI-edges (cited from [21]).
(a)
LNF68 Fe K
(b)
LNF68 Ni K
(c)
LCF71 Fe K
(d)
LCF71 Co K
(e)
LCdF96 Fe K
(f)
LCdF96 CdLI


## 3.1. Manganese PBA

Figure2 shows the open-current-voltage (OCV) discharge curve of NMF83 film against Li measured at 0.05 C. The discharge curve shows two plateaus at 3.8 (plateau I) and 3.5 V (plateau II). The observed capacity (=115 mAh/g) is comparable to the ideal value (=110 mAh/g).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]).Figure3 shows the XRD patterns of powered LFM83 against Li concentration (x). 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 x-region. The lattice constants (a) are refined by Rietveld analysis with the face-centered cubic (Fm3m: Z=4) model.Figure 3
XRD pattern of powered LMF83 against Li concentration (x). Values in parentheses represent indexes in the face-centered cubic setting (cited from [19]).Figure4(a) shows the XAS spectra of LMF83 films around the Fe K-edge against x. The peak energy at x=1.32 coincides with that of low-spin (LS) Fe2+ [30]. The blue-shift with decrease in x indicates partial formation of LS Fe3+. The peak energy at x=0.00 coincides with that of LS Fe3+ [30]. In other words, all the Fe sites are oxidized in the charge state. The electronic configuration at x=0.00 becomes Mn2.49+−Fe3+ if we assume the charge neutrality: Li1.32MnII[FeII(CN)6]0.83 → 1.6Li+ + MnII0.51MnIII0.49[FeIII(CN)6]0.83. The average Fe valence (VFe) is determined by the peak energy (E) as VFe=-6569.0+0.92204E. Figure 4(b) shows the XAS spectra of LMF83 films around the Mn K-edge against x. In the low x-region, a shoulder structure appears around 6553 eV. The absorption is ascribed to Mn3+ state. The Mn valence (VMn) is estimated from the relative intensity (I) at 6553 eV as VMn=2+0.49*[I(x)-I(0.00)]/[I(1.32)-I(0.00)].XAS spectra of LMF83 films againstx around the (a) Fe K- and (b) Mn K-edges (cited from [19]).
(a)
FeK
(b)
MnKThus obtained lattice constant (a), Mn valence, and the Co valence are plotted in Figure 5. In the plateau I (0.0<x<0.4), the Mn valence decreases while the Fe valence remains trivalent. In the plateau II (0.4x<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 Mn3+ and Fe3+, respectively. Surprisingly, LMF83 remains single cubic phase without structural phase transition nor phase separation in the entire x-region. In the plateau I, the lattice constant steeply increases from 10.40 A at x=0.00 to ~10.58 A at x~0.4. The expansion is ascribed to the bigger ionic radius (=0.83 A) of high-spin (HS) Mn2+ than that (=0.65 A) of HS Mn3+. On the other hand, the lattice constant slightly decreases with increasing in x in the plateau II. The decrease is probably due to the smaller size of [FeII(CN)6]4− than that of [FeIII(CN)6]3−. Actually, the FeII–N distance (=3.00-3.01 A) is shorter than the FeIII–N distance (=3.10 A) in RbMn[Fe(CN)6] [31].(a) Discharge curve, (b) lattice constant (a), (c) Fe valence, and (d) Mn valence of NMF83 againstx. Open (filled) marks in (b), (c), and (d) mean that the data are obtained in the charge (discharge) run (cited from [19]).
(a)
LMF83 0.05 C
(b)
(c)
(d)In manganese PBA, LixMn[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+y). Strictly speaking, however, the capacity increases with the initial Li concentration (x0), because x0 (=4y-2) is lower than 1+y in the entire y-region (0<y<1). Figure 6 shows the OCV discharge curves of manganese PBA films against Li: LMF83 (y=0.83), LMF87 (y=0.87), and LMF93 (y=0.93). As expected, the capacity increases with y: 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 Mn3+ and Fe3+, respectively. This assignments are confirmed by the infrared absorption (IR) spectroscopy around the CN stretching mode region [18].OCV discharge curves of (a) LMF83, (b) LMF87, and (c) LMF93 films against Li. For convenience of explanation, we define plateaus I and II (cited from [18]).
(a)
LMF83
(b)
LMF87
(c)
LMF93Figure7 shows the XRD patterns of (a) LMF83 and (b) LMF93 against x. Similarly to the case of LMF83, the XRD patterns of LMF87 and LMF93 in the high x-region can be indexed with the face-centered cubic setting. In the low x-region, however, two phase features are observed. The extra reflections are indexed with the face-centered cubic (Fm3m: Z=4) setting in LMF87, while they are indexed with the tetragonal (I4m2: Z=2) setting in LMF93. The lattice constants are refined by the Rietveld analysis with the single- and two-phase models.Magnified XRD patterns of (a) LMF87 and (b) LMF93 againstx. Values in the parentheses represent indexes in the face-centered-cubic setting (cited from [18]).
(a)
LMF87
(b)
LMF93Figures8(a) and 8(b) show the lattice constants against x. In plateau II, where the Fe sites are selectively reduced with x, the lattice constant remains nearly constant. In plateau I, where the Mn sites are selectively reduced with x, two-phase features are observed. In (a) LMF87, a phase separation into two cubic phases takes place below x=0.44. The volume fraction of the second phase increases as x decreases. In (b) LMF93, a phase separation into cubic and tetragonal phases takes place below x=0.26. The volume fraction of the second phase increases as x decreases.Discharge curve and lattice constant (a) of (a) LMF87 and (b) LMF93 againstx. Filled marks represent the second tetragonal phase (cited from [18]).
(a)
LMF87
(b)
LMF93The 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, LixFePO4 exhibits a phase separation into LiFePO4 and FePO4 in most of the x-region [32]. In the present manganese PBA, the coexistence of bigger Mn2+ and smaller Mn3+ may cause the local strain in the low x-region. In this situation, the system tends to exhibit a spontaneous phase separation into the Li-rich (Mn2+-rich) and Li-poor (Mn3+-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 Mn3+ causes the tetragonal distortion. More detailed discussions are described elsewhere [18].


## 3.2. Cobalt PBA

Figure9 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 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]).Figure10 shows the XRD patterns of powered LCF90 against x. All the reflections can be indexed with the face-centered cubic setting, as shown in parentheses. At x=1.2, two-phase feature is observed. In addition, the reflections discontinuously shift to the lower angle side between x=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: Z=4) model.Figure 10
XRD pattern of powered LCF90 againstx. Values in parentheses represent indexes in the face-centered cubic setting (cited from [20]).Figure11(a) shows the XAS spectra of LCF90 films around the Co K-edge against x. The XAS spectrum at x=0.0 coincides with that of LS Co3+, while the spectrum at 1.6 coincides with that of HS Co2+ [30]. The electronic configuration at x=0.00 becomes Co3+–Fe2.78+ if we assume the charge neutrality: Li1.6CoII[FeII(CN)6]0.90 → 1.6Li+ + CoIII[FeII0.33FeIII0.67(CN)6]0.90. In the intermediate x-region, the average Co valences are determined by the spectral decomposition as follows. The XAS spectra [ϕ(x)] at x are decomposed into ϕ(0.0) and ϕ(1.6) as (x)=χϕ(0.0)+(1-χ)ϕ(1.6), where χ is an adjustable parameter. The average Co valence is expressed as χ+2. Note that ϕ(0.6) [ϕ(1.4)] is essentially identical to ϕ(0.0) [ϕ(1.6)]. In other words, Co is divalent in 0.0<x<0.6 while it is trivalent in 1.4<x<1.6. Figure 4(b) shows the XAS spectra of LCF90 films around the Fe K-edge against x. The peak energy at x=1.6 coincides with that of LS Fe2+ [30]. The blue-shift with decrease in x indicates partial formation of LS Fe3+. The average Fe valence (VFe) is determined by the peak energy (E) as VFe=-6569.0+0.92204E. It is, however, difficult to extract any effective information on the Fe valence due to the big error bars.XAS spectra of LCF90 films againstx around the (a) Co K- and (b) Fe K-edges (cited from [20]).
(a)
CoK
(b)
FeKThus obtained lattice constant (a), Co valence, and the Fe valence are plotted in Figure12. The Co valence remains trivalent in plateau I (0.0<x<0.7), while it remains divalent in plateau III (1.1<x<1.6). On the other hand, the Co valance steeply decreases with x in plateau II (0.7<x<1.1). These observations suggest that the plateaus I, II, and III are ascribed to the reduction processes of Fe3+, Co3+, and Fe3+, 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.(a) Discharge curve, (b) lattice constant (a), (c) Co valence, and (d) Fe valence of NCF90 againstx. Open (filled) marks in (b), (c), and (d) mean that the data are obtained in the charge (discharge) run (cited from [20]).
(a)
LCF90
(b)
(c)
(d)The most probable scenario for the structural phase transition is a cooperative charge-transfer from Fe2+ to Co3+ or the variation of the electronic configuration from Fe2+-Co2+δ to Fe2+δ-Co3+. Actually, NaxCo[Fe(CN)6]0.713.8H2O [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 x = 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 Co2+ than that (=0.55 A) of LS Co3+. More detailed discussions are described elsewhere [20].


## 3.3. Other PBAs

Figure13 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.OCV discharge curves of (a) LNN68, (b) LCF71, and (c) LCdF96 films against Li (cited from [21]).
(a)
LNF68
(b)
LCF71
(c)
LCdF96Figure14 shows the XRD patterns of powered (a) LNF68 and (b) LCF71 against x. 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: Z=4) model. Unfortunately, the powdered LCdF96 films are seriously unstable in air, and many impurity reflections are observed in the XRD pattern.XRD pattern of powered (a) LNF68 and (b) LFC71 againstx. Values in parentheses represent indexes in the face-centered cubic setting (cited from [21]).
(a)
LNF68
(b)
LCF71Figures15(a) and 15(b) shows the XAS spectra of LNF68 films. The Fe K-edge spectrum exhibits red-shift with increase in x 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 x 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 x while the Cd LI-edge spectra are essentially unchanged. This indicates that the reduction site is Fe in LCdF96.XAS spectra of LNF68 films againstx around the (a) Fe K- and (b) Ni K-edges. XAS spectra of LCF71 films against x around the (c) Fe K- and (d) Co K-edges. XAS spectra of LCdF96 films against x around the (e) Fe K- and  (f) Cd LI-edges (cited from [21]).
(a)
LNF68 Fe K
(b)
LNF68 Ni K
(c)
LCF71 Fe K
(d)
LCF71 Co K
(e)
LCdF96 Fe K
(f)
LCdF96 CdLI


## 4. Na+ Intercalation

### 4.1. Manganese PBA

Figure16 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 (=−3.71V versus SHE) of Na/Na+ is higher than that (=−3.04 V 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 Mn3+ and Fe3+, respectively. This assignments are confirmed by the IR spectroscopy around the CN stretching mode region [34].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]).Figure17 show the XRD patterns of powered NFM83 against Na concentration (x). 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 x-region. The lattice constants (a) are refined by Rietveld analysis with the face-centered cubic (Fm3m: Z=4) model.Figure 17
XRD pattern of powered NMF83 against Na concentration (x). Values in parentheses represent indexes in the face-centered cubic setting (cited from [14]).Thus obtained lattice constant (a) is plotted in Figure 18. In the plateau I, the lattice constant steeply increases from 10.40 A at x=0.00 to ~10.58 A at x~0.3. The expansion is ascribed to the bigger ionic radius (=0.83 A) of HS Mn2+ than that (=0.65 A) of HS Mn3+. 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 guest-host 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.(a) Discharge curve, (b) lattice constant (a) of NMF83, and (c) lattice constant (a) of LMF83 againstx. Open (filled) marks in (b), and (c) mean that the data are obtained in the charge (discharge) run (cited from [14]).
(a)
NMF83
(b)
NMF83
(c)
LMF83


### 4.2. Cobalt PBA

Figure19 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 XAS around the Fe K- and Co K-edges reveal that the plateaus I and II are ascribed to the reduction processes of Fe3+ and Co3+, respectively [34].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]).Figure20 shows the XRD patterns of powered NCF90 against x. 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 x-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: Z=4) model.Figure 20
XRD pattern of powered NCF90 against Na concentration (x). Values in parentheses represent indexes in the face-centered cubic setting (cited from [15]).(a) Discharge curve, (b) lattice constant (a) of NCF90, and (c) a of LCF90 againstx. Open (filled) marks in (b), and (c) mean that the data are obtained in the charge (discharge) run (cited from [15]).
(a)
NCF90
(b)
NCF90
(c)
LCF90Thus 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 x~0.6 to ~10.16 A at x~1.6. The expansion is ascribed to the bigger ionic radius (=0.75 A) of HS Co2+ than that (=0.45 A) of LS Co3+. 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 (~0.02 A) bigger than those of LCF90.


## 4.1. Manganese PBA

Figure16 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 (=−3.71V versus SHE) of Na/Na+ is higher than that (=−3.04 V 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 Mn3+ and Fe3+, respectively. This assignments are confirmed by the IR spectroscopy around the CN stretching mode region [34].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]).Figure17 show the XRD patterns of powered NFM83 against Na concentration (x). 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 x-region. The lattice constants (a) are refined by Rietveld analysis with the face-centered cubic (Fm3m: Z=4) model.Figure 17
XRD pattern of powered NMF83 against Na concentration (x). Values in parentheses represent indexes in the face-centered cubic setting (cited from [14]).Thus obtained lattice constant (a) is plotted in Figure 18. In the plateau I, the lattice constant steeply increases from 10.40 A at x=0.00 to ~10.58 A at x~0.3. The expansion is ascribed to the bigger ionic radius (=0.83 A) of HS Mn2+ than that (=0.65 A) of HS Mn3+. 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 guest-host 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.(a) Discharge curve, (b) lattice constant (a) of NMF83, and (c) lattice constant (a) of LMF83 againstx. Open (filled) marks in (b), and (c) mean that the data are obtained in the charge (discharge) run (cited from [14]).
(a)
NMF83
(b)
NMF83
(c)
LMF83


## 4.2. Cobalt PBA

Figure19 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 XAS around the Fe K- and Co K-edges reveal that the plateaus I and II are ascribed to the reduction processes of Fe3+ and Co3+, respectively [34].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]).Figure20 shows the XRD patterns of powered NCF90 against x. 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 x-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: Z=4) model.Figure 20
XRD pattern of powered NCF90 against Na concentration (x). Values in parentheses represent indexes in the face-centered cubic setting (cited from [15]).(a) Discharge curve, (b) lattice constant (a) of NCF90, and (c) a of LCF90 againstx. Open (filled) marks in (b), and (c) mean that the data are obtained in the charge (discharge) run (cited from [15]).
(a)
NCF90
(b)
NCF90
(c)
LCF90Thus 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 x~0.6 to ~10.16 A at x~1.6. The expansion is ascribed to the bigger ionic radius (=0.75 A) of HS Co2+ than that (=0.45 A) of LS Co3+. 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 (~0.02 A) bigger than those of LCF90.


## 5. Characteristics of PBA

### 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 LiCoO2 causes the successive structural phase transitions and eventually produces CoO2 with CdI2 structure. In LiMn2O4. γ-MnO2 is produced at low Li concentration region. In LiFePO4, the Li deintercalation causes the phase separation into LiFePO4 and FePO4.In Table4, 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 x-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 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.Table 4
Experimental and calculated capacities of PBA films together with the structural responses.
Film
Capacity exp.
Capacity calc.
Ref.
Structural response
LMF83
115 mAh/g
110 mAh/g
[16]
Robust
LMF87
130 mAh/g
134 mAh/g
[16]
Phase separation
LMF93
143 mAh/g
153 mAh/g
[16]
Phase separation
LCF90
139 mAh/g
138 mAh/g
[22]
Phase transition
LCF71
70 mAh/g
72 mAh/g
[13]
Robust
LNF68
69 mAh/g
64 mAh/g
[13]
Robust
LCdF96
58 mAh/g
64 mAh/g
[13]
Robust
NMF83
130 mAh/g
103 mAh/g
[24]
Robust
NCF90
133 mAh/g
127 mAh/g
[25]
Robust


### 5.2. 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 LiFePO4, the Li+ deintercalation causes phase separation into LiFePO4 and FePO4 [32]. The flat working voltage of 3.5 V is determined by LiFePO4.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.


## 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 LiCoO2 causes the successive structural phase transitions and eventually produces CoO2 with CdI2 structure. In LiMn2O4. γ-MnO2 is produced at low Li concentration region. In LiFePO4, the Li deintercalation causes the phase separation into LiFePO4 and FePO4.In Table4, 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 x-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 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.Table 4
Experimental and calculated capacities of PBA films together with the structural responses.
Film
Capacity exp.
Capacity calc.
Ref.
Structural response
LMF83
115 mAh/g
110 mAh/g
[16]
Robust
LMF87
130 mAh/g
134 mAh/g
[16]
Phase separation
LMF93
143 mAh/g
153 mAh/g
[16]
Phase separation
LCF90
139 mAh/g
138 mAh/g
[22]
Phase transition
LCF71
70 mAh/g
72 mAh/g
[13]
Robust
LNF68
69 mAh/g
64 mAh/g
[13]
Robust
LCdF96
58 mAh/g
64 mAh/g
[13]
Robust
NMF83
130 mAh/g
103 mAh/g
[24]
Robust
NCF90
133 mAh/g
127 mAh/g
[25]
Robust


## 5.2. 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 LiFePO4, the Li+ deintercalation causes phase separation into LiFePO4 and FePO4 [32]. The flat working voltage of 3.5 V is determined by LiFePO4.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.


## 6. Summary

The SR XRD and XAS reveal the following characteristic features of PBA against Li+/Na+ intercalation/deintercalation.(1)
Host framework is robust 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 ofM–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 inter-ion distance (~5 A) as well as (2) the separation of the ions by the square window of the framework.



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*Source: 967285-2013-10-08.xml*