In situ observation of macroscopic phase separation in cobalt hexacyanoferrate film

Lithium-ion secondary batteries (LIBs) store electric energy via Li+ deintercalation from cathode materials. The Li+ deintercalation frequently drives a first-order phase transition of the cathode material as a result of the Li-ordering or Li-concentration effect and causes a phase separation (PS) into the Li-rich and Li-poor phases. Here, we performed an in situ microscopic investigation of the PS dynamics in thin films of cobalt hexacyanoferrate, LixCo[Fe(CN)6]0.9, against Li+ deintercalation. The thick film (d = 1.5 μm) shows a characteristic macroscopic PS of several tens of μm into the green (Li1.6Co[Fe(CN)6]0.9) and black (Li.6Co[Fe(CN)6]0.9) phases in the x range of 1.0 < x < 1.6. Reflecting the substrate strain, the thin film (d = 0.5 μm) shows no trace of the PS in the entire x region. Our observation suggests that the macroscopic PS plays a significant role in the charge/discharge dynamics of the cathode.

] 0.9 , is another ideal platform to investigate the PS dynamics against Li + deintercalation. In addition, yhe Li x Co[Fe(CN) 6 ] 0.9 film is a promising cathode material for LIB, showing a discharge capacity of 139 mAh/g and average voltage of 3.6 V 16 . Let us consider the structural correlation between Li x FePO 4 and Li x Co[Fe(CN) 6 ] 0. 9 . Li x FePO 4 is built up of two-dimensional (2D) sheets with [FeO 4 ] n formula of corner-sheared FeO 6 octahedra. These sheets are connected by PO 4 tetrahedra to make a three-dimensional (3D) skeleton. The Li + deintercalation oxidizes Fe 2+ to Fe 3+ and causes significant change in the Fe-O bond length, which leads to the PS. On the other hands, Li x Co[Fe(CN) 6 ] 0.9 is built up of [Fe(CN) 6 ] 4− octahedra. Similarly to the case of Li x FePO 4 , these octahedra are connected by Co 2+ ions to make a 3D skeleton. The Li + deintercalation oxidizes Co 2+ to Co 3+ and causes significant change in the Co-N bond length, which leads the PS into the green (high-x) and black (low-x) phases at x~1.2 16 . The green and black phases show the face-centered cubic structure and are formally expressed as Li 1.6 Co 2+ [Fe 2+ (CN) 6 ] 0.9 and Li 0.6 Co 3+ [Fe 2+ (CN) 6 ] 0.9 , respectively. Importantly, phase transformation into the black phase causes significant volume contraction: lattice constants (a) are 1.02 nm in the green phase and 1.00 nm in the black phase. The volume change is ascribed to the oxidization and resultant spin state transition of Co. Actually, the X-ray absorption near-edge structure (XANES) around the Co K-edge 16 indicates that Co 2+ and Co 3+ take the high-spin and low-spin states, respectively. Thus, in both the materials, the Li + deintercalation, and resultant oxidization of the 3D skeletons, causes the cooperative structural distortion and PS.
Here, we performed an in situ microscopic investigation of PS dynamics in the Li x Co[Fe(CN) 6 ] 0.9 films with use of the color difference between the green and black phases against Li + deintercalation. In thick film (d = 1.5 μ m), we observed a characteristic macroscopic PS of several tens of μ m into the original green and secondary black phases below x < 1.0. The length scale (several tens of μ m) is much larger than the crystal grain size (several hundreds of nm). We, however, observed no trace of the PS in thin film (d = 0.5 μ m) and ascribed the absence of the PS to the strain due to the substrate. Figure 1 shows absorption spectra of the Li x Co[Fe(CN) 6 ] 0.9 film against x. The film thickness (d = 1.0 μ m) was chosen so that the minimum transmittance (at 380 nm) becomes ~0.04. The spot of the light source is about 1 mm in diameter. Roughly speaking, the spectra at x = 1.6 and 1.0 corresponds to the green and black phases, respectively. In the green phase, the intense absorption observed around 380 nm is ascribed to the electron transfer from Fe 2+ to the neighboring Co 2+ 17 . In the black phase, the broad absorption observed around 540 nm is ascribed to the electron transfer from Fe 2+ to the neighboring Co 3+ 17 . The absorption intensity at 540 nm shows significant change in the phase transformation from the green to black phases. So, the 540 nm bands can be used as a sensitive monitor of the respective phases. The perpetration depth at the probe light wavelength is 0.4-1.0 μ m. The minimum transmittance at the probe light wavelength is 0.04 even for the thickest (d = 1.5 μ m) film. Figure 2 shows the charge curve of the Li x Co[Fe(CN) 6 ] 0.9 film (d = 1.5 μ m) at 0.7 C against x, together with the microscopic images. In the late stage (0.6 < x < 0.0) of the charge curve, a plateau is observed at around 4.0 V. This plateau is ascribed to the reduction process of Fe 2+ to Fe 3+ 16 . At x = 1.6, the microscopic image is homogeneous and green, indicating that the system is in the green phase (Li 1.6 Co 2+ [Fe 2+ (CN) 6 ] 0.9 ). With decreases in x, the black region appears (x = 1.4), increases in area (x = 1.2 and 1.0), and finally covers the entire image (x = 0.8). The black region corresponds to the black phase (Li 0.6 Co 3+ [Fe 2+ (CN) 6 ] 0.9 ) because the region does not transmit the green light (Fig. 1). Thus, we observed macroscopic PS in thick film. We performed Rietveld structural analysis (Rietan-FP 18 ) of the synchrotron-radiation X-ray powder diffraction pattern of Li 1.2 Co[Fe(CN) 6 ] 0.9 (Fig. 3S). The a values of the green and black phases are 1.01848 ± 0.00006 nm and 0.99535 ± 0.00007 nm, respectively. With further decrease in x below x = 0.8, the image gradually becomes bright. This is because parts of Fe 2+ , which is the final state of the optical transition, are oxidized to Fe 3+ with decrease in x. Looking at Fig. 2 (the x = 1.4, 1.2, and 1.0 images), the size of the green region gradually shrinks without changing the contrast, indicating that no additional nucleation of the black micro-domain occurs within the green region. That is, the transformation from green (Li 1.6 Co 2+ [Fe 2+ (CN) 6 ] 0.9 ) to black (Li 0.6 Co 3+ [Fe 2+ (CN) 6 ] 0.9 ) phases takes place at the phase boundary via selective Li + deintercalation. We emphasize that the length scale (several tens of μ m) of the PS is much longer than that (several hundred nm: see Figs S1 and S2) of the crystal grain size of the film. We consider that the volume contraction due to the phase transformation into the black phase is the main driving force of the macroscopic PS, as schematically shown in Fig. 3 The observed Δ L/L ( = − 0.013) value in the black phase is quantitatively consistent with that ( = − 0.023) evaluated from the lattice constants of the green and black phase. In other words, the lattice contraction due to the phase transformation propagates beyond the respective grains. Then, the lattice contraction causes a significant strain at the phase boundary. In such a region, the Li + deintercalation and subsequent phase transformation into the black phase is much easier than nucleation of a new micro-domain of Li 0.6 Co 3+ [Fe 2+ (CN) 6 ] 0.9 in another part of the green region. This scenario is essentially the same as the 'domino-cascade model' of Li x FePO 4 14 .

In Situ Observation of PS Dynamics
The PS dynamics are critically dependent on the film thickness. Figure 4 shows the charge curve of the Li x Co[Fe(CN) 6 ] 0.9 film (d = 0.5 μ m) at 0.9 C against x, together with the microscopic images. In the late stage (0.6 < x < 0.0) of the charge curve, a plateau due to the reduction process of Fe 2+ to Fe 3+ is observed at around 4.0 V. We observed no trace of the macroscopic PS. The image becomes dark with a decrease in x from x = 1.6 to 0.8. This is because parts of Co 2+ are oxidized to Co 3+ , which is the initial state of the optical transition, with decrease in x. With further decrease in x below 0.8, the image becomes bright again. This is because parts of Fe 2+ , which is the final state of the optical transition, are oxidized to Fe 3+ with decrease in x.

Normalized Absorption Intensity I n Against x
To investigate the PS dynamics in more detail, we quantitatively investigated the absorption intensity against x. Recall that the 540 nm absorption band is ascribed to the electron transfer from Fe 2+ to the neighboring Co 3+ . Then, the absorption intensity at x = 1.6 (Li 1.6 Co 2+ [Fe 2+ (CN) 6 ] 0.9 ) and at x = 0.6 (Li 0.6 Co 3+ [Fe 2+ (CN) 6 ] 0.9 )   6)]. Here, we assume a homogeneous Co oxidization in the x range of 1.6 > x > 0.6 and a homogeneous Fe oxidization in the x range of 0.6 > x > 0.0 (mean-field model). In this model, I n is expressed as 1.6 − x (1.6 > x > 0.6) and x + 0.4 (0.6 > x > 0.0), because I n is proportional to the probability of finding the Co 3+ site adjacent to the Fe 2+ site. The red lines in Fig. 5(a) and (b) are the results of the mean-field model. Figure 5(a) shows I n of the thick film against x in the black (A and A′ ), phase boundary (B and B′ ), and green (C and C′ ) regions. Data were averaged in 2 × 2 μ m 2 area, as indicated by squares in Fig. 5(c). In the x range of 1.6 > x > 0.6, the I n − x curves show significant position dependence and seriously deviate from the mean-field model (red lines). In the x range of 0.6 > x > 0.0, however, the I n − x curves overlap each other and nearly obey the mean-field model (red lines). In the black region (A and A′ ), I n steeply increases to ~1 with a decrease in x below x = 1.2, indicating selective Li + deintercalation and transformation into the black phase. The increase in I n gradually saturated below x = 1.2, indicating that the black region covers the entire 2 × 2 μ m 2 square. In the green region (C and C′ ), I n remains nearly zero in the x range of 1.6 < x < 1.0. With further decrease in x, I n steeply increases to ~1, indicating that the phase boundary reaches the square. In the boundary region (B and B′ ), I n shows an intermediate behavior between the two limiting cases. The increase of the I n − x curve, however, is rather gradual. This unexpected behavior implies finite width of the phase boundary due to the gradual change of x and/or inclination of the boundary. Figure 5(b) shows the I n − x curves of the thin film (0.5 μ m) at 0.9 C against x: The curve nearly obeys the mean-field model (red lines) in the entire x region, indicating that Co 2+ and Fe 2+ are homogeneously oxidized in the respective plateaus in the thin film.

Discussion
According to classical nucleation theory, Li deficiencies in the parent Li 1.6 Co[Fe(CN) 6 ] 0.9 pool together to form micro-clusters of Li 0.6 Co[Fe(CN) 6 ] 0.9 . The cluster deterministically grows when its size stochastically reaches a critical size, which is determined by the balance between the free energy gain due to the transformation and the strain loss at the interface. Unfortunately, the nucleation process is difficult to detect due to the limited spatial resolution ( = 1 μ m) of the optical microscopy. We investigated the microscopic image in the 1 st discharge process and found that the black region remains as islands even in the fully discharged state (Li 1.6 Co[Fe(CN) 6 ] 0.9 ) (the x = 1.6 image in Fig. S6). This is in sharp contrast with the initial homogeneous image (the x = 1.6 image in Fig. 2) of the ion-exchanged Li 1.6 Co[Fe(CN) 6 ] 0.9 . Such islands are probably stabilized by local compression or local Fe deficiency in the film. Thus, physical or chemical inhomogeneity of the cathode materials is advantageous for the PS. Finally, let us discuss the d-dependence of the PS dynamics. If the film were free-standing [ Fig. 3(a)] without any constraint, macroscopic PS would be possible even in the thin film. The actual film, however, consists of columnar crystal grains 19 . The bottom parts of the crystal pillars are strongly pinned at the indium tin oxide (ITO) substrate, as schematically shown in Fig. 3(b). We will call this model as "constraint model". Similarly to the case of the 1.5 μ m film, we evaluated Δ L/L between x = 1.6 and 1.4. The Δ L/L value is − 0.002 ± 0.006 [ Fig. S4(c)]. We observed no detectable displacement in the in-plane direction, which support the constraint model. In the constraint model, the Gibbs free energy change is expressed as Δ G = Δ G phase transformation + Δ G deformation . The first term is the Gibbs free energy change due phase transformation in the free-standing system, while the second term deformation energy of the pillars. To realize the PS (Δ G < 0), the energy gain (− Δ G phase transformation ) due to the phase transformation and the interfacial strain must surpass the energy loss (− Δ G deformation ) due to the pillar bending. The thicker the film becomes, the smaller − Δ G deformation becomes. Thus, the constraint model well explains why the PS appears in the thick film (Fig. 2) but is absent in the thin films (Fig. 4). Judging from the fact the 1. The thick film shows a characteristic macroscopic PS of several tens of μ m into the original green and secondary black phases below x < 1.0. We further found that the PS is absent in the thin film, reflecting the strain due to the substrate. This suggests that the external strain due to the surrounding environment crucially influences the PS dynamics within the respective particles, and hence the cycle and rate properties of the cathode. The X-ray diffraction patterns of the Na 1.6 Co[Fe(CN) 6 ] 0.9 films were obtained with a Cu Kα lines (Fig. S7). All the reflections can be indexed with the face-centered cubic structure. The lattice constants (a) were 1.027 nm for both the films. The morphologies of the Na 1.6 Co[Fe(CN) 6 ] 0.9 films were investigated with atomic force microscopy (AFM: Fig. S1) and scanning electron microscopy (SEM: Fig. S2). The films consist of crystalline grains of several hundred nm in diameter. The cross-sectional SEM image 19 indicates that the respective crystalline grains are columnar.

Method
Optical battery cell for microscopy. The optical battery cell has a structure of Li 1.6 Co[Fe(CN) 6 ] 0.9 film on an ITO glass/Teflon sheet with a square hole/anode. The anode was a small piece of Li metal attached on a cupper foil, which was sandwiched between the Teflon sheet and slide glass. The hole in the Teflon sheet was filled with electrolyte. The electrolyte was an ethylene carbonate (EC)/diethyl carbonate (DEC) solution containing 1 mol/L LiClO 4 . The cell was assembled under Ar atmosphere in an Ar-filled glove box and was sealed with Kapton tape. The charge/discharge behavior of the cell was stable and was consistent with the literature 16 even under air atmosphere for at least ten hours. It is difficult to precisely evaluate the capacity due to the bubbles of Ar gas which were inevitably introduced in the hole. Actually, some parts of the Li 1.6 Co[Fe(CN) 6 ] 0.9 film remained unchanged during the charge/discharge process. Therefore, we assume a fully charged and fully discharged state of x = 0.0 and 1.6, respectively.
In situ microscopic observation of the PS dynamics. The in situ microscopic PS dynamics were recorded with a microscopy system equipped with a charge-coupled device (CCD) camera for moving images. A halogen lamp was monochromized with a dichroic filter (DIF-50S-GRE: Sigma Koki, Co Ltd.) and used as the probe light source. The transmission range of the filter was 515-560 nm. The spatial resolution of the system was 1 μ m. The probe light sensitively monitored the absorption band due to the electron transfer from Fe 2+ to neighboring Co 3+