Invariant nature of substituted element in metal-hexacyanoferrate

The chemical substitution of a transition metal (M) is an effective method to improve the functionality of materials. In order to design the highly functional materials, we first have to know the local structure and electronic state around the substituted element. Here, we systematically investigated the local structure and electronic state of the host (M h) and guest (M g) transition metals in metal-hexacyanoferrate (M-HCF), Nax(M h, M g)[Fe(CN)6]y (1.40 < x < 1.60 and 0.85 < y < 0.90), by means of extended X-ray absorption fine structure (EXAFS) and X-ray absorption near-edge structure (XANES) analyses. The EXAFS and XANES analyses revealed that the local structure and electronic state around M g are essentially the same as those in the pure compound, i.e, M g-HCF. Such an invariant nature of M g in M-HCF is in sharp contrast with that in layered oxide, in which the M g valence changes so that local M g-O distance (d M-O g) approaches the M h-O distance (d M-O h).

structures. The M-HCFs are attracting current interest of material scientists, because they are promising materials for the lithium-ion secondary batteries (LIBs) [8][9][10] , SIBs 2,3,11-20 , electrochromism 21,22 , and thermoelectrics 23 . In SIBs, the rate and cycle properties of Mn-HCF are significantly improved by partial substitution of Fe, Co, and Ni for Mn 2,3 . Thus, M-HCF is a suitable system for investigation of the local structure and electronic state around M g and M h .
Here, we systematically investigated the local structure and electronic state around M g and M h in Na x (M h , M g ) [Fe(CN) 6 ] y (1.40 < x < 1.60 and 0.85 < y < 0.90) by means of the EXAFS and XANES analyses. The analyses revealed that the local structure and electronic state of M g are essentially the same as that in the pure material, i.e., M g -HCF. Such an invariant nature of M g in M-HCF is in sharp contrast with that in layered oxide, in which the M g valence changes so that d M-O g approaches d M-O h . We will discuss the origin for the difference in the substitution effect between M-HCF and the layered oxide.

EXAFS analysis
We performed careful EXAFS analysis on three pure (M-HCF) and six mixed (M h M g -HCF) compounds. Details of synthesis and characterization are described in the Method section. The x-ray diffraction (XRD) patterns for the nine compounds are shown in Fig. S1. In the EXAFS analyses, we included the contributions from the first-(N) and second-(C) nearest neighbor elements. In order to include the Fe(CN) 6 Table 1.    ) in the pseudo-cubic setting.

Electronic state
Now, let us proceed to the electronic state of M g and M h . Figure 4 shows the XANES spectra of the pure (M-HCF) and mixed (M h M g -HCF) compounds around the (a) Mn K-edge, (b) Co K-edge, and (c) Ni K-edge. The thick black curve represents the spectra of pure compounds. The thin solid and broken curves correspond to the spectra around M h and M g in the mixed compounds, respectively.  6 ] y . Red, blue and green colors represent the interatomic distances around Mn, Co, and Ni, respectively.
In the Mn K-edge spectra [ Fig. 4(a)], the main peak is attributable to the Mn1s-4p transition, whose position is a crude measures of the Mn valence. The blue-(red-) shift of the main peak suggests increase (decrease) in the Mn valence. In Mn-HCF (thick black curve), the main peak is observed at 6548.0 eV. We observed no detectable peak-shift in MnCo-and MnNi-HCFs, indicating that the Mn valence is robust against the partial substitution. Importantly, the peak positions of the substituted Mn in CoMn-and NiMn-HCFs are the same as that of Mn-HCF. Figure 4(d) shows magnified Mn K-edge spectra in the pre-edge region, which is dominated by the Mn1s-3d transition. We observed no detectable peak shift in MnCo-and MnNi-HCFs. These observations indicate that electronic states of the substituted Mn in MnCo-and MnNi-HCFs are the same as that in Mn-HCF. This is consistent with the fact that the ligand (CN − ) environments around substituted Mn in CoMn-and NiMn-HCFs are the same as that in Mn-HCF [Figs 1(b) and 3(b)].
Similarly to the case of the Mn K-edge spectra, we observed no detectable peak-shift in the Co K-and Ni-K-edge spectra. In Fig. 4(b), the peak positions of substituted Co in MnCo-and NiCo-HCFs are the same as that in Co-HCF. In Fig. 4(c), the peak positions of substituted Ni in MnNi-and CoNi-HCFs are the same as that in Ni-HCF. We observed no detectable peak shift in the respective pre-edge region [ Fig. 4(e) and (f)]. Thus, the electronic states of the substituted Co and Ni are the same as those in Co-and Ni-HCFs, respectively. This is consistent with the fact that the ligand (CN − ) environments around substituted Co and Ni are the same as those Co-and Ni-HCFs, respectively [see Fig. 1(b) and Fig. 3(b)].

Discussion
Now, let us discuss the difference in the local structures between the M-HCF and layered oxides. In M-HCF, the local structure around M g is essentially the same as that in the pure compound. In layered oxide, however, the M g valence changes so that  (Table S2). We found that d Fe-C (and d Fe-N ) is the same for the nine compounds within the experimental errors. By contract, in transition metal oxides, the hybridization between the O 2p and M 3d orbitals effectively causes the M-dependent charge exchange between O and M. Such a hybridization can modify the M g valence to minimize the Gibbs free energy. Secondary, the jungle-gym type network of M-HCF is flexible against the partial substitution. This is because the network is fairly sparse and has considerable Fe(CN) 6 vacancies. Actually, the density (~1.9 g/cm 3 ) of M-HCF is much smaller than that (=5.0 g/cm 3 6 ] and 4 M NaCl). In both the cases, the latter solution was stirred at 250 rpm with a magnetic stirrer during the instillation. The dropping rate ( = 100 ml/hour) was controlled with use of a tube pump. After the instillation, the solutions were kept for 12 hours. Then, the precipitates were gathered with a 0.1 μm filter, washed well with distilled water, and dried in air. The colors of the obtained powders were white (Mn-HCF), light yellow (MnNi-HCF), light green (Ni-, MnCo-, and CoMn-HCF), light blue (NiMn-HCF), and dark green (Co-, CoNi-, and NiCo-HCF).
The chemical compositions of the pure compounds were determined so as minimize the trial function:  Table 2.
Crystal structure and lattice constants. Synchrotron-radiation XRD measurements were performed at the BL8A beamline of the Photon Factory, KEK. The wavelength (=0.689028 Å) of the X-ray was calibrated by the lattice constant of standard CeO 2 powders. The samples were finely ground and placed in 0.3 mmφ glass capillaries. The capillaries were sealed and mounted on the Debye-Scherrer camera. The XRD patterns (Fig. S1) were detected with an imaging plate. The exposure time was 5 minutes. The XRD patterns of Ni-, NiCo-, and X-ray absorption spectroscopy. The X-ray absorption spectroscopy (XAS) measurements were conducted at BL-9C of the Photon Factory, KEK. The powder was finely ground, mixed with BN, and pressed into pellets with 5 mm in diameter. The XAS were recorded in a transmission mode with a Si(111) double-crystal monochromator at 300 K. The wavelengths of the monochromator were calibrated with the absorption edge of Fe, Mn, Co, and Ni foil. In X-ray absorption near edge structure (XANES) analyses, the background subtraction and normalization were performed using the ATHENA program 25 .

EXAFS analysis.
After the background subtraction and normalization of the XAS spectra, oscillatory components χ were extracted against the angular wavenumber k. k is defined by = − k m E E 2 ( )/ o  where m, E, and E 0 are the electron mass, energy of the incident X-ray, and absorption edge energy, respectively. Then, Fourier transformation of χ(k)k 3 was performed in the k-range from 3.0 to 11.0 Å −1 These data procedures were performed with use of ATHENA program 25 .
In order to refine the structural parameters, least-squares fittings are performed for the FT[χ(k)k 3 ] − R plots with use of ARTEMIS program 25 . In the plane wave and single-scattering approximation, χ(k) around the K-edge is expressed by the EXAFS equation as: , and ϕ j are the passive electron reduction factor, degeneracy of path, path length, effective scattering amplitude, mean square displacement, and effective scattering phase shift of the jth atom, respectively. The least-squares fittings were performed in the R range from 1 Å to 3.  Figure 2S shows prototypical examples of the fitting. The obtained structural parameters are listed in Table S1.In the analyses around the Fe K-edge, we included the contributions from the first-(C) and second-(N) nearest neighbor elements. Because of the linear Fe-C-N-M coordination, single (Fe-N-Fe), double (Fe-N-C-Fe), and triple (Fe-C-N-C-Fe) scattering paths were taken into account in the analyses of second nearest neighbor elements (N). We fixed N C and N N at 6. The obtained structural parameters are listed in Table S2.