Introduction

The partial substitution of the host transition metal (Mh) to the guest transition metal (Mg) is an effective method to improve the functionality of the materials, such as its electrochemical1,2,3,4,5,6, magnetic7,8,9, and dielectric10 properties. For example, NaFe0.5Co0.5O21 with an O3-type layered structure shows a high discharge capacity of 160 mAh/g and good cyclability, which is much higher than those of the parent O3-NaFeO2 and O3-NaCoO2. To microscopically comprehend the substitution effect, degree of distribution (random, attractive, and repulsive distribution: Fig. 1) of Mg is a crucial parameter. In the random distribution (Fig. 1a), the probability to find Mg at the nearest-neighboring site of Mg is the same as the mixing ratio (x) of Mg. The probability is higher than x in the attractive distribution (Fig. 1b) while it is lower than x in the repulsive distribution (Fig. 1c). Thus, we can describe the degree of distribution with parameter s that modifies the probability to find Mg at the nearest-neighboring site as sx. s = 1, > 1, < 1 represent the random, attractive, and repulsive distribution, respectively. Here, we propose that a systematic extended X-ray absorption fine structure (EXAFS) analysis against the Mg concentration can reveal the spatial distribution of Mg. The K-edge EXAFS analysis of 3d transition metals (Ms) is a powerful technique to determine the local intermetal distance around the corresponding M in the mixed compounds. Importantly, the observed intermetal distance [dMg–M(x)] around Mg is the probability-weighted average of dMg–Mg and dMg–Mh, because a difference between dMg–Mg and dMg–Mh is too small to separate. Then, we can extract the parameter s from systematic dMg–M(x) data against x.

Figure 1
figure 1

Distribution of the partial substituted element (Mg): (a) random, (b) attractive, and (c) repulsive distribution. In the present case, the mixing ratio x is 1/6. So, the probability to find Mg at the nearest-neighboring site is 1/6 in (a) random distribution, while it is higher (lower) than 1/6 in the (b) attractive [(c) repulsive] distribution.

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The O3-type layered transition metal oxides, O3-NaMO2 (M = Cr, Fe, and Co), show quite simple crystal structure with alternating MO2 layers and Na sheets11. The MO2 layer consists of edge-sharing MO6 octahedra formed by covalent bonding. Especially, O3-NaFeO2 and O3-NaCoO2 form solid solution in the entire composition range. O3-NaFeO2 has been investigated due to its electrochemical12, magnetic13,14 properties. On the other hand, O3-NaCoO2 has been investigated due to its electrochemical15, thermoelectric16, and superconductive17 properties. In addition, the ionic radius (r = 0.645 Å) of high-spin Fe3+ is much larger than that (r = 0.545 Å) of low-spin Co3+. In this sense, O3-NaCo1−xFexO2 is a suitable system for investigation of degree of distribution of Fe.

We chose NaCo1−xFexO2 as a prototypical transition metal compound and systematically investigated the local intermetal distance around the host Co [dCo–M(x)] and the guest Fe [dFe–M(x)] against x. The x-dependence of dFe–M(x) was analyzed by an empirical equation, \({d}_{\mathrm{F}\mathrm{e}-M}(x)=sxd_{\mathrm{F}\mathrm{e}-\mathrm{F}\mathrm{e}}+(1-sx)d_{\mathrm{F}\mathrm{e}-\mathrm{C}\mathrm{o}}\), where dFe–Fe and dFe–Co are the Fe–Fe and Co–Fe distances, respectively. The obtained s value (= 4.8) indicates aggregation tendency of guest Fe in NaCo1−xFexO2.

Results

Local structure around transition metal

Figure 2a,b show prototypical Fourier transformation of the χ(k)k3–R plots around the host Co and the guest Fe in NaCo0.998Fe0.002O2, respectively. χ and k are the oscillatory components of the normalized absorption and wavenumber, respectively. In the Co K-edge EXAFS spectra (Fig. 2a), two intense peaks are observed at around 1.5 Å and 2.4 Å (without phase shift correction), which are assigned to the paths to the first- (O) and second- (M) nearest neighbor elements, respectively (Fig. 2c). The corresponding peaks are observed in the Fe K-edge EXAFS spectra (Fig. 2b). With including contributions from first-(O), second-(M), and third-(Na) nearest neighbor elements, we performed least-squares fittings with the EXAFS equation in the R range from 1.0 to 3.22 Å. Thus, obtained parameters around Co and Fe are listed in Tables 1 and 2, respectively. The Co–O distance [dCo–O = 1.918(11) Å] and Co–Co distance [dCo–Co = 2.875(9) Å] in NaCoO2 are close to the crystallographic values, 1.935 Å and 2.890 Å18, within experimental error.

Figure 2
figure 2

Fourier transforms of k3-weighted (a) Co and (b) Fe K-edge EXAFS spectra for NaCo0.998Fe0.002 without phase shift correction. Red curves are the results of the least-squares curve-fitting with the EXAFS equation in the R range from 1.0 to 3.22 Å. (c) Schematic structure of O3-NaMO2. The first- (M–O), the second- (M–M), and the third (M–Na) scattering paths are indicated by allows.

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Table 1 Structural parameters of NaCo1−xFexO2 obtained by Co K-edge EXAFS analyses.
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Table 2 Structural parameters of NaCo1−xFexO2 obtained by Fe K-edge EXAFS analyses.
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Co and Fe K-edge X-ray absorption near edge structure (XANES) spectra for NaCo1-xFexO2 are shown in Figs. S1 and S2 in the supplementary information, respectively. We observed no detectable peak-shift in Co K-edge XANES spectra. We observed no detectable main peak shift for Fe K-edge XANES spectra, even though the spectral shape is slightly distorted due to the self-absorption effect19. These observations indicate that electronic states of the host Co and guest Fe are almost the same.

Interatomic distances (d Co–O and d Fe–O) to the nearest-neighboring oxygen

Figure 3 shows the Co–O (dCo–O) and the Fe–O (dFe–O) distances in NaCo1−xFexO2 against x. As indicated by the eye-guide straight lines, dCo–O and dFe–O are almost constant against x within experimental error. The larger error bars in dFe–O are originated in the lower concentration of Fe and the resultant worse S/N ratio of the EXAFS signal. The robust nature of dCo–O and dFe–O is ascribed to the fact that the Co (Fe) sites are surrounded by six oxygens as MO6 even in the mixed crystal. A similar robust nature of the interatomic distance to the first nearest elements is reported in the mixed crystal of metal-hexacyanides20, in which M is surrounded by six cyanide as M(NC)6.

Figure 3
figure 3

Co–O (dCo–O) and Fe–O (dFe–O) distance of NaCo1−xFexO2 against x. Straight lines are guides for the eye. Open and closed symbols represent the corresponding EXAFS data obtained in the transmission and fluorescence modes, respectively.

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Interatomic distances (dCo–M and dFe–M) to the nearest-neighboring transition metals

Figure 4 shows the Fe–M (dFe–M) and Co–M (dCo–M) distances in NaCo1−xFexO2 against x. dCo–O is apparently robust against x. This is partly because difference between dCo–Co [= 2.875(9) Å] and dCo–Fe [= 2.91 Å; extrapolated value of dFe–M(x) at x = 0] is too small to detect x-dependence of dCo–M(x). Looking at Fig. 4, one may notice that dFe–M(x) shows significant x-dependence and increases with x, reflecting larger ionic radius of high-spin Fe3+ than that of low-spin Co3+.

Figure 4
figure 4

Co–M (dCo–M) and Fe–M (dFe–M) distances of NaCo1−xFexO2 against x. Open and closed symbols represent the corresponding EXAFS data obtained in the transmission and fluorescence modes, respectively. Broken curves are calculated by \({d}_{\mathrm{C}\mathrm{o}-M}(x)=x{d}_{\mathrm{C}\mathrm{o}-\mathrm{F}\mathrm{e}}+(1-x){d}_{\mathrm{C}\mathrm{o}-\mathrm{C}\mathrm{o}}\) and \({d}_{\mathrm{F}\mathrm{e}-M}(x)=x{d}_{\mathrm{F}\mathrm{e}-\mathrm{F}\mathrm{e}}+(1-x){d}_{\mathrm{F}\mathrm{e}-\mathrm{C}\mathrm{o}}\), respectively. Red solid curve is the least-square fitting by the empirical equation; \({d}_{\mathrm{F}\mathrm{e}-M}(x)=sxd_{\mathrm{F}\mathrm{e}-\mathrm{F}\mathrm{e}}+(1-sx)d_{\mathrm{F}\mathrm{e}-\mathrm{C}\mathrm{o}}\) (s = 4.8).

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First, let us consider the situation of random distribution of the guest Fe. As explained in the introduction section, dCo–M(x) [dFe–M(x)] determined by the EXAFS analyses corresponds to the probability-weighted average of dCo–Co and dCo–Fe (dFe–Co and dFe–Fe). In the random distribution of Fe, the probability to find Fe (Co) at the nearest-neighboring transition metal site is x (1 − x). Then, dCo–M(x) [dFe–M(x)] is expressed as \({d}_{\mathrm{C}\mathrm{o}-M}(x)=x{d}_{\mathrm{C}\mathrm{o}-\mathrm{F}\mathrm{e}}+(1-x){d}_{\mathrm{C}\mathrm{o}-\mathrm{C}\mathrm{o}}\) [\({d}_{\mathrm{F}\mathrm{e}-M}(x)=x{d}_{\mathrm{F}\mathrm{e}-\mathrm{F}\mathrm{e}}+(1-x){d}_{\mathrm{F}\mathrm{e}-\mathrm{C}\mathrm{o}}\)], where dCo–Co (= 2.875(9) Å; Table 1), dCo–Fe (= dFe–Co), and dFe–Fe are Co–Co, Co–Fe, and Fe–Fe distances, respectively. We use the crystallographic value (= 3.022 Å18) of NaFeO2 for dFe–Fe while we used the extrapolated value (= 2.913 Å) of dFe–M at x = 0 for dFe–Co (see Fig. 4). The broken curves in Fig. 4 is the calculation of dCo–M (x) [dFe–M(x)]. Concerning to dCo–M(x), the calculation under random distribution satisfactory reproduces the experimental data. Concerning to dFe–M(x), the calculation fails to reproduce the experimental data. The deviation between experiment and calculation indicates deviation from the random distribution of Fe. Here, we modify the probability to find Mg at the nearest-neighboring site as sx. s = 1, > 1, < 1 represent the random, attractive, and repulsive distribution, respectively (Fig. 1). Then, we obtained empirical equation as

$${d}_{\mathrm{F}\mathrm{e}-M}\left(x\right)=sxd_{\mathrm{F}\mathrm{e}-\mathrm{F}\mathrm{e}}+\left(1-sx\right)d_{\mathrm{F}\mathrm{e}-\mathrm{C}\mathrm{o}}.$$
(1)

In general, an additional term such as constant*x(1 − x) is adopted to compensate the deviation between experimental data and the linear relation, because the term becomes zero at x = 0 and 1. We, however, applied a more straightforward expression (Eq. 1). The parameter (s) directly modifies the probability to find Fe at the nearest-neighboring site and has clear physical meaning. The red curve in Fig. 4 is the least-squares fitted results with Eq. (1). The fitted curve well reproduces the experimental data. The obtained s (= 4.8) is larger than unity, indicating that the Fe distribution has an aggregation tendency.

Discussion

The origin of the aggregation tendency of Fe is probably the distortion energy originated in the difference in the ionic radius between high-spin Fe3+ (r = 0.645 Å) than low-spin Co3+ (r = 0.545 Å). Actually, the lattice constant (a = 3.022 Å, c = 16.074 Å18) of NaFeO2 is much larger than those (a = 2.890 Å, c = 15.609 Å18) of NaCoO2. Then, the region where Fe and Co are mixed has extra distortion energy. Reflecting to this extra distortion energy, NaCo1−xFexO2 has the phase-separation instability, or, spatially decomposition into (1 − x)NaCoO2 and xNaFeO2. In the free energy point of view, the phase separation significantly decreases the entropy, and hence, is not realized unless the gain of the internal energy is huge enough. Even if the phase separation is not realized, there remains the phase separation tendency, that is, the aggregation tendency of the guest Fe, as observed in Fig. 4.

In addition, we point out the Kinetics effect in synthesis. NaCo1−xFexO2 were synthesized by sloid state reaction at relatively lower temperature (~ 850 K). In this situation, atomic migrations within the compound is not enough to reach the ground state. As a result, the compound remains in the metastable state with relatively random distribution. Amaha et al.21 investigated chemical and structural inhomogeneity of two sets of NaFe1/2Co1/2O2: one was prepared by quenching and the other was prepared by slowly-cooling after the synthesis at 1,173 K, respectively. They observed traces of inhomogeneity in the slowly-cooled compound while no trace of inhomogeneity was observed in the quenched one. This observation is consistent with the aggregation tendency of the guest Fe as detected the systematic EXAFS analyses against x in the present study.

Summary

We systematically investigated dCo–M(x) and dFe–M(x) of NaCo1−xFexO2 against x. We found that dFe–M(x) steeply increases with increases in x. The x-dependence of dFe–M(x) was analyzed by an empirical equation, \({d}_{\mathrm{F}\mathrm{e}-M}(x)=sxd_{\mathrm{F}\mathrm{e}-\mathrm{F}\mathrm{e}}+(1-sx)d_{\mathrm{F}\mathrm{e}-\mathrm{C}\mathrm{o}}\). The obtained s value (= 4.8) indicates the aggregation tendency of the guest Fe in NaCo1−xFexO2. Thus, systematic EXAFS analysis against Mg concentration is a highly sensitive method to detect deviation from the random distribution of Mg in partially substituted materials.

Methods

Sample preparation and characterization

Layered oxides NaCo1−xFexO2 were prepared by solid state reaction. Na2O2, Co3O4, and Fe2O3 were mixed in a 1.2:1–n:n atomic ratio and calcined at 858 K for 20 h in O2. n (= 0, 0.002, 0.005, 0.010, 0.020, and 0.005) is the nominal Fe content. Then, the product was finely ground, and again calcined in the same condition. The actual Fe content (x) in NaCo1−xFexO2 were determined by the inductively-coupled plasma (ICP) method as shown in Fig. S3 (x = 0, 0.002, 0.006, 0.012, 0.024, 0.060, respectively).

The X-ray diffraction (XRD) patterns were obtained using an X-ray powder diffractometer (MultiFlex, Rigaku, Tokyo, Japan) with the Bragg–Brentano (θ–2θ) geometry. The X-ray source was the Cu Kα line (λ = 1.54 Å) operated at 40 kV and 40 mA. The observed diffraction peaks can be indexed with O3-type structure (R \(\stackrel{-}{3}\) m; Z = 3) without detectable impurities such as defect-spinel phases (Fig. S4). The lattice constants a and c were refined by the Rietveld analysis (Rietan-FP22) with a trigonal model (R \(\stackrel{-}{3}\) m; Z = 3, hexagonal setting). Reflecting the larger ionic radius of Fe3+, a and c increase with x (Fig. S5).

Local structural analysis by EXAFS

The extended X-ray absorption fine structure (EXAFS) measurements were conducted at BL-9A beamline of the Photon Factory, KEK. The synchrotron radiation was monochromatized by a Si (111) double-crystal monochromator. The energy resolution (ΔE/E) was ~ 2 × 10−4 and the photon flux at sample position was ~ 4 × 1011 phs/s. The samples were finely ground, mixed with BN, and pressed into pellets with 5 mm in diameter. Co K-edge EXAFS spectra of NaCo1−xFexO2 with x = 0.000, 0.002, 0.006, 0.012, 0.024, and 0.060 and Fe K-edge EXAFS spectra of NaCo1−xFexO2 with x = 0.012, 0.024, and 0.060 were recorded in transmission mode with a gas-filled ion chamber at room temperature. Fe K-edge EXAFS spectra of NaCo1−xFexO2 with x = 0.002, 0.006, and 0.012 were recorded in fluorescence mode using a 19-element solid-state detector (SSD). Before the SSD, a Mn filleter was used to remove the background signal from Co Kα fluorescence.

The background subtraction, normalization and analyses of EXAFS spectra were performed using the ATHENA program and EXAFS analyses were performed using the ARTEMIS programs23 as described elsewhere18,20. First, the oscillatory components were extracted using the ATHENA program after background subtraction and normalization of the absorption spectra. Thus, we obtained χ(k)k3 – k plots, where χ and k are the oscillatory components of the normalized absorption and angular wavenumber, respectively. Co and Fe K-edge EXAFS oscillations without any modelling results for NaCo1-xFexO2 are shown in Figs. S6 and S7, respectively. The Fourier transformations of the χ(k)k3–R plots were performed in the k-range from 3.0 to 14.0 Å−1 at Co K-edge and from 2.0 to 8.5 Å−1 at Fe K-edge using the ATHENA program. In the plane wave and single-scattering approximation, χ(k) around the K-edge is expressed by the EXAFS equation as:

$$\upchi \left(k\right)=-{S}_{0}^{2}\sum_{j}\frac{{N}_{j}}{k{R}_{j}^{2}}{F}_{j}\left(k\right){e}^{-2{\sigma }_{j}{k}^{2}}\sin\left\{2k{R}_{j}+{\phi }_{j}\left(k\right)\right\},$$
(2)

where S0, Nj, Rj, Fj, σj2, and φj 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 k is defined by \(k=\sqrt{2m(E-{E}_{o})/\hslash }\) where m, E, and E0 are the electron mass, energy of the incident X-ray, and energy shift, respectively. In the least-squares curve fitting, we included the contribution from first (O), second (TM), and third (Na) nearest neighbor elements. We fixed Nj for the three elements at the crystallographic value (N1 = N2 = N3 = 6). We used the same S0 parameter for the three elements. The least-squares fittings were performed in q-space, which is inverse Fourier transformation in the R range from 1 to 3.22 Å. The best fitted results are shown in Figs. S8–S14.

Here, we consider the validity of the number of the free parameters (Nfp) in the EXAFS analysis. In general, Nfp should not exceed the maximum number of independent parameters (Nidp = 2ΔkΔR/π)24. For Co K-edge EXAFS, Nidp is 15 since Δk is 11 Å−1 and ΔR is 2.22 Å. For Fe K-edge EXAFS, Nidp is 9 since Δk is 6.5 Å−1 and ΔR is 2.22 Å. Even if we exclude the k-range less than 3 which is not relevant to the EXAFS, Nidp for Fe K-edge EXAFS is 8. The free parameters used for analysis are S02, E0, dFe–O, dFe–M, dFe–Na, σFe–O, σFe–M, σFe–Na for Fe K-edge EXAFS spectrum. Since S02 is common for six spectra, the substantial Nfp is 7 + 1/6 for each Fe K-edge EXAFS spectrum. Similarly, the free parameters used for analysis are S02, E0, dCo–O, dCo–M, dCo–Na, σCo–O, σCo–M, σCo–Na for Co K-edge EXAFS spectrum. The substantial Nfp is 7 + 1/6 for each Co K-edge EXAFS spectrum because S02 is common for six Co spectra. Therefore. Nfp (= 7 + 1/6) is less than Nidp for both the Co and Fe K-edge EXAFS spectra.

Here, let us consider the difference between the error bar (σr) of interatomic distance (r) obtained by the EXAFS analysis and the experimental resolution (Δr) in Fourier transformed R-space. σr (e.g. 0.005–0.011 Å for dFe-M) is determined by the least-squares fitting of the experimental data by EXAFS Eq. (2). In general, the χ2 statistic is defined as25

$${\chi }^{2}\equiv \sum_{i=1}^{n}\left\{\frac{1}{{\sigma }_{i}^{2}}{\left[{y}_{i}-y({x}_{i})\right]}^{2}\right\}$$
(3)

where yi, y(xi), and σi are the observed values, calculated values, and uncertainty in yi, respectively. In the present case, y(xi) are evaluated by the EXAFS Eq. (2) at xi. Then, σr is given by.

$${\sigma }_{r}=\sqrt{2{\left(\frac{{\partial }^{2}{\chi }^{2}}{\partial {r}^{2}}\right)}^{-1}}.$$
(4)

On the other hand, Δr is the lower limit value at which two peaks (shells) are separated and is given by Δr = π/2Δk, where Δk = kmax − kmin26. Δr for Fe (Co) K-edge EXAFS spectrum is 0.24 (0.14) Å. Thus, Δr is different from σr.