Inter-particle structural fluctuation of Prussian blue analogue as investigated by X-ray microbeam diffraction

Highly crystalline CoNi-PBA powder was prepared by citrate method ^34–36) from aqueous solutions containing Na⁺, Co²⁺, Ni²⁺, and [Fe(CN)₆]⁴⁻. In this method, the growth rate are reduced by storing Co²⁺ and Ni²⁺ in the form of citrate complex. Reflecting the slow growth rate, it is possible to obtain highly crystalline particles of uniform size (∼100 nm). CoNi-PBA were synthesized by slow dipping of solution A into solution B at 60 °C. The solution B was stirred at 300 rpm with a magnetic stirrer during the instillation. The dropping rate (=150 ml h⁻¹) was controlled with use of a tube pump. After the instillation, the solutions were kept for 1 h at 60 °C. Then, the precipitates were gathered with a 0.05 μm filter, washed well with distilled water, and dried in air. In Table I, we summarized the synthesis conditions of CoNi-PBA against the nominal Ni concentration (z_n). The chemical composition was determined using an inductively coupled plasma method. In Table II, we summarized the chemical composition of CoNi-PBA against z_n.

Figure S1 (available online at stacks.iop.org/JJAP/60/025502/mmedia) shows pictures of obtained CoNi-PBA. The color of the powder changes from light green at z = 0.0 (Co-PBA) to colorless at 1.0. Figure S2 shows scanning electron microscope (SEM) image of CoNi-PBA powders, obtained using a SEM equipment (JSM-IT200, JEOL Ltd.) with acceleration voltage of 2 kV. The powder composed of cubic particles with highly crystallinity and uniform size. With increase in z, the particle size gradually decreases from 489 ± 104 nm at z = 0.0 (Co-PBA) to 274 ± 56 nm at 1.0.

For structural characterization, synchrotron radiation X-ray diffraction (XRD) measurements were conducted at the BL02B2 beamline ^37,38) at SPring-8. The CoNi-PBA powder was filled into a 500 μmϕ glass capillary. The capillary, whose rotation axis was adjusted by a robot, was placed at the Debye-Scherrer camera. The XRD patterns were monitored using a Si microstrip solid-state detector (MYTHEN, Dectries Ltd.). The typical exposure time was 1 min. The wavelength (=0.618 970 Å) of the X-rays was calibrated using the cell parameter of a standard CeO₂ powder. Figure S3 shows XRD patterns of CoNi-PBA. In the whole region of z, the crystal structure was trigonal ($R\overline{3}m;$ Z = 3). The lattice constants, a and c, we refined by Rietveld method using Rietan-FP program. ³⁹⁾ In Table II, we summarized a and c of CoNi-PBA against z_n.

The system used for the X-ray microbeam diffraction measurements was installed in an experimental hutch of the BL40XU beamline at SPring-8. ^30–33,40) The energy of the fundamental synchrotron radiation can be set between 8 and 17 keV by changing the undulator gap. A further monochromatic X-ray beam (ΔE/E = 0.02%) was formed by using an Si (111) channel-cut monochromator. The wavelength of the X-ray beam was 0.829 91 Å. To obtain sufficient photon flux density, the monochromatic X-ray beam was focused by a phase zone plate with a 300 mm focal length. The photon flux and beam size at the sample were 9 × 10⁹ photons s⁻¹ and 1.06 × 2.88 μm², respectively. Diffraction images were reported using a Debye-Scherrer camera with a two-dimensional Si pixel array detector (EIGER X 1M, Dectries Ltd.). The camera length and 2θ position of the detector were 300.1 mm and 13.00 deg., respectively.

The CoNi-PBA powder was dispersed in liquid paraffin and thinly applied on a SiN membrane, whose window was 500 × 500 μm² in size and 0.5 μm in thickness. First, we carefully examined X-ray irradiation effect on the diffraction peak. We found that the diffraction peak gradually shifted to the high-2θ side in several seconds. The shift indicates that the X-ray irradiation causes volume shrinkage, probably due to the desorption of water molecules. Actually, Moritomo et al. ⁴¹⁾ reported that the lattice constant a decreases with decrease in the water concentration (w) in Na_0.50Co[Fe(CN)₆]_0.72 wH₂O. To avoid X-ray irradiation damage, the SiN membrane was continuously moved with a speed of 5 μm s⁻¹. Figure 1(a) shows picture of the SiN membrane around the window. The bright brown region contains CoNi-PBA powders. Square black and red line represent the scanned region (400 × 400 μm²) and scanned route, respectively. Diffraction image was recorded every second with an exposure time of 1 s.

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We further investigated X-ray irradiation effect on the inter-particle structural fluctuation. The Co-PBA powder was loosely filled into a 500 μmϕ glass capillary. Without swinging the ω axis of the capillary, the Co-PBA powder was X-ray irradiated for 180 s. During the X-ray irradiation, diffraction image was recorded every second with an exposure time of 1 s. After the measurements, the capillary was moved by 5 μm along the length direction. The same measurements were repeated 16 times.

Figure 1(b) shows prototypical example of the diffraction image of Co-PBA. Two diffraction peaks are observed as indicated by red arrows. These two diffraction peaks are the (012) reflections from two independent single particles that satisfy the Bragg's diffraction condition. We selected 50 diffraction peaks for each compound and investigated the inter-particle distribution of the spacing (d₀₁₂) of the (012) plane.

Figure 2 shows histogram of d₀₁₂ of CoNi-PBA against z. The average ($\overline{{d}_{012}}$) of d₀₁₂ gradually decreases with z; $\overline{{d}_{012}}=5.160$ Å at z = 0.00, 5.157 Å at 0.03, 5.153 Å at 0.12, 5.147 Å at 0.28, and 5.117 Å at 1.00. On the other hand, the standard deviation (σ) of d₀₁₂ remains small and nearly independent of z; σ = 0.006 Å at z = 0.00, 0.005 Å at z = 0.03, 0.005 Å at z = 0.12, 0.003 Å at z = 0.28, and 0.005 Å at z = 1.00. σ was evaluated by $\sqrt{\tfrac{1}{n}{\rm{\Sigma }}{({d}_{012}-\overline{{d}_{012}})}^{2}}$. Here, let us compare σ of d₀₁₂ with the average ($\overline{{{\rm{\Gamma }}}_{012}}$) of the full width of half maxima (Γ₀₁₂) of the (012) reflection. $\overline{{{\rm{\Gamma }}}_{012}}$ is nearly independent of z; $\overline{{{\rm{\Gamma }}}_{012}}=0.017$ Å at z = 0.00, 0.020 Å at 0.03, 0.018 Å at 0.12, 0.019 Å at 0.28, and 0.017 Å at 1.00. Thus, σ(≤0.006 Å) of d₀₁₂ is much smaller than $\overline{{{\rm{\Gamma }}}_{012}}$ (≈0.02 Å), indicating that the inter-particle structural fluctuation is negligible in the as-grown powder.

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Figure 3 shows X-ray irradiation time (t) dependence of d₀₁₂ of Co-PBA. Different symbols means values of the different single particles. The X-ray irradiation effect shows remarkable particle dependence. For the particle indicated by open circle, d₀₁₂ steeply decreases under X-ray irradiation from 5.15 Å at t = 1 s to 5.03 Å at 100 s. On the contrary, for the particle indicated by closed circle, d₀₁₂ hardly changes under X-rays irradiation. Figure S4 shows the corresponding diffraction images against t.

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Figure 4 shows histogram of d₀₁₂ of Co-PBA against t. $\overline{{d}_{012}}$ steeply decreases with t; $\overline{{d}_{012}}=5.156$ Å at t = 1 s, 5.138 Å at 30 s, 5.118 Å at 60 s, and 5.120 Å at 120 s. Surprisingly, σ of d₀₁₂ remarkably increases with t; σ = 0.006 Å at t = 1 s, 0.015 Å at 30 s, 0.031 Å at 60 s, and 0.031 Å at 120 s. We note that $\overline{{{\rm{\Gamma }}}_{012}}$ is nearly independent of t; $\overline{{{\rm{\Gamma }}}_{012}}=0.016$ Å at t = 1 s, 0.021 Å at 30 s, 0.019 Å at 60 s, and 0.019 Å at 120 s. Above t = 60 s, σ (≥0.031 Å) becomes larger than $\overline{{{\rm{\Gamma }}}_{012}}$ (=0.019 Å), indicating that the inter-particle structural fluctuation is induced by the X-ray irradiation. Here, we emphasize that the intra-particle structure remains homogeneous even under the X-ray irradiation, because $\overline{{{\rm{\Gamma }}}_{012}}$ (≈0.02 Å) remains small.

Here, let us briefly discuss the X-ray irradiation effects on $\overline{{d}_{012}}$ and σ. The decrease in $\overline{{d}_{012}}$ can be ascribed to the desorption of water molecules triggered by the X-ray irradiation, because lattice constant a decreases with decrease in the water concentration (w) in Na_0.50Co[Fe(CN)₆]_0.72 wH₂O. ⁴¹⁾ We ascribed the increase in σ to the distribution of the [Fe(CN)₆] deficiency (=15%) for each particle. We note that water molecules are to large (=3.80 Å) too pass through the window (∼5 × 5 Ų) of the PBA network. Then, the water molecules can only move through the crystal along the [Fe(CN)₆]-deficient path. Such a [Fe(CN)₆]-deficient path should strongly depend on the local growth environment for each particle. In particles where the path is linked from the inside to outside of the crystal, water molecules can be easily desorbed along the path. In particles where the path is terminated in crystal, water molecules cannot leave the crystal. In short, the easiness of the desorption of water molecules strongly depends on the particle. As a results, the water concentration within the crystal, and hence, d₀₁₂ is widely distributed after the X-ray irradiation. We note that the independence of $\overline{{{\rm{\Gamma }}}_{012}}$ on t indicates that both the distribution of the [Fe(CN)₆] deficiency and the amount of the crystal water has negligible effects on the intra-particle structural homogeneity. On the other hand, there exists a strong correlation between the amount of the crystal water and lattice constant, ⁴¹⁾ which causes the inter-particle structural fluctuation in the X-ray irradiated Co-PBA powder.