Journal ArticleDOI

# Hierarchical structure of niobate nanosheets in aqueous solution

21 Apr 2007-Journal of Applied Crystallography (International Union of Crystallography)-Vol. 40

AbstractThe hierarchical structure of an aqueous dispersion of niobate nanosheets was explored by using a combined method of ultra-small-angle and small-angle scattering of neutrons and X-rays. The concentration of the sheets studied was in the range where the dispersion exhibits a liquid-crystal phase as evidenced by observation between crossed polarizers in a previous report. The scattering data covered a wide q scale of more than four orders of magnitude [3 × 10−4 ≤ q ≤ 10 nm−1, where q = (4π/λ)sin(θ/2), λ and θ being the wavelength of the incident beam and the scattering angle, respectively], corresponding to the length scale l = 2π/q from ~1 nm to ~20 µm. The scattering analyses provided information on the hierarchical structural elements including: (i) single nanosheets as a structure element (hierarchy I), (ii) parallel stacks of the sheets (hierarchy II), and (iii) spatial arrangements of the stacks (hierarchy III), in order of increasing length scale. Hierarchy II is closely related to the liquid-crystal nature of the dispersion in which the spacing and the persistence length, normal and parallel to the stack surface, respectively, were disclosed. Hierarchy III gives rise to the low-q upturn in the scattering profile, which may be characterized by mass-fractal-like power-law scattering behavior. This finding is a surprise from the viewpoint of the liquid-crystal nature of the dispersion, a possible model of which is proposed in the text.

Topics: Scattering (57%), Length scale (53%), Dispersion (optics) (51%), Potassium niobate (50%)

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##### References
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4,586 citations

### "Hierarchical structure of niobate n..." refers background in this paper

• ...…scattering function of the particle form factor P(q) for randomly oriented thin discs of thickness d and radius R satisfying the criterion d << R (Guinier & Fournet, 1955), PðqÞ ¼ 4V2 20 2 q2R2 1 J1 2qRð Þ qR sin2ðqd=2Þ ðqd=2Þ2 ; ð1Þ where V is the volume of the particle, 0 is the scattering…...

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Journal ArticleDOI
Abstract: Introdzution. The shapes of colloidal particles are often reasonably compact, so that no diameter greatly exceeds the cube root of the volume of the particle. On the other hand, we know many coiloids whose particles are greatly extended into sheets (bentonite), rods (tobacco virus), or flexible chains (myosin, various Iinear polymers). In some instances, a t least, solutions of such highly anisometric particles are known to exhibit remarkably great deviations from Raoult’s law, even to the extent that an anisotropic phase may separate from a solution in which the particles themselves occupy but one or two per cent of the total volume (tobacco virus, bentonite). We shall show in what follows how such results may arise from electrostatic repulsion between highly anisometric particles. Most colloids in aqueous solution owe their stability more or less to electric charges, so that each particle will repel others before they come into actual contact, and effectively claim for itself a greater volume than what it actuaily occupies. Thus, we can understand that colloids in general are apt to exhibit considerable deviations from Raoult’s law and that crystalline phases retaining a fair proportion of solvent may separate from concentrated solutions. However, if we tentatively increase the known size of the particles by the known range of the electric forces and multiply the resulting volume by four in order to compute the effective van der Waal’s co-volume, we have not nearly enough to explain why a solution of 2 per cent tobacco virus in 0.005 normal NaCZ forms two phases.

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### "Hierarchical structure of niobate n..." refers background in this paper

• ...1(b) (Onsager, 1949)....

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• ...The huge nanosheets are ordered to form a liquid-crystalline phase, which is basically explained by Onsager’s theory (Onsager, 1949), as evidenced by observation between crossed polarizers (Miyamoto & Nakato, 2004)....

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### "Hierarchical structure of niobate n..." refers methods in this paper

• ...The absolute intensities for SAXS and USAXS were obtained using the nickel-foil method (Hendricks, 1972)....

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Journal ArticleDOI
Abstract: In this article, the authors review the studies on the photofunctions of intercalation compounds. (The structures and properties of host materials which have been used for immobilizing photoactive species have been summarized in the following section.) some of these studies are for the purpose of characterizing the properties of host materials and host-guest systems, and others are for the purpose of contributing to future practical applications. The well-defined layered structures as well as the ability to accommodate guest species on the surface of the layers are very useful for organizing photoactive species to evaluate and control the photofunctions. Table 1 summarizes the characteristics of typical host-guest systems studied for immobilizing photoactive species. Attention is mainly focused on the role of layered structure on the organization of photoactive species; the photofunctions of intercalation compounds are discussed only in connection with the microscopic structures. 321 refs.

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### "Hierarchical structure of niobate n..." refers background in this paper

• ...The semiconductive and photocatalytic nature inherent in the layered K4Nb6O17 crystal has potential applications for electronic devices (Ogawa & Kuroda, 1995)....

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Journal ArticleDOI
TL;DR: Small-angle neutron scattering from normal, compressed, and water-suspended powders of aggregates of fine silica particles has been studied and the intensity of scattering was found to scale with the correlation length in the manner expected for a fractal system.
Abstract: Small-angle neutron scattering from normal, compressed, and water-suspended powders of aggregates of fine silica particles has been studied. The samples possessed average densities ranging from 0.008 to 0.45 g/${\mathrm{cm}}^{3}$. Assuming power-law correlations between particles and a finite correlation length \ensuremath{\xi}, we derive the scattering function S(q) from specific models for particle-particle correlation in these systems. S(q) was found to provide a satisfactory fit to the data for all samples studied. The fractal dimension ${d}_{f}$ corresponding to the power-law correlation was 2.61\ifmmode\pm\else\textpm\fi{}0.1 for all dry samples, and 2.34\ifmmode\pm\else\textpm\fi{}0.1 for the water-suspended samples. The intensity of scattering was found to scale with the correlation length in the manner expected for a fractal system.

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### "Hierarchical structure of niobate n..." refers background in this paper

• ...The power-law scattering behavior has been often related to two kinds of fractal dimensions; one is the mass fractal dimension df and the other is the surface fractal dimension ds (Freltoft et al., 1986)....

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