A unified theory of absolute intensity measurements in small-angle X-ray scattering

Hendricks, R. W.

doi:10.1107/s0021889872009690

Cited by 93 publications

(73 citation statements)

References 9 publications

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“…The obtained SAXS profiles were corrected for background scattering and slitheight and slit-width smearings. The absolute SAXS intensity was obtained by the standard nickel foil method (Hendricks, 1972). Fig.…”

Section: Sans and Saxs Measurementmentioning

confidence: 99%

A combined small-angle scattering study of a chemical reaction at specific sites and reaction-induced self-assembly as a problem in open non-equilibrium phenomena

et al. 2007

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As a problem in open non-equilibrium phenomena, small-angle scattering (SAS) studies of chemical reactions at specific sites and reaction-induced selfassembly of a system which is obtained by mixing two stable solutions of palladium acetate [Pd(OAc) 2 ] in N,N-dimethylformamide and the secondgeneration polyamidoamine dendrimer in methanol are presented. The selfassembly was studied using a combination of neutron and X-ray SAS. The results revealed that the self-assembly involves the initial formation of aggregates of an average radius of 20 nm composed of the dendrimers and Pd(OAc) 2 followed by formation of palladium nanoparticles of a radius of 2.0 nm inside the aggregates. The aggregates were found to provide a special field for a chemical reaction for reduction of Pd(II) ions with methanol and for the self-assembly of the reduction products of Pd(0) atoms into nanoparticles. The nanoparticles are found to be trapped and stabilized in the aggregates.

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Section: Sans and Saxs Measurementmentioning

confidence: 99%

A combined small-angle scattering study of a chemical reaction at specific sites and reaction-induced self-assembly as a problem in open non-equilibrium phenomena

et al. 2007

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“…Background scattering arising from thermal diffuse scattering (TDS) (Vonk, 1973) was subtracted from the SAXS data. The absolute intensities for SAXS and USAXS were obtained using the nickel-foil method (Hendricks, 1972).…”

Section: Scattering Apparatusmentioning

confidence: 99%

Hierarchical structure of niobate nanosheets in aqueous solution

et al. 2007

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The 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.

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“…Equation (14) has found many important applications in the use of small-angle scattering for determination of internal surfaces. To use (14) to find the internal surface, however, the absolute small-angle scattering intensity (Hendricks, 1972) must be determined. It is worth mentioning the conditions necessary to obtain (14).…”

Section: Power-law Scattering From Non-fractal Scatterersmentioning

confidence: 99%

Small-angle scattering studies of disordered, porous and fractal systems

Schmidt¹

1991

J Appl Crystallogr

567

390

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Small-angle X-ray and neutron scattering are important techniques for studying the structure of fractals and other disordered systems on a scale of lengths from about 10 to 2000 A. This review begins with a brief outline of some properties of fractals. The small-angle scattering from fractal systems is then discussed and the effect of polydispersity is considered. The intensity of small-angle scattering from fractals and other disordered systems is often proportional to a negative power of the quantity q = 4~,t-Isin(0/2), where 0 is the scattering angle and ,~ is the X-ray or neutron wavelength. From the magnitude of the exponent that describes this type of scattering, which is often called power-law scattering, much important information can be obtained. Some situations in which power-law scattering can be expected are described. To illustrate the scattering from fractals and disordered systems, several experimental investigations of mass-fractal silicas and porous solids are reviewed and some calculations of the small-angle scattering from model fractal systems are outlined.

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A unified theory of absolute intensity measurements in small-angle X-ray scattering

Cited by 93 publications

References 9 publications

A combined small-angle scattering study of a chemical reaction at specific sites and reaction-induced self-assembly as a problem in open non-equilibrium phenomena

A combined small-angle scattering study of a chemical reaction at specific sites and reaction-induced self-assembly as a problem in open non-equilibrium phenomena

Hierarchical structure of niobate nanosheets in aqueous solution

Small-angle scattering studies of disordered, porous and fractal systems

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