Asymptotic Expansion of the Intensity of the Small‐Angle X‐Ray Scattering from Cylinders of Arbitrary Cross Section

1965 ◽  
Vol 6 (3) ◽  
pp. 424-431 ◽  
Author(s):  
Paul W. Schmidt
Keyword(s):  
Asymptotic Expansion ◽  
Cross Section ◽  
Small Angle ◽  
Arbitrary Cross Section ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

Characterization of TEMPO-oxidized cellulose nanofibers in aqueous suspension by small-angle X-ray scattering

2014 ◽  
Vol 47 (2) ◽  
pp. 788-798 ◽  
Author(s):  
Ying Su ◽  
Christian Burger ◽  
Benjamin S. Hsiao ◽  
Benjamin Chu
Keyword(s):  
Cross Section ◽  
Small Angle ◽  
Structural Information ◽  
Rectangular Cross Section ◽  
Aqueous Suspension ◽  
Cellulose Nanofibers ◽  
Weighted Average ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

Cellulose nanofibers, extracted from wood pulps using the (2,2,6,6-tetramethylpiperidine-1-yl)oxyl (TEMPO)-mediated oxidation method, are low-cost, sustainable and high-performance materials with potential usage in many applications. The structural information of these cellulose nanofibers in aqueous suspension was characterized by synchrotron small-angle X-ray scattering (SAXS). A simplified ribbon model having a near rectangular cross section was found to give the best fit to the SAXS results. The analytical expression of the ribbon model also led to a higher calculation efficiency compared with the more conventional parallelepiped model. The extracted structural information included the cross-section size and size distribution of the cellulose nanofibers. For example, for nanofibers prepared from the dried pulp of the maritime pine, the size-weighted averages of thickness and width were 3.2 and 12.7 nm, respectively, and the corresponding standard deviations were 2.2 and 5.5 nm, respectively. The scattering results of the size-weighted average of the nanofiber width are also consistent with those determined directly from transmission electron microscopy.

Small angle x-ray scattering metrology for sidewall angle and cross section of nanometer scale line gratings

2004 ◽  
Vol 96 (4) ◽  
pp. 1983-1987 ◽  
Author(s):  
Tengjiao Hu ◽  
Ronald L. Jones ◽  
Wen-li Wu ◽  
Eric K. Lin ◽  
Qinghuang Lin ◽  
...  
Keyword(s):  
Cross Section ◽  
Small Angle ◽  
Nanometer Scale ◽  
X Ray ◽  
X Ray Scattering ◽  
Scale Line ◽  
Sidewall Angle ◽  
Ray Scattering

Small-angle X-ray scattering from helical macromolecules

1971 ◽  
Vol 4 (4) ◽  
pp. 290-293 ◽  
Author(s):  
O. A. Pringle ◽  
P. W. Schmidt
Keyword(s):  
Cross Section ◽  
Small Angle ◽  
Dna Molecules ◽  
X Ray ◽  
X Ray Scattering ◽  
Good Agreement ◽  
Ray Scattering

An earlier calculation of the intensity of small-angle X-ray scattering from helical filaments is extended to give an expression for the intensity from helical macromolecules with a finite cross section. The results are in quite good agreement with an experimental scattering curve for a solution of DNA molecules.

Small-angle x-ray scattering cross-section measurements of imaging materials

2017 ◽  
Vol 3 (2) ◽  
pp. 025023 ◽  
Author(s):  
Nadia Alam ◽  
Mina Choi ◽  
Bahaa Ghammraoui ◽  
Eshan Dahal ◽  
Aldo Badano
Keyword(s):  
Cross Section ◽  
Small Angle ◽  
Scattering Cross Section ◽  
X Ray ◽  
Scattering Cross ◽  
X Ray Scattering ◽  
Ray Scattering

Small-Angle X-Ray Scattering Studies on the X-Ray Induced Aggregation of Malate Synthase Computer Simulations and Models

1980 ◽  
Vol 35 (11-12) ◽  
pp. 890-901 ◽  
Author(s):  
Peter Zipper ◽  
Helmut Durchschlag
Keyword(s):  
Cross Section ◽  
Small Angle ◽  
Two Dimensions ◽  
Distribution Functions ◽  
Malate Synthase ◽  
Weighted Averaging ◽  
X Ray ◽  
X Ray Scattering ◽  
Induced Aggregation ◽  
Ray Scattering

Malate synthase undergoes an X-ray induced aggregation which can be monitored in situ by small-angle X-ray scattering; the analysis of scattering curves, taken at subsequent stages of aggregation, has led to the establishment of a tentative model for an aggregation in two dimensions (Zipper and Durchschlag (1980) Rad. and Environm. Biophys., in press). This model was checked by comparison of appropriate theoretical curves with the experi­mental curves. The theoretical scattering curves for this comparison were obtained by weighted averaging over the scattering curves calculated for various species of hypothetical aggregates. Based on the approximation of the unaggregated enzyme particle by an oblate cylinder, the aggregates were assumed to be composed of 2, 3, 4 or 6 of such cylinders, associated side-by-side in one and later on in two linear rows. The weight fractions of the species were chosen so, that an optimum fit of the experimental mean radii of gyration and mean degrees of aggregation was achieved. The distance distribution functions calculated for the model are very similar to the functions derived from the scattering experiment. Cross-section Guinier plots of the scattering curves of the model reveal the occurrence of one and later on of two pseudo cross-section factors similar to those observed in the experimental scattering curves. The pseudo thickness factor of the model of the unaggregated particle is found to be retained in the model curves for all stages of aggregation. From these results it can be concluded that the model for the aggregation process is essentially consistent with the scattering behaviour of the aggregating enzyme. Small differences between the theoretical and experimental curves may be explained by the idealizations of the model. The comparison of theoretical curves for alternative models, assuming aggregation in three dimen­sions, suggests that these models are unlikely, though small amounts of three-dimensional aggregates cannot be ruled out completely.

The Morphology of Blends of Linear and Branched Polyethylenes by Small-Angle Neutron and X-Ray Scattering

1994 ◽  
Vol 376 ◽  
Author(s):  
J. D. Londono ◽  
G. D. Wignall ◽  
R. G. Alamo ◽  
L. Mandelkern ◽  
J. S.Lin
Keyword(s):  
Phase Separation ◽  
Solid State ◽  
Cross Section ◽  
Small Angle ◽  
Liquid State ◽  
Melt Structure ◽  
Slow Cooling ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

ABSTRACTThe solid-state morphology and liquid-state homogeneity of blends of high-density polyethylene (HDPE) and low-density polyethylene (LDPE) were investigated by small-angle neutron and x-ray scattering (SANS and SAXS). The solid state morphology was investigated as a function of composition and cooling rate from the melt. After slow cooling, the evidence indicated that the mixtures were either completely (HDPE-rich blends) or almost completely (LDPE-rich blends) phase separated into separate HDPE and LDPE lamellae over the whole compositional range. In contrast, for rapidly quenched blends the components are extensively co-crystallized for all concentrations, though the SANS data indicated that the branched component had a tendency to be preferentially located in the inter-lamellar regions. In the liquid state, the blends were homogenous at all compositions, showing that the solid state morphology is not determined by the melt structure, but is a function of the crystallization kinetics. Further evidence for blend homogeneity in the liquid is presented. In particular we examine the hypothesis that a phase separated mixture might give a scattering pattern similar to a homogenous blend if the domain sizes were larger that the maximum spatial resolution of the SANS experiment (D > 2π/Qmin ~ 2000Å). In this scenario, the differential scattering cross section dΣ/dΩ(Q) ~ Q-2, though phase separation decreases the cross section in this Q-range with respect to the homogenous blend. For HDPE/LDPE blends in the melt, this decrease in intensity was not observed, thus ruling out the possibility of phase separation.

A Revised O2 Reduction Model in Li-O2 Batteries as Revealed by in Situ Small Angle X-Ray Scattering

2019 ◽  
Author(s):  
Christian Prehal ◽  
Aleksej Samojlov ◽  
Manfred Nachtnebel ◽  
Manfred Kriechbaum ◽  
Heinz Amenitsch ◽  
...  
Keyword(s):  
Small Angle ◽  
Wide Angle ◽  
Reduction Mechanism ◽  
Reduction Model ◽  
X Ray ◽  
X Ray Scattering ◽  
O2 Reduction ◽  
Ray Scattering

<b>Here we use in situ small and wide angle X-ray scattering to elucidate unexpected mechanistic insights of the O2 reduction mechanism in Li-O2 batteries.<br></b>

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