Structure of a single particle from scattering by many particles randomly oriented about an axis: toward structure solution without crystallization?

Saldin, D. K.; Shneerson, V. L.; Howells, Malcolm R.; Marchesini, Stefano; Chapman, Henry N.; Bogan, Michael J.; Shapiro, Daniel B.; Kirian, Richard A.; Weierstall, Uwe; Schmidt, Kevin; Spence, John C. H.

doi:10.1088/1367-2630/12/3/035014

Cited by 53 publications

(60 citation statements)

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“…This is different from the analysis of CCFs performed in recent publications. 19,20 The authors of these publications proposed to average the angular CCF ͓Eq. ͑3͔͒ for a set of diffraction patterns measured on a large number of disordered systems, each containing a limited number of LSs in different positions and orientations.…”

Section: ͑26͒mentioning

confidence: 99%

X-ray cross-correlation analysis and local symmetries of disordered systems: General theory

2010

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In a recent paper ͓P. Wochner et al., Proc. Natl. Acad. Sci. U.S.A. 106, 11511 ͑2009͔͒ x-ray scattering intensity correlations around a ring, in the speckle diffraction pattern of a colloidal glass, were shown to display a remarkable ϳcos͑n ͒ dependence on the angular coordinate around the ring, with integer index n depending on the magnitude of the scattering wave vector. With an analytical derivation that preserves full generality in the Fraunhofer diffraction limit, we clarify the relationship between this result and previous x-ray studies of bond-orientation order, and provide a sound basis to the statement that the angular intensity correlations deliver information on local bond arrangements in a disordered ͑or partially ordered͒ system. We present a detailed analysis of the angular cross-correlation function and show its applicability for studies of a wide range of structural properties of disordered systems, from local structure to spatial correlations between distant structural elements.

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Section: ͑26͒mentioning

confidence: 99%

X-ray cross-correlation analysis and local symmetries of disordered systems: General theory

2010

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“…Several authors propose methods to describe the coherent scattering pattern and recover the three-dimensional structure of the scattering particle, based on the method proposed by Kam [78][79][80]. The proposed method for calculation of oriented scattering intensities can potentially be used to describe data from FEL experiments.…”

Section: Optimized Debye Equation For Oriented Particlesmentioning

confidence: 99%

Calculation of Small-Angle Scattering Patterns

Alves¹,

Oliveira²

2018

Small Angle Scattering and Diffraction

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Small-angle scattering (SAS) experiments applied to nano-scaled systems allow the investigation of the constituents' overall shape, size, internal structure and arrangement. A standard scattering experiment requires a relatively simple setup and is often applied to investigate a system of particles. In these cases, the measured scattering intensity represents an average over a large number of particles illuminated by the incoming beam. The calculation and modeling of the scattering intensity can be performed by the use of analytical/semi-analytical expressions or by the use of numerical methods. In this book chapter, an overview of current available simulation/modeling methods for SAS will be shown either for systems composed of oriented or for randomly oriented particles. Examples demonstrating the use of the finite element method are presented as well as a newly developed method for calculating scattering intensity for oriented particles.

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“…Under the aforementioned conditions, the measured scattering patterns will no longer be angularly isotropic, but will contain speckles. It can be shown that a large number of these scattering patterns can be used to estimate the average angular autocorrelation of the scattering pattern of a single particle (Kam et al, 1981;Saldin et al, 2010Saldin et al, , 2011.…”

Section: Introductionmentioning

confidence: 99%

Computation of fluctuation scattering profilesviathree-dimensional Zernike polynomials

et al. 2012

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Ultrashort X-ray pulses from free-electron laser X-ray sources make it feasible to conduct small-and wide-angle scattering experiments on biomolecular samples in solution at sub-picosecond timescales. During these so-called fluctuation scattering experiments, the absence of rotational averaging, typically induced by Brownian motion in classic solution-scattering experiments, increases the information content of the data. In order to perform shape reconstruction or structure refinement from such data, it is essential to compute the theoretical profiles from three-dimensional models. Based on the threedimensional Zernike polynomial expansion models, a fast method to compute the theoretical fluctuation scattering profiles has been derived. The theoretical profiles have been validated against simulated results obtained from 300 000 scattering patterns for several representative biomolecular species.

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Structure of a single particle from scattering by many particles randomly oriented about an axis: toward structure solution without crystallization?

Cited by 53 publications

References 0 publications

X-ray cross-correlation analysis and local symmetries of disordered systems: General theory

X-ray cross-correlation analysis and local symmetries of disordered systems: General theory

Calculation of Small-Angle Scattering Patterns

Computation of fluctuation scattering profilesviathree-dimensional Zernike polynomials

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