Numerical solution of the inverse problem in the analysis of neutron small angle scattering experiments

Magnani, M.; Puliti, Paolo; Stefanon, M.

doi:10.1016/0168-9002(88)90330-0

Cited by 48 publications

(19 citation statements)

References 5 publications

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“…Alternatively, knowledge on the particle size distribution and particle shape can result in a solution for the arrangement of the particles in space, as applied in structure resolving programs [187,147]. Lastly, by making a low-density packing assumption and given a known particle shape (from TEM), a unique particle size distribution remains [111,133,132,150,158].…”

Section: Scattering To Small Anglesmentioning

confidence: 99%

Everything SAXS: small-angle scattering pattern collection and correction

Pauw

2013

J. Phys.: Condens. Matter

170

136

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Section: Scattering To Small Anglesmentioning

confidence: 99%

Everything SAXS: small-angle scattering pattern collection and correction

Pauw

2013

J. Phys.: Condens. Matter

170

136

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“…Svergun, Semenyuk & Feigin (1988) realized the approach described above in a program package GNOM which allows for automatic estimation and refinement of the a value. In principle, the package has features similar to those of other indirect methods (Glatter, 1977;Moore, 1980;Provencher, 1982;Mangani, Puliti & Stefanon, 1988). It allows reliable solutions to be obtained, being stable with respect to the experimental errors and termination effects.…”

Section: Kp=jmentioning

confidence: 87%

Mathematical methods in small-angle scattering data analysis

Svergun¹

1991

J Appl Crystallogr

224

173

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Applications of modern mathematical methods to the problems of small-angle scattering data treatment and interpretation are considered. Special possibilities in data treatment, namely simultaneous treatment of data sets obtained with different experimental conditions and joint data processing for the anomalous-dispersion experiments, are presented. The methods are further developments of the indirect method based on the regularization technique [Svergun, Semenyuk & Feigin (1988). Acta Cryst. A44, 244-250]. Recent improvements in the shape-determination technique based on the multipole expansion theory [Stuhrmann (1970). Z. Phys. Chem. (Frankfurt am Main), 72,[177][178][179][180][181][182][183][184][185][186][187][188][189][190][191][192][193][194][195][196][197][198] are described. A new method is proposed for the determination of positioning and mutual orientation of subunits in complex particles using the spherical harmonics technique.

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“…[25][26][27][28][29] The use of contrast variation and the application of the same analysis to multiple datasets can go some way to overcoming these issues, by reducing the number of possible explanations for a given dataset. Additionally, other 'form-free' ways to analyse SANS data are available, for example the Indirect Fourier Transform (IFT) by Glatter 30 or the numerical methods suggested by Magnani et al 31 and recently Pauw et al 32 These yield probability distributions of the length-scales of the scattering objects and can be powerful, 'assumption-free' ways to determine information on particle shapes and sizes. For example, as shown in Fig.…”

mentioning

confidence: 99%

Practical applications of small-angle neutron scattering

Hollamby

2013

Phys. Chem. Chem. Phys.

125

116

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Recent improvements in beam-line accessibility and technology have led to small-angle neutron scattering (SANS) becoming more frequently applied to materials problems. SANS has been used to study the assembly, dispersion, alignment and mixing of nanoscale condensed matter, as well as to characterise the internal structure of organic thin films, porous structures and inclusions within steel.Using time-resolved SANS, growth mechanisms in materials systems and soft matter phase transitions can also be explored. This review is intended for newcomers to SANS as well as experts. Therefore, the basic knowledge required for its use is first summarised. After this introduction, various examples are given of the types of soft and hard matter that have been studied by SANS. The information that can be extracted from the data is highlighted, alongside the methods used to obtain it. In addition to presenting the findings, explanations are provided on how the SANS measurements were optimised, such as the use of contrast variation to highlight specific parts of a structure. Emphasis is placed on the use of complementary techniques to improve data quality (e.g. using other scattering methods) and the accuracy of data analysis (e.g. using microscopy to separately determine shape and size). This is done with a view to providing guidance on how best to design and analyse future SANS measurements on materials not listed below.

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Numerical solution of the inverse problem in the analysis of neutron small angle scattering experiments

Cited by 48 publications

References 5 publications

Everything SAXS: small-angle scattering pattern collection and correction

Everything SAXS: small-angle scattering pattern collection and correction

Mathematical methods in small-angle scattering data analysis

Practical applications of small-angle neutron scattering

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