Article (Scientific journals)
Small-angle scattering and scale-dependent heterogeneity
Gommes, Cédric
2016In Journal of Applied Crystallography, 49, p. 1-15
Peer Reviewed verified by ORBi
 

Files


Full Text
SAS_heterogeneity_paper_R1.pdf
Author preprint (778.64 kB)
Download

All documents in ORBi are protected by a user license.

Send to



Details



Keywords :
small-angle scattering; heterogeneity; hierarchical materials
Abstract :
[en] Although small-angle scattering is often discussed qualitatively in terms of material heterogeneity, when it comes to quantitative data analysis this notion becomes somehow hidden behind the concept of correlation function. In the present contribution, a quantitative measure of heterogeneity is defined, it is shown how it can be calculated from scattering data, and its structural significance for the purpose of material characterization is discussed. Conceptually, the procedure consists of using a finite probe volume to define a local average density at any point of the material; the heterogeneity is then quantitatively defined as the fluctuations of the local average density when the probe volume is moved systematically through the sample. Experimentally, it is shown that the so-defined heterogeneity can be estimated by projecting the small-angle scattering intensity onto the form factor of the chosen probe volume. Choosing probe volumes of various sizes and shapes enables one to comprehensively characterize the heterogeneity of a material over all its relevant length scales. General results are derived for asymptotically small and large probes in relation to the material surface area and integral range. It is also shown that the correlation function is equivalent to a heterogeneity calculated with a probe volume consisting of two points only. The interest of scale-dependent heterogeneity for practical data analysis is illustrated with experimental small-angle X-ray scattering patterns measured on a micro- and mesoporous material, on a gel, and on a semi-crystalline polyethylene sample. Using different types of probes to analyse a given scattering pattern enables one to focus on different structural characteristics of the material, which is particularly useful in the case of hierarchical structures.
Disciplines :
Physics
Materials science & engineering
Author, co-author :
Gommes, Cédric  ;  Université de Liège > Department of Chemical Engineering > Department of Chemical Engineering
Language :
English
Title :
Small-angle scattering and scale-dependent heterogeneity
Publication date :
2016
Journal title :
Journal of Applied Crystallography
ISSN :
0021-8898
eISSN :
1600-5767
Publisher :
Blackwell Publishing
Volume :
49
Pages :
1-15
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Available on ORBi :
since 28 June 2016

Statistics


Number of views
602 (13 by ULiège)
Number of downloads
305 (2 by ULiège)

Scopus citations®
 
10
Scopus citations®
without self-citations
9
OpenCitations
 
8

Bibliography


Similar publications



Contact ORBi