Particle and Particle Systems Characterization: Small-Angle Scattering (SAS) Applications, 1st Edition (Hardback) book cover

Particle and Particle Systems Characterization

Small-Angle Scattering (SAS) Applications, 1st Edition

By Wilfried Gille

CRC Press

336 pages | 164 B/W Illus.

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pub: 2013-11-22
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Small-angle scattering (SAS) is the premier technique for the characterization of disordered nanoscale particle ensembles. SAS is produced by the particle as a whole and does not depend in any way on the internal crystal structure of the particle. Since the first applications of X-ray scattering in the 1930s, SAS has developed into a standard method in the field of materials science. SAS is a non-destructive method and can be directly applied for solid and liquid samples.

Particle and Particle Systems Characterization: Small-Angle Scattering (SAS) Applications is geared to any scientist who might want to apply SAS to study tightly packed particle ensembles using elements of stochastic geometry. After completing the book, the reader should be able to demonstrate detailed knowledge of the application of SAS for the characterization of physical and chemical materials.


"This is a useful monograph on applications of observed wave and particle interference patterns to reconstruct structural details of scattering materials. It can equally serve as a comprehensive textbook to graduate students and as a reference book to professionals in the field."

Zentralblatt MATH 1323

Table of Contents

Scattering experiment and structure functions; particles and the correlation function of small-angle scattering

Elastic scattering of a plane wave by a thin sample

SAS structure functions and scattering intensity

Chord length distributions and SAS

SAS structure functions for a fixed order range L

Aspects of data evaluation for a specific L

Chord length distribution densities (CLDDs) of selected elementary geometric figures

The cone case–an instructive example

Establishing and representing CLDDs

Parallelepiped and limiting cases

Right circular cylinder

Ellipsoid and limiting cases

Regular tetrahedron (unit length case a = 1)

Hemisphere and hemisphere shell

The Large Giza Pyramid as a homogeneous body

Rhombic prism Y based on the plane rhombus X

Scattering pattern I(h) and CLDD A(r) of a lens

Chord length distributions of infinitely long cylinders

The infinitely long cylinder case

Transformation 1: From the right section of a cylinder to a spatial cylinder

Recognition analysis of rods with oval right section from the SAS correlation function

Transformation 2: From spatial cylinder C to the base X of the cylinder

Specific particle parameters in terms of chord length moments: The case of dilated cylinders

Cylinders of arbitrary height H with oval RS

CLDDs of particle ensembles with size distribution

Particle-to-particle interference—a useful tool

Particle packing is characterized by the pair correlation function g(r)

Quasi-diluted and non-touching particles

Correlation function and scattering pattern of two infinitely long parallel cylinders

Fundamental connection between γ(r), c and g(r) Cylinder arrays and packages of parallel infinitely long circular cylinders Connections between SAS and WAS Chord length distributions: An alternative approach to the pair correlation function Scattering patterns and structure functions of Boolean models

Short-order range approach for orderless systems

The Boolean model for convex grains

Inserting spherical grains of constant diameter

Size distribution of spherical grains

Chord length distributions of the Poisson slice model

Practical relevance of Boolean models

The "Dead Leaves" model

Structure functions and scattering pattern of a puzzle cell (PC)

The uncovered "Dead Leaves" model

Tessellations, fragment particles and puzzles

Tessellations: original state and destroyed state

Puzzle particles resulting from DLm tessellations

Punch-matrix/particle puzzles

Analysis of nearly arbitrary fragment particles via their CLDD

Predicting the fitting ability of fragments from SAS

Porous materials as "drifted apart tessellations"

Volume fraction of random two-phase samples for a fixed order range L from γ(r,L) The linear simulation model

Analysis of porous materials via ν-chords The volume fraction depends on the order range L The Synecek approach for ensembles of spheres Volume fraction investigation of Boolean models About the realistic porosity of porous materials

Interrelations between the moments of the chord length distributions of random two-phase systems

Single particle case and particle ensembles

Interrelations between CLD moments of random particle ensembles

CLD concept and data evaluation: Some conclusions

Exercises on problems of particle characterization: examples

The phase difference in a point of observation P

Scattering pattern, CF and CLDD of single particles

Structure functions parameters of special models

Moments of g(r), integral parameters and c

About the Originator

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Physics
SCIENCE / Solid State Physics