Statistical Analysis of Microstructures in Materials Science

by Ohser, Joachim; Mü; cklich, Frank

• ISBN13: 9780471974864
• ISBN10: 0471974862
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-12-19
• Publisher: WILEY

Summary

The investigation of the origin and formation of microstructures and the effect that microstructure has on the properties of materials are important issues in materials science and technology. Geometrical analysis is often the key to understanding the formation of microstructures and the resulting material properties. The authors make use of mathematical morphology, spatial statistics, image processing, stereology and stochastic geometry to analyze microstructures arising in materials science. * Quantitative microstructure analysis is one of the most successful experimental techniques in materials science * Uses examples to demonstrate the techniques * Program code included enables the reader to apply the numerous algorithms * Accessible to material scientists with limited statistical knowledge Primarily aimed at applied materials scientists, the book will also appeal to those working and researching in earth sciences, material technology, mineralogy, petrography, image analysis, cytology and biology.

Author Biography

Joachim Ohser holds a Chair at University of Applied Sciences, Darmstadt, Germany, where he is a professor in the field of image processing. He has long experience with characterization and geometric modelling of microstructures. Since 1999 he heads the working group on quantitative microstructural analysis of the German Materials Society. His research focuses on stochastic and discrete geometry, image analysis and simulation of materials properties.

Table of Contents

Dedication to Gunter Bach	ix
Preface	xi
Series Preface	xiii
Acknowledgements	xv
List of Notation	xvii
List of Source Codes	xxi
Introduction	1	(8)
What is this book about?	1	(1)
Spatial microstructure in materials science?	1	(4)
How is this book organized?	5	(4)
Methodological Tools	9	(48)
Points, sets, and morphological transformations	10	(15)
Points and vectors	10	(1)
Rotation and motion	11	(2)
An introduction to set theory	13	(4)
Morphological transformations	17	(8)
Characteristics of particles and section profiles	25	(9)
Particle parameters	27	(3)
Characteristics of planar section profiles	30	(1)
The Minkowski functionals	31	(3)
The orientation of objects	34	(4)
Crofton formulae for spatial objects	34	(3)
The Crofton formula for planar objects	37	(1)
Parallel sections of sets	38	(8)
Describing objects by functions	46	(11)
Steiner formulae	47	(1)
Covariance and chord length distribution function	48	(3)
Functions for planar objects	51	(6)
Statistical Estimation of Basic Characteristics	57	(50)
Definition of the basic characteristics	61	(6)
Basic stereological methods	67	(18)
The point-count method	70	(3)
Lineal analysis	73	(2)
The area method	75	(3)
Thin sections	78	(2)
Serial section analysis	80	(5)
Representation of textures	85	(11)
Texture characteristics related to surface density	86	(2)
Statistical analysis of anisotropic structures	88	(1)
Textures of homogeneously deformed structures	88	(6)
A further aspect of anisotropy	94	(2)
Textures in planar sections	96	(1)
Describing components by functions	96	(11)
Distance distributions	97	(3)
Distance distributions of planar sections	100	(2)
The chord length distribution	102	(5)
Basic Characteristics and Digitalization	107	(34)
Analysis of spatial images	109	(15)
Volume and volume density	113	(1)
The specific surface area	114	(3)
The specific integral of mean curvature	117	(4)
The specific integral of total curvature	121	(3)
Analysis of planar images	124	(17)
Area and area fraction	126	(1)
Length of total projection and specific line length	127	(2)
Euler number and integral of curvature per unit area	129	(4)
Digital resolution and fractal dimension	133	(2)
Algorithm and implementation	135	(6)
Covariance and Spectral Density	141	(22)
The covariance function	142	(10)
Definition and basic properties	142	(3)
Exponential covariance: asymptotic formulae	145	(5)
Estimating the covariance function	150	(2)
Fourier transform and spectral analysis	152	(11)
Fourier transform	152	(2)
The Wiener-Khinchin theorem	154	(2)
The isotropic case	156	(5)
Estimating the power spectrum	161	(2)
Size Distribution of Spherical Particles	163	(36)
Estimation of sphere diameter distribution	166	(12)
Planar sections	167	(9)
Thin sections	176	(2)
More about statistical estimation	178	(12)
Numerical solution of the stereological equations	181	(6)
A comparative study of stereological estimation	187	(3)
Moments of sphere diameters	190	(9)
Moments of sphere diameters from planar sections	191	(2)
Moments of sphere diameters from thin sections	193	(6)
Nonspherical Particles of Constant Shape	199	(38)
The continuous model	201	(1)
Discretization	202	(8)
Logarithmic discretization	202	(2)
Linear estimation	204	(6)
Improved linear estimation	210	(4)
Cubic particles	214	(8)
Conventional linear estimation	214	(1)
Additional observation of the vertices number	215	(3)
Using full shape information	218	(4)
Weighted size distributions	222	(15)
Weighted size distributions for compact particles	224	(3)
Thickness distribution of lamellae	227	(10)
Size-Shape Distribution of Particles	237	(26)
On spheroids and prisms	239	(15)
Spheroids	242	(3)
Regular prisms	245	(9)
Single-phase polyhedral microstructures	254	(9)
Arrangement of Objects	263	(50)
First-and second-order characteristics	270	(17)
The covariance function of point fields	271	(3)
Estimation of the K-function	274	(5)
Estimation of the pair correlation function	279	(3)
The Bartlett spectrum	282	(3)
The mark correlation function	285	(1)
Anisotropic point fields	286	(1)
Distance distributions	287	(9)
Nearest-neighbor distance distribution	288	(5)
Contact distributions	293	(3)
Planar point fields	296	(7)
Second-order characteristics	297	(2)
Stereological estimation of the pair correlation function	299	(4)
Mathematical models for particle arrangements	303	(10)
The spatial Poisson field	303	(5)
The planar Poisson field	308	(2)
The Matern hard-core point field	310	(1)
The Matern cluster point field	311	(2)
Single-Phase Polyhedral Microstructures	313	(38)
Formulae for basic characteristics	317
Planar tessellations	317	(3)
Spatial tessellations	320
Statistics for planar tessellations	223	(103)
Voronoi tessellations	326	(12)
The planar Poisson-Voronoi tessellation	328	(4)
The spatial Poisson-Voronoi tessellation	332	(6)
Planar sections through spatial tessellations	338	(9)
Planar section of the spatial Poisson-Voronoi tessellation	339	(6)
Stereological formulae	345	(2)
Generalized Voronoi tessellations	347	(4)
Appendix A Characteristics of Geometric Objects	351	(8)
Appendix B Software Utilities	359	(4)
References	363	(12)
Index	375