The Quantitative Description of the Microstructure of Materials

TLDR: In this article, a method for estimating the density of volume elements by a method of size distribution reconstruction is presented. But the method is limited to the case of 2D lines on a plane.

Abstract: Introduction Elements of the Microstructures of Materials Size and Shape The Influence of Microstructure on the Properties of Materials Stochastic Character of the Geometry of Microstructures Observations of the Microstructure of Materials About the Book Rerferences Basic Concepts, Definitions, Techniques, and Relationships Populations, Individual Microstructural Elements, and Distribution Functions Distribution Functions Parameters of the Populations Normal and Log-Normal Distribution Sampling Size of the Samples Microstructural Homogeneity General Characterization of Material Microstructures Geometrical Probing Random and Oriented Sections Random Oriented Lines Point Testing Number and Weighted Distributions Notation Volume Fraction Determination Density of Two-Dimensional Features in Space Density of Lines on a Plane Density of Lines in Space Density of Elements and Average Properties Modification for Anisotropic Lines and Surfaces Anisotropic Distribution of Lines Estimation of the Density of Volume Elements, NV, by a Method of Size Distribution Reconstruction Description of Particle Agglomeration Curvature of Lines on a Plane References Modern Stereology Disector-New Approach to Particle Density Selector-Particle Volume Distribution Point Sampled Intercepts Second Order Statistics-Methods for Estimating the Variance of Particle Volume Fractionator Nucleator Vertical Sectioning-Area of the Surfaces Orientator Trisector References Computer Aided Characterization of the Microstructures of Materials Image Processing Computer Aided Procedures of Data Analysis Elements of a System for Image Analysis References Characterization of Linear and Planar Elements of Microstructures Dislocations Internal Surfaces External Surfaces Quantitative Characterization of Thin Film Structures References The Geometry of Grains and Its Effect on the Properties of Polycrystals Introduction Grains as Space Filling Volumetric Elements Stochastic Character of Grains Geometry The Relationship Between 3-D Grains and Their 2-D Sections Grain Size Grain Area Distribution Function and Its Relationship to Grain Volume Distribution Mean Size of Grains Relationship Between Linear Parameters of Grain Size Degree of Grain Size Uniformity Data for Metallic Polycrystals Grain Size Effect Geometry of Grains and Physical Properties of Grain Boundaries References Changes in the Geometry of Grains and Grain Boundaries Under the Action of External and Internal Factors Tensile Test Changes in the Geometry of Grains in Strained Polycrystals-Uniform Deformation Approximation Spherical Grains Approach Stochastic Geometry Modelling Statistically Compatible Deformation Localized Deformation An Application to the Studies of Plastic Deformation Mechanisms Grain Geometry Evolution Under the Action of Internal Factors Annealing of Deformed Materials References Particles, Pores, and Other Isolated Volumetric Elements of the Microstructure Particle Sampling and Choice of Parameters General Characteristics of Particle Populations: Volume, Surface Area, Curvature, and Number Individual Properties of Particles: Mean Volume and Coefficient of Variation Particle Arrangements and Orientations Description of Particle Shapes Shape of Particle Sections Fourier Analysis of Sections Shape References