Fractals in Materials Science

Author: Su Yanjing Chu Wuyang Su Yanjing Gao Kewei Gao Kewei
Publisher:
Publish Date: 2004-07-01
Features: This book introduces the concept of fractals and their applications in materials science in a clear and accessible language. The first three chapters cover the basic concepts of self-similar and self-affine fractals and the measurement of fractal dimensions. The last three chapters explore the applications of fractals in materials science and the quantitative relationship between fractal dimensions and material properties. The book aims to enable more materials scientists to understand and master the fundamentals of fractals, inspire interest in fractal research through various examples, and contribute innovative work in material structure, improving material performance, and material development. This book is suitable for materials workers, undergraduate and graduate students, and teachers in material science and physics departments, as well as readers with an interest in material fractals.
Table of Contents:
Chapter 1 Self-Similar Fractals and Fractal Dimensions
1.1 Strictly Self-Similar Fractals
1.2 Fractal Dimensions of Self-Similar Fractals
1.3 Fractals in Nature (Approximately Self-Similar)
1.4 Differences Between Strictly Self-Similar and Approximately Self-Similar Fractals
1.5 Topological Dimension and Fractal Dimension
1.6 Definition of Fractal Dimension
1.7 Definition of Self-Similar Fractals
Chapter 2 Measurement of Fractal Dimensions
2.1 Box Counting Method
2.2 Variable Scale Length Measurement
2.3 Island Method
2.4 Power Spectrum Method
2.5 Measurement of Fractal Dimensions of Point Fractals
2.6 Physical Methods for Measuring Fractal Dimensions
Chapter 3 Self-Affine Fractals
3.1 Self-Affine Fractal Patterns
3.2 Brownian Motion
3.3 Self-Affine Fractal Functions
3.4 Fractal Dimensions of Fractional Brownian Curves
3.5 R/S Method and Fractals
Chapter 4 Fractal Growth
4.1 Fractal Growth Models
4.2 Electrodeposition
4.3 Thin Film Deposition
4.4 Crystallization
Chapter 5 Fractal Problems in Materials Science
5.1 Fractals in Thin Films and Surfaces
5.2 Fractals in Polymers
5.3 Amorphous Materials
5.4 Fractal Structures of Martensite
5.5 Fractals in Quasicrystals
Chapter 6 Fracture and Fractal Dimensions
6.1 Fracture Surfaces, Cracks, and Fractal Dimensions
6.2 Fracture Toughness and Fracture Surface Fractal Dimensions
6.3 Ductile Fracture and Fractal Dimensions
6.4 Environmental Fracture and Fractal Dimensions
6.5 Crack Nucleation, Propagation, and Fractal Characteristics