Image-Based Fractal Description of Microstructures / Edition 1

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Fractal analysis has rapidly become an important field in materials science and engineering with broad applications to theoretical analysis and quantitative description of microstructures of materials. Fractal methods have thus far shown great potential in engineering applications in quantitative microscopic analysis of materials using commercial microscopes. This book attempts to introduce the fundamentals and the basis methods of fractal description of microstructures in combination with digital imaging and computer technologies. Basic concepts are given in the form of mathematical expressions. Detailed algorithms in practical applications are also provided. Fractal measurement, error analysis and fractal description of cluster growth, thin films and surfaces are emphasized in this book. Image-Based Fractal Description of Microstructures provides a comprehensive approach to materials characterization by fractal from theory to application and is therefore an essential source of reference for university professors, professional engineers and research students.

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Product Details

  • ISBN-13: 9781441953704
  • Publisher: Springer US
  • Publication date: 12/7/2010
  • Edition description: Softcover reprint of hardcover 1st ed. 2003
  • Edition number: 1
  • Pages: 272
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.60 (d)

Table of Contents

Preface. Acknowledgements.
1: Introduction. 1.1. Classification of basic elements in microstructures. 1.2. Image and image processing. 1.3. Image-based measurement of basic elements. 1.4. Parameter estimation. 1.5. Relationship between properties and irregularity of microstructures of materials.
2: Digital Images of Microstructures. 2.1. Light optical microscope. 2.2. Scanning electron microscope. 2.3. Transmission electron microscope. 2.4. Scanning tunnelling microscope. 2.5. Atomic force microscope. 2.6. Magnetic force microscope.
3: Image Processing. 3.1. Image pre-processing. 3.2. Object abstraction. 3.3. Image post-processing.
4: Fundamental Statistics. 4.1. Populations, sampling and probability. 4.2. Statistical measures for population. 4.3. Probability distribution. 4.4. Some useful theorems. 4.5. Simple linear regression analysis.
5: Fractal Fundamentals. 5.1. Definitions of fractals. 5.2. Dimension. 5.3. Properties of a fractal set. 5.4. Examples of fractals.
6: Fractal Measurements of Projection Microstructures. 6.1. Fractal measurements. 6.2. Length of fractal curve. 6.3. Perimeter-area and area-volume relations. 6.4. Mass method. 6.5. Box-counting method. 6.6. Multifractal measurements of cluster growth.
7: Fractal Measurements of Topographical Images from 3D Surfaces. 7.1. Fractal nature of material surfaces. 7.2. Fractal-based methods for the description ofsurfaces. 7.3. Variation-correlation method for the description of 3D surfaces.
8: Irregularity of Graphite Nodules. 8.1. Conventional description of nodules. 8.2. Measurement procedures. 8.3. Quantitative analysis.
9: Fractal Growth of Graphite Nodules. 9.1. Growth of graphite nodules. 9.2. Fractal growth of graphite nodules. 9.3. Fractal growth models of graphite nodules. 9.4. Interpretation of fractal growth of graphite nodules.
10: Fractal-based Study of Magnetic Thin Films. 10.1. Magnetic thin films. 10.2. Preparation of magnetic thin films. 10.3. Description of the surfaces of magnetic thin films. 10.4. Description of the magnetic microstructures of magnetic thin films.
11: Fractal-based Study of Fracture Surfaces. 11.1. Fractography. 11.2. Fracture and fractals. 11.3. Physical meaning of the secondary electron image. 11.4. Influence of SEM parameters on Dcor. 11.5. Influence of noise on Dcor. 11.6. Fractal characteristics and mechanical properties. 11.7. Quantitative fractography. References. Index.

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