Diffusion Phenomena: Cases and Studies Second Edition

This authoritative test introduces the basic aspects of diffusion phenomena and their methods of solution through physical examples. It emphasizes modeling and methodology, bridging the gap between physico chemical statements of certain kinetic processes and their reduction to diffusion problems. Author Richard Ghez draws upon his experience in the areas of metallurgy and semiconductor technology to present physically significant examples that will prove of interest to a wide range of scientists — physicists, chemists, biologists, and applied mathematicians. Prerequisites include a rigorous year of calculus and a semester of thermodynamics.
The opening chapter on the diffusion equation is succeeded by chapters on steady-state examples, diffusion under external forces, and simple time-dependent examples. An introduction to similarity is followed by explorations of surface rate limitations and segregation, a user's guide to the Laplace transform, and further time-dependent examples.

Richard Ghez worked for more than 20 years in IBM's T. J. Watson Research Center and has more recently been on the faculty of the Department of Materials Science and Engineering at the Tachnion-Israel Institute of Technology at Haifa. He has served as an Editor for the Journal of Crystal Growth and is the author of approximately 100 scientific papers.

Contents
1. The Diffusion Equation 
1.1. The Isotropic One-Dimensional Random Walk 
1.2. Continuum Equations 
1.3. Elementary Properties of the Diffusion Equation 
1.4. Numerical Methods 
1.5. A Numerical Example 
1.6. Higher Dimensions and Coordinate Systems
1. 7. Other Instances of the Diffusion Equation 
1.8. General Balance Laws and Constitutive Relations.  
Notes  
References
2. Steady-State Examples 
2.1. The Steady State Is Not the Equilibrium State
2.2. General Solutions for Rotationally Symmetric Cases
2.3. The Thermal Oxidation of Silicon
2.4. A Few Considerations Concerning Capillarity
2.5. The Precipitation of Spherical Particles
2.6. Crystal Growth According to the Theory of Burton, Cabrera, and Frank 
Notes 83 References
3. Diffusion Under External Forces
3.1. The Anisotropic One-Dimensional Random Walk
3.2. Diffusivity and Mobility Coefficients.
3.3. An Introduction to Double Layers References
4. Simple Time-Dependent Examples
4.1. The Gaussian and One of Its Relatives
4.2. The Gaussian and Another of Its Relatives.
4.3. Two Applications of Error Functions to One-Dimensional Phases
4.4. The Gaussian Has Yet More Relatives
4.5. Crystal Growth Under Conditions of Constant Cooling Rate
4.6. Product Solutions for Higher-Dimensional Problems Notes
References
5. An Introduction to Similarity
5.1. Similarity Solutions
5.2. Boltzmann's Transformation
5.3. Two Applications of Similarity to Spheres
5.4. Variable Diffusivity and Boltzmann's Transformation
5.5. Analytic Solutions for Variable Diffusivity Notes References
6. Surface Rate Limitations and Segregation
6.1. What Are Boundary Conditions? 
6.2. Gibbs's Dividing Surface 
6.3. Nonequilibrium Behavior of Dividing Surfaces
6.4. Grain Boundary Diffusion According to Whipple
6.5. Grain Boundary Diffusion According to Benoist and Martin 
6.6. The Radiation Boundary Condition and a Typical Diffusion Problem
Notes
References