Diffusion Phenomena: Cases and Studies

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