Skip to main content

A Primer of Diffusion Problems

A Primer of Diffusion Problems

Richard Ghez

ISBN: 978-3-527-60283-4

Jan 2005

264 pages

Select type: O-Book

Description

The only elementary text to provide a complete introduction to diffusion theory and the various analytical and numerical methods of solution. Presents an integrated set of real-life problems taken mainly from metallurgy and device processing, and offers an overview of the solution of diffusion problems in practical cases, with clear explanations of the interrelationships between mathematical solutions, and the underlying physics and chemistry. Covers oxidation theory, error functions, Laplace transforms, and similarity, a topic of current research interest. Also covers Green's functions and integral equations, rarely discussed in introductory texts.
Partial table of contents:

THE DIFFUSION EQUATION.

Isotropic One-dimensional Random Walk.

Elementary Properties of the Diffusion Equation.

Higher Dimensions and Coordinate Systems.

STEADY STATE EXAMPLES.

The Steady State is Not the Equilibrium State.

The Thermal Oxidation of Silicon.

The Precipitation of Spherical Particles.

DIFFUSION UNDER EXTERNAL FORCES.

One-dimensional Anisotropic Random Walk.

Diffusivity and Mobility Coefficients.

An Introduction to Double-layers.

SIMPLE TIME-DEPENDENT EXAMPLES.

The Gaussian and One of Its Relatives.

Two Applications of Error Functions to One-dimensional Phases.

Crystal Growth under Conditions of Constant Cooling Rate.

AN INTRODUCTION TO SIMILARITY.

Boltzmann's Transformation.

Boltzmann's Transformation and Variable Diffusivity.

Analytic Solutions for Variable Diffusivity.

A USER'S GUIDE TO THE LAPLACE TRANSFORM.

Elementary Properties and Further Examples.

The Convolution Theorem.

A Few Words on Asymptotics.

FURTHER TIME-DEPENDENT EXAMPLES.

Laser Processing.

Thermally Stimulated Diffusion.

Application to the Numerical Solution for Nonlinear Surface Conditions.

Appendix A: Random Walks in Higher Dimensions.

Appendix B: The Phase Rule and Some of Its Consequences.

Appendix C: Moments of Distributions and Asymptotic Behavior.

Index.