Book contents
- Frontmatter
- Contents
- Preface
- Notation
- Part I Basic Thermodynamics and Kinetics of Phase Transformations
- 1 Introduction
- 2 Temperature–Composition Phase Diagrams
- 3 Diffusion
- 4 Nucleation
- 5 Effects of Diffusion and Nucleation on Phase Transformations
- Part II The Atomic Origins of Thermodynamics and Kinetics
- Part III Types of Phase Transformations
- Further Reading
- References
- Index
3 - Diffusion
from Part I - Basic Thermodynamics and Kinetics of Phase Transformations
Published online by Cambridge University Press: 24 April 2020
- Frontmatter
- Contents
- Preface
- Notation
- Part I Basic Thermodynamics and Kinetics of Phase Transformations
- 1 Introduction
- 2 Temperature–Composition Phase Diagrams
- 3 Diffusion
- 4 Nucleation
- 5 Effects of Diffusion and Nucleation on Phase Transformations
- Part II The Atomic Origins of Thermodynamics and Kinetics
- Part III Types of Phase Transformations
- Further Reading
- References
- Index
Summary
Chapter 3 begins by describing mechanisms of atomic diffusion in crystals, with emphasis on how their rates depend on temperature. Characteristic diffusion lengths and times are explained. The diffusion equation is derived for the chemical composition in space and time, c(r,t). The mathematics for solving the diffusion equation in one dimension are developed by standard approaches with Gaussian functions and error functions. The method of separation of variables is presented for three-dimensional problems in Cartesian and cylindrical coordinates. Typical boundary value problems for diffusion are solved with Fourier series and Bessel functions.
- Type
- Chapter
- Information
- Phase Transitions in Materials , pp. 59 - 82Publisher: Cambridge University PressPrint publication year: 2020