Phase transformations are among the most intriguing and technologically useful phenomena in materials, particularly with regard to controlling microstructure.
After a review of thermodynamics, this book has chapters on Brownian motion and the diffusion equation, diffusion in solids based on transition-state theory, spinodal decomposition, nucleation and growth, instabilities in solidification, and diffusionless transformations. Each chapter includes exercises whose solutions are available in a separate manual.
This book is based on the notes from a graduate course taught in the Centre for Doctoral Training in the Theory and Simulation of Materials. The course was attended by students with undergraduate degrees in physics, mathematics, chemistry, materials science, and engineering. The notes from this course, and this book, were written to accommodate these diverse backgrounds.
Author(s): Dimitri D. Vvedensky
Series: IOP Concise Physics
Publisher: IOP Publishing
Year: 2019
Language: English
Pages: 184
City: Bristol
PRELIMS.pdf
Preface
Author biography
Dimitri Dimitrievich Vvedensky
CH001.pdf
Chapter 1 Overview of thermodynamics
1.1 Basic concepts and terminology
1.1.1 Systems and boundaries
1.1.2 Equilibrium and state variables
1.1.3 Processes
1.2 The laws of thermodynamics
1.2.1 The zeroth law of thermodynamics
1.2.2 The first law of thermodynamics
1.2.3 The second law of thermodynamics
1.2.4 The third law of thermodynamics
1.3 Fundamental equations
1.3.1 The Gibbs function
1.3.2 The Helmholtz function
1.4 Thermal, mechanical, and chemical equilibria
1.5 Phase equilibria
1.5.1 The Clausius–Clapeyron equation
1.5.2 The Gibbs phase rule
1.6 Summary
Further reading
Exercises
References
CH002.pdf
Chapter 2 Brownian motion, random walks, and the diffusion equation
2.1 Random walks and Brownian motion
2.1.1 Brownian motion
2.1.2 The random walk and the diffusion equation
2.2 Fick’s laws and the diffusion equation
2.2.1 Fick’s first law
2.2.2 The continuity equation
2.2.3 Fick’s second law and the diffusion equation
2.3 Fundamental solution of the diffusion equation
2.3.1 Differential equation for Fourier components
2.3.2 The fundamental solution
2.3.3 Solution of the initial-value problem
2.4 Examples
2.5 Summary
Further reading
Exercises
References
CH003.pdf
Chapter 3 Atomic diffusion in solids
3.1 Defects in solids
3.1.1 Point defects
3.1.2 Line defects
3.1.3 Plane defects
3.1.4 Volume defects
3.2 Thermodynamics of point defects
3.3 Diffusion mechanisms
3.4 Transition-state theory11This section is based on the unpublished lecture notes of Hannes Jónsson.
3.4.1 Assumptions of classical transition-state theory
3.4.2 Equilibrium statistical mechanics
3.4.3 The dividing surface
3.4.4 The rate constant
3.4.5 The harmonic approximation
3.5 Analysis of diffusion experiments
3.5.1 Diffusion processes
3.5.2 Arrhenius diagrams
3.6 Summary
Further reading
Exercises
References
CH004.pdf
Chapter 4 Spinodal decomposition
4.1 The Bragg–Williams model
4.2 The phase diagram
4.2.1 Thermodynamic stability
4.2.2 Stable, metastable, and unstable phases
4.2.3 Kinetics of unmixing
4.3 The Cahn–Hilliard equation
4.3.1 Spatially-varying concentrations
4.3.2 The fundamental equations
4.3.3 Functional derivative of the free energy
4.3.4 Evolution equation for the concentration
4.4 Experiments on spinodal decomposition
4.5 Summary
Further reading
Exercises
References
CH005.pdf
Chapter 5 Nucleation and growth
5.1 Classical nucleation theory
5.1.1 Metastability
5.1.2 Homogeneous formation of nuclei
5.2 Nucleation rate of solid-state transformations
5.3 Homogeneous versus heterogeneous nucleation
5.3.1 Heterogeneous nucleation on a surface
5.3.2 Elastic effects in solid-state nucleation
5.4 Overall transformation rate
5.4.1 Kolmogorov–Johnson–Mehl–Avrami theory
5.4.2 Derivation of the KJMA equation
5.4.3 Determination of nucleation mechanisms
5.4.4 Graphene
5.5 Summary
Further reading
Exercises11Exercises 1-4 are adapted from Markov (1995), pp 13–14
References
CH006.pdf
Chapter 6 Instabilities of solidification fronts
6.1 Solidification of a pure liquid
6.1.1 The heat equation
6.1.2 Velocity of the liquid–solid interface
6.1.3 The Gibbs–Thomson equation
6.1.4 Equations for the dimensionless temperature
6.2 Motion of a spherical solidification front
6.2.1 Solution for shape-preserving growth
6.3 Linear stability of spherical front
6.3.1 Solution of the heat equation
6.3.2 The Gibbs–Thomson relation
6.3.3 The conservation equation
6.3.4 The dispersion relation
6.3.5 Numerical simulation of two-dimensional instabilities
6.4 Constitutional supercooling
6.5 Summary
Further reading
Exercises
References
CH007.pdf
Chapter 7 Diffusionless transformations
7.1 Martensitic transformations
7.1.1 Crystallographic considerations
7.1.2 Free energy changes
7.2 Shape memory alloys and pseudoelasticity
7.3 Theory of pseudoelasticity
7.3.1 Ginzburg–Landau free energy functional
7.3.2 Nucleation of critical ‘true twin’ droplets
7.4 Summary
Further reading
Exercises
References
APP1.pdf
Chapter
APP2.pdf
Chapter
APP3.pdf
Chapter
