| Kinetic Processes in Materials |
| 3.21 Spring 2002 |
| Professor Sam Allen |
Professor Craig Carter |
|---|
| Department of Materials Science and Engineering |
| Massachusetts Institute of Technology |
| 77 Massachusetts Institute of Technology |
| Cambridge, MA 02139 |
Below is a tentative schedule.
An updated
schedule can be found at
http://pruffle.mit.edu/ccarter/3.21
Introduction
- Thermodynamics and Kinetics
- Averaging
- Fields, Variations, and Continuum Limits
- Fluxes and Accumulation
- Conserved and Nonconserved Quantities
Building Teamwork Skills
Reading: Distributed in Lecture
- How to Succeed in 3.21 and Still Have Time for 3.23
Homework 1 handed out.
Principles of Irreversible Thermodynamics
Reading: KPIM Chapter 2
- Entropy and Entropy Production
- Basic Postulate of Irreversible Thermodynamics
- Linear Irreversible Thermodynamics
- Onsager's Symmetry Hypothesis
Driving Forces and Fluxes for Diffusion
Reading: KPIM Chapter 3
- Diffusion in a Concentration Gradient
- Laboratory and Lattice Reference Frames, Marker Velocity
- Relation of diffusivity to mobility
- Interdiffusion, Intrinsic Diffusion and Self-Diffusion
Diffusion in the Presence of Stress
Reading: KPIM Chapter 3.
- Effect of Stress on Mobilities
- Formation of Solute Atmospheres around Dislocations
- Diffusional Creep
Diffusion Resulting from other Gradients
Homework 1 due, Homework 2 handed out.
Reading: KPIM Chapter 3.
- Electrical potential gradients
- Thermal gradients
- Capillarity effects
- Darcy's flaw
The Diffusion Equation
Reading: KPIM Chapter 4.
- Flux and Divergence
- The Constant Diffusivity Case
- Scaling of the Diffusion Equation
- Superposition of Solutions
- Fundamental Point-Source Solutions
- Time-Dependent Diffusivity
Solutions to the Diffusion Equation
Reading: KPIM Chapters 4 & 5.
- Anisotropic Diffusion
- Steady-State Solutions
- Time-Dependent Solutions
- Point Sources; Error Function
Methods of Solution to Diffusion Equation
Homework 2 due, Homework 3 handed out.
Reading: KPIM Chapter 5)
- Method of separation of variables
- Method of Laplace transforms
Methods of Solution to Diffusion Equation
Reading: KPIM Chapter 28 (Appendix D).
- Numerical Methods for Solving Differential Equations
- Treatment of Boundary Conditions
- Solutions Using Canned Software Packages: Maple, Mathcad,
Mathematica, etc.
- Examples
Activated Jump Processes
Reading: KPIM Chapter 6.
- One-Particle Model
- Many-Body Model
Diffusion Resulting from Discrete Jumps
Homework 3 due, Homework 4 handed out.
Reading: KPIM Chapter 6.
- Computer demo
- Mean Square Displacement from a Point Source
- Diffusion and Random Walks
- Diffusion with Correlated Jumps
Diffusion in Crystals
Reading: KPIM Chapter 7.
- Diffusion mechanisms
- Atomic Models for Diffusion Coefficients: Metals
Diffusion in Crystals
Reading: KPIM Chapter 7.
- Atomic Models for Diffusion Coefficients: Ionic Crystals
Diffusion Along Crystal Imperfections
Homework 4 due, Homework 5 handed out.
Reading: KPIM Chapter 8.
- The Diffusion Spectrum
- Diffusion along Grain Boundaries
Diffusion Along Crystal Imperfections
Reading: KPIM Chapter 8.
- Diffusion along Dislocations
Diffusion in Noncrystalline Solids
Reading: KPIM Chapter 9.
- Diffusion in Liquids
- Diffusion in Amorphous Metals
- Diffusion of Small Solutes in Glassy Polymers
Diffusion in Noncrystalline Solids
- Diffusion of Polymer Chains
Motion of Dislocations
Reading: KPIM Chapter 10.
- Forces on Dislocations
- Dislocation Glide
- Dislocation Climb
Homework 6 handed out
Morphological Evolution of Surfaces
Reading: KPIM Chapter 13
- Smoothing of a free surface by surface diffusion
- Surface rearrangements by evaporation-condensation
Sintering
Reading: KPIM Chapter 14
- Sintering mechanisms and rates
- Scaling laws
- Sintering of powders
Competetive Growth: Particle Coarsening
Reading: KPIM Chapter 15, Section 15.1
- Diffusion control--mean-field theory
- Experimental studies
- Source/sink control
Competetive Growth: Grain Growth
Reading: KPIM Chapter 15, Section 15.2
- Grain growth in two dimensions
Homework 6 due; homework 7 handed out.
Continuous Transformations--Introduction
Reading: KPIM Chapters 18-19
- Order parameters
- Conserved and non-conserved field variables
- Diffuse interfaces
Continuous Transformations--Kinetics
Reading: KPIM Chapter 19
- Evolution equations
- Kinetics and morphology of spinodal decompositon
- Continuous ordering
Homogeneous Nucleation
Reading: KPIM Chapter 20, Section 20.2.
- Steady-state nucleation
- Factors influencing nucleus shape
Homework 7 due; homework 8 handed out.
Heterogeneous nucleation
Reading: KPIM Chapter 20, Section 20.3.
- Nucleation in polycrystalline microstructures
- Nucleation on dislocations
Morphological Instabilities in Growth
Reading: KPIM Chapter 21, Section 21.4.
- Instability of a solid/liquid interface in a pure material
- Instabilities in alloy solidification
Homework 8 due; homework 9 handed out.
Momentum Diffusion by Viscous Shear
The Substantial Derivative and the Navier-Stokes Equations
Laminar Boundary Layer and the Friction Factor/Drag Coefficient
Homework 9 due, Homework 10 handed out.
Estimating Heat and Mass Transfer Coefficients
Reading:
Concurrent Nucleation and Growth Kinetics
Reading: KPIM Chapter 22, Section 22.1.
Time-Temperature-Transformation Diagrams
Reading: KPIM Chapter 22, Section 22.3.
- Temperature dependence of the rate of spinodal decomposition
Solidification
Reading: KPIM Chapter 23.
- Plane-front solidification
- Zone refining and zone leveling
- Cells and dendrites
- Casting microstructures
Homework 10 due
Martensitic Transformations
Reading: KPIM Chapter 24.
- Characteristics
- Crystallographic theory
Shape-Memory Alloys
- Deformation of martensite and austenite
- Deformation/temperature cycling and shape memory
- Ferromagnetic shape-memory alloys
Coverage: KPIM Chapters 13-15; 18-24
Summary and Review
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