3.21 | Spring 2006 | Graduate
Kinetic Processes in Materials

Lecture Notes

The following table presents a thorough summary of each lecture session.

L1 Introduction: Fields and Gradients; Fluxes; Continuity Equation (PDF)  
L2 Irreversible Thermodynamics (PDF)  
L3 Driving Forces and Fluxes for Diffusion; Self-Diffusion and Interdiffusion (PDF)

Scalar Fields, Fluxes, and Accumulation, scalar_field.nb (NB) (Courtesy of Prof. Craig Carter. Used with permission.)

Illustrates the behavior of the concentration around a line source that is diffusing into an infinite isotropic medium.

L4 Interdiffusion; Effects of Electrical Potential, Capillarity, and Stress on Diffusion Potential (PDF)  
L5 Effects of Capillarity and Stress on Diffusion (PDF)  
L6 The Diffusion Equation (PDF)  
L7 Solutions to the Diffusion Equation - I (PDF)  
L8 Solutions to the Diffusion Equation - II (PDF)  
L9 Solutions to the Diffusion Equation - III (PDF)

Solutions to the Diffusion Equation, diffusion_soln.nb (NB) (Courtesy of Miguel Marioni. Used with permission.)

Numerical work illustrating some solutions to diffusion boundary-value problems; plots of closed form solutions as well as solutions by finite differences.

L10 Activated Jump Processes (PDF)  
L11 Diffusion Resulting from Discrete Jumps (PDF)  
L12 Diffusion in Crystals (PDF)  
L13 Atomic Models for Diffusivities - I (PDF)  
L14 Atomic Models for Diffusivities - II (PDF)  
L15 Short-Circuit Diffusion in Crystals (PDF)  
L16 Diffusion in Noncrystalline Materials (PDF)  
L17 Surface Evolution Due to Capillary Forces (PDF)  
L18 Particle Coarsening (PDF)  
L19 Grain Growth (PDF)  
L20 Diverse Short Topics: Anisotropic Surfaces, Diffusional Creep, and Sintering (PDF)  
L21 General Features of Phase Transformations (PDF)  
L22 Spinodal Decomposition and Continuous Ordering (PDF)

BCC Alloys in the Bragg-Williams Approximation, bcc_alloys.nb (NB)

Free energy model for BCC and CsCl structure with first-neighbor interactions. Calculates miscibility gap for W < 0 and excess free energy per unit area of diffuse interface.

L23 Spinodal Decomposition Kinetics (PDF)

Kinetics of Spinodal Decomposition, spinodal.nb (NB)

Extension of the prior lecture’s Mathematica notebook, to cover kinetics of spinodal decomposition including kinetic and thermodynamic wavenumbers, temperature dependence, etc.

L24 Nucleation (PDF)  
L25 Heterogeneous Nucleation (PDF)  
L26 Diffusional Growth (PDF)  
L27 Morphological Stability of Moving Interfaces (PDF)

Diffusional Growth, diffusion_growth.nb (NB)

This Mathematica notebook covers growth of a spherical precipitate from supersaturated solution. Calculates rate constant for diffusional growth, interfacial velocity, concentration profile in matrix using exact solution. Explores using stationary-field approximation to calculate interface velocity and concentration profile. Introduces spherical harmonic functions for describing shape perturbations of a sphere.

Ni-Cr Equilibrium Diagram, CrNi.tif (TIF) (Reprinted with permission of ASM International®. All rights reserved.)

This illustration accompanies the Mathematica notebook on Diffusional Growth. To load in the notebook, place this file in your user directory.

L28 Kinetics of Nucleation and Growth Transformations (PDF)