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Abstract/Syllabus:
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Russell, Kenneth, and Samuel Allen, 3.21 Kinetic Processes in Materials, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 07 Jul, 2010). License: Creative Commons BY-NC-SA
Kinetic Processes in Materials
Spring 2006
Nucleation is the onset of a phase transition, e.g. from liquid to gas, in a small but stable region. In this photo, bubbles in a soft drink each nucleate independently, responding to a decrease in pressure. (Photo courtesy of Wikipedia.)
Course Highlights
This course features a complete set of lecture summaries in the lecture notes section, and a complete set of exams with solutions.
Course Description
This course presents a unified treatment of phenomenological and atomistic kinetic processes in materials. It provides the foundation for the advanced understanding of processing, microstructural evolution, and behavior for a broad spectrum of materials. The course emphasizes analysis and development of rigorous comprehension of fundamentals. Topics include: irreversible thermodynamics; diffusion; nucleation; phase transformations; fluid and heat transport; morphological instabilities; gas-solid, liquid-solid, and solid-solid reactions.
Technical Requirements
Special software is required to use some of the files in this course: .nb and .tif.
Syllabus
This page presents various course policies and a course calendar.
Prerequisites
3.012, 3.022, 3.044, or permission of instructor.
Textbook
Balluffi, R. W., S. M. Allen, and W. C. Carter. Kinetics of Materials. New York, NY: John Wiley & Sons, 2005. ISBN: 9780471246893.
Homework
For most class sessions, homework problems will be suggested from the course textbook. These problems will not be graded, but students are strongly encouraged to work through them and consult the solutions in the book as needed.
Exams
Three 90 minute exams will be given during the term.
Grading Policy
The course grading is based on equal weight among the three exams (1/3 each).
Course Calendar
The calendar below provides information on the course's lecture (L) and recitation (R) sessions.
Course calendar.
| SES # |
TOPICS |
| L1 |
Introduction: Fields and Gradients; Fluxes; Continuity Equation |
| R1 |
Recitation |
| L2 |
Irreversible Thermodynamics |
| L3 |
Driving Forces and Fluxes for Diffusion; Self-Diffusion and Interdiffusion |
| R2 |
Recitation |
| L4 |
Interdiffusion; Effects of Electrical Potential, Capillarity, and Stress on Diffusion Potential |
| L5 |
Effects of Capillarity and Stress on Diffusion |
| L6 |
The Diffusion Equation |
| R3 |
Recitation |
| L7 |
Solutions to the Diffusion Equation - I |
| L8 |
Solutions to the Diffusion Equation - II |
| L9 |
Solutions to the Diffusion Equation - III |
| R3 |
Recitation |
| L10 |
Activated Jump Processes |
| L11 |
Diffusion Resulting from Discrete Jumps |
| L12 |
Diffusion in Crystals |
| R4 |
Recitation |
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Exam 1 |
| L13 |
Atomic Models for Diffusivities - I |
| L14 |
Atomic Models for Diffusivities - II |
| R5 |
Recitation |
| L15 |
Short-Circuit Diffusion in Crystals |
| L16 |
Diffusion in Noncrystalline Materials |
| L17 |
Surface Evolution Due to Capillary Forces |
| R6 |
Recitation |
| L18 |
Particle Coarsening |
| L19 |
Grain Growth |
| L20 |
Diverse Short Topics: Anisotropic Surfaces, Diffusional Creep, and Sintering |
| R7 |
Recitation |
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Exam 2 |
| L21 |
General Features of Phase Transformations |
| R8 |
Recitation |
| L22 |
Spinodal Decomposition and Continuous Ordering |
| L23 |
Spinodal Decomposition Kinetics |
| R9 |
Recitation |
| L24 |
Nucleation |
| L25 |
Heterogeneous Nucleation |
| L26 |
Diffusional Growth |
| R10 |
Recitation |
| L27 |
Morphological Stability of Moving Interfaces |
| L28 |
Kinetics of Nucleation and Growth Transformations |
| R11 |
Recitation |
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Exam 3 |
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Further Reading:
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Readings
This following table lists readings assigned for each lecture session, plus supplemental readings. Most assigned readings are from the course textbook:
[KoM] = Balluffi, R. W., S. M. Allen, and W. C. Carter. Kinetics of Materials. New York, NY: John Wiley & Sons, 2005. ISBN: 9780471246893.
The table below provides information on the course's lecture (L) and recitation (R) sessions.
Course readings.
| SES # |
TOPICS |
READINGS |
| L1 |
Introduction: Fields and Gradients; Fluxes; Continuity Equation |
KoM, chapter 1. |
| R1 |
Recitation |
|
| L2 |
Irreversible Thermodynamics |
KoM, chapter 2.
Christian, J. W. "Irreversible Thermodynamics." In Theory of Transformations in Metals and Alloys, Part 1: Equilibrium and General Kinetic Theory. Kidlington, UK: Pergamon Press, 1975. ISBN: 9780080180311. |
| L3 |
Driving Forces and Fluxes for Diffusion; Self-Diffusion and Interdiffusion |
KoM, section 3.1.
Poirier, D. R., and G. H. Geiger. Transport Phenomena in Materials Processing. Warrendale, PA: Minerals, Metals & Materials Society, 1994. ISBN: 9780873392723. See pp. 185-189 and 281-282 on Heat Conduction, and pp. 417-434 on Diffusion. |
| R2 |
Recitation |
|
| L4 |
Interdiffusion; Effects of Electrical Potential, Capillarity, and Stress on Diffusion Potential |
KoM, sections 3.2-3.5. |
| L5 |
Effects of Capillarity and Stress on Diffusion |
KoM, sections 3.4-3.5. |
| L6 |
The Diffusion Equation |
KoM, sections 4.1-4.1.2 and 4.2. |
| R3 |
Recitation |
|
| L7 |
Solutions to the Diffusion Equation - I |
KoM, sections 4.3-4.5. |
| L8 |
Solutions to the Diffusion Equation - II |
KoM, sections 5.1-5.2.4. |
| L9 |
Solutions to the Diffusion Equation - III |
KoM, sections 5.2.4-5.2.6. |
| R4 |
Recitation |
|
| L10 |
Activated Jump Processes |
KoM, sections 7.1-7.1.2 and 7.2. |
| L11 |
Diffusion Resulting from Discrete Jumps |
KoM, section 7.2. |
| L12 |
Diffusion in Crystals |
KoM, sections 8.1-8.2.1. |
| R5 |
Recitation |
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| |
Exam 1 |
|
| L13 |
Atomic Models for Diffusivities - I |
KoM, section 8.2.
Allen, S. M., and E. L. Thomas. "Point Imperfections in Ionic Crystals." Section 5.1.6 in The Structure of Materials. 1999. ISBN: 9780471000822. |
| L14 |
Atomic Models for Diffusivities - II |
KoM, section 8.2. |
| R6 |
Recitation |
|
| L15 |
Short-Circuit Diffusion in Crystals |
KoM, chapter 9. |
| L16 |
Diffusion in Noncrystalline Materials |
KoM, chapter 10. |
| L17 |
Surface Evolution Due to Capillary Forces |
KoM, section 14.1. |
| R7 |
Recitation |
|
| L18 |
Particle Coarsening |
KoM, sections 15.1 and C.4. |
| L19 |
Grain Growth |
KoM, sections 15.2 and 13.3.5. |
| L20 |
Diverse Short Topics: Anisotropic Surfaces, Diffusional Creep, and Sintering |
KoM, sections 14.2, 16.1, 16.3, and C.3. |
| R8 |
Recitation |
|
| |
Exam 2 |
|
| L21 |
General Features of Phase Transformations |
KoM, chapter 17. |
| R9 |
Recitation |
|
| L22 |
Spinodal Decomposition and Continuous Ordering |
KoM, chapter 18. |
| L23 |
Spinodal Decomposition Kinetics |
KoM, chapter 18. |
| R10 |
Recitation |
|
| L24 |
Nucleation |
KoM, chapter 19. |
| L25 |
Heterogeneous Nucleation |
KoM, section 19.2. |
| L26 |
Diffusional Growth |
KoM, chapter 20. |
| R11 |
Recitation |
|
| L27 |
Morphological Stability of Moving Interfaces |
KoM, chapter 20.
See Mathematica notebook on Diffusional Growth in lecture notes section. |
| L28 |
Kinetics of Nucleation and Growth Transformations |
KoM, chapter 21. |
| R12 |
Recitation |
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Exam 3 |
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Supplemental Readings
Students are encouraged to consult an applied math book as needed, such as: Hildebrand, F. B. Advanced Calculus for Applications. Upper Saddle River, NJ: Prentice-Hall, 1976.
Balluffi, R. W. "In Pursuit of the Lattice Vacancy." MRS Bulletin (February 1991): 23-28.
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