| Lecture slides (PDF) |
Videos on YouTube w/ closed caption (CC) |
Additional Info |
| Lecture 00 Course info |
Instructor, textbook, policy, website, and grading |
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| Hw1 answers & hints |
Course objectives |
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Thermodynamics quick refresher |
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Kinetics & phase transformation vs thermodynamics |
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Example – steel hardness vs cooling rate |
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Example – B4C morphology vs synthesis condition |
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Topics covered and schedule |
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Application examples for kinetics & phase transformation |
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| Lecture 01 Diffusion – introduction |
Diffusion definition and diffusing species |
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Different ways to classify diffusion phenomena |
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Descriptions-applications-characteristics of diffusion |
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Down-hill diffusion |
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Up-hill diffusion |
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Binary phase diagrams with miscibility gap |
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Additional considerations on down-hill vs up-hill diffusion |
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| Lecture 02 Atomistic mechanism of diffusion |
Diffusion mechanism: Vacancy vs Interstitial |
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Atomistic model for interstitial diffusion & Fick’s 1st law |
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Crystal structure and concentration effects on interstitial diffusion coefficient |
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C interstitial diffusion in FCC-Fe |
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Thermal activation of diffusion |
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| Lecture 03 Steady-state & non-steady-state diffusion – Fick’s 2nd law |
Steady state diffusion and concentration profile |
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Non-steady state diffusion and Fick’s 2nd Law |
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Change of concentration profile with time |
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Diffusion example – Homogenization |
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Diffusion example – Spin-on dopant |
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Diffusion example – Infinite diffusion couple |
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Diffusion example – Carburization and Decarburization |
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Diffusion length |
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Random walk and Diffusion length |
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| Lecture 04 Self-diffusion & vacancy diffusion |
Self diffusion |
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Self diffusion coefficient and examples |
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Vacancy diffusion and relationship with self diffusion |
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| Lecture 05 Substitutional diffusion in alloys |
Kirkendall effect |
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Atoms asymmetric movement wrt a lattice plane |
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Darken’s equations and Interdiffusion coefficient |
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Considerations on interdiffusion coefficient |
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Mobility and Diffusion coefficient relationship |
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Thermodynamic factor & relationships between self-intrinsic-inter diffusion coefficients |
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| Lecture 06 Determine diffusion coefficient & Matano analysis |
Determine D when independent of concentration |
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Boundary conditions for general isothermal interdiffusion |
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Boltzmann transformation |
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Matano analysis for D changing with concentration |
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Matano interface and its significance |
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| Lecture 07 Short-circuit diffusion & reaction diffusion |
Grain boundary diffusion |
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Temperature effect on grain bulk vs grain boundary diffusion |
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Diffusion along dislocations |
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Reaction diffusion |
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Reaction diffusion – Interface velocity |
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Down-hill diffusion in a single-phase region |
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Down-hill diffusion involving a two-phase region |
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| Lecture 08 Diffusion – other problems |
Expectations about diffusion |
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D for interstitial carbon atoms in iron: BCC-Fe vs FCC-Fe |
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Successful jump frequency |
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Kirkendall interface moving velocity |
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Example for use of Darken’s equations |
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| Lecture 09 Surface energy |
Classification of interfaces |
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Liquid-gas interfacial energy & Surface tension |
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Surface energy for FCC (111) plane |
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Surface energy for FCC (002) plane |
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Surface energy for FCC (220) plane |
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Surface energy for a plane rotating away from a low index plane |
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Wuff construction and crystal equilibrium shape |
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| Lecture 10 Grain boundaries |
Tilt grain boundary & Twist grain boundary |
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Small angle grain boundaries |
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Tilt GB energy vs misorientation angle |
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Twin boundaries |
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Measure GB energy vs misorientation angle |
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Driving force for general GB migration |
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Driving force for GB straightening |
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Driving force for GB rotation |
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Boundary between three neighboring grains |
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Stability of grain shape |
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Grain growth kinetics |
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Grain boundary segregation |
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| Lecture 11 Interfaces and precipitate shape |
Coherent interface |
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Semi-coherent interface |
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TiC-ZrC semi-coherent interface from
Li et al. Ceram Int 41(10) 14258 (2015) |
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Incoherent interface |
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Shapes of fully coherent and incoherent precipitates |
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Shapes of partially coherent precipitates |
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Shapes of precipitates at GB |
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Volume strain on precipitate shape and Coherence loss in growth |
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Solid-liquid interfaces |
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| Lecture 12 Solidification via homogeneous nucleation |
Solidification and Nucleation-growth process |
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Classification of nucleation-growth type phase transformations |
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Solidification examples |
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Barriers in reaction or phase transformation |
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Solidification via homogeneous vs heterogeneous nucleation |
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Free energy change in solidification via homogeneous nucleation |
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Driving force vs undercooling in solidification |
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Critical nucleus size vs undercooling in solidification |
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Nucleation barrier vs undercooling in solidification |
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Critical nucleus size vs Max cluster size – Nucleation temperature |
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Homogeneous nucleation rate |
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| Lecture 13 Solidification via heterogeneous nucleation |
Free energy change and critical nucleus size for solidification via heterogeneous nucleation |
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S factor for solidification via heterogeneous nucleation |
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Heterogeneous nucleation rate for solidification |
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Other factors influencing heterogeneous nucleation rate |
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Two growth modes of solid from liquid for a pure element |
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Continuous growth for a pure element solid |
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Lateral growth for a pure element solid |
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Planar growth of a pure element solid into superheated liquid |
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Dendritic growth of a pure element solid into supercooled liquid |
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| Lecture 14 Alloy solidification |
Alloy EQUILIBRIUM solidification |
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Alloy solidification with stirring |
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Alloy solidification with stirring – Coring |
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Alloy solidification with stirring – Concentration profile change |
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Alloy solidification with stirring – Analytical solution |
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Alloy solidification – NO stirring in liquid |
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Constitutional supercooling in alloy solidification |
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| Lecture 15 Solidification other issues |
Eutectic solidification |
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Zones formed during solidification and controlling cast structure |
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Expectations for solidification and homogeneous/heterogeneous nucleation |
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| Lecture 16 Diffusional phase transformation |
Introduction to solid state phase transformation |
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Characteristics of solid state phase transformation |
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1st & 2nd order phase transformation |
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Phase diagrams and common solid state phase transformations |
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| Lecture 17 Nucleation in precipitation |
Introduction to precipitation in solid |
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Homogeneous nucleation in solid |
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Driving force for homogeneous nucleation in solid precipitation |
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Nucleation rate for homogeneous precipitation |
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Nose-shaped curve of nucleation rate for homogeneous precipitation |
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Heterogeneous precipitation |
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| Lecture 18 Growth of precipitates |
Precipitate growth and shape |
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Diffusion controlled planar growth of incoherent precipitate |
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Nose-shaped rate curve for precipitates growth |
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Growth of other precipitates |
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| Lecture 19 Spinodal decomposition |
Introduction to Spinodal decomposition |
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Solid miscibility gap – example of Cu-Ni |
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Spinodal decomposition – free energy-composition curve |
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Spinodal decomposition – Composition change over time |
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Nucleation-growth within miscibility gap |
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Spinodal decomposition vs nucleation-growth |
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Driving force for spinodal decomposition |
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Interfacial chemical energy and coherent strain energy |
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Coherency strain and coherent spinodal |
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Wavelength for composition modulation from spinodal decomposition |
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| Lecture 20 Massive transformation and particle coarsening |
Introduction to other phase transformations |
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Precipitate coarsening |
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Massive transformation |
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Order-disorder transformation |
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| Lecture 21 Martensite transformation |
Fe-Fe3C phase diagram and Martensite transformation |
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Martensite transformation – At low T to meta-stable phase |
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Martensite transformation – Surface roughness and microstructures |
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Martensite transformation – Diffusionless and Athermal |
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Lattice misfit of C in Fe and BCT structure |
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Crystallography considerations for Martensite transformation in carbon steel |
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| Lecture 22 Kinetics trivia |
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| Lecture 23 Models for transformation kinetics |
TTT and CT curves |
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Nucleation and growth kinetics for very low conversion |
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Nucleation and growth kinetics for high conversion – JMA equation |
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Nucleation and growth kinetics with site saturation |
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Nucleation and growth kinetics with diffusion control |
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Interpretations of JMA equation exponent factor n |
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Diffusion controlled 1D growth kinetics |
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Diffusion controlled shrinking core model |
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Interface controlled shrinking core model |
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Summary of kinetic models |
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| Lecture 24 Example of SiC formation kinetics and mechanism |
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| Lecture 25 Expectations about solid state phase transformation |
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