CSU – MSE 505 Kinetics Materials

Course Information

Principles of kinetics and phase transformations for engineering materials and their applications

Course Objective

The main objective of Kinetics of Materials is to introduce graduate-level principles and practical applications of kinetics and phase transformation for engineering materials involving phenomena including diffusion, movement of interfaces, solidification, and nucleation and growth.  The course also aims to provide graduate-level training in critical thinking, mathematical analysis, and written communication skills focusing on problems of interest involving kinetics and phase transformation of engineering materials

Course Syllabus with Suggested Schedule

EMA 5001 Physical Properties of Materials SYLLABUS

Lecture Slides & Videos

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