FIU – EMA5001 Kinetics of Materials

Course Information

The physical properties of materials, focusing on principles of kinetics in phase transformations for engineering materials and their applications

Course Objective

The main objective of EMA5001 Kinetics of Materials (listed as Physical Properties 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 interests 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)Videos on YouTube w/ closed caption (CC)Additional Info
Lecture 00  Course infoInstructor, textbook, policy, website, and gradingBk
Hw1 answers & hintsCourse objectivesBk
 Thermodynamics quick refresherBk
 Kinetics & phase transformation vs thermodynamicsBk
 Example – steel hardness vs cooling rateBk
 Example – B4C morphology vs synthesis conditionBk
 Topics covered and scheduleBk
 Application examples for kinetics & phase transformationBk
Lecture 01  Diffusion – introductionDiffusion definition and diffusing speciesBk
 Different ways to classify diffusion phenomenaBk
 Descriptions-applications-characteristics of diffusionBk
 Down-hill diffusionBk
 Up-hill diffusionBk
 Binary phase diagrams with miscibility gapBk
 Additional considerations on down-hill vs up-hill diffusionBk
Lecture 02  Atomistic mechanism of diffusionDiffusion mechanism: Vacancy vs InterstitialBk
 Atomistic model for interstitial diffusion & Fick’s 1st lawBk
 Crystal structure and concentration effects on interstitial diffusion coefficientBk
 C interstitial diffusion in FCC-FeBk
 Thermal activation of diffusionBk
Lecture 03  Steady-state & non-steady-state diffusion – Fick’s 2nd lawSteady state diffusion and concentration profileBk
 Non-steady state diffusion and Fick’s 2nd LawBk
 Change of concentration profile with timeBk
 Diffusion example – HomogenizationBk
 Diffusion example – Spin-on dopantBk
 Diffusion example – Infinite diffusion coupleBk
 Diffusion example – Carburization and DecarburizationBk
 Diffusion lengthBk
 Random walk and Diffusion lengthBk
Lecture 04 Self-diffusion & vacancy diffusionSelf diffusionBk
 Self diffusion coefficient and examplesBk
 Vacancy diffusion and relationship with self diffusionBk
Lecture 05  Substitutional diffusion in alloysKirkendall effectBk
 Atoms asymmetric movement wrt a lattice planeBk
 Darken’s equations and Interdiffusion coefficientBk
 Considerations on interdiffusion coefficientBk
 Mobility and Diffusion coefficient relationshipBk
 Thermodynamic factor & relationships between self-intrinsic-inter diffusion coefficientsBk
Lecture 06  Determine diffusion coefficient & Matano analysisDetermine D when independent of concentrationBk
 Boundary conditions for general isothermal interdiffusionBk
 Boltzmann transformationBk
 Matano analysis for D changing with concentrationBk
 Matano interface and its significanceBk
Lecture 07  Short-circuit diffusion & reaction diffusionGrain boundary diffusionBk
 Temperature effect on grain bulk vs grain boundary diffusionBk
 Diffusion along dislocationsBk
 Reaction diffusionBk
 Reaction diffusion – Interface velocityBk
 Down-hill diffusion in a single-phase regionBk
 Down-hill diffusion involving a two-phase regionBk
Lecture 08  Diffusion – other problemsExpectations about diffusionBk
 D for interstitial carbon atoms in iron: BCC-Fe vs FCC-FeBk
 Successful jump frequencyBk
 Kirkendall interface moving velocityBk
 Example for use of Darken’s equations Bk
Lecture 09  Surface energyClassification of interfacesBk
 Liquid-gas interfacial energy & Surface tensionBk
 Surface energy for FCC (111) planeBk
 Surface energy for FCC (002) planeBk
 Surface energy for FCC (220) planeBk
 Surface energy for a plane rotating away from a low index planeBk
 Wuff construction and crystal equilibrium shapeBk
Lecture 10  Grain boundariesTilt grain boundary & Twist grain boundaryBk
 Small angle grain boundariesBk
 Tilt GB energy vs misorientation angleBk
 Twin boundariesBk
 Measure GB energy vs misorientation angleBk
 Driving force for general GB migrationBk
 Driving force for GB straighteningBk
 Driving force for GB rotationBk
 Boundary between three neighboring grainsBk
 Stability of grain shapeBk
 Grain growth kineticsBk
 Grain boundary segregationBk
Lecture 11  Interfaces and precipitate shapeCoherent interfaceBk
 Semi-coherent interfaceBkTiC-ZrC semi-coherent interface from
Li et al. Ceram Int 41(10) 14258 (2015)
 Incoherent interfaceBk
 Shapes of fully coherent and incoherent precipitatesBk
 Shapes of partially coherent precipitatesBk
 Shapes of precipitates at GBBk
 Volume strain on precipitate shape and Coherence loss in growthBk
 Solid-liquid interfacesBk
Lecture 12  Solidification via homogeneous nucleationSolidification and Nucleation-growth processBk
 Classification of nucleation-growth type phase transformationsBk
 Solidification examplesBk
 Barriers in reaction or phase transformationBk
 Solidification via homogeneous vs heterogeneous nucleationBk
 Free energy change in solidification via homogeneous nucleationBk
 Driving force vs undercooling in solidificationBk
 Critical nucleus size vs undercooling in solidificationBk
 Nucleation barrier vs undercooling in solidificationBk
 Critical nucleus size vs Max cluster size – Nucleation temperatureBk
 Homogeneous nucleation rateBk
Lecture 13 Solidification via heterogeneous nucleationFree energy change and critical nucleus size for solidification via heterogeneous nucleationBk
 S factor for solidification via heterogeneous nucleationBk
 Heterogeneous nucleation rate for solidificationBk
 Other factors influencing heterogeneous nucleation rateBk
 Two growth modes of solid from liquid for a pure elementBk
 Continuous growth for a pure element solidBk
 Lateral growth for a pure element solidBk
 Planar growth of a pure element solid into superheated liquidBk
 Dendritic growth of a pure element solid into supercooled liquidBk
Lecture 14 Alloy solidificationAlloy EQUILIBRIUM solidificationBk
 Alloy solidification with stirringBk
 Alloy solidification with stirring – CoringBk
 Alloy solidification with stirring – Concentration profile changeBk
 Alloy solidification with stirring – Analytical solutionBk
 Alloy solidification – NO stirring in liquidBk
 Constitutional supercooling in alloy solidificationBk
Lecture 15 Solidification other issuesEutectic solidificationBk
 Zones formed during solidification and controlling cast structureBk
 Expectations for solidification and homogeneous/heterogeneous nucleationBk
Lecture 16 Diffusional phase transformationIntroduction to solid state phase transformationBk
 Characteristics of solid state phase transformationBk
 1st & 2nd order phase transformationBk
 Phase diagrams and common solid state phase transformationsBk
Lecture 17 Nucleation in precipitationIntroduction to precipitation in solidBk
 Homogeneous nucleation in solidBk
 Driving force for homogeneous nucleation in solid precipitationBk
 Nucleation rate for homogeneous precipitationBk
 Nose-shaped curve of nucleation rate for homogeneous precipitationBk
 Heterogeneous precipitationBk
Lecture 18  Growth of precipitatesPrecipitate growth and shapeBk
 Diffusion controlled planar growth of incoherent precipitateBk
 Nose-shaped rate curve for precipitates growthBk
 Growth of other precipitatesBk
Lecture 19  Spinodal decompositionIntroduction to Spinodal decompositionBk
 Solid miscibility gap – example of Cu-NiBk
 Spinodal decomposition – free energy-composition curveBk
 Spinodal decomposition – Composition change over timeBk
 Nucleation-growth within miscibility gapBk
 Spinodal decomposition vs nucleation-growthBk
 Driving force for spinodal decompositionBk
 Interfacial chemical energy and coherent strain energyBk
 Coherency strain and coherent spinodalBk
 Wavelength for composition modulation from spinodal decompositionBk
Lecture 20  Massive transformation and particle coarseningIntroduction to other phase transformationsBk
 Precipitate coarseningBk
 Massive transformationBk
 Order-disorder transformationBk
Lecture 21  Martensite transformationFe-Fe3C phase diagram and Martensite transformationBk
 Martensite transformation – At low T to meta-stable phaseBk
 Martensite transformation – Surface roughness and microstructuresBk
 Martensite transformation – Diffusionless and AthermalBk
 Lattice misfit of C in Fe and BCT structureBk
 Crystallography considerations for Martensite transformation in carbon steelBk
Lecture 22 Kinetics trivia  
Lecture 23 Models for transformation kineticsTTT and CT curvesBk
 Nucleation and growth kinetics for very low conversionBk
 Nucleation and growth kinetics for high conversion – JMA equationBk
 Nucleation and growth kinetics with site saturationBk
 Nucleation and growth kinetics with diffusion controlBk
 Interpretations of JMA equation exponent factor nBk
 Diffusion controlled 1D growth kineticsBk
 Diffusion controlled shrinking core modelBk
 Interface controlled shrinking core modelBk
 Summary of kinetic modelsBk
Lecture 24 Example of SiC formation kinetics and mechanism  
Lecture 25 Expectations about solid state phase transformation