{"id":1962,"date":"2025-01-15T19:45:51","date_gmt":"2025-01-15T19:45:51","guid":{"rendered":"https:\/\/www.engr.colostate.edu\/laboratories\/ceramics\/?page_id=1962"},"modified":"2025-12-09T23:07:19","modified_gmt":"2025-12-09T23:07:19","slug":"csu-mse-505","status":"publish","type":"page","link":"https:\/\/www.engr.colostate.edu\/laboratories\/ceramics\/csu-mse-505\/","title":{"rendered":"CSU \u2013 MSE 505 Kinetics of Materials"},"content":{"rendered":"

Course Information<\/h2>\n

Principles of kinetics and phase transformations for engineering materials and their applications<\/p>\n

Course Objective<\/h2>\n

The main objective of Kinetics of Materials is to introduce graduate-level principles and practical applications of kinetics and phase transformation<\/strong> for engineering materials involving phenomena including diffusion, movement of interfaces, solidification, and nucleation and growth.\u00a0 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<\/p>\n

Course Syllabus with Suggested Schedule<\/h2>\n

EMA 5001 Physical Properties of Materials SYLLABUS<\/a><\/p>\n

Lecture Slides & Videos<\/h2>\n\n\n
Lecture slides (PDF)<\/strong><\/td>Lecture videos (To be updated)<\/strong><\/td>Other Info<\/strong><\/td><\/tr>
Lecture 00\u00a0 Course info<\/a><\/td>Instructor, textbook, policy, website, and grading<\/a><\/td>Lecture 00 homework answers & hints<\/a><\/td><\/tr>
<\/td>Course objectives<\/a><\/td><\/td><\/tr>
 <\/td>Thermodynamics quick refresher<\/a><\/td><\/td><\/tr>
 <\/td>Kinetics & phase transformation vs thermodynamics<\/a><\/td><\/td><\/tr>
 <\/td>Example – steel hardness vs cooling rate<\/a><\/td><\/td><\/tr>
 <\/td>Example – B4<\/sub>C morphology vs synthesis condition<\/a><\/td><\/td><\/tr>
 <\/td>Topics covered and schedule<\/a><\/td><\/td><\/tr>
 <\/td>Application examples for kinetics & phase transformation<\/a><\/td><\/td><\/tr>
Lecture 01\u00a0 Diffusion – introduction<\/a><\/td>Diffusion definition and diffusing species<\/a><\/td><\/td><\/tr>
 <\/td>Different ways to classify diffusion phenomena<\/a><\/td><\/td><\/tr>
 <\/td>Descriptions-applications-characteristics of diffusion<\/a><\/td><\/td><\/tr>
 <\/td>Down-hill diffusion<\/a><\/td><\/td><\/tr>
 <\/td>Up-hill diffusion<\/a><\/td><\/td><\/tr>
 <\/td>Binary phase diagrams with miscibility gap<\/a><\/td><\/td><\/tr>
 <\/td>Additional considerations on down-hill vs up-hill diffusion<\/a><\/td><\/td><\/tr>
Lecture 02\u00a0 Atomistic mechanism of diffusion<\/a><\/td>Diffusion mechanism: Vacancy vs Interstitial<\/a><\/td>Lecture 02 homework answers & hints<\/a><\/td><\/tr>
 <\/td>Atomistic model for interstitial diffusion & Fick’s 1st law<\/a><\/td><\/td><\/tr>
 <\/td>Crystal structure and concentration effects on interstitial diffusion coefficient<\/a><\/td><\/td><\/tr>
 <\/td>C interstitial diffusion in FCC-Fe<\/a><\/td><\/td><\/tr>
 <\/td>Thermal activation of diffusion<\/a><\/td><\/td><\/tr>
Lecture 03\u00a0 Steady-state & non-steady-state diffusion – Fick’s 2nd law<\/a><\/td>Steady state diffusion and concentration profile<\/a><\/td>Lecture 03 homework answers & hints<\/a><\/td><\/tr>
 <\/td>Non-steady state diffusion and Fick’s 2nd Law<\/a><\/td><\/td><\/tr>
 <\/td>Change of concentration profile with time<\/a><\/td><\/td><\/tr>
 <\/td>Diffusion example – Homogenization<\/a><\/td><\/td><\/tr>
 <\/td>Diffusion example – Spin-on dopant<\/a><\/td><\/td><\/tr>
 <\/td>Diffusion example – Infinite diffusion couple<\/a><\/td><\/td><\/tr>
 <\/td>Diffusion example – Carburization and Decarburization<\/a><\/td><\/td><\/tr>
 <\/td>Diffusion length<\/a><\/td><\/td><\/tr>
 <\/td>Random walk and Diffusion length<\/a><\/td><\/td><\/tr>
Lecture 04 Self-diffusion & vacancy diffusion<\/a><\/td>Self diffusion<\/a><\/td><\/td><\/tr>
 <\/td>Self diffusion coefficient and examples<\/a><\/td><\/td><\/tr>
 <\/td>Vacancy diffusion and relationship with self diffusion<\/a><\/td><\/td><\/tr>
Lecture 05\u00a0 Substitutional diffusion in alloys<\/a><\/td>Kirkendall effect<\/a><\/td><\/td><\/tr>
 <\/td>Atoms asymmetric movement wrt a lattice plane<\/a><\/td><\/td><\/tr>
 <\/td>Darken’s equations and Interdiffusion coefficient<\/a><\/td><\/td><\/tr>
 <\/td>Considerations on interdiffusion coefficient<\/a><\/td><\/td><\/tr>
 <\/td>Mobility and Diffusion coefficient relationship<\/a><\/td><\/td><\/tr>
 <\/td>Thermodynamic factor & relationships between self-intrinsic-inter diffusion coefficients<\/a><\/td><\/td><\/tr>
Lecture 06\u00a0 Determine diffusion coefficient & Matano analysis<\/a><\/td>Determine D when independent of concentration<\/a><\/td><\/td><\/tr>
 <\/td>Boundary conditions for general isothermal interdiffusion<\/a><\/td><\/td><\/tr>
 <\/td>Boltzmann transformation<\/a><\/td><\/td><\/tr>
 <\/td>Matano analysis for D changing with concentration<\/a><\/td><\/td><\/tr>
 <\/td>Matano interface and its significance<\/a><\/td><\/td><\/tr>
Lecture 07\u00a0 Short-circuit diffusion & reaction diffusion<\/a><\/td>Grain boundary diffusion<\/a><\/td><\/td><\/tr>
 <\/td>Temperature effect on grain bulk vs grain boundary diffusion<\/a><\/td><\/td><\/tr>
 <\/td>Diffusion along dislocations<\/a><\/td><\/td><\/tr>
 <\/td>Reaction diffusion<\/a><\/td><\/td><\/tr>
 <\/td>Reaction diffusion – Interface velocity<\/a><\/td><\/td><\/tr>
 <\/td>Down-hill diffusion in a single-phase region<\/a><\/td><\/td><\/tr>
 <\/td>Down-hill diffusion involving a two-phase region<\/a><\/td><\/td><\/tr>
Lecture 08\u00a0 Diffusion – other problems<\/a><\/td>Expectations about diffusion<\/a><\/td>Lecture 08 homework answers & hints<\/a><\/td><\/tr>
 <\/td>D for interstitial carbon atoms in iron: BCC-Fe vs FCC-Fe<\/a><\/td><\/td><\/tr>
 <\/td>Successful jump frequency<\/a><\/td><\/td><\/tr>
 <\/td>Kirkendall interface moving velocity<\/a><\/td><\/td><\/tr>
 <\/td>Example for use of Darken’s equations<\/td><\/td><\/tr>
Lecture 09\u00a0 Surface energy<\/a><\/td>Classification of interfaces<\/a><\/td><\/td><\/tr>
 <\/td>Liquid-gas interfacial energy & Surface tension<\/a><\/td><\/td><\/tr>
 <\/td>Surface energy for FCC (111) plane<\/a><\/td><\/td><\/tr>
 <\/td>Surface energy for FCC (002) plane<\/a><\/td><\/td><\/tr>
 <\/td>Surface energy for FCC (220) plane<\/a><\/td><\/td><\/tr>
 <\/td>Surface energy for a plane rotating away from a low index plane<\/a><\/td><\/td><\/tr>
 <\/td>Wuff construction and crystal equilibrium shape<\/a><\/td><\/td><\/tr>
Lecture 10\u00a0 Grain boundaries<\/a><\/td>Tilt grain boundary & Twist grain boundary<\/a><\/td><\/td><\/tr>
 <\/td>Small angle grain boundaries<\/a><\/td><\/td><\/tr>
 <\/td>Tilt GB energy vs misorientation angle<\/a><\/td><\/td><\/tr>
 <\/td>Twin boundaries<\/a><\/td><\/td><\/tr>
 <\/td>Measure GB energy vs misorientation angle<\/a><\/td><\/td><\/tr>
 <\/td>Driving force for general GB migration<\/a><\/td><\/td><\/tr>
 <\/td>Driving force for GB straightening<\/a><\/td><\/td><\/tr>
 <\/td>Driving force for GB rotation<\/a><\/td><\/td><\/tr>
 <\/td>Boundary between three neighboring grains<\/a><\/td><\/td><\/tr>
 <\/td>Stability of grain shape<\/a><\/td><\/td><\/tr>
 <\/td>Grain growth kinetics<\/a><\/td><\/td><\/tr>
 <\/td>Grain boundary segregation<\/a><\/td><\/td><\/tr>
Lecture 11\u00a0 Interfaces and precipitate shape<\/a><\/td>Coherent interface<\/a><\/td>Lecture 11 homework answers & hints<\/a><\/td><\/tr>
 <\/td>Semi-coherent interface<\/a><\/td>Bk<\/a>TiC-ZrC semi-coherent interface<\/a> from
Li et al. Ceram Int 41(10) 14258 (2015)<\/a><\/td><\/tr>
 <\/td>Incoherent interface<\/a><\/td><\/td><\/tr>
 <\/td>Shapes of fully coherent and incoherent precipitates<\/a><\/td><\/td><\/tr>
 <\/td>Shapes of partially coherent precipitates<\/a><\/td><\/td><\/tr>
 <\/td>Shapes of precipitates at GB<\/a><\/td><\/td><\/tr>
 <\/td>Volume strain on precipitate shape and Coherence loss in growth<\/a><\/td><\/td><\/tr>
 <\/td>Solid-liquid interfaces<\/a><\/td><\/td><\/tr>
Lecture 12\u00a0 Solidification via homogeneous nucleation<\/a><\/td>Solidification and Nucleation-growth process<\/a><\/td><\/td><\/tr>
 <\/td>Classification of nucleation-growth type phase transformations<\/a><\/td><\/td><\/tr>
 <\/td>Solidification examples<\/a><\/td><\/td><\/tr>
 <\/td>Barriers in reaction or phase transformation<\/a><\/td><\/td><\/tr>
 <\/td>Solidification via homogeneous vs heterogeneous nucleation<\/a><\/td><\/td><\/tr>
 <\/td>Free energy change in solidification via homogeneous nucleation<\/a><\/td><\/td><\/tr>
 <\/td>Driving force vs undercooling in solidification<\/a><\/td><\/td><\/tr>
 <\/td>Critical nucleus size vs undercooling in solidification<\/a><\/td><\/td><\/tr>
 <\/td>Nucleation barrier vs undercooling in solidification<\/a><\/td><\/td><\/tr>
 <\/td>Critical nucleus size vs Max cluster size – Nucleation temperature<\/a><\/td><\/td><\/tr>
 <\/td>Homogeneous nucleation rate<\/a><\/td><\/td><\/tr>
Lecture 13 Solidification via heterogeneous nucleation<\/a><\/td>Free energy change and critical nucleus size for solidification via heterogeneous nucleation<\/a><\/td><\/td><\/tr>
 <\/td>S factor for solidification via heterogeneous nucleation<\/a><\/td><\/td><\/tr>
 <\/td>Heterogeneous nucleation rate for solidification<\/a><\/td><\/td><\/tr>
 <\/td>Other factors influencing heterogeneous nucleation rate<\/a><\/td><\/td><\/tr>
 <\/td>Two growth modes of solid from liquid for a pure element<\/a><\/td><\/td><\/tr>
 <\/td>Continuous growth for a pure element solid<\/a><\/td><\/td><\/tr>
 <\/td>Lateral growth for a pure element solid<\/a><\/td><\/td><\/tr>
 <\/td>Planar growth of a pure element solid into superheated liquid<\/a><\/td><\/td><\/tr>
 <\/td>Dendritic growth of a pure element solid into supercooled liquid<\/a><\/td><\/td><\/tr>
Lecture 14 Alloy solidification<\/a><\/td>Alloy EQUILIBRIUM solidification<\/a><\/td><\/td><\/tr>
 <\/td>Alloy solidification with stirring<\/a><\/td><\/td><\/tr>
 <\/td>Alloy solidification with stirring – Coring<\/a><\/td><\/td><\/tr>
 <\/td>Alloy solidification with stirring – Concentration profile change<\/a><\/td><\/td><\/tr>
 <\/td>Alloy solidification with stirring – Analytical solution<\/a><\/td><\/td><\/tr>
 <\/td>Alloy solidification – NO stirring in liquid<\/a><\/td><\/td><\/tr>
 <\/td>Constitutional supercooling in alloy solidification<\/a><\/td><\/td><\/tr>
Lecture 15 Solidification other issues<\/a><\/td>Eutectic solidification<\/a><\/td><\/td><\/tr>
 <\/td>Zones formed during solidification and controlling cast structure<\/a><\/td><\/td><\/tr>
 <\/td>Expectations for solidification and homogeneous\/heterogeneous nucleation<\/a><\/td><\/td><\/tr>
Lecture 16 Diffusional phase transformation<\/a><\/td>Introduction to solid state phase transformation<\/a><\/td><\/td><\/tr>
 <\/td>Characteristics of solid state phase transformation<\/a><\/td><\/td><\/tr>
 <\/td>1st & 2nd order phase transformation<\/a><\/td><\/td><\/tr>
 <\/td>Phase diagrams and common solid state phase transformations<\/a><\/td><\/td><\/tr>
Lecture 17 Nucleation in precipitation<\/a><\/td>Introduction to precipitation in solid<\/a><\/td><\/td><\/tr>
 <\/td>Homogeneous nucleation in solid<\/a><\/td><\/td><\/tr>
 <\/td>Driving force for homogeneous nucleation in solid precipitation<\/a><\/td><\/td><\/tr>
 <\/td>Nucleation rate for homogeneous precipitation<\/a><\/td><\/td><\/tr>
 <\/td>Nose-shaped curve of nucleation rate for homogeneous precipitation<\/a><\/td><\/td><\/tr>
 <\/td>Heterogeneous precipitation<\/a><\/td><\/td><\/tr>
Lecture 18\u00a0 Growth of precipitates<\/a><\/td>Precipitate growth and shape<\/a><\/td><\/td><\/tr>
 <\/td>Diffusion controlled planar growth of incoherent precipitate<\/a><\/td><\/td><\/tr>
 <\/td>Nose-shaped rate curve for precipitates growth<\/a><\/td><\/td><\/tr>
 <\/td>Growth of other precipitates<\/a><\/td><\/td><\/tr>
Lecture 19\u00a0 Spinodal decomposition<\/a><\/td>Introduction to Spinodal decomposition<\/a><\/td><\/td><\/tr>
 <\/td>Solid miscibility gap – example of Cu-Ni<\/a><\/td><\/td><\/tr>
 <\/td>Spinodal decomposition – free energy-composition curve<\/a><\/td><\/td><\/tr>
 <\/td>Spinodal decomposition – Composition change over time<\/a><\/td><\/td><\/tr>
 <\/td>Nucleation-growth within miscibility gap<\/a><\/td><\/td><\/tr>
 <\/td>Spinodal decomposition vs nucleation-growth<\/a><\/td><\/td><\/tr>
 <\/td>Driving force for spinodal decomposition<\/a><\/td><\/td><\/tr>
 <\/td>Interfacial chemical energy and coherent strain energy<\/a><\/td><\/td><\/tr>
 <\/td>Coherency strain and coherent spinodal<\/a><\/td><\/td><\/tr>
 <\/td>Wavelength for composition modulation from spinodal decomposition<\/a><\/td><\/td><\/tr>
Lecture 20\u00a0 Massive transformation and particle coarsening<\/a><\/td>Introduction to other phase transformations<\/a><\/td><\/td><\/tr>
 <\/td>Precipitate coarsening<\/a><\/td><\/td><\/tr>
 <\/td>Massive transformation<\/a><\/td><\/td><\/tr>
 <\/td>Order-disorder transformation<\/a><\/td><\/td><\/tr>
Lecture 21\u00a0 Martensite transformation<\/a><\/td>Fe-Fe3C phase diagram and Martensite transformation<\/a><\/td><\/td><\/tr>
 <\/td>Martensite transformation – At low T to meta-stable phase<\/a><\/td><\/td><\/tr>
 <\/td>Martensite transformation – Surface roughness and microstructures<\/a><\/td><\/td><\/tr>
 <\/td>Martensite transformation – Diffusionless and Athermal<\/a><\/td><\/td><\/tr>
 <\/td>Lattice misfit of C in Fe and BCT structure<\/a><\/td><\/td><\/tr>
 <\/td>Crystallography considerations for Martensite transformation in carbon steel<\/a><\/td><\/td><\/tr>
<\/td> <\/td> <\/td><\/tr>
Lecture 23 Models for transformation kinetics<\/a><\/td>TTT and CT curves<\/a><\/td><\/td><\/tr>
 <\/td>Nucleation and growth kinetics for very low conversion<\/a><\/td><\/td><\/tr>
 <\/td>Nucleation and growth kinetics for high conversion – JMA equation<\/a><\/td><\/td><\/tr>
 <\/td>Nucleation and growth kinetics with site saturation<\/a><\/td><\/td><\/tr>
 <\/td>Nucleation and growth kinetics with diffusion control<\/a><\/td><\/td><\/tr>
 <\/td>Interpretations of JMA equation exponent factor n<\/a><\/td><\/td><\/tr>
 <\/td>Diffusion controlled 1D growth kinetics<\/a><\/td><\/td><\/tr>
 <\/td>Diffusion controlled shrinking core model<\/a><\/td><\/td><\/tr>
 <\/td>Interface controlled shrinking core model<\/a><\/td><\/td><\/tr>
 <\/td>Summary of kinetic models<\/a><\/td><\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"

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.\u00a0 The course also aims…Read more <\/a><\/p>\n","protected":false},"author":28,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page_narrow.php","meta":{"footnotes":""},"class_list":["post-1962","page","type-page","status-publish","hentry"],"yoast_head":"\nCSU \u2013 MSE 505 Kinetics of Materials - Dr Zhe CHENG Group<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.engr.colostate.edu\/laboratories\/ceramics\/csu-mse-505\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"CSU \u2013 MSE 505 Kinetics of Materials - 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