2017 Microstructure Evolution and Diffusion in Metals

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Academic unit or major
Graduate major in Energy Science and Engineering
Kimura Yoshisato  Nakada Nobuo 
Class Format
Media-enhanced courses
Day/Period(Room No.)
Mon3-4(J234)  Thr3-4(J234)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
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Course description and aims

This course focuses on the ability to understand the diffusion theory as a basis of the microstructure of metals and alloys, involving the formation mechanism and temperature and time dependent changes, from the viewpoint of phase equilibria and kinetics, and it also focuses on how the microstructural factors, such as lattice defects and phase interfaces, affect mechanical properties and functional properties of metallic materials. Physical, mechanical, and functional properties of metallic materials are governed not only by chemical compositions but also by materials’ microstructure in the multi length scale. First of all, physical and thermodymanical background is explained for phase diagrams which are necessary to understand microstructure formation. Then, students acquire how to correctly comprehend information related to the phase equilibrium and microstructure formation, and how to improve functions and properties of metallic materials by controlling microstructure including phase interfaces and lattice defects. Microstructure change is generally proceeds as the diffusion rate controlled phenomena at high temperature range in which atomic diffusion can be sufficiently activated. In this course, fundamental theory of diffusion is precisely explained for metals and alloys using simple mathematical approaches, for instance, how to solve the diffusion equation based on the Fick’s law is introduced. Moreover, the methodology will be discussed over how to understand the dynamical behavior of microstructure changes using solutions of the diffusion equation from the viewpoint of phase equilibrium.

Student learning outcomes

By the end of this course, students will be able to:
1) Understand alloy phase diagrams, from binary to ternary systems, as a basis of microstructure, and to comprehend information related to the phase equilibrium correctly together with the understanding of thermodynamical background.
2) Explain the process of solidification microstructure depending on crystallographic orientation, and the processes of solidification and precipitation due to the heterogeneous nucleation, based on the understanding of the classical nucleation and growth theory.
3) Explain features of solidification microstructure of invariant reactions, eutectic and peritectic reactions, and to explain the relationship between eutectoid microstructure and mechanical properties of steels.
4) Explain the aging process of aluminum alloys including microstructure change due to the precipitation from supersaturated solid solution matrix and precipitation hardening mechanism, and also to explain the coherency of phase interfaces depending on the precipitation particle size.
5) Explain microstructure formed by the athermal martensitic transformation in steels, and shape memory effect and superelasticity originated from the thermal martensitic transformation in NiTi alloys.
6) Explain processes of recovery, recrystallization, and coarsening as temperature and time dependent changes of plastically deformed microstructure.
7) Explain features of fracture surface due to elastic deformation and brittle deformation, and features of dislocation substructure and fracture surface due to fatigue, cyclic deformation.
8) Explain the theory of diffusion phenominon based on Fick's law.
9) Explain the solution of diffusion equation and the determination of diffusion coefficient.


Phase diagram, Gibbs phase rule, Phase equilibrium, Phase transformation, Invariant reaction, Solidification, Precipitattion, Diffusion, Fick's law

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Exercise problems are assigned to students at the beginning of each class, and group discussion is held during the class according to topics to be learned. This course is devided in the first half and the second half, and understanding level is checked at the end of each half as midterm and final exams. Students should read the course schedule to check topics covered on that day, and preparation and reveiw are required.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Phase Equilibrium and Phase Stability in Binary Phase Diagrams Understand how to comprehend binary phase diagrams about phase stability and phase region, and explain phase equilibrium conditions using chemical potential together with thermodynamical meaning.
Class 2 Invariant Reaction and Gibbs Phase Rule Explain formation of microstructure by binary invariant reactions; eutectic and eutectoid reactions, and peritectic and peritectoid reactions. Also explain how to expand from binary to ternary system in terms of invariant reactions according to the Gibbs phase rule.
Class 3 Solidification Microstructure Explain heterogeneous nucleation with understanding of classical theory of nucleation and growth. And explain the relationship between crystallographically preferred growth direction and dendritic growth.
Class 4 Expansion of Phase Diagrams from Binary to Ternary Systems Comprehend alloy compositions, isotherms, and isopleths of ternary phase diagrams, and explain phase equilibrium condition in ternary systems, as extended from binary systems.
Class 5 Invariant Reactions and Reaction Scheme in Ternary Phase Diagrams Comprehend three types of invariant reactions, reaction schemes, and projections of liquidus surface of ternary phase diagrams, and explain phase equilibrium condition in ternary systems.
Class 6 Precipitation Microstructure Explain the precipitation in supersaturated solid solution matrix phase and the aging hardening mechanism in aluminum alloys, and explain the characteristics of the grain boundary reaction cellular microstructure formed by the discontinuous precipitation.
Class 7 Time- and Temperature-Dependent Change of Microstructure Explain changes in microstructure due to severe plastic deformation and consecutive recovery, recrystallization, and coarsening process. Explain the characteristics of ductile and brittle fracture surfaces, and the characteristics of microstructure and fracture surface formed by cyclic fatigue.
Class 8 Understanding level check-up examination, Review, and Supplement Evaluate the understanding level for the first half of this lecture (Class 1 through 7), and review the topics for insufficient understanding level.
Class 9 Fick's fiarst law understand Fick's first law staing that diffusion flux is proportional to a concentration gradient under sttedy state.
Class 10 Fick's second law understand Fick's second law staing that a development of concentration distribution is discribed with respect to mass balance.
Class 11 Solution of diffusion equation by separation of variables understand that diffusion equation can be analytically solved via separation of variables.
Class 12 Solution of diffusion equation by Laplace transformation understand that diffusion equation can be analytically solved via Laplace transformation.
Class 13 Boltzmann-Matano method understand Boltzmann-Matano method for determining the diffusion coefficient from concentration profiles when it is concentration dependent.
Class 14 Darken method understand the interdiffusion coefficient as defined in Darken's equation.
Class 15 Relation among various diffusion coefficients learn various diffusion coefficients, such as body diffusion, grain boundary diffusion, pipe diffusion, and their relations.



Reference books, course materials, etc.

Nishizawa, Taiji. Tamura, Imao. Sudo, Hajime. Metallography (Kinzokusoshikigaku). Tokyo: MARUZEN Co.,Ltd.; ISBN-13: 978-4621082430, (Japanese), Nishizawa, Taiji. Thermodynamics of Microstructure (Mikurososhiki-no-Netsurikigaku). Sendai: The Japan Institute of Metals and Materials; ISBN-13: 978-4889030280. (Japanese),Kohda, Shigeyasu. Introduction to Metal Physics (Kinzoku-buturigaku-joron). Tokyo: CORONA Publishing Co.,Ltd.; ISBN-13: 978-4339042870. (Japanese).

Assessment criteria and methods

Students' knowledge of followings will be assessed; diffusion related laws, solution of the diffusion equation, analysis of diffusion coefficient, comprehension of phase diagrams regarding microstructure formation as phase equilibrium, kinetics of microstructure formation, microstructure formation processes through solidification, precipitation, phase transformation. Understanding level check-up test and final exam 60%, and exercise problems 40%. The first half classes 50% and the second half classes 50%, and credits require 60 scores and higher out of 100.

Related courses

  • Themodynamics of Phase Equilibrium
  • Phase Transformation and Microstructure Control
  • Transport Phenomena at HighTemperature
  • Advanced Microstructure Design of Ferrous Materials
  • Advanced Microstructure Design of Non-ferrous Materials
  • Environmental Degradation of Materials

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Not applied.

Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

Kimura: kimura.y.ac[at]m.titech.ac.jp, 045-924-5157
Nakada: nkada.n.aa[at]m.titech.ac.jp, 045-924-5622

Office hours

Will be noticed on the first day of the lecture. It is basically recommended to contact by e-mail or telephone in advance to schedule an appointment.

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