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2021　Phase Diagram and Stability in Metals

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Academic unit or major
Undergraduate major in Materials Science and Engineering
Instructor(s)
Hosoda Hideki  Kimura Yoshisato 
Class Format
Lecture / Exercise     
Media-enhanced courses
Day/Period(Room No.)
Tue1-2(W331)  Fri1-2(W331)  
Group
-
Course number
MAT.M207
Credits
2
Academic year
2021
Offered quarter
3Q
Syllabus updated
2021/3/19
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

This course focuses on how to comprehend phase diagrams for understanding the phase equilibrium information, in the first half, and it covers the fundamentals of thermodynamical and physical background to understand the constructions of phase diagrams, in the second half. Topics include how to comprehend the phase equilibrium information in the binary alloy phase diagram by developing better understanding of the Gibbs’ phase rule, solubility curves, phase boundaries, and phase fields. The invariant reactions which characterize the types of binary phase diagram are explained with corresponding microstructure formation. Students cultivate deep understanding of the fundamentals of thermodynamics such as the Gibbs energy, chemical potential, and equilibrium conditions between phases, so that they can explain the physical background of phase diagrams. Moreover, the concept will be described how the alloy systems can be extended from binary to ternary.
In the metallurgical engineering and materials science fields, the ability to comprehend and to draw important pieces of information about phase equilibria from phase diagrams, which play a role of maps for matters and materials, is required to successfully achieve the materials design both for structural and functional materials. Since mechanical properties as well as functional properties can be controlled by microstructure, it is necessary to acquire the knowledge of phase diagrams in order to understand the formation mechanism and the time- and temperature-dependent changes of microstructure from the viewpoint of phase equilibria and phase stability. Microstructure of metals and alloys is formed through various paths such as solidification, precipitation, phase transformation, and so forth, according to the reaction scheme which is provided by the phase diagram. To acquire practical knowledges and skills of microstructure control methods focusing on lattice defects and phase interfaces, students should learn, in this course, the phase equilibrium on the phase diagrams together with the kinetics of the formation process of microstructure in a wide variety.

Student learning outcomes

By the end of this course, students will be able to:
1) understand the Gibbs phase rule in binary phase diagrams, and be able to correctly comprehend information which is related to phase fields and phase equilibrium from binary phase diagrams.
2) explain solid solution and phase separation by understanding the meaning of solubility curves, and be able to explain the volume fractions of co-existing two phases using the lever rule.
3) understand what the invariant reactions in binary system, the eutectic (eutectoid) reaction and the pretectic (peritectoid) reaction are, and be able to explain the formation process and the distinctive feature of each microstructure which is formed by those reactions.
4) understand the relationship between Gibbs energy and chemical composition, and temperature, as the thermodynamics background of binary phase diagrams, and be able to explain the chemical potential.
5) explain the conditions of two-phase (and three-phase) equilibrium in the binary system using the chemical potential which is evaluated from the relation between Gibbs energy and chemical composition, and also be able to explain the thermodynamical meaning of common tangent law.
6) understand and explain the concept of how to expand phase diagrams from a binary system to a ternary system.
7) explain at least some examples of the microstructure control from the viewpoint of phase diagrams for the practical materials design used for representative alloy systems (such as steels, aluminum alloys and titanium alloys).

Keywords

Alloy phase diagram, Phase equilibrium, Gibbs phase rule, phase transformation, invariant reaction, Chemical potential, Microstructure control, Materials design

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 check-up test is scheduled as the summery at the end of each half.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 Introduction: Why we need to learn phase diagams? – Relationship between microstructure and mechanical properties Understand how phase diagrams are playing important roles for the design of structural and functional materials.
Class 2 Comprehensions of Phase Diagrams (1); three states of matter, allotropic transformation, The phase diagram of water, The Gibbs' phase rule Explain Gibbs phase rule by deriving its equation, and revewing three states of matter using the phase diagram of water.
Class 3 Comprehensions of Phase Diagrams (2); Solid solution phases, Intermediate (Intermetallic) phases, Single- and two-phase fields Specify a primary solid solution phase, an intermediate phase, and single- and two-phase fields in binary phase diagrams.
Class 4 Comprehensions of Phase Diagrams (3); All-proportion miscible type phase diagrams, Solubility curves, The lever rule Understand the all-propertion miscible type phase diagram, solubility curves, and solidsolution and phase separation, and explain valume fractions of two phases using the lever rule.
Class 5 Comprehensions of Phase Diagrams (4); Binary invariant rections and solidification microstructure I – Eutectic reaction and eutectoid reaction Understand and explain the formation process of the eutectic microstructure and the eutectoid microstructure.
Class 6 Comprehensions of Phase Diagrams (5); Binary invariant rections and solidification microstructure II – Peritectic reaction and peritectoid reaction Understand and explain the formation process of the peritectic microstructure and the peritectoid microstructure.
Class 7 Comprehensions of Phase Diagrams – Understanding level check-up, Review, Supplement Evaluate the understanding level for the comprehension of binary phase diagrams (class 1 through 6) by examination 1, and review the topics for insufficient understanding level.
Class 8 Microstructure Control of Practical Alloys based on Phase Diagrams – Fundamental of Iron and Steels Summarize various microstructure controls used for steels based on phase diagrams, and categorize them according to phase transitions and heat treatments applied.
Class 9 Microstructure Control of Practical Alloys based on Phase Diagrams – Fundamental of Aluminum alloys and Titanium alloys Summarize microsturucture changes of aging process and related precipitation hardening mechanism of aluminum alloys, and two-phase microstructure control and peculiar properties of titaniumu alloys.
Class 10 Constructions of Phase Diagrams (1); Composition and temperature dependence of the Gibbs free energy Understand the relationship between Gibbs energy and chemical composition, and temperature, in a binary system, and explain its correspondence with a phase diagram.
Class 11 Constructions of Phase Diagrams (2); The Gibbs free energy and its partial molar quantity of chemical potential Derive the chemical potential from Gibbs energy-chemical composition curves, and understand that the chemical potential is a partial molar quantity of Gibbs energy.
Class 12 Constructions of Phase Diagrams (3); Equilibrium condition of two phases, Common tangent law on the Gibbs free energy–composition curves Eexplain the conditions of two-phase (and three-phase) equilibrium in a binary system using the chemical potential based on the common tangent law, together with the correspondence with a phase diagram.
Class 13 Constructions of Phase Diagrams (4); Ternary phse diagrams – How to comprehend ternary phase diagrams, Equilibrium of Three phases, Invariant reactions Explain the concept of how to expand phase diagrams from a binary system to a ternary system, and comprehend three-phase equilibrium and invariat reactions in ternary phase diagrams.
Class 14 Constructions of Phase Diagrams – Understanding level check-up, Review, Supplement Evaluate the understanding level for the constructions of binary phase diagrams (class 8 through 13) by examination 2, and review the topics for insufficient understanding level.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

Handouts

Reference books, course materials, etc.

Nishizawa, Taiji. Tamura, Imao. Sudo, Hajime. Metallography (Kinzokusoshikigaku). Tokyo: Maruzen; 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)
Miura, Kenji. Fukutomi, Hiroshi. Onodera, Hidehiro. Read and Interpret: Alloy Phase Diagrams (Mikata-Kangaekata: Goukin-Joutaizu). Tokyo: Ohmsha; ISBN-13: 978-4274087448. (Japanese)

Assessment criteria and methods

Students' knowledge of comprehension of binary phase diagrams, microstructure formation mechanisms by the invariat reactions, phase equilibrium conditions based on Gibbs energy, the relationship between microstructure control and phase diagrams in aluminum alloys and ferrous alloys (steels) will be assessed. Understanding level check-up tests (twice) (28%), final exams (38%), exercise problems (24%) and two homework reports (10%). The two check-up tests, the two reports, the final exam and at least 2/3 attendance of exercise problems are necessary to take the credits, regardless of total scores. Credits require 60 scores and higher out of 100. 　

Related courses

  • Thermodynamics of Materials
  • Crystallography
  • Crystal Growth and Microstructure
  • Science and Engineering of Ferrous Materials I
  • Science and Engineering of Ferrous Materials II
  • Science and Engineering of Non-ferrous Materials

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

Applicants are required to attend the first lecture due to grouping. If you could not attend it due to illness for example, but would like to register, contact Prof. Hosoda by e-mail by noon the next day after the first lecture.

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

Hosoda: hosoda.h.aa[at]m.titech.ac.jp, 045-924-5057
Kimura: kimura.y.ac[at]m.titech.ac.jp, 045-924-5157

Office hours

It is basically recommended to contact by e-mail or telephone in advance to schedule an appointment.

Other

The class will be divided into several groups for the exercise and presentation. The grouping is based on the first attendees and the list of credits taken at the first lecture. For this reason, applicants must attend the first lecture. In case of withdrawing, contact Prof. Hosoda by e-mail as soon as possible, at least by noon the next day.

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