2018 Physical Chemistry in Metals

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Academic unit or major
Undergraduate major in Materials Science and Engineering
Susa Masahiro  Hayashi Miyuki  Kawamura Kenichi  Ueda Mitsutoshi  Kobayashi Yoshinao 
Course component(s)
Mode of instruction
Day/Period(Room No.)
Mon3-4(S8-101)  Thr3-4(S8-101)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

This course consists of 'thermodynamics' and 'kinetics' parts, which are lectured in parallel. The 'thermodynamics' part starts with review on the first to third laws including thermodynamic functions such as Gibbs energy, followed by the topics, the chemical potential and the Gibbs phase rule, the latter being applied to phase diagrams and also systems involving chemical reactions. The concept of activity is introcuded along with standard states for components in gas and condensed phases, the latter including Raoultian, Henrian and 1mass% Henarian activities. The Elligham diagram is also touched on as an example of applications of thermodynamics. The kinetics part starts with its importnace in steelmaking and the concept of mass, momentum and energy flows, followed by the topics, diffusion rate and chemical reaction rate. Fick's first and second laws are introduced to quantitatively describe diffusion fluxes in steady and unsteady states. Chemical reaction rates are explained in relation to heterogeneous reaction which is very important to steelmaking, along with the concepts of elementary steps and rate-determining step using the unreacted core model.
 'Physical Chemistry in Metals' is a basis of many other courses provided in Undergraduate Major 'Materials Science and Engineering' and is also important for research and development of high temperature materials and processing. Production of materials must be considered from two perspectives of thermodynamics and kinetics.Thermodynamics can predict a condition where a material is formed spontaneouly, and kinetics can predict the production rate of the material. Students are expected to apply the concepts given in this course to your own research as well.

Student learning outcomes

By the end of this course, students will be able to:
1) Calculate internal energy, enthalpy, entropy and Gibbs energy changes of reactions.
2) Apply the Gibbs phase rule to discuss intensive parameters requied to establish phase equilibrium and chemical equilibrium.
3) Understand the concept of activity and calculate chemical equilibria using the Gibbs energy change and equilibrium constants.
4) Understand how to make the Ellingham diagram as well as how to use it.
5) Understand the concepts of mass, momentum and energy flows.
6) Describe diffusion fluxes in steady and unsteady states quantitatively.
7) Understand the concepts of elementary steps and rate-determining step and calculate heterogeneous reaction rates.


First to third laws of thermodynamics, Internal energy, Enthalpy, Entropy, Gibbs energy, Chemical potential, Chemical equilibrium, Gibbs phase rule, Activity, Standard state, Interaction parameter, Ellingham diagram, Flux, Steady state, Unsteady state, Fick's law, Diffusion coefficient, Reaction rate, Arrhenius equation, Activitaion energy,Elementary step, Rate-determining step, Heterogeneous reaction

Competencies that will be developed

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

Class flow

At the beginning of each class, solutions to exercise problems that were assigned during the previous class are reviewed. Towards the end of class, students are given exercise problems related to the lecture given that day to solve. To prepare for class, students should read the course schedule section and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purposes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 First law of thermodynamics - Difference between internal energy and enthalpy Understand the calculation of internal energy and enthalpy changes
Class 2 What is flow? - Definition of flux (mass, momentum, energy) and Fick's first law Understand the importance of kinetics in steelmaking and calculate diffusion flux in steady state
Class 3 Second and third laws of thermodynamics - Entropy changes of universe, system and surroundings Calculate entropy changes of system associated with expansion and temperature change
Class 4 Definition of diffusion coefficient and equation of mass balance - Kirkendall effect, Darken's method and Fick's second law Derive the general equation of mass balance
Class 5 Gibbs energy and chemical equilibrium -Definition of Gibbs energy and its physical meaning Calculate the Gibbs energy change of reaction
Class 6 Diffusion in steady state - Diffusion in gas and liquid phases and diffusion involving chemical reaction Calculate diffusion fluxes in gas and liquid phases in steady state and diffusion fluxes invloving chemical reaction
Class 7 Chemical potential and Gibbs phase rule - How to consider the numbers of components, phases and degrees of freedom Apply the Gibbs phase rule to phase diagrams and systems involving chemical reactions
Class 8 Diffusion in unsteady state - Analytical solutions of Fick's second law and determination of interdiffusion coefficient Calculate diffusion flux in unsteady state
Class 9 Concept of Activity - Raoultian and Henrian activities Determine the activity from vapor poressure and calculate chemical equilibrium involving liquid phase
Class 10 Boltzmann-Matano method and up-hill diffusion - Diffusion coefficient as function of concetration Calculate diffusion coefficient using the Boltzmann-Matano method
Class 11 1mass% Henrian activity and interaction parameter - Chemical potential difference between standard states Calculate chemical equilibria in solutions containing dilute solutes
Class 12 Chemical reaction kinetics - Chemical reaction rate constant and kinetic equation Calculate the rates of the first-order and second-order reactions, step reaction and interfacial reaction
Class 13 Ellingham diagram - Themodynamics of oxidation of metals Make the Ellingham diagram and use it
Class 14 Analysis of heterogeneous reaction - Rate-determining step,unreacted core model, slag-metal reaction and gas-metal reaction Calculate topochemical reaction rate
Class 15 Test level of understanding with exercise problems to summarize the course - Solve exercise problems covering the contents of classes 1-14 Test level of understanding and self-evaluate achievement for classes 1-14


Handouts relevent to the lecture are provided.

Reference books, course materials, etc.

Atkins: 『Physical Chemistry 8th edn Parts 1&2』 Tokyo Kagaku Dojin,ISBN: 978-4-8079-0695-6, ISBN: 978-4-8079-0696-3 (Japanese)
The Japan Institute of Metals 『Physical Chemistry of Metals』 Maruzen, ISBN: 4-88903-011-5 (Japanese) 

Assessment criteria and methods

Students' knowledge of thermodynamics laws, thermodynamic functions, Gibbs phase rule, activity, Elligham diagram, diffusion flux, chemical reaction rate and their ability to apply them to problems will be assessed.
Final exams 70%,exercise pronlems 30%

Related courses

  • MAT.A204 : Thermodynamics of Materials
  • MAT.M203 : Chemical Reaction Dynamics(M)
  • MAT.M202 : Statistical Mechanics(M)
  • MAT.M207 : Phase Diagram and Stability in Metals
  • MAT.M304 : Crystal Growth and Structure Formation

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

Students must have successfully completed both Thermodynamics of Materials (MAT.A204) and Chemical Reaction Dynamics (MAT.M203) or have equivalent knowledge.

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

Susa: susa.m.aa[at]m.titech.ac.jp
Hayashi: hayashi[at]mtl.titech.ac.jp

Office hours

Susa: Contact by e-mail in advance to schedule an appointment.
Hayashi: Contact by e-mail in advance to schedule an appointment.

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