2017　Statistical Mechanics (Ceramics course)

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Undergraduate major in Materials Science and Engineering
Instructor(s)
Kamiya Toshio  Matsuishi Satoru
Class Format
Lecture
Media-enhanced courses
Day/Period(Room No.)
Tue7-8(S7-202)  Fri7-8(S7-202)
Group
-
Course number
MAT.C203
Credits
2
2017
Offered quarter
3Q
Syllabus updated
2017/3/17
Lecture notes updated
-
Language used
Japanese
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Course description and aims

This course starts from reviwing thermodynamics and aims to learn statistical mechanics from the microscopic point of view. Starting from Maxwell-Boltzmann distribution, which is applied to statistics of gasous atoms and molecules, studients will learn fundamental and applications of general classical and quantum statistical phyisics.

Student learning outcomes

At the end of this course, students will be able to:
(1) Know how to treat many body systems statistically.
(2) Understand the relationship between the microscopic statistical mechanics and the macroscopic thermodynamics.
(3) Understand which quantum statistics can be applied to what problems.

Keywords

Ergodic hypothesis, Maxwell-Boltzmann distribution、Boltzmann distribution, Fermi-Dirac distribution, Bose-Einstein distribution, thermodynamic functions, free energy, distribution function

Competencies that will be developed

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

Class flow

Students would be given exercise problems when required. At the beginning of each class, solusions to exercise problems are reviewed. Questions are accepted anytime during each class.

Course schedule/Required learning

Course schedule Required learning
Class 1 First law of thermodynamics Understand the first law of thermodynamics
Class 2 Second law of tehrmodynamics, thermodynamic functions Understand the second law of thermodynamics and important thermodynamic functions
Class 3 Kinetic theory of gases Understand the thermal equillibrium statistics of gasous atoms and molecules
Class 4 Fundamental of classical statistical mechanics I Derivate distribution function for gasous atoms and molecules at thermal equillibrium
Class 5 Fundamental of classical statistical mechanics II Explain the concept of ergodic hypothesis, derivate distribution function in the phase space
Class 6 Canonical distribution and grand canonical distribution Derive distribution functions for gases with interaction
Class 7 Midterm review of the first half of this course Review the 1st to 6th classes
Class 8 Fundamental of quantum statistical mechanics I Derive Fermi-Dirac distribution for anti-symmetric particles
Class 9 Fundamental of quantum statistical mechanics II Derive Bose-Einstein distribution for symmetric particles
Class 10 Theory of ideal Bose gas and specific heat of solids Derive the theory of specific heat of solids based on phonon distribution
Class 11 Theory of thermal radiation Derive the theory of thermal distribution based on Bose-Einstein statistics of photons
Class 12 Theory of ideal Fermi gas and electrons in metal Derive the electronic properties of metals based on Fermi-Dirac distribution and free electron model
Class 13 Theory of electrons in semiconductor Derive the electronic properties of semiconductors considering band structure with forbidden gap
Class 14 Magnetic susceptibility Apply Fermi-Dirac distribution to spin systems and derive their magnetic properties
Class 15 Bose-Einstein condensation Learn what happens if electrons make Cooper paiers that follows Bose-Einstein distribution

Textbook(s)

Textbook will be specified at the class. Related text and materials will be distributed.

Assessment criteria and methods

Students will be evaluated by exerciese problems given in the classes and by a term-end examination

Related courses

• MAT.A204 ： Thermodynamics of Materials
• MAT.P204 ： Physical Chemistry (Thermodynamics)
• MAT.P301 ： Solid State Physics (Lattice)
• MAT.P303 ： Solid State Physics (Electrons)
• MAT.P205 ： Physical Chemistry (Phase Diagram)

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

Students must have successfully completed Thermodynamics of Materials (MAT.A204) or have equivalent knowledge.
Statistical Mechanics(M)(MAT.M202) and Physical Chemistry (Statistical Mechanics)(MAT.P305) cannot be taken if one taks Statistical Mechanics(C).

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

Toshio Kamiya　kamiya.t.aa[at]m.titech.ac.jp
Satoru Matsuishi　matsuishi.s.aa[at]m.titech.ac.jp

Office hours

(Kamiya, Matsuishi) Contact by e-mail in advance to schedule an appointment.