2023 Faculty Courses School of Materials and Chemical Technology Undergraduate major in Materials Science and Engineering
Statistical Mechanics (Ceramics course)
- Academic unit or major
- Undergraduate major in Materials Science and Engineering
- Instructor(s)
- Toshio Kamiya / Seiichiro Izawa
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 7-8 Tue (S7-201) / 7-8 Fri (S7-201)
- Class
- -
- Course Code
- MAT.C203
- Number of credits
- 200
- Course offered
- 2023
- Offered quarter
- 3Q
- Syllabus updated
- Jul 8, 2025
- Language
- Japanese
Syllabus
Course overview and goals
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.
Course description and aims
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.
(4) Understand how to calculate physical properties using statistical distribution functions
Keywords
Ergodic hypothesis, Maxwell-Boltzmann distribution, Boltzmann distribution, Fermi-Dirac distribution, Bose-Einstein distribution, thermodynamic functions, free energy, distribution function, physical properties
Competencies
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Review of thermodynamics | Review thermodynamics to be needed to understand statistical physics |
| Class 2 | Kinetic theory of gases, Maxwell distribution | Understand the thermal equilibrium statistics of gaseous atoms and molecules |
| Class 3 | Maxwell distribution, fundamental of classical statistical physics I | Understand the thermal equilibrium statistics of gaseous atoms and molecules under potential |
| Class 4 | fundamental of classical statistical physics II | Explain the concept of ergodic hypothesis, derivate distribution function in the phase space |
| Class 5 | Canonical theory, principle of equal a priori probabilities for quantum statistical physics | Understand the canonical theory and the principle of equal a priori probabilities for quantum statistical physics |
| Class 6 | Grand canonical distribution, fundamental of quantum statistical physics | Understand the grand canonical distribution and fundamental of quantum statistical physics |
| Class 7 | Fundamental of quantum statistical physics, applications of classical statistical physics | Understand the fundamental of quantum statistical physics and applications of classical statistical physics |
| Class 8 | Review of distribution functions | Review the 1st to 7th classes |
| Class 9 | Theory of ideal Bose gas and specific heat of solids | Derive the theory of specific heat of solids based on phonon distribution |
| Class 10 | Theory of thermal radiation | Derive the theory of thermal distribution based on Bose-Einstein statistics of photons |
| Class 11 | 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 12 | Theory of electrons in semiconductor | Derive the electronic properties of semiconductors considering band structure with forbidden gap |
| Class 13 | Phase transition | Understand phase transitions from the viewpoints of statistical physics |
| Class 14 | Review | Review of statistical physics |
Study advice (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)
Textbook will be specified at the class. Related text and materials will be distributed.
Reference books, course materials, etc.
R.P. Feynman, Statistical Mechanics, Addison-Wesley
Evaluation methods and criteria
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
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
Sei-ichiro Izawa izawa.s.ac[at]m.titech.ac.jp
Office hours
(Kamiya, Izawa) Contact by e-mail in advance to schedule an appointment.