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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Physics
- Instructor(s)
- Hirahara Toru
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue5-6(H115) Fri1-2(H115)
- Group
- -
- Course number
- PHY.C441
- Credits
- 2
- Academic year
- 2017
- Offered quarter
- 1Q
- Syllabus updated
- 2017/3/17
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
This course gives an introduction on how one can deduce the point group or space group of a crystal starting from the basics of crystallography such as stereo projection. The concept of three-dimensional real and reciprocal lattices will be presented and applied to real crystals such as metals or semiconductors. The relation between macroscopic physical properties of crystals represented as tensor quantities and the point group symmetry will be discussed. The basics of X-ray and electron diffraction will be given based on kinematic approximations. The relation between Fourier transformations and simple periodic structures as well as disordered ones will be discussed.
Crystal structures and diffraction phenomenon are taught in Quantum Mechanics, Solid State Physics, and Chemical Physics classes as well as in physical laboratory classes. But none treats them in a comprehensive way, and thus the aim of the lecture is to systematically organize this knowledge.
Student learning outcomes
By the end of this course, students will be able to:
1) Understand that the basic structure of materials are periodic arrangements of atoms.
2) Explain that the symmetry and macroscopic properties of materials are strongly interconnected.
3) Explain the principles of experimental diffraction/microscopy techniques.
Keywords
Crystals, lattice, Point/Space groups, Symmetry, Electron diffraction, X-ray diffraction
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
Two-thirds of each class is devoted to fundamentals and the rest to advanced content or application. To allow students to get a good understanding of the course contents and practice application, problems related to the contents of this course will be provided occasionally.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Introduction: What are crystals? | Understand the purpose of the present lecture and describe the properties of materials by comparing them to non-crystals. |
| Class 2 | Fundamentals of crystallography | Learn how to describe the symmetry of materials and apply them to real systems. |
| Class 3 | Point group | Learn how to describe the symmetry of materials using group theory. |
| Class 4 | Space and reciprocal lattices | Understand the concept of reciprocal lattices. |
| Class 5 | Space group | Understand the concept of space groups and learn how to use the International Tables for crystallography. |
| Class 6 | Crystal structure 1 (Chemical bondings and ionic radius) | Learn the chemical bonding that constitute the crystal structure. |
| Class 7 | Crystal structure 1 (fcc, bcc, hip lattices, complicated crystal structures) | Understand real crystal structures as well as relevant ones. |
| Class 8 | Crystal symmetry and physical properties 1 (Tensor representation of physical quantities, point group transformation, Neumann's principle) | Understand the basics of the relation between physical properties of crystals and its symmetry. |
| Class 9 | Crystal symmetry and physical properties 2 (Vectors, tensors) | Be able to explain the physical properties of crystals based on symmetry using vectors and tensors. |
| Class 10 | Atomic scattering factor and crystal structure factor 1 (Kinematic representation of diffraction, Bragg reflection and reciprocal lattices) | Understand the fundamental theory of diffraction. |
| Class 11 | Atomic scattering factor and crystal structure factor 2 (Crystal symmetry and Extinction rule) | Understand the relation between diffraction spots and crystal symmetry. |
| Class 12 | Application of Fourier analysis to crystal structures (Self-correlation function, disordered structure, fluctuation, dynamical structure factor) | Learn the application of Fourier transformation to structure analysis. |
| Class 13 | Observing crystal structures 1 (Principles of various diffraction methods and basics of experimental details) | Understand the basic principles of various diffraction methods. |
| Class 14 | Observing crystal structures 2 (Principles of scanning probe microscopy and basics of experimental details) | Understand the basic principles of scanning probe microscopes and be able to explain the experimental data. |
| Class 15 | Observing crystal structures 3 (State-of-art structure analysis methods) | Understand the structure determination techniques used in state-of-art research. |
Textbook(s)
Toyohiko Konno, "Crystal symmetry and group theory", Kyoritsu-shuppan (in Japanese)
Toyohiko Konno, "Fundamentals of diffraction from crystals and its imaging", Kyoritsu-shuppan (in Japanese)
Y. Waseda, E. Matsubara, K. Shinoda “X-ray diffraction crystallography”, Springer （Available online freely inside the campus）
C. Malgrange, C. Ricolleau, M. Schlenker “Symmetry and Physical Properties of Crystals”, Springer
M. S. Dresselhaus, G. Dresselhaus, A. Jorio, “Group Theory-Application to the Physics of Condensed Matter”, Springer
(Available online at http://web.mit.edu/course/6/6.734j/www/group-full02.pdf)
Reference books, course materials, etc.
Handouts will be distributed at the beginning of class when necessary and elaborated on using PowerPoint slides. Students are expected to use these documents for preparation and review purposes.
Assessment criteria and methods
Evaluation will be based on examination or report submission
Related courses
- PHY.Q438 ： Quantum Mechanics of Many-Body Systems
- PHY.C340 ： Basic Solid State Physics
- PHY.C341 ： Condensed Matter Physics I
- PHY.C342 ： Condensed Matter Physics II
- PHY.L202 ： Experiments in Physics A
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students must have basic knowledge of quantum mechanics, statistical mechanics, and solid state physics.
Other
There are many things to memorize so please review the lecture on your own and understand the meaning of the technical terms.
