To understand the origin of solid state physics, crystal and phonon are essential. The concept of crystal structure based on symmetry can easily explain the solid state composed a lot of atoms. To acquire the quantized phonon from the wave of lattice vibration comes from ordered arrangement of atomic coordination in crystals, students can contribute to develop a variety of materials support our society. From an idea of solid, students can grasp structures on atomic or molecular scale, and reach the comprehensive solid state physics.
At the end of this course, students will be able to understand and explain the solid state physics of lattice vibration and its quantization based on the common concept of geometric crystallography and symmetry of crystals. And also, students will apply the fundamental knowledge of atomic coordinationand lattice vibration in crystals to predict material properties.
This course focuses on symmetry, point group and space group determined crystal structures, and covers fundamental knowledge of solid state physics such as wave of lattice vibration, Brilluouin zone, phonon, specific heat, heat conductivity.
Crystal, Lattice, Symmetry, Point Group, Space Group, Lattice Vibration, Phonon, Specific Heat, Heat Conductivity
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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This lecture is given by distribution of necessary handout and blackboard demonstration. Students are given exercise problems related to the lecture given that day to solve. Required learning should be completed outside of the classroom for preparation and review purposes.
Course schedule | Required learning | |
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Class 1 | Crystals: Relationship of Crystal Lattice, Primitive Lattice, and Atomic Coordination | Introduction of atomic coordination in crystals |
Class 2 | Point Lattice and Bravais Lattice | Relationship of 13 Bravais lattice |
Class 3 | Crystal Plane, Index and Orientation for Direct Lattice | Explanation of rules for representation of crystals |
Class 4 | Relationship of Reciprocal Lattice and Direct Lattice | To understand the concept of reciprocal lattice |
Class 5 | Symmetry Operation and Symmetry Elements | Types of symmetry operation |
Class 6 | Stereographic Projection and Point Group | Notation of 32 point groups |
Class 7 | Space Group and the Extinction Rule | Relationship of Space group and diffraction condition |
Class 8 | Space Group, Point Group, and Material Property | Relationship of crystal structure and material property |
Class 9 | Vibration of Monoatomic Lattice | Lattice vibration from thermal motion of monoatom and its quantization |
Class 10 | Vibration of Diatomic Lattice | Lattice vibration from thermal motion of diatom and its quantization |
Class 11 | Quantization of Lattice vibration and Momentum of Phonon | Lattice vibration and momentum of phonon for real crystals |
Class 12 | Lattice Specific Heat: Einstein Model | Introduction of lattice specific heat from classical model and Einstein model |
Class 13 | Lattice Specific Heat: Debye Model | Introduction of lattice specific heat from Debye Model |
Class 14 | Anhamonic Interaction in Crystals (Thermal Expansion) | Anhamonic oscillator and diffusion of phonon |
Class 15 | Heat Conductivity | Heat conductivity and heat resistance |
None required.
Toyohiko Konno, Materials Symmetry and Group theory, Kyoritsu Publisher, Hikaru Terauchi and Terutaro Nakamura, Solid State Physics, Tokaidaigaku Publisher
Students will be assessed on their understanding of crystal symmetry, point group, space group, lattice vibration, phonon, specific heat, and heat conduction, and their ability to apply them to solve problems. The student's course scores are based on final exams (80%) and exercises (20%).
No prerequisites
Takaaki Tsurumi: ttsurumi[at]ceram.titech.ac.jp
Takuya Hoshina: thoshina[at]ceram.titech.ac.jp
No office hours are necessary, but students with questions can be accepted at any time at professor's offices (S7-509 or S7-508).