2017 Crystal and Phonon

Font size  SML

Register update notification mail Add to favorite lecture list
Academic unit or major
Undergraduate major in Materials Science and Engineering
Tsurumi Takaaki  Ikoma Toshiyuki 
Course component(s)
Day/Period(Room No.)
Tue5-6(S7-201)  Fri5-6(S7-201)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

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.

Student learning outcomes

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

Competencies that will be developed

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

Class flow

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

  Course schedule Required learning
Class 1 Crystals: Relationship of Crystal Lattice, Primitive Lattice, and Atomic Coordination Introduction of atomic coordination from crystals learned in high school
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.

Reference books, course materials, etc.

Toyohiko Konno, Materials Symmetry and Group theory, Kyoritsu Publisher, Hikaru Terauchi and Terutaro Nakamura, Solid State Physics, Tokaidaigaku Publisher

Assessment criteria and methods

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%).

Related courses

  • MAT.C301 : Crystal Chemistry (Ceramics course)
  • MAT.C302 : Spectroscopy
  • MAT.C306 : Dielectric Materials Science
  • MAT.C305 : Semiconductor Materials and Device
  • MAT.C307 : Magnetic Materials Science

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

No prerequisites

Page Top