2023 Crystal Physics

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Academic unit or major
Graduate major in Physics
Uchida Masaki 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Tue1-2(S2-201(S224))  Fri1-2(S2-201(S224))  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

In crystal physics, crystals are considered as an anisotropic medium from a macroscopic point of view. The concept of tensors is important for discussing physical properties of crystals. After giving an overview of crystal physics, we discuss transformations and second-order tensors. We next discuss characteristics of magnetic susceptibility, permittivity, stress, and strain tensors as equilibrium properties of crystals. We further discuss characteristics of thermal and electrical conductivity tensors as transport properties of crystals. Symmetry elements and point groups of crystals are also explained.

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) Understand that symmetry and macroscopic properties of materials are strongly interconnected.


Crystals, lattice, point groups, symmetry, tensors

Competencies that will be developed

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

Class flow

Lectures will be given in board format. Questions and comments are submitted as a questionnaire at the end of each lecture.

Course schedule/Required learning

  Course schedule Required learning
Class 1 The groundwork of crystal physics (scalars, vectors, tensors, transformations) Understand the groundwork of crystal physics
Class 2 The groundwork of crystal physics (definition of a tensor, the representation quadric) Understand the groundwork of crystal physics
Class 3 The symmetry of crystals (symmetry elements, point groups, crystal classes, crystal systems) Understand the symmetry of crystals
Class 4 The effect of crystal symmetry on crystal properties Understand the effect of crystal symmetry on crystal properties
Class 5 Transformations and second-rank tensors Understand transformations and second-rank tensors
Class 6 Vector product (polar and axial vectors) Understand vector product
Class 7 The Mohr circle construction Understand the Mohr circle construction
Class 8 Magnetic susceptibility tensor Understand magnetic susceptibility tensor
Class 9 Permittivity tensor Understand permittivity tensor
Class 10 Stress tensor Understand stress tensor
Class 11 Strain tensor Understand strain tensor
Class 12 Thermal conductivity tensor Understand thermal conductivity tensor
Class 13 Electrical conductivity tensor Understand electrical conductivity tensor
Class 14 Summary Understand crystal physics

Out-of-Class Study Time (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.


J. F. Nye “Physical Properties of Crystals: Their Representation by Tensors and Matrices” (Oxford University Press)

Reference books, course materials, etc.

We use lecture materials as needed.

Assessment criteria and methods

Evaluation will be based on report submission.

Related courses

  • PHY.C340 : Basic Solid State Physics
  • PHY.C341 : Condensed Matter Physics I
  • PHY.C342 : Condensed Matter Physics II

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

Students must have basic knowledge of electromagnetism and solid state physics.

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