2022 Crystal Physics

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Academic unit or major
Graduate major in Physics
Satoh Takuya 
Class Format
Lecture    (Livestream)
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Tue1-2()  Fri1-2()  
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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 the physical properties of crystals. After giving an overview of crystal physics, we discuss transformations and second-order tensors. Next, we consider the anisotropy of paramagnetic and diamagnetic susceptibility and electric polarization as the characteristics of the equilibrium state of crystals. The point group of crystals and symmetry operations 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) Explain that the symmetry and macroscopic properties of materials are strongly interconnected.


Crystals, lattice, point group, 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 (Scalar, 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) Understand the symmetry of crystals
Class 4 The symmetry of crystals (Crystal systems) Understand the symmetry of crystals
Class 5 The effect of crystal symmetry on crystal properties Understand the effect of crystal symmetry on crystal properties
Class 6 Transformations and second-rank tensors Understand transformations and second-rank tensors
Class 7 Vector product (Polar and axial vectors) Understand vector product
Class 8 The Mohr circle construction Understand the Mohr circle construction
Class 9 Paramagnetic and diamagnetic susceptibility Understand paramagnetic and diamagnetic susceptibility
Class 10 Electric Polarization Understand electric Polarization
Class 11 Pyroelectricity and ferroelectricity Understand pyroelectricity and ferroelectricity
Class 12 Crystal optics (birefringence) Understand crystal optics
Class 13 Optical activity Understand optical activity
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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