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.
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
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
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 | |
---|---|---|
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 |
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)
We use lecture materials as needed.
Evaluation will be based on report submission.
Students must have basic knowledge of electromagnetism and solid state physics.