Topics of this course include (1) basics of crystal structures, (2) classification of the Bravais lattice, (3) reciprocal lattice, (4) classification of crystals in terms of the formation mechanisms, (5) lattice vibrations (phonons), (6) electronic states in crystals and their band structure, (7) fundamental properties of metals and semiconductors.
Through this course, students will understand basic properties of crystals based on quantum mechanics, and how they correspond to experiments.
Through this course, students will be able to (1) calculate various properties (including translation vectors and reciprocal vectors) for a given crystal structure, (2) explain various crystals in terms of the formation mechanisms (such as ionic and covalent crystals), (3) explain basic properties of electronic band structures in crystals, (4) explain basic properties of semiconductors, and (5) explain basics of superconductivity and various magnetisms.
translation vector, unit cell, Bravais lattice, reciprocal vector, Brillouin zone, phonon, metal, insulator, band structure, semiconductor
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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At the end of some classes, small tests will be given to test comprehension. Preparation and review for each class are recommended.
Course schedule | Required learning | |
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Class 1 | Crystal structure and translation vectors | Explanation on crystal sturcture and translation vectors |
Class 2 | Reciprocal vectors and Brillouin zone | Explanation on reciprocal vectors and Brillouin zone |
Class 3 | Reciprocal vectors and X-ray diffractions | Explanations on reciprocal vectors and X-ray diffractions |
Class 4 | Examples of Bravais lattices and reciprocal bectors | Explanations on examples of Bravais lattices and reciprocal bectors |
Class 5 | Various formation mechanisms of crystals | Explanations on metals, covalent crystals, ionic crystals, van der Waals interaction and hydrogen bond |
Class 6 | Phonon I: classical description of lattice vibration, quantization | Explanations on classical description of lattice vibration and quantization of phonons. |
Class 7 | Phonon II: thermodynamic and transport properties of phonons | Explanations on thermodynamic and transport properties of phonons |
Class 8 | Free-electron model of metals | Explanations on free-electron model of metals |
Class 9 | Electrons in periodic potentials and Bloch theorem | Explanations on electrons in periodic potentials and Bloch theorem |
Class 10 | Band structure of electrons in crystals | Explanations on band structure of electrons in crystals |
Class 11 | Fermi surfaces in metals | Explanations on Fermi surfaces in metals |
Class 12 | Energy gaps and semiconductors | Explanations on energy gaps and semiconductors |
Class 13 | impurities and pn junctions in semiconductors | Explanations on impurities and pn junctions in semiconductors |
Class 14 | optical properties of solids | Explanations on optical properties of solids |
Class 15 | superconductivity, magnetism | Explanations on superconductivity and magnetism |
Textbooks, if any, will be given in the class.
References and course materials, if any, will be given in the class.
examinations and small tests
Basic knowledge on electromagnetism, statistical physics and quantum mechanics