This course pursues to lay down firm foundation on the basic concept of crystal structure, crystallographic computation, and symmetry (point groups and space groups). The concept of reciprocal space is also introduced for its application to coordinate transformation and diffraction phenomenon. The concept of materials’ tensor properties is finally introduced to represent the anisotropic physical properties of solids and to explain lattice dynamics.

응용선형대수

1) Attendance: 3%
2) Homework: 10%
3) Q&A: 2%
4) Presentation: 10%
5) Mid-term Exam: 35%
6) Final Exam: 40%

Structure and Dynamics, M. T. Dove, Oxford, 2003

강의:
I. Atomic arrangements (crystal structure): Chapters 1 to 6 and Chapter 8
II. Measurement of crystal structure: Chapter 7
III. Crystal structure and physical properties: Chapters 9 and 10

1. Crystal lattices (2 Weeks)
1.1 Space lattice
1.2 Crystal systems
1.3 Bravais lattices
1.4 Crystal structure: convolution
1.5 Direction: metric tensor
1.6 Lattice planes
1.7 Rhombohedral (R) - centered hexagonal

2. Reciprocal space (1.5 Weeks)
2.1 Reciprocal basis vectors
2.2 Reciprocal space and lattice planes
2.3 Reciprocal metric tensor
2.4 Non-primitive lattices
2.5 Reciprocal lattice: Fourier transform of a crystal lattice
2.6 Brillouin zone

3. Coordinate transformation (2 Weeks)
3.1 Vector cross product
3.2 Relations between direct and reciprocal spaces
3.3 Coordinate transformations
3.4 Stereographic projection

4. Crystal symmetry (1.75 Weeks)
4.1 Symmetry of a hexagon
4.2 Symmetry operations
4.3 Combinations of symmetry operations
4.4 Point symmetry

5. Point groups (1.75 Weeks)
5.1 What is a group?
5.2 3-D crystallographic point symmetries
5.3 General remarks
5.4 2-D point groups

6. Space groups (1 Week)
6.1 Combining translations with point group symmetry
6.2 Plane groups in 2-D
6.3 Space groups
6.4 The International Tables for Crystallography

7. Diffraction (1 Week)
7.1 Diffraction
7.2 Diffraction and Fourier analysis
7.3 Symmetry and diffraction

8. Crystal structures (1 W)
8.1 Classification of structures
8.2 Parent structures
8.3 Derivative structures
8.4 Other crystal structures

9. Tensors in physical properties (1 Week)
9.1 Tensors
9.2 First-rank tensors
9.3 Second-rank tensors
9.4 3rd-rank tensors
9.5 4th-rank tensors

10. Lattice dynamics (1 Week)
10.1 The harmonic approximation
10.2 Lattice vibrations of 1-D monatomic crystals
10.3 Lattice vibrations of crystals with several atoms in a unit cell

1. Lecture (55 min)
2. Group discussion (10 min)
3. Presentation (10 min)

75분 수업은 강의(55분), 조별토의(10분), 토의내용발표(10분)로 운영됨.

"조별토의":
- 그날 강의에서 배운 내용에 대해, 교수 강의 후에 조별로 토의함.(한 조는 5~6명 정도)
- 조별로 조장이 토의를 주관. (조장은 매번 돌아가며 맡음)
- 각 조의 조장은 토의 요약(PPT)을 제출 (마감: 다음 수업일 전날 자정까지) (*** 모든 조의 조장이 제출해야 함)

"토의내용발표": 다음 수업시간에 발표
- 매 수업 별로 한 조가 (조별토의에서 논의된 내용을 정리하여) 돌아가며 발표함. (예: 첫 발표는 A조 발표, 다음 번에는 B조 -> C조 -> D조 -> A조.......순서로 발표해 감)
- 발표시간: 5분 (+ 5분 질의)