Study program:
Minerology and Crystallography (VII semester -MsC) |
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Name of subject: Geometrical Crystallography |
Instructors:
Prof. Sabina Kovač |
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Status: Compulsory |
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ECTS: 5 |
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Prerequisites: - |
Course Objectives:
During the course, students will learn the laws of symmetry. They will introduce simple and complex symmetric operations and all elements of symmetry, the morphological characteristics of crystals as a result of the three-dimensional periodicity of the crystal structure. By applied knowledge, they will be able to determine the symmetry of the crystals measured on the optical goniometer and to determine the appropriate crystal system and one of the 32 crystalline classes. They will learn to distinguish single crystals, twins, and types of twinning. Students will learn 17 two-dimensional and 230 space groups, which is a fundamental for understanding crystal structures. |
Learning Outcomes:
During this course students will learn: the laws of symmetry, macro-symmetry operations and elements of symmetry. They will know to determine the symmetry of crystal models or crystals measured on the optical goniometer, and will know to determine which crystal systems and class of the crystal. Students will teach basic 2D and 3D space groups, which are fundamental for understanding the arrangement of atoms and ions within crystalline structures. |
Content:
Theory teaching
Symmetry of crystals. Boundary elements of the crystal. Crystallographic laws of symmetry. Goniometry. Stereographic and gnomonic projection of crystals. Nomenclature and systematization of 7 crystal systems within the 32 crystal classes. The crystal twinning. Free symmetry operations. Complex symmetry operations. Space lattice. Haji-Brave (Hauy-Bravais) theory. The concept of nodes and unit cell in simple and complex Brave lattices. Complex symmetrical operations at the crystal lattice. Screw axis of symmetry. Glide planes. Unit cell parameters. Number of formula units in a unit cell. Principle of performing 230 space groups of symmetry and their connection with 17 two-dimensional space groups. Practical teaching
Exercises are followed by lectures according to the method units. |
Suggested Reading List:
- Karanović, Lj., Poleti, D., (2003) Rendgenska strukturna analiza, Zavod za udžbenike i nastavna sredstva, Beograd.
- International Tables for Crystallography, (1983) Vol. A, Space-Group Symmetry, IUCr, U.K.
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Conduct of the Course:
Students will learn from lectures, exercises, assignments and seminars. |
Fund hours:
| Lectures |
Exercises |
Other forms of teaching |
Study research |
| 2 |
2 |
0 |
0 |
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Assessment:
| Final Exam |
ECTS |
| Oral Exam | 50 |
| Classwork Assessment |
ECTS |
| Class Participationа | 5 | | Practical Classes | 5 | | Written tests | 30 | | Seminars | 10 |
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Additional Assessment Criteria: - |
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