Crystallography A

obligatory courses

Presenting the basic information about symmetry, necessary to describe chemical objects and/or crystals. The basic information concerning X-ray structural analysis that will allow students to use and understand scientific literature will also be presented.

The course covers the definition of the crystal and the most important properties of the crystalline state, the definition of the unit cell, crystal lattices, lattice directions and planes, crystal systems, Bravais lattice, Miller indices. The other important issues relevant to the study of crystallography are also included. These are: properties of symmetry of solids, unit cells, and lattices; spherical and stereographic projection, symmetry operations, point symmetry, translational symmetry, complex symmetry elements, coexistence of symmetry elements; point groups and space groups (Hermann-Mauguin and Schönflies classification; close and the closest packing of spheres, reciprocal space – definition and properties, Ewald sphere construction. Properties of X-rays. Laue and Bragg’s diffraction theories. Symmetry of diffraction pattern, Intensity of reflections as a source of information about arrangement of atoms and/or ions in the crystal unit cell. Phase problem. Experimental methods of X-ray crystallography: Laue method, oscillation method, goniometric methods; determination of unit cell parameters; Powder diffraction. Crystallization techniques, crystal growth theories, imperfect crystals, energetic aspects of the crystals structures, classification of solids (ionic, covalent, metallic, molecular) their characteristics. Elements of crystallophysics. Interpretation of the crystal and molecular structure based on crystallographic databases.

1. Z. Trzaska Durski, H. Trzaska Durska, Podstawy krystalografii strukturalnej i rentgenowskiej, Wydawnictwo Naukowe PWN, Warszawa, 1994 (in Polish).

2. Z. Bojarski, M. Gigla, K. Stróż, M. Surowiec, Krystalografia. Podręcznik wspomagany komputerowo, Wydawnictwo Naukowe PWN, Warszawa, 1996, 2001, 2007 (in Polish).

3. Z. Trzaska Durski, H. Trzaska Durska, Podstawy krystalografii, Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa 2003 (in Polish).

4. P. Luger, Rentgenografia strukturalna monokryształów, PWN, Warszawa 1989 (in Polish).

5. M. van Meerssche i J. Feneau-Dupont, Krystalografia i chemia strukturalna, PWN, Warszawa 1984 (in Polish).

6. P. Luger, Modern X-ray Analysis on Single Crystals, Walter de Gruyter and Co., Berlin 1980 (in English).

7. C. Giacovazzo, H. Z. Monaco, D. Biterbo, F. Scordari, G. Gilli, G. Zanotti, M. Catti, Fundamentals of Crystallography, IUCR, Oxford University Press, 2000 (in English).

The aim of the course is to present the basic information about symmetry analyses of the crystal models, analyses of point groups and selected space groups. The problems concern also spherical and stereographic projection, point symmetry, the rules of coexistence of symmetry elements, complex symmetry elements, crystal systems and Bravais lattices. Students get also practical skills how to interpret of the information taken from International Tables for Crystallography.

Exam requirements:

- The definition of the unit cell, crystal lattices, lattice directions and planes, crystal systems, Bravais lattice, Miller indices.

-Geometric crystallography: spherical and stereographic projection, symmetry operations, point symmetry, translational symmetry, complex symmetry elements, coexistence of symmetry elements; point groups and space groups (Hermann-Maugin and Schönflies classification

- Properties of X-rays. Laue and Bragg’s diffraction theories. Reciprocal space. Basic experimental methods of X-ray crystallography.

- Symmetry of diffraction pattern, Intensity of reflections as a source of information about arrangement of atoms and/or ions in the crystal unit cell.

- phase problem and ways to solve it.

- experimental methods of X-ray crystallography: Laue method, oscillation method, goniometric methods; determination of unit cell parameters;

- powder diffraction.

- Elements of crystallophysics.

- energetic aspects of the crystals structures, classification of solids (ionic, covalent, metallic, molecular)

- crystallization techniques, crystal growth theories,

- Interpretation of the crystal and molecular structure based on crystallographic databases

Not applicable