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Course, academic year 2018/2019
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Fundamentals of Crystallography - NFPL107
Title in English: Základy krystalografie
Guaranteed by: Department of Condensed Matter Physics (32-KFKL)
Faculty: Faculty of Mathematics and Physics
Actual: from 2015 to 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:1/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information:
Guarantor: prof. RNDr. Radomír Kužel, CSc.
doc. RNDr. Stanislav Daniš, Ph.D.
Classification: Physics > Solid State Physics
Annotation -
Last update: T_KFES (23.05.2001)
Specialized lecture on crystallography. Symmetry of crystal structures, crystal lattices, point groups, space groups, Miller indices, reciprocal lattice, macroscopic symmetry, stereographic projection, International Tables for Crystallography and their application, symmetry and physical properties. Further applications in X-ray structure analysis can be found in lecture FPL 049.
Course completion requirements - Czech
Last update: prof. RNDr. Radomír Kužel, CSc. (06.10.2017)

Účast na výuce, zpracování zadaných úloh během semestru.

Literature -
Last update: prof. RNDr. Radomír Kužel, CSc. (10.05.2019)

Václav Valvoda, Milena Polcarová, Pavel Lukáč: Základy strukturní analýzy. Univerzita Karlova. Praha 1992.

I. Kraus: Úvod do strukturní rentgenografie. Academia. Praha 1985.


Maureen M. Julian: Foundations of Crystallography with Computer Applications. CRC Press. Taylor and Francis Group. 2015

Boris K. Vainshtein: Modern crystallography. Vol. 1. Fundamentals of crystals. Symmetry, and methods of structural crystallography. (Second enlarged edition.) Berlin: Springer-Verlag, 1994

Robert E. Newnham: Properties of Materials. Anisotropy. Symmetry. Structure. Oxford University Press. 2005

Marc de Graaf and Michael McHenry: Structure of Materials. An Introduction to Crystallograhy, Diffraction and Symmetry. Cambridge University Press. 2007

Requirements to the exam - Czech
Last update: prof. RNDr. Radomír Kužel, CSc. (06.10.2017)

Zkouška je převážně ústní z probírané látky + příklady zaměřené na symetrii krystalů, rovinné a prostorové grupy.

Syllabus -
Last update: T_KFES (21.05.2004)
I. Crystals and their symmetry.
Historic introduction. Local symmetry of atoms in solids, directional and isotropic bonds of atoms. Construction of crystals with the aid of the atomic layers with different symmetry - close packed structures, primitive and centered structures. Interstitial structures. Crystal representation with the aid of projections - crystallographic planes.

II. Representation of symmetry of ordered structures
Translation periodicity of crystals. Plane and space (Bravais) lattices. Crystallogrpahic classes. Notation of planes, directions and points. Reciprocal lattice. Miller indeces. Crystallographic symmetry elements. Matrix representation of symmetry elements. Macroscopic symmetry of crystals and point group. Plane and space groups. Stereographic projection.

III. Representation of crystallographic groups
Introduction to group theory. Basic definitions. Crystallogrpahic groups. Sub-groups and super-groups. Examples of groups. Classification of plane and space groups in International Tables of Crystallography.

International (Hermann-Mauguin) and Schoenflies symbols. Diagrams of space groups. Generators. Wyckoff positions.

IV. Symmetry and physiacl properties of crystals
Anisotropy of physical properties and their tensor description. Anisotropic temperature factor. Electric and elastic properties of crystals - pyroelectricity, dielectric and optical properties, piezoelectricity

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