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Course, academic year 2018/2019
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Methods of Solving and Refining Monocrystal Structures - NFPL039
Title in English: Metody řešení a upřesňování krystalových struktur monokrystalů
Guaranteed by: Department of Condensed Matter Physics (32-KFKL)
Faculty: Faculty of Mathematics and Physics
Actual: from 2015
Semester: summer
E-Credits: 3
Hours per week, examination: summer 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
Guarantor: RNDr. Václav Petříček, CSc.
prof. RNDr. Miloslav Dušek, Dr.
Classification: Physics > Solid State Physics
Annotation -
Last update: T_KFES (23.05.2003)

Elementary crystallographic concepts. Review of basic experimental methods. Heavy-atom method (Patterson function, Fourier synthesis). Statistics of reflections. Direct methods of phase problem solutions. Structure refinement. Modulated and composite structures.
Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

V. Valvoda, M. Polcarová, P. Lukáč : Základy strukturní analýzy. Karolinum. Praha 1992 J.Loub : Krystalová symetrie a rentgenová difrakce, Skripta

odborné články

Syllabus -
Last update: T_KFES (26.05.2003)

1. Fundamentals of crystallography.

Translation symmety, lattice, lattice parameters, reduced lattice. Symmetry, restrictions of rotational and translational operators, point group, space group, symbols of space groups. Structure factor, influence of symmetry on structure factors, extinction.

2. Basic experimental methods.

Photographic and diffractometric methods of structure analysis of single crystals. Modern sources of X-rays. Determination of Laue group and space group. Systematic measurement of integrated intensities integrálních. Automatization of experiment. Determination of structure factor from integrated intensities of reflections, Lorentz correction, polarization correction and absorption corection. Phase problem of structure analysis.

3. Heavy-atom method.

Patterson function, its properties and symmetry, Harker cross-sections, lokalization of heavy atom. Lokalization of light atoms, Fourier synthesis.

4. Statistics of reflections.

Normalization of structure factors, Wilson plot, estimation of scale and temperature factor. Distribution of structure factors in dependence on symmetry, centrosymmetric and non-centrosymetric distribution. Structure invariants and semi-invariants.

5. Direct methods of solution of phase problem.

Choice of origin in dependence on symmetry of crystal, fixation of enantiomorphy. Symbolic addition, Sayre equation, tangent formula. Strategy of application of direct methods.

6. Crystal structure refinement.

Basic parameters of description of crystal structure, least-squares method, quality of refinement.

7. Modulated and composite structures.

Satelite reflections, position and occupational modulation, composite crystals, deWolffova construction, superspace, generalized electron density. Methods of solution and refinement of modulated and composite structures.

8. Twinning in crystals.

Merohedry a pseudomerohedry, general twinning, partial and total overlapping, inclusion of twinning into structure determination and refinement.


Examples of procedures of crystal structure determination and practical applications on selected examples.

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