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Course, academic year 2019/2020
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Structure of Solids and Diffraction - NFPL012
Title in English: Struktura látek a difrakce záření
Guaranteed by: Department of Condensed Matter Physics (32-KFKL)
Faculty: Faculty of Mathematics and Physics
Actual: from 2006
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information: http://krystal.karlov.mff.cuni.cz/FPL012
Guarantor: prof. RNDr. Radomír Kužel, CSc.
doc. RNDr. Miroslav Cieslar, CSc.
Classification: Physics > Solid State Physics
Is incompatible with: NFPL025
Annotation -
Last update: T_KFES (23.05.2001)
Basic course for pre-graduated students, mainly for the students of the solid state physics. The lectures cover the fundamentals of kinematic and dynamic diffraction theory, fundamentals of crystallography and basic principles of the X-ray structure analysis and its most frequent applications. A special attention is paid to the physical principles of interaction of radiation with matter and to the relationship between the structure of matter and its physical properties. The second part of the course is devoted to the transmission electron microscopy and electron diffraction. The following topics are discussed: Thomson and Compton scattering, atomic scattering factor, structure factor, Bragg equation, atomic displacement and vibrations, crystal lattices, reciprocal space and reciprocal lattices, Friedel's law, Laue classes, space groups, symmetry operations and Laue conditions for diffraction. The applications illustrate the orientation of crystals, qualitative and quantitative phase analysis, measurement of lattice parameters and the basic methods of structure solution (Patterson function, heavy atom method and isomorphic substitution). It is recommended to combine this lecture with the exercises FPL035.
Course completion requirements - Czech
Last update: prof. RNDr. Václav Holý, CSc. (07.06.2019)

Nutnou podmínkou připuštění ke zkoušce je získání zápočtu. Zkouška se sestává z písemné a ústní části. Písemná část spočívá ve vyřešení velmi snadného problému, který nevyžaduje dlouhé počítání (max. 30 min). Ústní část navazuje na řešení zmíněného problému a trvá max. 45 min. Známka zkoušky se stanoví ze souhrnného hodnocení písemné a ústní části. Požadavky zkoušky odpovídají sylabu předmětu v rozsahu, který byl odpřednášen.

Literature - Czech
Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)
  • V. Valvoda, M. Polcarová, P. Lukáč: Základy strukturní analýzy, Karolinum, Praha, 1992
  • V. Valvoda: Rentgenografické difrakční metody (skriptum), SPN, Praha, 1979
  • V. Valvoda: Rentgenová strukturní analýza (skriptum), SPN, Praha, 1982
  • V. Valvoda: Základy krystalografie (skriptum), SPN, Praha, 1982
  • P. Lukáč a kol.: Praktikum fyziky kovů (skriptum), kapitola: Elektronová mikroskopie, SPN, Praha, 1982. B. Smola: Transmisní elektronová mikroskopie ve fyzice pevnych látek (skriptum), SPN, Praha, 1983

V. Valvoda, M. Polcarová, P. Lukáč: Základy strukturní analýzy, Karolinum, Praha 1992

V. Valvoda: Rentgenografické difrakční metody (skripta), SPN, Praha 1979

V. Valvoda: Rentgenová strukturní analýza (skripta), SPN, Praha 1982

R.B. Heslop, K. Jones: Anorganická chemie, SNTL, Praha 1982

B.K. Vajnštejn: Sovremennaja krystallografija, Nauka, Moskva 1979 (Tom 1-3)

P. Lukáč a kol.: Praktikum fyziky kovů (skripta), kap.: Elektronová mikroskopie, SPN, Praha, 1982

B. Smola: Transmisní elektronová mikroskopie ve fyzice pevných látek (skripta), SPN, Praha, 1983oubka. Meze platnosti kinematické aproximace. Kikuchiho linie.

V. Analýza poruch krystalové mříže v elektronové mikroskopii.

13. Vznik kontrastu na ideálním krystalu. Sloupcová aproximace. Intenzita přímého a difraktovaného svazku. Efektivní odchylka od Braggovy polohy. Intenzita difraktovaného svazku v porušeném krystalu. Kontrast na úplných dislokacích, vrstevných chybách, plošných poruchách a precipitátech. Viditelnost a neviditelnost poruch v elektronovém mikroskopu. Reflexní (dvousvazková) poloha.

14. Konstrukce a vlastnosti elektronového mikroskopu. Vady a vlastnosti magnetických čoček. Korekce vad. Rozlišovací schopnost, hloubka ostrosti. Zobrazení a difrakce v transmisním elektronovém mikroskopu. Světlé a tmavé pole. Difrakce z vybrané plochy.

  • V. Valvoda, M. Polcarová, P. Lukáč: Základy strukturní analýzy, Karolinum, Praha, 1992
  • V. Valvoda: Rentgenografické difrakční metody (skriptum), SPN, Praha, 1979
  • V. Valvoda: Rentgenová strukturní analýza (skriptum), SPN, Praha, 1982
  • V. Valvoda: Základy krystalografie (skriptum), SPN, Praha, 1982
  • P. Lukáč a kol.: Praktikum fyziky kovů (skriptum), kapitola: Elektronová mikroskopie, SPN, Praha, 1982. B. Smola: Transmisní elektronová mikroskopie ve fyzice pevnych látek (skriptum), SPN, Praha, 1983

V. Valvoda, M. Polcarová, P. Lukáč: Základy strukturní analýzy, Karolinum, Praha 1992

V. Valvoda: Rentgenografické difrakční metody (skripta), SPN, Praha 1979

V. Valvoda: Rentgenová strukturní analýza (skripta), SPN, Praha 1982

R.B. Heslop, K. Jones: Anorganická chemie, SNTL, Praha 1982

B.K. Vajnštejn: Sovremennaja krystallografija, Nauka, Moskva 1979 (Tom 1-3)

P. Lukáč a kol.: Praktikum fyziky kovů (skripta), kap.: Elektronová mikroskopie, SPN, Praha, 1982

B. Smola: Transmisní elektronová mikroskopie ve fyzice pevných látek (skripta), SPN, Praha, 1983

Requirements to the exam - Czech
Last update: prof. RNDr. Václav Holý, CSc. (07.06.2019)

Požadavky zkoušky odpovídají sylabu předmětu v rozsahu, který byl odpřednášen.

Syllabus -
Last update: T_KFES (26.05.2003)

I. Crystal structure and symmetry.

1. History of crystallography and structure analysis. Translation periodicity of crystals. Plane and space lattices. Symmetry operations. Hermann-Mauguin symbols. Elementary cells. Notation of directions and planes. Transformation of axes and plane indices. Stereographic projection. Groups.

2. Point groups. Crystallographic systems. Laue classes. Bravais lattices. Reciprocal lattice. Brillouin zones.

3. Space groups. Equivalent positions. Matrix description of symmetry operations. Wyckoff notation. International tables of crystallography. Examples of simple structures.

4. Influence of crystal symmetry on properties of compounds. Tensors and anisotropy of macroscopic properties. Neumann principle. Voigt principle. Curie principle.

II. Diffraction theory.

1. Geometric principles of diffraction. Reciprocal lattice. Laue conditions. Ewald construction.

2. Interaction of X-rays with matter. Absorption of radiation in material. Plane and spherical wave. Thomson and Compton scattering. Scattering on atom and ensamble of atoms. Atomic scattering factor, anomalous dispersion and absorption. Introduction of structure factor. Electron density and Fourier transformation. Basic atributes of diffraction peaks (position, intensity, width, shape) in kinematic theory of diffraction.

3. Static and dynamic displacements, temperature factor. Coherence length of photon. Crystals of finite dimensions.

4. Dynamic theory of diffraction. Wave equation for periodic medium. Single wave and two wave approximation. Some experimental effects - Pendellösung, Borrmann effect. Wave field in the diffracting crystal.

5. Comparison of scattering by X-rays, neutrons and electrons.

III. Structure analysis by diffraction

1. X-ray sources, detectors and monochromators.

2. Single crystal methods. Film methods. Orientation of crystal by Laue method. Space group determination - diffraction symbol. Single crystal diffractometers.

3. Phase problem. Structure determination (Patterson function, heavy-atom method, isomorphous replacement, direct methods). Study of deformation electron density due to bonding.

4. Powder diffraction. Information in powder diffraction pattern and its evaluation. Different diffraction geometries.

5. Application of structure analysis in materials research: phase identification, phase analysis, texture, stress, strain, crystallite size.

IV. Kinematic theory of high-energy electrons.

1. Kinematic approximation. Elastic and inelastic scattering. Wavelength of electrons. Electron scattering in potential field. Fresnel zones method. Amplitude-phase diagram. Phase shift of scattered wave. Elastic scattering on atom, elementary cell, distorted and undistorted crystal. Deviation from the Bragg position.

2. Interpretation of high-energy electron diffraction. Diffraction pattern from a single crystal and polycrystal. Intensity distribution in reciprocal lattice. Dimensional and shape effect. Extinction length. Limitations of kinematic theory. Kikuchi lines.

V. Lattice defects analysis in electron microscopy.

1. Phase contrast in ideal crystal. Column approximation. Intensity of the direct and diffracted beam. Effective deviation from the Bragg position. Intensity of diffracted beam in distorted crystal. Contrast on dislocations, stacking faults and precipitates. Visibility and invisibility of lattice defects in electron microscope. Reflection (two-beam) position.

2. Construction and properties of electron microscope. Faults and properties of magnetic lens. Correction of faults. Resolution, depth of sharpness. Imaging and diffraction in transmission electron microscope. Bright and dark field. Diffraction from selected area.

 
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