Materials Science and Engineering

**Syllabus Not Found**

## Short Course Description

Tentative topics of the lectures

Lecture 1: Generation, properties and scattering of X-rays. History and physical principles of generation of X-rays. Typical wavelengths, characteristic and continuous parts of the X-ray spectrum.

Lecture 2. Mathematical description of electromagnetic waves and their interference. Scattering of X-rays by electrons. Polarization factor. Scattering of X-rays by atoms. Atomic scattering factors. Scattering of X-rays by molecules. Investigation of structures of diatomic molecules by X-ray scattering.

Lecture 3. Kinematical theory of X-ray diffraction: DIffraction of X-rays by crystals. Laue interference function. Structure factor. Reciprocal space. Ewald sphere.

Lecture 4. Experimental methods of X-ray diffraction by crystals. Rocking curve. Rotation photographs. Laue diffraction. Powder diffraction. Electron diffraction and neutron scattering.

Lecture 5. Instruments and detectors: single crystal and powder diffractometers, Bragg-Brentano geometry, monochromator, detection of X-rays. Structural, microstructural and instrumental contributions to the X-ray diffraction.

Lecture 6. Geometrical methods of structure analysis: reconstruction of reciprocal space, determination of crystal orientation, indexing of reflections, identifying Bravais types of lattices and determination of lattice parameters.

Lecture 7. Space group determination: 230 space groups, the relationship between space groups and structure factors. Systematic extinctions. International Tables for X-ray crystallography, Volume A. Friedel?s law.

Lecture 8. Structure analysis of centrosymmetric and non-centrosymmetric crystals: Intensity statistics. Application of resonant scattering.

Lecture 9. Solutions of the phase problem of X-ray crystallography: trial structures, Fourier synthesis. Patterson function. History and development of the direct methods for the solution of the phase problem.

Lecture 10. Thermal motion and structural disorder: Thermal displacement of atoms in crystals. Debye-Waller factors. Static disorder. Average and local structures of crystals.

Lecture 11. Structure refinement and least-square minimization algorithms: Single crystal and powder structure refinement. Introduction to Rietveld refinement.

Leture 12. Materials analytics using synchrotron radiation: generation and properties of synchrotron radiation. The advantage of synchrotron radiation over the laboratory X-ray sources. Typical research at synchrotrons.

Recommended literature:

[1]. Marc De Graef and Michael E. McHenry. Structure of Materials. An Introduction to Crystallography, Diffraction and Symmetry. Cambridge University Press. 2012

[2]. Christopher Hammond. The basics of crystallography and diffraction. Cambridge University Press. 2012.

[3]. Carnelio Giacovazzo. Fundamentals of Crystallography. Oxford University Press, 1992

[4]. International Tables for Crystallography, Volume B. International Union of Crystallography, 2016.

Full syllabus is to be published

**Final Exam**

Students may be required to submit additional assignments

Full requirements as stated in full syllabus

**Introduction to Crystallo**(05814132)