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Phonon properties of materials with a different structural complexity

complexity Lecture will start with a brief introduction into a harmonic oscillator, its quantization, its application to a general system of coupled atoms/ions by harmonic forces and to the notion of phonons. The structural complexity of materials can be result of a long range aperiodicity, a non-commensurate lattice distortion, the defect presence (local and extended ones), etc. Usually, realistic studies of phonon properties in structurally complex systems involve numerically intense calculations and/or heavy mathematical formalism. In this lecture we shall cover only very simple cases which can be done analytically. These simple cases can be generalized in order to get an insight into more complex situations. Particular attention will be paid to long wave limit where generally complex equation of motion can be simplified. Some of these results will be applied to calculation of few thermodynamic and transport properties. Tutorial will consist of numerical calculations and simulations with already prepared python scripts. Participants would be able to investigate how calculation/simulation results depends on the parameters in the problem under consideration. Knowledge of python programming language is recommended but it is not required.

Phonon properties, disordered medium, quasi-crystals

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