The purpose of the lecture is to provide a basic knowledge on Brillouin zone-centre phonon spectroscopy and its application in structural analysis of solids. The emphasis will be put on the relation between crystal symmetry and spectral features. Theoretical explanations will be combined with practical exercises of normal crystal mode determination, using the Bilbao Crystallographic Server.

Outlines:

• Atomic vibrations in crystals: phonons, optical and acoustic modes, longitudinal and transverse modes
• Interaction processes between light and solids: IR absorption and Raman scattering
• Character tables and correlation between molecular symmetry, site symmetry and crystal symmetry.
• Group-theory analysis of normal phonon modes. Bilbao Crystallographic Server: Solid State Theory Applications - SAM (Spectral Active Modes).
• Beyond the "standard" symmetry analysis. Complex materials: one-mode and two-mode behaviour, LO-TO splitting. How the Bilbao Crystallographic Server can help us.
• How to conduct an experiment to gain the desired structural information information. The use of SAM to plan the experiment.

The exercises will include:

• Explanation of the normal mode nomenclature.
• Determinations of the Raman and IR modes of two minerals with the same chemistry and different structure: calcite and aragonite
• Complex perovskite-type materials: determination of the Raman and IR active modes of the paraelectric and possible ferroelectric phases. Determination of atomic vector displacements for a given phonon mode.
• LO-TO splitting in Bi₄Ge₃O₁₂

Supplementary Material