1. Periodic crystal structure, primitive cell, symmetry operations, types of 2D and 3D lattices. 2. Consequences of crystal periodicity - reciprocal space, Brillouin zone and periodic boundary conditions. X-Ray difraction in periodic structures, experimental methods of difraction. 3. Crystal bond - nature of interatomic interactions, potential energy, pair potentials, bonding in rare gas crystals, ionic bond, covalent and metal crystals, hydrogen bond. 4. Defects in crystal lattice, dislocations and polycrystalline materials. Vibrational, thermal and mechanical properties of crystals from classical point of view. 5. Quantum description of crystal - wave function, Schrödinger equation, elementary quantum systems (free particle, particle in a box, harmonic oscillator, hydrogen atom), Schrödinger equation for solid state and usual approximations for its solution. 6. Sommerfeld model of free electrons, conductivity of metals. 7. Quantum theory in solid state, band structure, semiconductors and isulating materials. 8. Properties of surfaces, absorption on a surface. 9. Harmonic vibrations of crystal lattice, phonons, electrical and heat conductivity, thermal expansion. 10. Optical properties of solids, spectroscopic methods, x-ray spectrography. 11. Response to external forces and fields, dielectric tensor, stress and strain tensors, elastic constants. 12. Nanocrystals, two-dimensional materials (graphene), quantum dots.
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