Hard Matter: Fundamentals and Applications

Electrons in solids

Simple models of metals and basic transport properties (DC and AC conductivity, magneto-transport and Hall effect, thermal conductivity, thermopower). Fermi-Dirac distribution, Fermi sphere, density of states. Crystal structure, lattices, basis vectors, and unit cells. Direct and reciprocal lattices. Electrons in periodic potentials, Bloch's theorem, Bloch functions, and band structure. Examples: Graphene, Dirac cones, chiral fermions.
Inertia of filled bands, electrons and holes, effective mass tensor, DC and AC transport in the diffusive regime. Semiconductors. n-type and p-type doping in semiconductors and heterostructures. Applications of semiconductors to materials science. Density Functional Theory: Hohenberg-Kohn theorem and Kohn-Sham approach. Exchange and correlation functionals.

Computational Laboratory

Pseudopotentials, Brillouin zone sampling. Plane waves and atomic orbitals. DFT in action: key parameters of a periodic DFT calculation. Density of states, local density of states, simulation of STM tomography. 1D Systems: Peierls distortion in cumulenes, carbon nanotubes. 2D Systems: Graphene. 3D Systems: Metals, graphite. Magnetic ordering: Fe(bcc), Fe(fcc). Magnetic anisotropy.

Thermodynamics of Transformations

Phase Diagrams: Single- and two-component systems with the formation of intermediate compounds and partial or complete solid solutions. Phase transitions from both thermodynamic and structural perspectives. Kinetics of phase transitions.
Defects and Reactivity: Point defects in metals, semiconductors, stoichiometric and non-stoichiometric compounds. Diffusion of matter and charge. Measurement techniques for DC and AC conductivity. Impedance spectroscopy.
Investigation Techniques

Thermodynamic, structural, microstructural, and spectroscopic characterization techniques for solids, including XRPD, SEM/EMPA, TEM/EELS, AFM, XPS, IS, UV, and DSC, will be introduced with particular focus on their applications in materials science.

Experimental Laboratory

Two systems will be studied: (i) silver iodide (AgI) undergoes a polymorphic phase transition that transforms it into a "fast ionic conductor." This phase transition will be examined from thermodynamic, structural, and transport property perspectives, highlighting the deep interconnection between these properties; (ii) mixed oxide nanoparticles of interest for energy and catalysis will be synthesized and thoroughly characterized using diffraction, electron microscopy, and spectroscopic techniques.