Crystal state. X-ray diffraction. Metals. Electrons in a weak periodic potential. Band structure of the solids. Semiconductors. Lattice dynamics. Cohesion energy. Specific heat of solids. Nuclear spin interactions. Zeeman Interaction. Radiofrequency pulses. Carbon-detection. Relaxation in the presence of coherent modulations. Paramagnetism. Multidimensional experiments. Pulse sequences. Practicals on sample handling, acquisition and processing of spectra under magic angle spinning.
Title: Solid State Physics. Authors: Neil W. Ashcroft e N. David Mermin
(any edition)
Title: Introduction to solid state physics. Author: Charles kittel
(any edition)
Title: NMR of Paramagnetic Molecules. Authors: Ivano Bertini, Claudio Luchinat, Giacomo Parigi, Enrico Ravera
(2nd edition)
Additional material will be provided through the e-learning platform.
Learning Objectives
To provide basic knowledge of the solid state physics, with particular attention to the crystal state. Study of several experimental techniques for the analysis of the crystal state. Illustration of models for the description of electronic properties in molecular solids with examples of metals and semiconductors. To provide an in-depth knowledge of magnetic resonance spectroscopy and related topics. To provide the tools for understanding simple or complex pulse sequences for solution state and solid state magnetic resonance spectroscopy. To provide state-of-the-art knowledge of experimental methods for the characterization of biomolecules, drugs and materials.
Prerequisites
No
Teaching Methods
Lectures and practicals. The students, depending on their number, will be asked to select and discuss one or more scientific papers pertaining the topics of the course.
Type of Assessment
Oral exam. The student is called to discuss two arguments taken from each series of lessons in which the course is structured.
Course program
States of the matter. Amorphous solids. Crystal solids. Bravais Lattice and primitive vectors. Examples of Bravais lattices. Coordination number and nearest neighbors. Primitive and unit cells. Wigner-Seitz primitive cell. Lattice with a basis. Reciprocal lattice. First Brillouin zone. Lattice planes. Miller indices. Classification of Bravais lattices. Symmetry operations. Space and point groups of a Bravais lattice. Crystal systems. X-ray diffraction. Bragg and von Laue formulations of the X-ray diffraction by a crystal. Intensity of the X-ray radiation. Metals. Free electron model for metals. Fermi energy and Fermi sphere. Energy, heat capacity and conductivity of a free electron gas. Ohm law. Periodic potential model for metals. Block theorem. Periodic boundary conditions of Born-von Karman. Schroedinger equation and wavefunction for Block electrons. Fermi surface. Electrons in a weak periodic potential. Equivalence with the free electron model. Energy and wavefunction of a isolated electronic state and a group of isolated states. The case of two electronic states. Band structure and band energy gap. Semiconductors. Law of mass action. Donors and accettors. p and n type semiconductors. Lattice dynamics. Normal modes of a monodimensional lattice. Cohesion energy of crystals. Specific heat of solids: Einstein and Debye approaches. Nuclear spin interactions. Differences between solution and solid state NMR. Zeeman interaction. Strong magnetic fields. Longitudinal relaxation. Radiofrequency pulses, NMR instrumentation, transverse relaxation, selective or broadband excitation. Chemical shielding and its anisotropy, effects of mechanical rotation of the samples, mathematical treatment and experimental needs. Heteronuclear dipole-dipole interactions. Use of dipole-dipole interactions for structural and dynamical characterization. Nuclear quadrupole interactions. Homonuclear dipole-dipole interactions. Effect of homonuclear dipole-dipole interactions on proton spectra. Carbon detection. Sensitivity enhancement. Relaxation in the presence of coherent modulations. Effect of interference between coherent and non-coherent motions Paramagnetism. Hyperfine interaction: contact shift and pseudocontact shift. Homogeneous and inhomogeneous broadening in paramagnetic solids. NMR-crystallography. Multidimensional experiments and pulse sequences. Decoupling and recoupling of nuclear interactions for structural determination. Practicals on sample handling, acquisition and processing of spectra under magic angle spinning. Applications to biological systems and materials science.