84583 - PHYSICS OF CONDENSED MATTER AND RADIATION

Scheda insegnamento

Anno Accademico 2017/2018

Conoscenze e abilità da conseguire

At the end of the teaching activities, all students will be able to understand and analyze: - the phenomenology of the interaction between radiation and matter, and its description in a classical context; - the quantum physics related to the interaction between radiation and matter when exposed to semi-classical approximation (photoelectric absorption and the diffusion of atoms; the absorption and diffusion related to vibrational and rotational stimulation of molecules); - the description of direct and reciprocal crystal lattices, as well as the description of their elements of symmetry; - the fundamentals on defects both on point and on extended basis; - the basics of physics of electron states in crystalline solids; - the description of elastic waves in lattices, the knowledge related to physics of phonons and its relation with the models of both Einstein and Debye; - all introductory notions of the physics of magnetism of solid state; - all introductory notions of the thermodynamics statistics in the phases of transition.

Programma/Contenuti

1. Atomic Structure

1.1. Introduction to symmetry

Symmetry in crystallography. Isometric transformations. Direct and opposite congruence. Symmetry operations. Matrix description.

1.2. Crystal structures in 2 D.

Bravais lattices in 2 D. Primitive vectors. The five 2 D bravais lattices. 2D crystal structures. Unit cells: primitive, conventional and Wigner & Seitz. Point groups. The seventeen space groups in 2 D (plane groups).

1.3. Crystal structures in 3 D.

Crystal structures in 3 D. Coordination number. The fourteen Bravais lattices and seven crystal systems. Stereograms, the thirty two crystallographic point groups and two hundred and forty space groups. Relation between atomic structure and physical properties.

1.4. Structural determination by particle and wave scattering

X-rays, electrons and neutrons. Scattering by single atoms, by an ensemble of atoms and by a lattice. Laue conditions. Reciprocal lattice. Lattice planes and Miller indeces. Diffraction from a lattice with a basis, geometrical structure factor.

2. Electronic structure

2.1. The free electron gas

2.1.1. Hamiltonian for condensed matter.

2.1.2. Free electron gas. Born – von Karman boundary conditions. Fermi sphere. Fermi Dirac distrubutions. Sommerfeld expansione. Specific heat.

2.2. Non interacting electrons in a periodic potential.

2.2.1. Consequences of translational symmetry. Bloch theorem. Schroedinger equation in reciprocal space. Band index, lattice momentum. Energy bands. Energy gap. The ground state and the difference between metals and insulators. Density of states. Van Hove singularities. Velocity of Bloch electrons.

2.2.2. Nearly free electrons. Independent electrons in a weak periodic potential. Bragg planes. Representation of energy bands in three schemes. Fermi surfaces. Higher order Brillouin zone.

3. Vibrations and phonons.

3.1. Adiabatic approximation. Separation of the Schroedinger equation in two equations describing nuclear and electronic motions. Harmonic approximation.

3.2. Lattice vibrations in the harmonic approximation: classical description.

Atomic chain, dispersion relation. Vibrations in 3 D. Equation of motion and dynamical matrix; eigenvalues and eigen vectors. Acoustic and optical branches.

3.3. Lattice vibrations in the harmonic approximation: quantum description.

Hamiltonian of the harmonic crystal in terms of creation and destruction operators. Phonons. Bose – Einstein statistics. Lattice specific heat. High temperature limit and the Dulong and Petit law. Low temperature limit, T^3 dependence. Einstein and Debye Models.

3.4. Inelastic neutron scattering.

Thermal neutrons. Conservation of energy and momentum in inelastic scattering.

4. Interaction between radiation and matter

General aspects and classical description. Attenuation coefficient and cross section. The dielectric response of matter, phenomenology. Permittivity and susceptibility. Index of refraction: dispersion and attenuation. Weak interaction limit. Model dielectric function for static polarization. Kramers – Heisenberg dielectric function. Kramers Kronig relations. Scattering from a damped harmonic oscillator. High and low frequency limits. Resonant scattering.

Quantum description. Fermi’s golden rule. Semiclassical approximation, Coulomb gauge. Vector potential for a polarized plane wave. Interaction Hamiltonian: linear and quadratic terms in the vector potential. Photoelectric absorption cross section in the dipole approximation. Selection rules. Scattering of radiation. Density of states for photons and derivation of the scattering cross section. Elastic scattering of linearly polarized radiation from a hydrogen – like atom in the ground states. High and low energy limits.

5. Introduction to magnetism in solids (Dr. Laura Basiricò)

Classical description of magnetic phenomena. Orbital and spin magnetic moment. Magnetization. Magnetostatics in ponderable matter. Magnetic materials: properties, operational definition of magnetic field; diamagnetic, paramagnetic and ferromagnetic materials. Microscopic interpretation of magnetization in ponderable matter: Larmor diamagnetism, Langevin paramagnetism; Curie – Weiss law for ferromagnetism. Hysterisis curves and Weiss domains in ferromagnetic materials.

Quantum interpretation. Quantum theory of paramagnetism and diamagnetism: Brillouin function. Quantum magnetic susceptibility. Larmor diamagnetism. Magnetization density as a function of the Helmholtz free energy. Hund’s rule for the atomic ground states. Van Vleck paramagnetism. Susceptibility of metals: Pauli paramagnetism and Landau diamagnetism. Quantum theory of ferromagnetism. Mean field theory. Curie – Weiss law. Exchange interaction and Heisenberg model. Magnons. MAgnetic neutron scattering. Antiferromagnetic ordering. Ferromagnetic domains and Bloch walls.

Testi/Bibliografia

Ashcroft & Mermin: Neil W. Ashcroft and N. David Mermin, Solid State Physics, Saunders College Publishing (1976)

Bassani & Grassano: G.F. Bassani e U. Grassano Fisica dello Stato Solido, Bollati Boringhieri (2000), In Italian.

Cotton: F. Albert Cotton, Chemical Applications of Group Theory, Third Edition, Wiley.

Giacovazzo: Carmelo Giacovazzo (editor), Fundamentals of Crystallography, Third Edition, Oxford University Press (2011).

Grosso & Pastori Parravicini: Giuseppe Grosso and Giuseppe Pastori Parravicini, Solid State Physics, Second Edition, Academic Press (2014)

Kittel: Charles Kittel, Introduction to Solid State Physics, Eighth Edition, Wiley (2005);
Introduzione alla Fisica dello Stato Solido, Casa Editrice Ambrosiana (2008).

Marder: Michael P. Marder, Condensed Matter Physics, Second Edition, Wiley (2010)

Rigamonti & Carretta: A. Rigamonti and P. Carretta, Structure of Matter, Spinger (2015)

Tinkham: Michael Tinkham, Group Theory and Quantum Mechanics, Dover (2003) oppure McGraw Hill (1964).

Metodi didattici

Formal lectures and group discussions

Modalità di verifica dell'apprendimento

Oral exam

Strumenti a supporto della didattica

Powerpoint presentations, a copy o which is available on campus.unibo.it

Orario di ricevimento

Consulta il sito web di Federico Boscherini

Consulta il sito web di Laura Basiricò