OVERVIEW

The third year teaching in the degree course in Materials Science introduces to the basic knowledge of Physics of Solids. Particular importance is given to the ability to interpret the physical properties of solids with the help of appropriate simplifications and mathematical models identifying the validity limits of the model. The program provides an introduction to Crystal structure, electronic structure and vibrational states of Solids.

AIMS AND CONTENT

LEARNING OUTCOMES

The coursw aims to provide the basic knowledge of the physics of solids in its experimental and theoretical aspects as well as a solid working methodology and an interdisciplinary approach oriented towards problem solving

AIMS AND LEARNING OUTCOMES

Know how to apply the basic knowledge of classical physics, modern physics and chemistry to the introductory study of Physics of Solids 

To be familiar with the mathematical tools necessary to make models useful to describe the behaviour of crystalline solids and to understand its structural, vibrational and electronic properties.

To propose examples of the application of models to solids;

Know how to integrate the knowledge and languages ​​of the various disciplines       

PREREQUISITES

Basic knowledge of classical physics, infinitesimal calculus and modern physics

TEACHING METHODS

Classroom lessons with examples and applications. The course includes about 64 hours of lectures. Student's  participation is required in the discussion that highlights the characteristics of the various models used and their adequacy to interpret the properties of crystalline solids.

SYLLABUS/CONTENT

Brief introductory review of solid-state characteristics and crystal structure.

Elements of solid-state statistical physics
Boltzmann statistics and specific heat in the classical limit (Dulong and Petit's law). Quantum assumptions and Einstein and Debye models for specific heat at low temperatures. Debye's interpolation formula for intermediate temperatures. Drude's model for electronic  conduction in metals. Thermal transport. Fermi-Dirac statistics and Sommerfeld free-electron model. Fermi sea and Fermi surface. Fermi energy. Density of states. Electronic specific heat and Pauli paramagnetism.

Lattice vibrations in one-dimensional systems.
Simple examples to introduce the concept of normal mode of vibration. Elasticity, thermal expansion. Monoatomic linear chain: direct lattice and . k-Space.Normal modes of oscillation. Dispersion relation and consequences. Quanta of vibration (phonons). Bose statistics, statistical considerations and discussion of the Debye model. Crystalline momentum. Linear diatomic chain. Dispersion relation. Acoustic (speed of sound) and optical modes. Extended and reduced zone representation. Zone edges.

Electronic states in one-dimensional systems
Method of linear combination of atomic orbitals. Electronic states of a linear monatomic chain (Tight Binding Method). Dispersion relation (bands). Permitted and prohibited energy intervals (gaps). Band filling criteria. Fermi surface. Effective mass, group velocity. Density of states.

Crystal structures.
Lattices. Conventional, primitive, unitary cells. Lattice with bases. Structures with cubic symmetry. Other symmetries. Reciprocal lattice in three dimensions. Lattice planes and Miller indices. Brillouin zone: construction and properties. Waves in crystals Diffraction experiments for the study of crystal structures. Laue and Bragg conditions. Scattering amplitudes. Comparison of X-ray diffraction and neutron diffraction.

Phonons and electrons in crystalline solids.
Phonon branches. Experimental methods for verifying phonon dispersion curves. Electrons in periodic potential. Bloch's theorem. Free and quasi-free electrons. Bands. Insulators, metals and semiconductors. Experimental methods for determining band structure. 3D Fermi surfaces.

RECOMMENDED READING/BIBLIOGRAPHY

S.H. Simon Oxford Solid State Basics

Readings

N. W. Ashcroft N. David Mermin   Solid State Physics

 C. Kittel Introduction to Solid State Physics

  H. P. Myers  Introductory  Solid State Physics

TEACHERS AND EXAM BOARD

Exam Board

MAURIZIO CANEPA (President)

FRANCESCA TELESIO

LESSONS

LESSONS START

last week september 2023

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The examination consists of an oral test with two questions on the core topics of the course (structure, lattice vibrations, electronic states) aimed at assessing knowledge of the fundamental topics and the ability to apply the knowledge to practical situations.  The duration of the interview is approximately forty minutes.

 In the event of difficulty, a third question is proposed.

ASSESSMENT METHODS

The oral examination aims to ascertain the degree of achievement of the following learning outcomes: knowing and understanding the fundamental aspects of the Physics of Solids (structure, lattice vibrations, electronic states), being able to apply the knowledge by making examples, and to express oneself in a coherent language using appropriate mathematical tools.  The assessment takes all these aspects into account.

Exam schedule