OVERVIEW

The course introduces the basic concepts and models of the Physics of Solids. Emphasis is placed on the ability to interpret the physical properties of solids with the help of appropriate simplifications and mathematical models, identifying the limits of validity of the approximations introduced. The program includes an introduction to the structure, vibrational and electronic states of solids, with special reference to crystalline solids.

AIMS AND CONTENT

LEARNING OUTCOMES

Achieve basic knowledge of the physics of solids in its experimental and theoretical aspects as well as sound working methodology and an interdisciplinary problem-solving-oriented approach

AIMS AND LEARNING OUTCOMES

Know how to apply basic knowledge of classical physics, modern physics and chemistry to the study at the introductory level of the Physics of Solids.  To be familiar with the mathematical tools needed to develop models useful for describing the behavior of crystalline solids and understanding their thermal, vibrational and electronic properties; to know how to exhibit examples of the application of models to solids; to integrate the knowledge and languages of the various disciplines.

PREREQUISITES

Basic knowledge of general and modern physics, mathematical analysis and vector algebra.

TEACHING METHODS

Classroom lectures with examples and applications.  The teaching involves approximately 64 hours of lectures. Active student participation is solicited in discussions that highlight the characteristics of the various models used and their appropriateness for interpreting the properties of crystalline solids.

SYLLABUS/CONTENT

Brief introductory review of the characteristics of solid state and crystal structure with recalls of atomic and molecular physics. 

Elements of statistical physics of the solid state
Boltzmann statistics and specific heat in the classical limit (Dulong and Petit's law). Quantum assumptions and Einstein and Debye models for specific heat. 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. Density of electronic states. Fermi sphere and energy..Electronic specific heat. Pauli paramagnetism.

Vibrational and electronic states in one-dimensional systems. 

Introduction to the method of linear combination of atomic orbitals (Tight Binding): diatomic molecule. Chain of three atoms: vibrational modes and electronic states.

Monoatomic linear chain
Direct lattice and reciprocal lattice. Space -k.
Vibrations : Normal modes of oscillation. Dispersion relation and consequences.  Comparison with Debye's model.  Quanti of vibration (phonons).
Electronic states. Dispersion relation (bands) in Tight Binding approximation. Representation in extended zone and reduced zone. Allowed and forbidden energy intervals (gaps).  Density of states. Effective mass, group velocity.  

Linear diatomic chain. Direct lattice and reciprocal lattice. Vibrational modes. Dispersion relation. Acoustic (speed of sound in crystals) and optical modes. .Electronic bands. Criteria of band filling. 

Crystal structures
Lattices. Direct lattice: conventional, primitive, unitary cells. Lattice with base. reciprocal lattice.  Brillouin zone: construction and properties. Insights into cubic symmetry structures.  Waves in crystals. Diffraction experiments for the study of crystal structures. Laue and Bragg conditions. 

Phonons  Experimental methods for verifying phonon dispersions. Examples of phonon dispersion curves. 

Bands Electrons in periodic potential. Bloch's theorem. Strongly bound electrons: bands in insulating materials.  Approximation of nearly free electron and bands in metals. Fermi surfaces in simple metals and comparison with Sommerfeld's model. .Semiconductors. Experimental methods for determining band structure.

RECOMMENDED READING/BIBLIOGRAPHY

Recommended

S.H Simon Oxford Solid State Basics

Other texts

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

 C. Kittel, Introduzione alla fisica dello stato solido

https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Mathematical_Methods_in_Chemistry_(Levitus)

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

Second half of september

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written test with discussion of two exercises and demonstrations carried out in the course.

Oral test. Discussion of two topics. One topic is the student's choice.

ASSESSMENT METHODS

Written test: verification of accuracy, precision and completeness. A score is given in thirtieths (maximum 30)

Oral test: verification of accuracy, precision and completeness. A score from 0 to 10 is assigned.

The final grade is obtained from the sum of the marks obtained in the two tests.

Honors are granted if the total score reaches 37 points.