Teaching activity/Attivita' didattica prof. A. Di Cicco 2012-2022

Lectures during academic years 2012-2022

Corsi relativi agli anni accademici 2012-2022

Lectures for the first degree in Physics/Lezioni per il Corso di Laurea in Fisica (triennale):

• Physics of fluids+Thermodynamics/Fisica dei Fluidi e Termodinamica (2011-2022, 6 crediti): program/programma

Lectures for the Master degree in Physics/Lezioni per il Corso di Laurea Magistrale in Fisica (biennale):

• Solid State Physics/Fisica dei Solidi (2002-2022, 6 crediti): program/programma, Exercises/ESERCIZI
• Advanced Physics Laboratory (2012-2016 4 credits of 12 total, from 2016-2022 6 credits of 12 total): program/programma (last academic years) and teaching material/Materiale didattico.
  Programs and teaching material of the previous academic years: Program and teaching material/Materiale didattico 2012-13,Program and teaching material/Materiale didattico 2013-14, Program and teaching material/Materiale didattico 2014-15, Program and teaching material/Materiale didattico 2015-16, Program and teaching material/Materiale didattico 2016-2022.
  

corso di TERMODINAMICA E FISICA DEI FLUIDI (Laurea triennale in Fisica)

Docente: prof. Di Cicco Andrea

1-Solidi e fluidi
Proprietà meccaniche dei solidi. Definizione di sforzo e deformazione. Modulo di Young. Sforzo di taglio. Compressibilità. Pressione in un fluido in equilibrio. Tensione superficiale. Forze di adesione e di coesione. Capillarità.

2-Moto di fluidi
Moto di un fluido in regime stazionario. Equazione di continuità. Conservazione dell'energia (teorema di Bernoulli). Applicazioni al fluido in quiete, allo scorrimento orizzontale (fenomeno di Venturi), alla portanza in un profilo alare. Corrente fluida viscosa, definizione di viscosità.

3-Termodinamica: concetti generali Concetti di base: sistemi termo dinamici, trasformazioni, parametri di stato. Temperatura. Termometri, termometri a gas. Gas perfetto. Calore. Lavoro. Calore Specifico. Propagazione del calore.

4-Termodinamica: primo principio Primo principio della termodinamica. Sviluppi analitici del primo principio. Calore specifico a pressione costante Cp ed a volume costante Cv. Applicazione del primo principio al caso del gas perfetto: rapporto Cp/Cv, equipartizione dell'energia e calore specifico a volume costante, trasformazioni adiabatiche.

5-Termodinamica: secondo principio Enunciati del secondo principio della termodinamica. Equivalenza tra i due enunciati. Il ciclo di Carnot. Rendimento di una macchina ideale. Teorema di Carnot. Temperatura termodinamica assoluta. Cicli termodinamici reversibili e irreversibili. Integrale di Clausius. Entropia. Sviluppi analitici del secondo principio. Energia interna di un gas perfetto. Entropia di un gas perfetto. Espressione analitica del secondo principio (enunciato di Kelvin). Interpretazione statistica dell'Entropia. Teorema di Nerst (terzo principio). Il calore specifico nei solidi.

6-Transizioni di fase e potenziali termodinamici Eq. di Van Der Waals. Transizioni di fase: calori latenti, diagramma di fase, equazione di Clapeyron. Potenziali termodinamici: Entalpia, Energia Libera di Helmoltz e Gibbs. Proprieta' e relazioni tra le funzioni termodinamiche. Condizioni d'equilibrio (minimo di Energia libera) e applicazione alle transizioni di fase. Regola delle fasi.

Testi consigliati:

Mencuccini, Silvestrini, Fisica I (Liguori, 1987).

[1-3] P . A. Tipler, Fisica 1 (3nd ed.) (Zanichelli , 1995).

per la fisica dei Fluidi vedere anche T. Papa, "Lezioni di Fisica" [15-17] (editore Kappa).

E. Fermi, "Termodinamica" (Boringhieri, 1962)

SOLID STATE PHYSICS (Master degree in Physics)

Docente: prof. Di Cicco Andrea

1) Structure and properties of solids. Crystallization. Materials and methods of solid state physics. Experimental conditions for the study of solid materials. Periodic table and fundamental properties of solids. Potential energy and cohesion in typical classes of solids. Crystal structures. Ideal crystalline lattice. Primitive cell. Basis. Allowed and forbidden symmetries. Classification of Bravais lattices according to symmetry operations. Miller indices. [1]
[1] [Mye] Chapt. 1, 2, see also [Kit] Chapt. 1 or [Ash] Chapt. 4,7.

2) Diffraction of radiation in general. "Scattering" of photons, neutrons and electrons: similarities and differences. Amplitude and intensity of scattered radiation in x-ray diffraction. Atomic form factors. Relationship with the charge density. Diffraction by crystals. Laue equations, equivalence with the Bragg condition. Reciprocal lattice and interplanar distances. Symmetries. Calculation of the scattering amplitude. Structure factor. Laue equations. Examples of the calculation for the structure factor for simple solids. Forbidden reflections. X-ray generators, basic principles. [1,2] Synchrotron radiation. Spectrometers and detectors, sample preparation. [3] Single-crystal and powder diffraction. [1]
[1] [Kit] Chapt. 2.
[2] [War] Chapt. 1-5.
[3] More in: "Practical Surface Analysis", D. Briggs and M. P. Seah, Wiley and sons (1983); Par. 2.4; "X-ray determination of Electron Distributions", R. J. Weiss, North-Holland (1966), Chapt. 3; website of the European Synchrotron Radiation Facility: www.esrf.fr

3) Adiabatic approximation: separation of the ion and electron motions. Conditions for the validity of such approximation in solids. [1] Perfect crystals: consequences for translational invariance (Bloch theorem). Bloch theorem for a generic periodic potential. Periodic boundary conditions, counting of states. Volume of the primitive cell of the reciprocal lattice. [2]
[1] [Bas] Chapt. 3.1,3.3,3.4,3.5. [Mad] Chapt. 1.2
[2] [Ash] Chapt. 8 (p. 132-136)

4) Lattice dynamics. Three-dimensional Bravais lattice with basis: harmonic approximation. Consequences of translational symmetry. Construction of the dynamical matrix. Eigenvalues and eigenvectors. Equations of motion, general characteristics. Acoustic and optical branches. [1,2] Normal modes in one dimension: dispersion relations for monatomic and diatomic chains. Phase and group velocity. Brillouin zones.[2,3]
[1] [Mar] Chapt. II.1, p. 6-10,17-21.
[2] [Ash] Chapt. 22 (422-442).
[3] [Kit] Chapt. 5 (158-170).

5) Quantum theory of the harmonic crystal. Phonons. Internal energy and specific heat (lattice vibrations) classical limit. Quantum and anharmonic corrections. Specific heat at low temperature. Models for intermediate temperatures (Debye, Einstein), definition and meaning of the Debye temperature. Lattice and electronic contributions to the specific heat. Typical Debye temperatures of simple solids. Phonon density of states. Van Howe singularities. Density of states in the Debye and Einstein approximations, comparison with realistic density of states.[1,2]
[1] [Ash] Chapt. 23, App. L.
[2] Reading [Kit] Chapt. 5 (151-158), Chapt. 6 (182-196).

6) Neutron scattering: differential cross-section. Dynamical structure factor S (q,ω). Crystal structures with thermal disorder. Debye-Waller factor and elastic diffusion. One-phonon contribution. Multi-phononic terms. Peak width of single phonon contributions. [1] Inelastic scattering of X-rays [2] Optical measurements of phonon spectra (Brillouin lines). Differences and similarities between scattering of x-rays, neutrons and light. [1]
[1] [Ash] Chapt. 24, App. N.
[2] [Bas] Chapt. 7.5

7) Electronic properties. Drude model for metals. Discussion of the free-electron approximation. Density of electron states and Fermi energy. Typical values for metals. Plasmons. [1,2]
[1] [Mye] Chapt. 6.1, 6.2.
[2] [Ash] Chapt. 1 (p. 2-6), Chapt.2 (p. 30-40)

8) Energy and specific heat of an electron gas. Specific heat of metals at low temperature. [1] Electrical conductivity in metals. [1,2] Hall effect and magnetoresistance. High-frequency conductivity and optical properties of metals. Heat conductivity and thermopower in metals. [3] Compressibility.
[1] [Kit] Chapt. 7 (220-237)
[2] [Mye] Chapt. 6.4.
[3] [Ash] Chapt. 1 (11-25)

9) Limits of the free electron approximation. Periodic potentials. Nearly-free electrons. Bloch states. Fermi surface. Density of electron states. "Weak" potential approximation and perturbative approach. Energy levels close to a Bragg plane. Energy bands and formation of the energy gap in one-dimensional and three-dimensional systems. "Tight-binding" models. LCAO, linear combinations of atomic orbitals. Application to s-like bands. General characteristics of the valence levels. Wannier functions. Methods for the calculation of the band structure in the approximation of independent electrons. Cellular methods. Augmented Plane Wave (APW) method. Orthogonalized plane wave method (OPW). Non-local potentials and pseudopotentials. [1]
[1] [Ash] Chapt. 3, 8 (137-145), 9, 10 , 11.

10) Semiconductors. Valence and conduction bands. Density of holes and electrons, temperature-dependent. Chemical potential. Intrinsic semiconductors. Law of mass action. Doped semiconductors.[1,2]
[1] [Kir] Chapt. 3.
[2] [Ash] App. E, Chapt. 28, Chapt. 29 (reading).

Bibliography:

[Ash] N. Ashcroft, D. Mermin, "Solid state physics", Saunders (1976).
[Bas] F. Bassani e U. M. Grassano, Fisica dello Stato Solido, Boringhieri (2000).
[Cus] N. E. Cusack, "The Physics of Structurally Disordered Matter", Adam Hilger IOP (1987).
[Kir] P. R. Kireev, "Semiconductor Physics", MIR Publ ().
[Kit] C. Kittel, "Introduzione alla fisica dello stato solido", Boringhieri (1982).
[Mad] O. Madelung, "Introduction to Solid-State Theory" Springer-Verlag (1978).
[Mar] A. A. Maradudin, E. W. Montroll, G. H. Weiss, e I. P. Ipatova, "Theory of lattice dynamics in the harmonic approximation", 2nd edition, Academic Press (1971).
[Mye] H. P. Myers, "Introductory Solid State Physics", Taylor and Francis (1990).
[War] B. E. Warren, "X-ray Diffraction", Dover (1990).
[Zim] J. M. Ziman, "Principle of the Theory of Solids", 2nd ed., Cambridge Univ. Press (1972).

Written reports and exam (up to 2017)

Some topics were not deeply discussed during the 2016-2017 lectures, due to the known problems caused by the earthquake series in Camerino. Students are expected to produce a short written report about 3 of the following topics, a few days before the oral examination: 1) The adiabatic approximation. Conditions for the validity of such approximation in solids. 2) Bloch theorem for a generic periodic potential. 3) Hall effect and magnetoresistance. 4) Heat conductivity and thermopower in metals. 5) Compressibility in metals. 6) Semiconductors. Valence and conduction bands. Intrinsic semiconductors. Law of mass action. Doped semiconductors.

  Questions to be answered in written form (2015).

2015/2016. A short written dissertation concerning at least 2 of the 4 questions proposed should be submitted a few days before the oral examination. Discussion of one of the chosen problems, and of two arguments of the program will be part of the oral examination.

2017. A short written dissertation concerning at least 3 of the 6 topics proposed should be submitted a few days before the oral examination. Discussion of one of the chosen problems, and of two arguments of the program will be part of the oral examination.

Written reports (since 2018)

Students can produce short written reports about 3 of the following topics, a few days before the oral examination (not mandatory): 1) The adiabatic approximation. Conditions for the validity of such approximation in solids. 2) Bloch theorem for a generic periodic potential. 3) Hall effect and magnetoresistance. 4) Heat conductivity and thermopower in metals. 5) Compressibility in metals. 6) Semiconductors. Valence and conduction bands. Intrinsic semiconductors. Law of mass action. Doped semiconductors.

Exam (since 2018)

2018/2019. The program does not include part 10 (semiconductors). The exam is oral and usually will be carried out discussing 2 or 3 arguments of the general program. The student can present a short written report (see above) concerning at least 3 of the 6 topics proposed should be submitted a few days before the oral examination. Discussion of one of the chosen problems, and of two arguments of the program will be part of the oral examination.

UP

ADVANCED PHYSICS LABORATORY (Master degree in Physics)

Lectures by A. Di Cicco

Program A.Y. 2012/13

Basic knowledge about theory and methods

X-ray fluorescence (XRF). Experimental set-up: x-ray source, optics, detectors. Theory of photoabsorption. Fluorescence yield. Methods for quantitative x-ray fluorescence analysis. Raman scattering. Experimental set-up: laser source, optics, spectrometer, detectors. Peak-fitting analysis.

Bibliography:
See ``Quantitative X-ray Spectrometry'' by Ron Jenkins, R. W. Gould, and Dale Gedcke (2nd edition, 1995).

Laboratory sessions

Measurements of the XRF spectra of several samples of unkwown chemical composition. The students will acquire the necessary expertise for running the experimental set-up (sample positioning, managing the power-supply, the detector, the multi-channel analyser and related software). The collected XRF data will be subsequently converted in a suitable energy scale (calibration) and the chemical species of the samples identified (qualitative XRF analysis). Full data-analysis, including fitting of the relevant fluorescence peaks over the background signal, will allow the students to measure the relative intensity of the individual components. By application of the theoretical framework concerning the photon-in photon-out process a detailed quantitative analysis will be performed with the aim of determining the concentration of the chemical species inside the given samples. Measurements of Raman scattering spectra of a Sulphur sample using a laser source and an optical spectrometer. The students will acquire the necessary expertise for running the experimental set-up (alignment of the laser beam and calibration, positioning, managing the CCD detector and related software). The collected Raman scattering data (images) will be subsequently converted in a suitable scale (calibration) and the vibrational levels identified. The students will acquire the necessary expertise for XRF and Raman data-analysis including theoretical modeling and evaluation of physical data with their statistical uncertainty.