84541 - X-RAY AND SYNCHROTRON RADIATION PHYSICS

Conoscenze e abilità da conseguire

At the end of the course the student will learn the basic notions regarding the physical mechanisms of the interaction between X-rays and condensed matter in both a macroscopic and microscopic approach and the most important properties of synchrotron radiation sources, with emphasis on the underlying physics. Moreover, the student will learn the basics of the main experimental X-ray methods (such as X-ray diffraction, X-ray absorption spectroscopy and photoemission) and their recent application to current research topics.

Contenuti

The objective of the course is to describe the physical mechanisms of the interaction between x-rays and matter and the main experimental methods used in modern research in condensed matter physics and related areas such biophysics, medical physics, cultural heritage and environmental science.

Module 1: Federico Boscherini

• Introduction to X-ray physics.
  • X-rays in the wave and particle description.
  • Comparison of the main physical properties of x-rays with the corresponding ones of atoms, molecules and solids in the domains of length, energy, momentum, angular momentum.
• Classical approach.
  • Macroscopic description of interaction.
    • Dielectric response. Electrical susceptibility and dielectric function. Dispersion and attenuation. Index of refraction. Linear attenuation coefficient.
    • Model dielectric functions. Static case. Dielectric response of an ensemble of damped harmonic oscillators. Near resonant behaviour. X-ray limit. Kramers – Kronig relations.
  • Microscopic description of interaction.
    • Cross section.
    • Elastic scattering from a free electron and from an atom (atomic form factor).
    • Photoelectric absorption in atoms and solids.
  • Relation between macro and micro description, between index of refraction and atomic form factor. Optical theorem.
  • Scattering from a damped harmonic oscillator. Limits: low energy, resonance and high energy.
• Semiclassical theory of the interaction between radiation and hydrogen – like atoms.
  • Fermi’s golden rule for transitions to discrete and continuum states.
  • Vector potential for a plane monochromatic and linearly polarized EM wave.
  • Interaction Hamiltonian in the Coulomb gauge. Dipole approximation.
  • Photoelectric absorption cross – section. Selection rules. Lifetime broadening.
  • Photoemission cross – section.
  • Scattering cross – section. Contribution of the term (X-ray limit). The Kramers – Heisenberg cross – section; limits: low energy, resonance, high energy.

Module 2: Francesco Borgatti

• Synchrotron radiation and free electron laser sources
  • Synchrotron Radiation Sources
    • Electromagnetic radiation emitted from accelerated particles
    • Storage Ring Elements
      • Sources of synchrotron radiation (Bending Magnet, Undulator, wiggler)
      • RF cavity
      • Beamlines and basics of x-ray optics
    • General characteristics of Synchrotron Radiation
      • Brilliance
      • Diffraction limit and Coherence lengths
    • SR historical review
  • Free Electron Laser Sources
    • General properties – comparison with synchrotron radiation sources
    • SASE Mechanism of coherent emission - The microbunching process
• Photoemission spectroscopy
  • The Photoelectric effect
  • Experimental Setup
  • Theoretical Description
  • Primary and secondary structures occurring in the photoemission spectra
  • Photoelectron Spectroscopy of solids
  • Quantitative Analysis
  • Hard x-ray Photoelectron Spectroscopy

  Module 3: Raffaello Mazzaro

• X-ray absorption fine structure
  • Phenomenology of X-ray absorption spectroscopy
  • Main experimental layouts
  • Physical origin of the fine structure (self-interference phenomenon)
  • Golden rule and further approximations
  • Approximate derivation of EXAFS (Muffin-tin approximation for two atomic system)
  • Correction terms for the EXAFS function and final relation.
  • EXAFS data analysis and resulting structural parameters
  • XANES phenomenological description
  • Chemical shift of the absorption edge
  • Linear dichroism in XANES and EXAFS
• X-ray diffraction
  • Classical theory for elastic scattering (free electron and single atom)
  • Atomic form factor and anomalous correction
  • Relation between diffused intensity and electronic density in extended samples.
  • Crystal structure and reciprocal space (notion)
  • Kinematic diffraction theory from crystals
  • Laue conditions and Bragg’s law
  • The role of structure factor on diffraction intensity
  • XRD Debye Waller factor
  • XRD experimental setup
  • Single crystal and powder diffraction.
  • Surface XRD
  • Interpretation of scattered intensity in terms of radial distribution function and application to non-crystalline materials.

 

Testi/Bibliografia

• Copia delle presentazioni utilizzate a lezione, reperibili su iol.unibo.it.
• P. Fornasini, lezione X – ray absorption spectroscopy, reperibile sul sito www.synchrotron-radiation.it (Attività SILS/ scuola di Luce / Grado 2013).
• C. Meneghini, lezione The XANES Region, reperibile sul sito reperibile sul sito www.synchrotron-radiation.it (Attività SILS/ scuola di Luce / Grado 2013).

Libri testo di approfondimento:

• J. Als – Nielsen and D. McMorrow, Introduction to Modern X-ray Physics, Wiley, New York, 2001.
• D. Attwood, Soft X-rays and extreme ultraviolet radiation, Cambridge University Press (1999).
  
• A. Balerna and S. Mobilio, Introduction to Synchrotron Radiation, in “Synchrotron Radiation: Basics, Methods and Applications”, a cura di S. Mobilio, F. Boscherini e C. Meneghini, Springer (2015).
  
• P. Fornasini, Introduction to X-ray absorption spectroscopy, in “Synchrotron Radiation: Basics, Methods and Applications”, a cura di S. Mobilio, F. Boscherini e C. Meneghini, Springer (2015).
• B. Bunker, Introduction to XAFS: a practical guide to X-ray absorption spectroscopy, Cambridge University Press (2010).
  
• B.E. Warren, X-ray diffraction, Dover, New York, 1990.
• S.J.L. Billinge e E.S. Bozin, Pair distribution function technique: principles and methods, in Diffraction at the nanoscale, a cura di A. Guagliardi & N. Masciocchi, Insubria University Press.
• A. Guinier, X-ray diffraction in crystals, imperfect crystals, and amorphous bodies, Dover, New York, 1994.
• S. Hüfner, Photoelectron Spectroscopy – Principles and Applications, 3rd ed. (Berlin, Springer, 2003)
  
• C. Mariani e G. Stefani, Photoemission Spectroscopy: fundamental aspects in “Synchrotron Radiation: Basics, Methods and Applications”, a cura di S. Mobilio, F. Boscherini e C. Meneghini, Springer (2015)

Metodi didattici

Lezioni frontali alla lavagna e con presentazioni tramite PC e videoproiettore. 

Modalità di verifica e valutazione dell'apprendimento

Esame orale, consistente in due parti. Nella prima parte lo studente illustrerà a scelta uno dei metodi sperimentali descritti a lezione, affrontando i fondamenti fisici, gli aspetti sperimentali, le caratteristiche e qualche esempio di applicazione. La seconda parte verterà sugli aspetti generali del programma: proprietà dei raggi X, sorgenti di luce di sincrotrone, interazione raggi X - materia.

Iscrizione alla lista d'esame tramite almaesami in gruppi di 3 studenti ogni ora e mezza, 12 studenti al giorno.

Strumenti a supporto della didattica

Presentazioni powerpoint, copia delle quali è disponibile per gli studenti on line

Orario di ricevimento

Consulta il sito web di Federico Boscherini

Consulta il sito web di Francesco Borgatti

Consulta il sito web di Raffaello Mazzaro