84541 - X-Ray and Synchrotron Radiation Physics

Learning outcomes

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.

Course contents

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.

Readings/Bibliography

• Lecture presentations available on iol.unibo.it.
• P. Fornasini, X – ray absorption spectroscopy, available at www.synchrotron-radiation.it (Attività SILS/ scuola di Luce / Grado 2013).
• C. Meneghini, The XANES Region, available at www.synchrotron-radiation.it (Attività SILS/ scuola di Luce / Grado 2013).

Textbooks for in depth description of course topics:

• 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 aspectsin “Synchrotron Radiation: Basics, Methods and Applications”, a cura di S. Mobilio, F. Boscherini e C. Meneghini, Springer (2015)

Teaching methods

Lectures with powerpoint presentations, a copy of which is available on the web site iol.unibo.it.

Assessment methods

Oral exam, in two parts. In the first part, each student will illustrate one of the experimental methods (student's choice), focussing on physics fundamentals, experimantal aspects, characteristics and examples. The second part will deal with the fundamental part of the course: properties of x-rays, synchrotron radiation soursces, interaction of x-rays with matter.

The exam must be booked via almaesami, 3 students every hour and a half slot, 12 students a day.

Teaching tools

Presentations. Slides are available to registered students on line

Office hours

See the website of Federico Boscherini

See the website of Francesco Borgatti

See the website of Raffaello Mazzaro