91239 - Materials Spectroscopy

Learning outcomes

At the end of the course, the student has acquired the fundamentals of materials spectroscopy, quantum theory of solids, as well as spectroscopic techniques based on absorption/emission, light scattering, and magnetic properties.

Course contents

Main topics

• The crystalline state: crystalline structures, direct and reciprocal lattice.
• Linear, planar and spatial space groups.
• Quantum theory of solids, Bloch theorem and functions.
• Elastic and inelastic scattering of photon and mass particles.
• Reticular motions, phonons, vibrational spectroscopy. 
• Quasi-crystals
• Optical properties of crystals.

Calendar

• 19/09/2023 TH
  Ideal crystal, direct lattice, basis of atoms, convolution function, translational symmetry, Bloch's theorem.
• 20/09/2023 TH
  Bloch's theorem, Bloch's functions, reciprocal space, reciprocal lattice, Voronoi primitive unit cell, Wiegner-Seitz cell, first Brillouine zone, eigenvalues and eigenfunctions of a free-particle upon periodic potential constraint in a unidimensional lattice.
• 26/09/2023 TH
  Quantum mechanical calculation of the molecular orbitals of linear Be37 as a model for linear crystals.
  
• 27/09/2023 TH
  Relation between the primitive translation vectors in the direct and reciprocal lattices (2D and 3D). Eigenvalues and eigenfunctions of a free-particle upon periodic potential constraint in two- and three-dimensional lattices. Density of states and Fermi's energy.
  
• 03/10/2023 TH
  Periodic Born von Karman conditions. Point group symmetry of the k-space.
  
• 10/10/2023 LAB
  Plane waves and pseudopotentials. Electronic bands of Si with Quantum Espresso.
• 10/10/2023 TH
• Fourier series for a 2pi periodic function.
• 11/10/2023 TH
  Fourier series for a periodic function. Euler notation. Fourier transform.
  
• 17/10/2023 LAB
  Quantum mechanical calculations on solids with Quantum Espresso.
  
• 17/10/2023 TH
  Fourier transform of the exponential decay function. Convolution theorem.
  
• 18/10/2023 TH
  Correlation and autocorrelation theorems. Apodization and aliasing. Multidimensional Fourier series and transform.
  
• 24/10/2023 TH
  Vibrational motions in monoatomic crystals.
  
• 25/10/2023 TH
• Vibrational motions in monoatomic crystals.
• 31/10/2023 TH
  Density of states. Phonons. Vibrational motions in biatomic crystals.
  
• 02/11/2023 LAB
  Calculation (G16) and analysis of the vibrational normal modes of a monoatomic chain.
  
• 07/11/2023 TH
  Vibrational motions in biatomic crystals.
  
• 08/11/2023 TH
  Acoustical and optical branches. Case study: TiO2.
• 14/11/2023 TH
  Neutron scattering.
• 15/11/2023 TH
  
• Photon scattering. Symmetry representation of the vibrational normal modes of carbonate anion.
• 21/11/2023 TH
  Symmetry representation of the vibrational normal modes of 2 carbonate anions system.
  
• 22/11/2023 TH
  Vibrational normal modes of calcite.
  28/11/2023 TH
  Determination of the vibrational normal modes of calcite and aragonite using the utilities of the Bilbao Crystallographic Server.
  
• 29/11/2023 TH
  Case study: analysis of the vibrational motions in TiO2 (rutile, anatase, brookite).
• 05/12/2023 TH
  Diffraction condition.
  
• 06/12/2023 TH
• 07/12/2023 TH (ex laser)
• 11/12/2023 TH (ex laser)
• 12/12/2023 TH

Anonymous statistical survey

Once 2/3 of the lessons have been completed, a survey will be carried out to know students' opinions on the course, in order to make it more effective. Reference links:

• https://opinionistudenti.unibo.it
• https://val.unibo.it/ (student)
• https://val.unibo.it/demo.php (survey)
• https://gestioneval.unibo.it (lecturer)

Readings/Bibliography

• C. Kittel
  Introduction to Solid State Physics
  John Wiley & Sons, Inc.
• P. F. Bernath
  Spectra of Atoms and Molecules
  Oxford University Press, 1995
• D.R.VI
  Handbook of Applied Solid-State Spectroscopy
  Springer-Verlag, 2003
• H. Luth and H. Ibach
  Solid-State Physics: An Introduction to Principles of Materials Science
  Springer-Verlag, 3rd Ed. 2003
  
• J. M. Ziman
  I Principi della Teoria dei Solidi
  Tamburini Editore, 1975.
• H. Kuzmany
  Solid-State Spectroscopy
  Springer-Verlag, 3rd Ed. 1998
• J. I. Gersten and F. W. Smith
  The Physics and Chemistry of materials
  J. Wiley ans Sons, Inc. 2001, Canaa
• Nguyen Tuan Hung, Ahmad R.T. Nugraha , Riichiro Saito
  Quantum ESPRESSO Course for Solid-State Physics
  Jenny Stanford Publishing, 1st Ed. 2022
  Ebook: https://dx.doi.org/10.1201/9781003290964
  Repository: https://github.com/topics/quantum-espresso?l=roff
• Bilbao Crystallographic Server
  https://www.cryst.ehu.es/
• American Mineralogist Crystal Structure Database
  http://rruff.geo.arizona.edu/AMS/amcsd.php
• Crystallography Open Database
  https://www.crystallography.net/cod/
  

Teaching methods

Lectures and computational simulations.

As concerns the teaching methods of this course unit, all students must attend Module 1, 2 on Health and Safety online: 

• https://www.unibo.it/en/services-and-opportunities/health-and-assistance/health-and-safety/online-course-on-health-and-safety-in-study-and-internship-areas

Assessment methods

Oral examination.

Teaching tools

Blackboard (lectures and exercises) and video-projector.

Computational laboratory.

Lecture notes are available in electronic format on the course's institutional website:

• https://virtuale.unibo.it/course/view.php?id=47166

Students who need compensatory tools because of disabilities or specific learning disorders (SLD) can contact:

• https://site.unibo.it/studenti-con-disabilita-e-dsa/en

to agree on the adoption of the most appropriate measures.

Office hours

See the website of Assimo Maris