MAS.020UF Introduction to Solid State Physics


Crystal Structure

Crystal Physics




Exam questions






Phonons are quantized particles of sound. Similar to photons, the phonon energy is related to the frequency of the sound waves $E=hf$ and the phonon momentum is related to the wavelength of the sound waves $p=h/\lambda$.

Read the Normal Modes and Phonons section of the outline.
Kittel chapter 4: Crystal vibrations and Kittel chapter 5: Phonons and lattice vibrations
R. Gross und A. Marx: Dynamik des Kristallgitters und Thermische Eigenschaften des Kristallgitters

    For the exam
  • Be able to write down Newton's law for a periodic arrangement of atoms connected by linear springs. Know the form of the eigenfunction solutions that solve these equations.
  • Be able to draw the dispersion relation for crystals such as Ag, NaCl, or TiO2. There are always three acoustic branches. The acoustic branches are linear near k = 0. There are 3p - 3 optical branches where p is the number of atoms in the primitive unit cell. All acoustic and optical branches meet the Brillouin zone boundary at 90°.
  • Know how to calculate the density states and from the dispersion relation and how to calculate the internal energy, Helmholtz free energy, specific heat, and entropy.
  • Be able to define: Einstein model, Debye model, and Umklapp scattering.
  • Be able to describe how the phonon dispersion relation can be measured with neutron scattering.
  • Be able to describe how kinetic theory can be used to describe the phonon contribution to the thermal conductivity.

Table summarizing the properties of phonons