Crystal Vibrations (Phonons)

Atomic motions in molecules and crystals are organized into vibrational modes. In crystals these modes are called phonons (Phonon Wiki). As with molecules, quantum mechanics requires that vibrational energy in a crystal is gained or lost in discrete packets, or quanta, of energy, corresponding to hν, where h is Planck's constant (6.626x10–34 J•sec) and ν is the frequency of a vibration. In addition, a half-quantum (hν/2) of vibrational energy will be present in each mode even at absolute zero temperature. The quantum-mechanical nature of phonon energy drives isotopic fractionation in crystals, causes discrete infrared absorption bands, and Raman scattering. It also controls superconductivity (when phonons couple with electronic motion), temperature-variable heat capacity, and heat conduction.

Large-wavelength crystal vibrations are routinely measured by infrared and Raman spectroscopy, while shorter wavelength vibrations can usually only be examined with more difficult neutron- or x-ray-scattering techniques. Very little is known about effects of isotopic substitution on vibrational frequencies in crystals, so it is almost always necessary to create force-field models to estimate isotope fractionations.
  
Recent theoretical and computational developments have made it possible to calculate crystal phonon frequencies from first principles, using density functional theory. This page links to some results of calculations made with ABINIT. Another (much more professional-looking) web page showing calculations made with the semi-commercial code CRYSTAL06 can be found here.

Aragonite (CaCO3)

Aragonite unit cell

Witherite (BaCO3)

Witherite Structure

Quartz (SiO2)

 
a-quartz structure

Magnesium Silicate Perovskite (MgSiO3)
Cubic (Pm-3m)

Silicate Perovskite Structure

Fe3Si

Fe3Si Structure


Nahcolite (NaHCO3)
e.g., baking soda

Nahcolite Structure

Phonons animations were created using Jmol, a free Java molecular graphics package. You may need to install or upgrade Java on your computer to see these animations. 

The research shown on these pages was made possible by support from the National Science Foundation, the NASA Astrobiology Institute, and UCLA.