Phonon Visualization

In crystalline solids, atoms oscillate about their equilibrium positions in a periodic manner. When these lattice vibrations are treated quantum mechanically, they are described as discrete vibrational quanta, known as phonons, which behave as bosonic quasiparticles.

In this section, the lattice vibrations of a unit cell of a respective crystal structure are visualized. More specifically, we consider optical phonons at the Γ-point of the Brillouin zone of the corundum crystal structure, which is, for example, found in sesquioxides such as α-Ga₂O₃ or α-In₂O₃ (see also the section Novel Oxides).

The trigonal rhombohedral corundum crystal structure exhibits a total of 13 IR or Raman active phonon modes, which are as follows:

IR active modes: E_u(1), E_u(2), E_u(3), E_u(4) and A_2u(1), A_2u(2)

Raman active modes: E_g(1), E_g(2), E_g(3), E_g(4), E_g(5) and A_1g(1), A_1g(2)

In the following, all phonon modes are displayed by one static figure of the unit cell, containing arrows to indicate the displacement of each atom, and one dynamic animated GIF that directly shows the vibrations. In all cases, all atoms exhibit vibrational motion. If static figures do not show arrows for all atoms, this is because the vibration amplitude is too small to be visible compared to that of other atoms in the same mode. If atomic bonds appear to vanish during the animated vibration, this is due to the choice of bond length in the animation software and does not reflect actual physical behavior. Note also that for E phonon modes, which are doubly degenerate, only one of the two modes is shown.

All static and dynamic figures presented here were generated from the eigendisplacements obtained from ABINIT calculations of the phonon density of states of α-In₂O₃ by Cuscó et al., Appl. Phys. Lett. 121, 062106 (2022), using XCrySDen (See: Kokalj, J. Mol. Graphics Modelling, 1999, 17, 176--179.)