Phonons and reciprocal space

Vibrations

Recall that vibrations are dene as the oscillation (or movement) of atoms in a molecule (or crystal) in periodic motion. In the crystalline case, these periodic vibrations are known as phonons. The simplest approximation to describe this periodic motion (i.e. phonons) is that of the harmonic oscillator that is shown in Fig. 1 and described by Eq. 1.

	$x(t) = Acos(\omega t + \phi)$ (Eq. 1)
Fig. 1: Animation of a simple harmonic oscillator.	$A$ and $\phi$ is the amplitud and the phase respectively and $\omega$ is the angular frequency