Normal modes in glasses

Thermal energy causes the ions in a metallic glass, as in a crystal, to vibrate about their mean positions; in a glass there may be additional ionic motion in which ions actually shift between two or more sites but we ignore this for the present. The complex vibrational motion can, as a first approximation, be resolved into a superposition of normal modes, each of which is to this approximation a harmonic motion independent of all the other modes. This ignores anharmonicity and tunnelling modes, which can be very important in glasses. For our present purposes we take the normal mode description as adequate but bear in mind its limitations. These modes introduce into the solid changes in charge density that are periodic in time and cause corresponding changes to the potential seen by the conduction electrons. These changes scatter the electrons.

When such harmonic motions are quantised we associate with each mode phonons in accordance with the intensity of the particular mode. In disordered materials the normal modes of vibration exist although they are not necessarily extended waves; some may be localised to the neighbourhood of particular ions. As long as the vibrations are quasiharmonic, however, phonons are a valid concept in disordered materials although it may not be possible to assign to them a well-defined wave vector if the mode is strongly localised.