Inelastic Neutron Scattering and Dynamics in Solids and Liquids

Abstract

The concept of lattice waves, called phonons, propagating through single crystals goes back to Debye and Born-von Kármán (1912). In fact, it can be traced back even further. The phonons appear as the elementary excitations of the lattice, and each one is characterized by its wave vector, frequency, and polarization direction. In the simplest case, where we have only one atom per unit lattice cell, there are for each wave vector three different phonons, one essentially longitudinal and two essentially transverse. These are called acoustic phonons. For more than one atom per unit cell, there are a greater number of phonons for a given wave vector. In the alkali halides, which contain two atoms per unit cell, we have three acoustic branches and three other branches, called optical phonons. They represent motions where neighboring atoms move out of phase even for long-wavelength vibrations and thus give rise to an oscillating electric dipole moment within each unit cell. For this reason, the very-long-wavelength optical phonons are responsible for strong infrared absorption in alkali halides. The long-wavelength acoustic phonons affect the elastic properties of the crystal, and the short-wavelength acoustic phonons determine the thermodynamic properties of the lattice—that is, the free energy, specific heat, entropy, etc.