Phonon Studies
Authors: Delaire Olivier A. , Stassis C. 
Published: October 2012

Until the beginning of the 20th century, the models used to understand the properties of solids were based on the assumption that atomic nuclei are fixed at their equilibrium positions. These models have been very successful in explaining many of the low‐temperature properties of solids, and especially those of metals, whose properties are determined to a large extent by the behavior of the conduction electrons. Many well‐known properties of solids (such as sound propagation, specific heat, thermal expansion, thermal conductivity, melting, and superconductivity), however, cannot be explained without considering the vibrational motion of the nuclei around their equilibrium positions. The study of lattice dynamics ‐‐or phonons, which are the quanta of the vibrational field in a solid ‐‐ was initiated by the seminal papers of Einstein, Debye, and Born and von Kármán. Initially, most of the theoretical and experimental studies were devoted to the study of phonons in crystalline solids, as the name lattice dynamics implies. At present, the field encompasses the study of the dynamical properties of solids with defects, surfaces, and amorphous solids. It is impossible in a single article to present even a brief overview of this field. The discussion that follows will therefore be limited to a brief outline of the neutron scattering techniques used for the study of phonons in crystalline solids.

Indirect information about the lattice dynamical properties of solids can be obtained from a variety of macroscopic measurements. For instance, in some cases, the phonon contribution to the specific heat or resistivity can be easily separated from other contributions and can provide important information about the lattice dynamical properties of a solid. In addition, measurements of sound velocities are particularly useful, since they provide the slopes of the acoustic phonon branches. Since such macroscopic measurements are relatively easy and inexpensive to make in a modern materials science laboratory, they should, in principle, be performed before one undertakes a detailed phonon study by spectroscopic techniques. Direct measurement of the frequencies of long‐wavelength optical phonons can be obtained by Raman scattering and infrared spectroscopy. These experiments provide essential information for solids containing several atoms per unit cell and should be performed, if possible, before one undertakes a time‐consuming and expensive detailed neutron scattering study. Also, for simple solids, information about the phonon dispersion curves can be obtained from x‐ray diffuse scattering experiments.

Presently, the most powerful technique for the study of phonons is the inelastic scattering of thermal neutrons. The technique directly determines the dispersion relation, that is, the relationship between the frequency and propagation vector of the phonons. Its power was demonstrated by Brockhouse and Stewart, who, following a suggestion put forward by Placzek and Van Hove, measured the dispersion relation of aluminum. The triple‐axis neutron spectrometry (TAS) developed by Brockhouse has since been the work‐horse technique for dispersion measurements. More recently, intense pulsed neutron sources have enabled time‐of‐flight spectrometry (TOF) to map single‐crystal excitations across large volumes in reciprocal space, offering great complementarity with the more focused TAS measurements. Additionally, inelastic x‐ray scattering, based on principles similar to the triple‐axis neutron technique, now enables the study of considerably smaller crystals.