Low-temperature acoustics

Solid materials

Acoustic measurements have been used to characterize the properties of a wide variety of solid-state materials, such as metals, dielectric crystals, amorphous solids, and magnetic materials. A measurement of the velocity of sound in a substance gives information on its elastic properties, while the attenuation of the sound characterizes the interaction of the lattice vibrations with the electronic and structural properties of the material. Ultrasonic frequencies, in the range from 20 kHz to 100 MHz and above, are commonly employed in these measurements because of the ease of generating and detecting the sound with piezoelectric quartz crystals.

Because the sound velocity effectively measures elastic constants, such measurements are used to characterize phase transitions in crystals where the structure of the lattice changes. The attenuation of sound in many crystals is due to defects and impurities in the crystal lattice and provides information on such structures. In a metal at very low temperatures, the dominant source of attenuation is the interaction of the sound with the conduction electrons. See Crystal, Lattice vibrations, Phase transitions, Phonon, Sound absorption

A large variety of magnetoacoustic effects are observed in metals and crystals. In these measurements, changes in the sound attenuation occur as the strength of a magnetic field applied to the sample is increased. One example is the phenomenon of nuclear acoustic resonance, resulting from the interaction of the nuclear spins in a crystal with vibrations of the lattice. There are also a number of other magnetoacoustic effects in metals which are useful in determining the orbits followed by the conduction electrons in the metal. See De Haas-van Alphen effect

Sound propagation is useful for studying amorphous materials. In materials such as silica glass (amorphous silicon dioxide, SiO₂), only two quantum energy levels are found to be important at low temperatures. These levels correspond to two nearly equivalent arrangements of the atoms, with one arrangement having slightly higher energy. An imposed sound field can cause a transition from one arrangement to the other. If the relaxation rate back to the original configuration is comparable to the sound frequency, there will be a net absorption of energy from the sound wave. A peak in the attenuation in silica glass near 50 K (-370°F) has been identified as being due to this process, and measurements as a function of frequency allow a determination of the relaxation rate. See Amorphous solid

When a metal is cooled below its superconducting transition temperature, there are striking changes in the attenuation of sound. At the transition some of the electrons near the Fermi surface begin to pair together, due to the attractive electron-phonon coupling. Once this occurs, the electrons can no longer exchange momentum with the lattice, and hence have zero resistance. This also means that the paired electrons no longer absorb energy from the sound wave, and the attenuation is from the remaining unpaired normal electrons. As the temperature is lowered well below the transition, the density of the unpaired electrons drops rapidly, and the attenuation becomes very small. See Superconductivity

Superfluid helium

Sound propagation has been extensively used to probe many of the unusual properties of superfluid helium. The novel features of the superfluid (zero viscosity and entropy) give rise to a rich variety of different types of sound which can propagate in the superfluid helium. Five distinct sound modes have been identified and observed experimentally. The sound velocities of a number of these modes are shown in the illustration as a function of temperature.

First sound is a pressure wave which propagates in the bulk liquid. It is quite similar to sound in ordinary fluids.

Second sound is an unusual type of wave: it is a temperature wave in the bulk superfluid. In this mode the normal fluid and superfluid move in opposite directions. This keeps the density constant, and hence there are no pressure oscillations in the wave (as in first sound); but because only the normal fluid carries entropy, there are oscillations in the entropy and thus in the temperature of the liquid. See Second sound

Third sound is a wave which propagates in very thin films of helium. The third sound is a wave in which the thickness of the film varies, somewhat like waves in a tank of water. Because the films are so thin, only the superfluid can move, the normal fluid being immobilized by its viscosity.

Fourth sound is a pressure wave which propagates in superfluid helium when it is confined in a porous material such as a tightly packed powder. In such a situation the normal fluid is immobilized, and only the superfluid can flow freely because of its zero viscosity (the porous materials are often called superleaks for this reason). The fourth sound is analogous to first sound because it involves density and pressure oscillations.

Fifth sound is a temperature wave which can propagate in helium confined in a superleak. It is analogous to second sound, except that again only the superfluid component can flow. See Liquid helium, Superfluidity