Hypersound

elastic waves with frequencies ranging from 10⁹ to 10¹² or 10¹³ Hz; the high-frequency portion of the spectrum of elastic waves. The physical nature of hypersound is no different from that of ultrasound, whose frequency ranges from 2 x 10⁴ to 10⁹ Hz. However, owing to the higher frequencies—and therefore shorter wavelengths—of hypersound as compared to ultrasound, the interaction between hypersound and the quasiparticles of the medium, such as electrons, phonons, and magnons, becomes considerably more important.

The hypersonic frequency range corresponds to the frequencies of electromagnetic oscillations in the decimeter, centimeter, and millimeter ranges (the so-called superhigh frequencies, or SHF). By using the techniques for generating and receiving SHF electromagnetic oscillations, it has been possible to obtain and begin the study of hypersonic frequencies of ~ 10¹¹ Hz.

A frequency of 10⁹ Hz in air at normal atmospheric pressure and room temperature corresponds to a hypersonic wavelength of 3.4 x 10^-5 cm, that is, this length is on the same order as the mean free path of molecules in air under these conditions. Since elastic waves can only propagate in an elastic medium when their wavelengths are noticeably longer than the mean free path in gases (or longer than the interatomic distance in liquids and solids), hypersonic waves do not propagate in air and gases at normal atmospheric pressure. In liquids the attenuation of hypersound is very high and the propagation range is small. Solids in the form of single crystals are relatively good conductors of hypersound but mainly at low temperatures only. Thus, for example, even in a single crystal of quartz, which has notably low attenuation for elastic waves, a longitudinal hypersonic wave at a frequency of 1.5 x 10⁹ Hz propagating along theZ-axis of the crystal is reduced in amplitude by a factor of 2 over a distance of only 1 cm at room temperature. However, there are better hypersonic conductors than quartz, in which the attenuation of hypersound is considerably smaller (for example, single crystals of sapphire, lithium niobate, and ferric-yttrium garnet).

For a long time hypersonic waves could not be produced by artificial means (this being one of the reasons that “hypersound” was isolated from the rest of the elastic wave spectrum), and therefore the hypersound produced thermally was studied. A solid crystalline body can be represented by a certain three-dimensional space-lattice with atoms or ions at the lattice points. The thermal motion is a continuous and random vibration of these atoms about their equilibrium positions. Such vibrations can be regarded as a totality of longitudinal and transverse plane elastic waves of varied frequencies—from the lowest natural frequencies of the elastic vibrations of a given body up to frequencies of 10¹²—10¹³Hz (the elastic wave spectrum ends here)—that propagate in all possible directions. These waves are known as Debye waves, or thermal phonons.

A phonon is an elementary excitation of a crystal lattice or quasiparticle with an energy hv and momentum hv/c, where v is the frequency, c is the velocity of sound in the crystal, and h is Planck’s constant. A plane elastic wave of a certain frequency corresponds to a phonon just as a plane electromagnetic wave of a certain frequency corresponds to a photon. Thermal phonons have a broad frequency spectrum whereas artificially produced hypersound can have one specific frequency. Consequently, artificially generated hypersound can be represented as a flux of coherent phonons. In liquids the thermal motion has characteristics resembling those of the thermal motion in solids so that in liquids, just as in solids, the thermal motion continuously generates incoherent hypersonic waves.

Until it became possible to produce hypersound artificially, the study of hypersonic waves and their propagation in liquids and solids was carried out chiefly by an optical method. The presence of thermally produced hypersound in an optically transparent medium causes light to be scattered with the formation of several spectral lines that are displaced by the hypersonic frequency v, the so-called Mandel’-shtam-Brillouin scattering (combination scattering). Studies of hypersound in a number of liquids has led to the discovery of the dependence of the velocity of the propagation of hypersound in them on frequency and anomalous absorption.

The modern methods of generating and receiving hypersound are based mainly on the use of piezoelectric phenomena (the formation of electric charges on the surface of a piezoelectric crystal, such as a quartz plate that is cut in a certain direction when acted upon by mechanical deformation and vice versa, the deformation of a crystal when placed in an electric field) and magnetostriction phenomena (changes in the shape and dimensions of a body when magnetized and changes in the magnetization with deformation).

One of the most common methods of generating hypersound is to excite it from the surface of a piezoelectric crystal. For this purpose, the end face of the piezoelectric crystal is placed in that part of a resonator where the intensity of the SHF electric field is at a maximum. If the crystal is not piezoelectric, a thin piezoelectric film such as cadmium sulfide is deposited on its end face. Under the action of the SHF electric field, an alternating deformation is produced at the same frequency, and this propagates in the crystal in the form of a longitudinal or shear wave at a hypersonic velocity. The plane surface of the crystal itself serves in this case as the source of this wave. In turn, a mechanical deformation causes an electric charge to appear on the crystal’s surface and, consequently, the reception of hypersound can thus be achieved.

When elastic waves are propagated in the crystals of dielectrics that do not contain free charge carriers, these waves are attenuated due to their nonlinear interaction with thermal phonons. The nature of this interaction and, consequently, the nature of the attenuation depend on the frequency of the propagating waves. If the frequency is low (the ultrasonic region), the wave only disturbs the equilibrium distribution of the thermal phonons, which is then restored by the random inelastic collisions among the thermal phonons; here there is an energy loss in the wave. For high hypersonic frequencies, direct nonlinear interaction occurs between the hypersound that is artificially produced and the hypersound of thermal origin. The coherent phonons collide inelastically with the thermal phonons and transfer their energy to them, thus causing a loss of energy. As the temperature decreases, the thermal phonons become “frozen” and decrease in number. Accordingly, the attenuation of both ultrasound and hypersound is reduced substantially as the temperature is decreased.

When hypersound propagates in crystals of semiconductors and metals where there are conduction electrons, it interacts with the electrons as well as with the thermal phonons. An elastic wave that propagates in such crystals almost always carries a local electric field with it at the velocity of sound. This is related to the fact that the wave deformation of the crystal lattice displaces the atoms or ions from their equilibrium position, which causes a change in the intracrystalline electric fields. The electric fields thus developed change the motion of the conduction electrons and their energy spectrum. On the other hand, if for any reason changes in the state of the conduction electrons occur, the intracrystalline fields are altered, thus causing deformations in the crystal. In this manner, the interaction of conduction electrons with the phonons is accompanied by an absorption or emission of phonons.

The study of hypersonic attenuation by conduction electrons in metals has made it possible to investigate such important properties of metals as relaxation time, the Fermi surface, and the energy gap in superconductors.

The interaction between artificial, or coherent, phonons and electrons becomes important in the ultrasonic frequency region and especially in the hypersonic frequency region in semiconductors having piezoelectric properties (for instance, cadmium sulfide crystals, which have a very strong interaction between phonons and conduction electrons). If a constant electric field is applied to the crystal with a strength such that the velocity of the electrons is somewhat greater than that of the elastic wave, the electrons will then overtake the elastic wave, thus transferring their energy to it and strengthening it—that is, the elastic waves will be amplified. The interaction between coherent phonons and electrons also results in the acoustoelectric effect, a phenomenon in which phonons, while transferring their momentum to the electrons, create in the crystal a constant potential and direct current. In the case where electrons transfer energy to the elastic wave, an acoustic electromotive force is also produced, but it has the opposite sign.

In considering the interaction between hypersound and electrons, attention must be given to the fact that electrons have, in addition to a mass and a charge, an intrinsic mechanical moment (spin) and the associated magnetic moment as well as an orbital magnetic moment. A spin-orbit interaction occurs between the orbital magnetic moment and the spin: if the inclination of the orbit changes, the direction of the spin also changes to some extent. The passage of hypersound of appropriate frequency and polarization can produce a change in the magnetic state of the atoms. Thus, at hypersonic frequencies on the order of 10¹⁰ Hz, the interaction between hypersound and the spin-orbital system in paramagnetic crystals is expressed, for example, in the phenomenon of acoustic paramagnetic resonance (APR), which is similar to electron paramagnetic resonance (EPR), and consists in the selective absorption of hypersound caused by the transition of atoms from one magnetic level to another. With the aid of APR, it is possible to study the transitions between such levels in the atoms of paramagnets that are forbidden for EPR.

By using the interaction between coherent phonons and the spin-orbit system, it is possible at low temperatures to amplify and generate hypersonic waves in paramagnetic crystals using a principle similar to that of quantum generators. In magnetically ordered crystals (ferromagnetics, anti-ferromagnetics, and ferrites) the propagation of hypersonic waves causes spin waves to appear (a change in the magnetic moment that is transmitted in the form of a wave) and vice versa, a spin wave causes a hypersonic wave to appear. Thus, one type of wave creates another type so that in the general case neither pure spin nor elastic waves are propagated in such crystals, but rather coupled magnetoelastic waves.

The interaction between hypersound and light is manifested, as mentioned above, in the scattering of light on the hypersound of thermal origin, but the effect of this interaction is very low. However, by employing a powerful light source such as a pulse from a powerful ruby laser, it is possible to obtain a pronounced amplification of an elastic wave by the incident light. As a result, an intense hypersonic wave with a power of several tens of kW can be generated in a crystal. In turn, the amplified elastic wave will scatter the incident light so that under certain conditions the intensity of the more strongly scattered light may be on the same order of magnitude as the incident light; this phenomenon is known as induced Mandel’shtam-Brillouin scattering.

Thus, the properties of hypersound permit it to be used as a tool for studying the state of matter. It is of particularly great value in solid-state physics. In technological applications, which are only now beginning to be developed, it has already found an important use in so-called acoustic delay lines for the SHF region (ultrasonic delay lines).