Current Problems in the Application of Ultrasound

S. Ya. Sokolov

In recent years ultrasonic waves have found broad application in various fields of physics and technology. In turn, the brilliant successes of physics and radio engineering have contributed to the rapid development of ultraacoustics. At the present time the nature of ultrasonic vibrations, their properties, and the phenomena associated with the action of ultrasound on matter have been studied in sufficient depth. The range of ultrasonic frequencies has been considerably expanded; methods have been developed for obtaining ultrahigh (hypersonic) frequencies on the order of \(f = 1.3 \cdot 10^9\) Hz. This frequency, of course, is not the limit, and the near future will show what can be achieved in this direction. It is to be hoped that it will be possible to obtain ultrasonic vibrations close in frequency to long infrared rays.

The production of hypersonic waves opens up new, far-reaching possibilities for studying the nature of thermal vibrations and the mechanism of scattering of light by a medium. In addition, they will evidently find a number of important technical applications.

The present article considers the principal questions of the application of ultrasound being developed in our laboratory, as well as the results achieved by us in this field up to the present time.

1. Absorption of Ultrasonic Vibrations in Solids

The absorption of ultrasonic waves in solids has been considered theoretically more than once; however, experimentally it has been studied very little, since the technique for obtaining high-frequency ultrasonic vibrations had not until recently been sufficiently developed. Therefore the theoretical predictions still require experimental verification to a considerable extent.

Most theoretical work is devoted to questions of the propagation and absorption of hypersonic waves of frequencies on the order of \(10^{10}\)—\(10^{12}\) cps and higher in crystals. At the present time the frequency of ultrasonic vibrations obtained in our laboratory has come considerably closer to the indicated value. Below we briefly set forth the results of experiments on the propagation and absorption of ultrasound in various media.

If the medium under investigation is homogeneous (for example, single crystals), then the absorption of ultrasonic waves is small and is determined by the coefficients of viscosity and thermal conductivity. If the medium is inhomogeneous (for example, metals), then the absorption of ultrasound increases as the degree of inhomogeneity grows and may become very large, which is especially noticeable in metals of coarse-grained structure.

This influence of the degree of inhomogeneity of the medium on the absorption of ultrasound should evidently be explained as follows.

In a metal, elastic inhomogeneities arise at the boundaries of contact of the crystals composing it, the development of which depends on the size of the crystals and their orientation. During the propagation of ultrasonic waves, temperature fluctuations are formed at the boundaries of contact of the crystals; these lead to the formation of local heat flows, which increases the entropy of the oscillating body, i.e., increases the losses of ultrasonic energy.

Since the thermoelastic properties depend on the sizes of the crystals and their orientation, the arising losses \(\Delta E\) of ultrasonic energy will likewise depend on the sizes of the crystals and their orientation, i.e., on the structure of the medium. Therefore

\[ \Delta E=\varphi(d,a), \]

where \(d\) is the average grain size and \(a\) is a parameter determining the orientation of the grains.

The losses of ultrasonic energy also depend on the wavelength \(\lambda\), more precisely, on the parameter \(k\), where

\[ k=F(d/\lambda). \]

It follows from experiment that, as the ratio \(d/\lambda\) increases, the energy losses increase, becoming noticeable already at \(d/\lambda<1\).

In metals whose structure is such that the sizes of the crystals are comparable with the wavelength or greater than it \((d/\lambda \geq 1)\), especially strong absorption of ultrasound is observed and the medium becomes “slightly transparent” to it. In this case, the strong absorption of ultrasound is explained not only by the reasons indicated above, but chiefly by the influence of diffuse scattering of ultrasonic waves, whose propagation under these conditions may be likened to the propagation of light in a turbid medium, which is confirmed by corresponding measurements. However, in meas—

...one should take into account that ultrasonic waves are repeatedly reflected from crystal faces, are superposed on one another with different amplitudes and phases, and produce a certain resultant amplitude. In this case the amplitudes and phases of the vibrations must be regarded as random independent quantities, and theoretically the problem of the propagation of ultrasound in the medium should be treated as a statistical one.

In order, as far as possible, to avoid the influence of multiple reflection from crystal faces, we used ultrasonic pulses of duration \(1\ \mu\text{sec}\) at a frequency \(f = 18 \cdot 10^6\ \text{cps}\), which we had previously used for defectoscopy1. The ultrasonic pulses passed through the medium under investigation, were amplified, and were recorded by a cathode-ray oscillograph.

In a homogeneous medium with a small absorption coefficient, ultrasonic pulses, slowly attenuating, are repeatedly reflected from the opposite faces of the specimen. In this case, on the oscillograph screen we see a series of regular pulses equidistant from one another. This phenomenon is similar to the reverberation of sound in an enclosed room.

The influence of elastic anisotropy on the absorption of ultrasound was investigated on various specimens of iron, copper, and other metals of fine-grained and coarse-grained structure. The latter was obtained by thermal and mechanical treatment of the specimens. In addition, specimens with pronounced anisotropy were prepared from Armco iron; these were “examined by transmission” in the direction of the elongated fibers and perpendicular to them.

It was observed that, in the direction of the elongated fibers, ultrasonic pulses penetrated through the specimen, whereas in the direction perpendicular to the fibers the pulses were completely absorbed (their penetration through the specimen was not observed on the oscillograph). Nor was penetration of pulses detected through other specimens with a coarse-grained structure.

The same metal specimens were investigated a second time by passing through them ultrasonic vibrations of a lower frequency, \(f = 4 \cdot 10^6\ \text{cps}\). At this frequency the penetration of pulses was recorded, which should be explained by a reduction of diffuse scattering as a result of a decrease in the ratio \(d/\lambda\) by approximately a factor of 4.

In order to elucidate further the influence of grain size on the absorption of ultrasound, iron specimens with different structures were investigated. Ultrasonic waves of frequency \(f = 4 \cdot 10^6\ \text{cps}\) were passed through each specimen, and with the aid of the oscillograph the relative magnitude of the pulses emerging from the metal was measured.

The results of the measurements are shown in the curve of Fig. 1, a, where the abscissa axis gives the average grain sizes in the specimens, and the ordinate axis the magnitudes of the pulses that had passed through the specimens.

On Fig. 1, b and 1, c are shown photographs of polished sections of specimens corresponding to points b and c on the curve of Fig. 1, a.

From the experiments performed, which so far have had a qualitative character, it follows that the absorption of ultrasound depends extremely strongly on the presence in the medium of elastic inhomogeneities and on their dimensions.

The mechanism of absorption of ultrasonic vibrations in a fine-crystalline medium may be explained approximately as follows². If the dimensions of the individual crystallites are considerably smaller than the wavelength of the ultrasound \((d \ll \lambda)\), then it may be assumed, to a good approximation, that each crystallite is under the action of a uniformly distributed pressure, which, owing to the anisotropy of the crystallite and the boundary conditions at its surface, produces in it a nonuniform deformation. Thus, the deformation will vary appreciably over distances of the order of \(d\). The arising

Fig. 1. a—dependence of the absorption of an ultrasonic pulse on the dimensions of crystalline grains; b and c—microphotographs of polished sections of specimens corresponding to points b and c on curve a.

temperature gradient will be of the order of \(T/d\), where \(T\) is the temperature difference arising as a result of the deformation. Therefore the influence of thermal conductivity increases strongly, while the influence of viscosity remains the same, so that the absorption due to thermal conductivity becomes considerably greater than the absorption due to viscosity. According to this theory, the coefficient of ultrasound absorption does not depend on the frequency in the case when the temperature equalization time (the thermal-conductivity relaxation time) \(\tau = d^2/\sigma\), where \(\sigma\) is the coefficient of thermal conductivity, is large in comparison with the period of vibration; if \(\tau\) is small in comparison with the period of vibration, then the absorption coefficient is proportional to the square of the frequency,

If heat exchange is taken into account not only within the crystallite, but also at the boundaries between individual crystallites, then the absorption coefficient for \(d \ll \lambda\) will be proportional to the square root of the frequency.

As has already been indicated above, if the absorption of ultrasound in a medium is small, then multiple reflection of gradually decaying pulses from the opposite faces of a crystal is observed. The number of observed reflections can serve as a measure of the absorption of ultrasonic waves. The attenuation is especially small and, correspondingly, the number of observed reflections is large if the ultrasonic waves propagate in such a homogeneous medium as single crystals. This provides a convenient method for measuring the absorption of ultrasound.

The observations were carried out at frequencies lying in the range from \(f = 1.6 \cdot 10^7\) Hz to \(f = 1 \cdot 10^9\) Hz. Single crystals containing no internal inhomogeneities were selected. A quartz plate (pressed tightly against the single crystal) with dimensions many times smaller than those of the crystal under investigation was excited and served as the source of ultrasonic waves. In this case the ultrasonic pulse was reflected from two opposite faces tens and even hundreds of times.

In Fig. 2, \(a\) an oscillogram is shown of pulses repeatedly reflected from the faces of a quartz single crystal; the ultrasonic waves had frequency \(f = 10^8\) Hz and propagated in the direction of the optical axis. The pulses were absorbed considerably more strongly, and the number of reflected pulses decreased sharply, if inhomogeneities (twinning) were present in the quartz crystal.

The propagation in quartz single crystals of ultrasonic waves with frequency \(f = 10^9\) Hz was also investigated, the absorption being somewhat greater. The corresponding picture for propagation along the optical axis is shown in Fig. 2, \(b\).

The frequency \(f = 10^9\) Hz was obtained from a small piezoquartz plate excited at the sixteenth overtone. The length of the ultrasonic wave in quartz at this frequency is

\[ \lambda = \frac{c}{f} = \frac{5 \cdot 10^5}{10^9} = 5 \cdot 10^{-4}\ \text{cm} = 5\ \mu . \]

Let us note that the described method of observing multiply reflected pulses can be used practically to identify the degree of inhomogeneity of single crystals. If the crystal is homogeneous and contains no inclusions, twins, etc., then the pattern of reflected pulses will be uniform, with gradual attenuation of the pulses. If, however, inhomogeneities are present in the single crystals, then the pulse pattern will be irregular; the pulses will be located at unequal distances and their magnitude will change discontinuously, with sharp attenuation.

a

b

Fig. 2. Multiple reflection of pulses of ultrasonic waves during propagation along the optical axis of a quartz single crystal:
a—at frequency \(f = 10^8\) Hz, b—at frequency \(f = 10^9\) Hz.

It should be pointed out that in a large number of the quartz single crystals we tested, both longitudinal and transverse waves were excited simultaneously. In Fig. 3, a, which pertains to such a case, the difference in the propagation velocity of the longitudinal and transverse waves is clearly visible.

a

Of particular interest is the pattern of the arrangement of the pulses in Fig. 3, b. As can be seen from the figure, there are two groups of pulses here. The group of pulses closely adjacent to one another and located in the left-hand part of the figure corresponds to the longitudinal type of waves. The second group of pulses, spaced much more sparsely (approximately by a factor of 4.5), evidently corresponds to another type of waves, propagating with a velocity 4.5 times smaller. Similar phenomena were observed on many quartz specimens. Should this phenomenon be attributed to a new type of waves (of the capillary type), propagating in quartz with a velocity on the order

b

Fig. 3. Simultaneous excitation of two types of waves.

1250 m/sec, or whether this phenomenon should be explained by interference causes, will be shown by further experiments.

Figure 4 shows ultrasonic pulses in single crystals of NaCl and KBr.

Experiments on the propagation of ultrasonic waves in single crystals of piezoelectric quartz in the direction of the three axes (optical, electrical, and mechanical) showed that the absorption coefficient of ultrasound has an anisotropic character, i.e., it has different values for different directions[^4]. Its minimum value was observed in the direction of the optical axis, and its maximum value in the direction of the electrical axis.

a

b

Fig. 4. Ultrasonic pulses in single crystals of NaCl (a) and KBr (b).

In some single crystals of quartz the anisotropy of the absorption coefficient was expressed extremely strongly; for example, in the direction of the optical axis the absorption coefficient of ultrasound was tens of times smaller than in the direction of the electrical axis. The corresponding pattern of multiple reflection of pulses of frequency \(f = 10^8\) Hz is shown in Fig. 5. In the direction of the optical axis (Fig. 5, a) the number of observed reflections was of the order of 50, while in the direction of the electrical axis (Fig. 5, b) it was of the order of 7. Fig. 5, c refers to the direction of the mechanical axis.

The anisotropy of ultrasound absorption, evidently, should be attributed partly to the piezoelectric properties of the crystals. In this connection it is necessary to take into account the considerations given in the work of Shaposhnikov[^6], where the possibility of the existence of a new type of relaxation phenomena is indicated. The phenomena arising in a crystal under the action—

Fig. 5. Anisotropy of the absorption coefficient:
a—reflections observed during propagation along the optical axis, b—along the electrical axis, c—along the mechanical axis.

...under the action of ultrasonic compression and rarefaction waves will produce piezoelectric polarization. If the crystal possesses electrical conductivity, this should lead to more intense absorption of ultrasonic waves and to the dispersion associated with it. However, to refine the data on this phenomenon, additional investigations are required.

Without going into the details of the dependence of ultrasonic absorption in single crystals on frequency, it should be pointed out that the expression for the absorption coefficient of longitudinal waves in an isotropic medium\(^5\)

\[ \gamma_l=\frac{\omega^2}{2\rho c_l^3} \left[ \left(\frac{4}{3}\eta+\zeta\right) + \frac{\chi T a^2\beta^3\left(c_l^2-\frac{4}{3}c_t^2\right)}{c_p^2} \right] \]

must, for the case of an anisotropic medium (piezoelectric single crystals), be replaced by another one, in which, instead of the first and second viscosity coefficients \(\eta\) and \(\zeta\), there will enter the components of the symmetric viscosity tensor of rank 4.

2. SCATTERING OF LIGHT BY ULTRASONIC WAVES

The study of the scattering of light by ultrasonic waves propagating in an elastic medium is of extremely great importance, since it makes it possible to understand more deeply the mechanism of scattering of light by inhomogeneities of the medium. Rayleigh\(^7\) showed that, if light is scattered by particles whose dimensions are much smaller than the wavelength of the scattered light, then the coefficient of scattering of light decreases inversely proportional to the fourth power of the wavelength and depends on the scattering angle \(\varphi\):

\[ K=\frac{\pi^2(\mu^2-1)^2}{2Nr^2\lambda^4}(1+\cos^2\varphi). \tag{2.1} \]

Subsequently Smoluchowski and Einstein\(^8\) considered the scattering of light by density fluctuations whose dimensions are small. The formula obtained by them for the case of an ideal gas coincides with Rayleigh’s formula.

For inhomogeneities whose dimensions are comparable with the wavelength or exceed it, Rayleigh’s law is not applicable, and the scattering coefficient depends substantially on the ratio of the dimensions of the inhomogeneities to the wavelength.

Brillouin\(^9\) considered the scattering of light as the result of multiple specular reflection from the fronts of thermal elastic waves propagating in the medium. Fluctuations of the density of the medium, produced by thermal elastic waves, cause corresponding changes in the refractive index of light. The intensity of light scattering in a given direction is determined by the wavelengths of the hypersonic waves \(\Lambda\). As in the case of reflection of X-rays from the planes of a crystal (condition

Bragg–Wulff), the beam of light scattered in this direction will have maximum intensity only when reflection occurs from “planes” located one from another (in the given direction) at a distance equal to half the wavelength of light \(\lambda\). This condition for light scattered at an angle \(\varphi\) has the form

\[ \sin \frac{\varphi}{2}=\frac{\lambda}{2\Lambda}. \tag{2.2} \]

Since the refractive index varies periodically in time, in accordance with the change in the density of the medium, the diffracted beam, as Brillouin and Mandelstam\({}^{10}\) showed, will be modulated, i.e., in addition to the fundamental frequency \(\nu_0\), side frequencies \(\nu_1\) and \(\nu_2\) will appear, equal to

\[ \nu_0 \pm \Delta \nu=\nu_0\left(1 \pm \frac{2v}{c}\sin \frac{\varphi}{2}\right), \tag{2.3} \]

where \(v\) and \(c\) are the velocities of propagation of sound and light in the medium\({}^{11}\). These side frequencies in the spectrum of the scattered light were observed experimentally. Measurements of \(\Delta \nu\) made it possible to determine the velocities of propagation of longitudinal and transverse hypersonic waves in a quartz single crystal.

When ultrasonic waves propagate in an elastic medium, regularly distributed and successive condensations and rarefactions are produced. In accordance with the periodic distribution of condensations and rarefactions of the medium, its refractive index also changes periodically. This occurs both for traveling and for standing waves. Thus, if the medium is transparent, these condensations and rarefactions form a kind of “diffraction grating.” The optical properties of such a grating change from point to point, to a first approximation, according to a sinusoidal law. The grating constant is equal to half the wavelength of the ultrasonic wave in the given medium. To obtain a diffraction pattern, it is necessary that the wavelength of the ultrasonic wave be sufficiently small.

The phenomenon of diffraction of light by ultrasonic waves was discovered almost simultaneously by Debye and Sears\({}^{12}\) and by Lucas and Biquard\({}^{13}\). Since at present it is possible to obtain ultrasonic waves with frequencies of the order of \(f=10^9\) Hz, the study of the diffraction of light by very short elastic waves is of particular interest. The scheme of the optical and electrical arrangement that makes it possible to detect this phenomenon is shown in Fig. 6.

Light from source 1 passes through a monochromator and, with the aid of lens 2, is focused on the slits 3 of the collimator. After the collimator, the light is transformed by a lens into a parallel beam and passes through the medium 5, in which ultrasonic oscillations have been excited. Upon emerging from the medium, the light falls on lens 6 and is collected in its focal plane 7. Here, on a screen (or

in the microscope) an image of the slit is observed. The direction of propagation of the ultrasonic waves is perpendicular or almost perpendicular to the direction of the light.

When ultrasonic oscillations are not excited in the medium, in the focal plane of lens 6 only the image of the slit is observed (the spectrum of zero order). When ultrasonic oscillations are excited, in addition to the zero-order spectrum, a number of side spectra of higher orders appear in the focal plane. In Fig. 7 diffraction patterns corresponding to different frequencies of ultrasonic waves are shown*).

Fig. 6. Diagram of the setup for observing diffraction of light by ultrasonic waves.

The distances between the spectra depend on the wavelength of the light and the wavelength of the ultrasound. At low frequencies of ultrasonic oscillations the diffraction spectra are located almost continuously, forming a blurred spot; as the frequency increases, the distances between the diffraction spectra increase.

The phenomenon of diffraction of light in such a grating can, in essence, be likened to diffraction on an ordinary optical grating. In 1932 Debye\(^{14}\) created an approximate theory which makes it possible to calculate the intensity of the first-order spectra. According to this theory, the intensity of the first-order spectra is proportional to the square of the amplitude of the ultrasonic wave. This dependence was confirmed experimentally for the case of very small amplitudes.

In an ultrasonic wave the dielectric constant of the medium \(\varepsilon\), and correspondingly the refractive index \(\mu\), vary periodically. Let

\[ \varepsilon = \varepsilon_0 + \varepsilon'; \qquad \mu = \mu_0 + \mu', \]

*) It is interesting to note that the quartz plate in which the phenomenon of diffraction of light at the frequency \(f = 2.98 \cdot 10^8\) cps was observed had a fundamental-tone frequency \(f = 2.67 \cdot 10^5\) cps.

Thus, the plate oscillated at an overtone of order

\[ n = \frac{2.98 \cdot 10^8}{2.67 \cdot 10^5} = 1120. \]

where \(\varepsilon_0\) and \(\mu_0\) are the mean values of the dielectric constant and the refractive index. For weak ultrasonic oscillations

Fig. 7. Diffraction of light by ultrasonic waves in quartz:
\(a\)—at frequency \(f = 2.98 \cdot 10^8\) Hz,
\(b\)—at frequency \(f = 4.81 \cdot 10^8\) Hz.

a linear dependence of \(\mu'\) on the density of the medium is assumed. Consequently, for sinusoidal traveling and standing waves one may write:

\[ \begin{aligned} \mu' &= \mu_1 \cos [\Omega t - (\mathbf{k}\mathbf{r})],\\ \mu' &= 2\mu_1 \cos \Omega t \cos (\mathbf{k}\mathbf{r}). \end{aligned} \tag{2.4} \]

Here \(\Omega\) and \(\mathbf{k}\) are the cyclic frequency and wave vector of the ultrasonic wave \((k=2\pi/\Lambda)\).

Under the assumption that \(\Omega \ll \omega\), i.e., that the change in \(\mu\) occurs very slowly in comparison with the frequency of light \(\omega\), the diffraction field is given by the formula

\[ E= -\frac{\mu_1}{\mu_0}\cdot \frac{k^2}{4\pi}\cdot \frac{x_0y_0z_0}{R_0}\, e^{i[(\omega\pm\Omega)t-(\kappa R_0)]} \frac{ \sin\left[\dfrac{\pi z_0}{\lambda}(\cos\theta-\cos\varphi)\right] }{ \dfrac{\pi z_0}{\lambda}(\cos\theta-\cos\varphi) } \times \]

\[ \times \frac{ \sin\left[\dfrac{\pi x_0}{\lambda}\left(\sin\theta-\sin\varphi\mp\dfrac{\lambda}{\Lambda}\right)\right] }{ \dfrac{\pi x_0}{\lambda}\left(\sin\theta-\sin\varphi\pm\dfrac{\lambda}{\Lambda}\right) } \cdot e^{\,i\kappa z_0/\lambda\,(\cos\theta-\cos\varphi)} . \tag{2.5} \]

Here \(\theta\) is the diffraction angle, \(\varphi\) is the angle of incidence of the light beam, \(R_0\) is the radius vector of the observation point, \(z_0\) is the path length of the light in the ultrasound region, and \(x_0\) is the width of the ultrasonic region.

The solution gives a satisfactory description of the diffraction of light for the case in which there are only spectra of the \(\pm 1\)-st order.

Raman and Nath\({}^{15}\) assumed that a light ray, passing through an ultrasonic grating, remains rectilinear. On the path between the planes \(z=0\) and \(z=z_0\), different rays traverse different optical thicknesses and leave the region of the ultrasonic waves with different phases. As a result, the electric field in the plane \(z=z_0\) has a constant amplitude and is modulated only in phase.

The assumption of phase modulation of the light rays easily explains the presence of higher-order spectra. It makes it possible, both for traveling and for standing ultrasonic waves, to give a simple calculation of the intensities of the spectra and of their frequency and phase relations.

The theory of Raman and Nath leads to the following conclusions:

1. The directions corresponding to the principal diffraction maxima are determined by the expression

\[ \sin\theta-\sin\varphi=\frac{n\lambda}{\Lambda}, \qquad n=0,\ \pm1,\ \pm2. \tag{2.6} \]

1. The intensity of the \(n\)-th spectrum in diffraction by a traveling wave is proportional to

\[ I_n^2\left[ \frac{2\alpha\Lambda}{\lambda\sin\varphi} \sin\left(\frac{\pi z_0}{\Lambda}\operatorname{tg}\varphi\right) \right]; \qquad \alpha=\frac{\mu_1}{\mu_0}, \tag{2.7} \]

where \(I_n\) is the Bessel function of the \(n\)-th order; in the case of normal incidence the intensity is proportional to

\[ I_n^2\left(\frac{2\pi\alpha z_0}{\lambda}\right). \tag{2.8} \]

1. The diffracted beams are monochromatic, and the frequency of the \(n\)-th spectrum is equal to

\[ \omega_n=\omega+n\Omega . \tag{2.9} \]

1. In the case of diffraction by a standing wave, the intensities of the diffracted beams change with time.

The positions of the spectra of higher orders, as well as their intensity, depend on the angle between the direction of the light beam and the direction of the ultrasonic waves, i.e., on the length of the path of the light in the ultrasonic field.

From (2.7) it is seen that the energy is distributed among the spectra symmetrically. However, the symmetry of the diffraction pattern with respect to the spectrum of zero order is not confirmed by experiment. As a more rigorous consideration shows, the Raman and Nath theory is applicable only in the case of long ultrasonic waves satisfying the condition

\[ \frac{k z_0}{\Lambda}\ll 1 . \tag{2.10} \]

S. M. Rytov\(^{16}\) investigated the case of small angles of incidence. He showed, theoretically and experimentally, that as the ultrasonic wavelength decreases the diffraction pattern approaches that which obeys the Bragg–Wulff condition and corresponds to selective reflection.

The transparent medium is divided by ultrasonic waves into a series of reflecting planes located at equal distances \(\Lambda/2\) from one another, onto which light waves fall at a certain angle. In those directions in which the light waves reflected from different planes coincide in phase, they reinforce one another, and thus the intensity of the light in these directions will be maximal. Thus, the maximum light intensity will be observed in those directions in which the path difference between two neighboring reflected rays is equal to an integral number of wavelengths. This path difference is equal to \(\Lambda \sin \varphi\), where \(\varphi\) is the angle between the direction of propagation of the light and the reflecting plane (the so-called “glancing angle”). When the grating constant and the wavelength of the incident light are changed, the maximum light intensity is obtained already at other glancing angles.

For observing the phenomenon of light diffraction by short ultrasonic waves,\(^{17}\) we first selected quartz plates which were readily excited and gave intense diffraction spectra of higher orders (more than 30 orders). A thin parallel beam of light, limited by a circular diaphragm, was passed through the plate. An electric voltage was applied to the quartz plate by means of a pair of electrodes of small dimensions. The light beam could be displaced in such a way that any region could be illuminated.

plates. The intensity of the diffraction spectra of higher orders was measured with the aid of a photocell.

As was to be expected, the greatest intensity of the diffraction spectra corresponded to the case when the light passed through the regions located between the electrodes. In this way it was possible to study the curve of the distribution of deformations in the quartz plate for a given arrangement of the electrodes.

The intensity and number of diffraction spectra depend on the temperature of the plate. To study this question, the quartz plate was placed in a special furnace, the temperature of which was varied from room temperature to \(600^\circ\text{C}\). When the temperature was increased from room temperature to \(210^\circ\text{C}\), the intensity and the number of spectra increased. With a further increase in temperature, a decrease in the intensity of the diffraction spectra became noticeable. The spectra became blurred. At a temperature of \(490^\circ\text{C}\), only a weak diffraction spectrum of the first order was observed, while at a temperature of \(535^\circ\text{C}\) the diffraction spectra disappeared entirely.

Since the distance between the diffraction spectra is a measure of the velocity of propagation of ultrasound in the medium under investigation, by measuring the distance between the spectra obtained from plates of different cuts one can obtain for them the ratio of the velocities of sound propagation.

In this way it was established that the ratio of the velocities of sound propagation for the parallel and perpendicular cuts has the following value:

\[ \frac{c_{\parallel}}{c_{\perp}} = 1.21 \div 1.25, \]

where \(c_{\parallel}\) and \(c_{\perp}\) are the velocities of sound propagation in the directions of oscillation, respectively for the parallel and perpendicular cuts.

In some quartz plates, when they were excited at one frequency, diffraction spectra of higher orders corresponding to two types of oscillations were observed simultaneously; this could be readily established by measuring the distances between spectra of the same order. The simultaneous excitation of longitudinal and transverse waves was noted, which we had previously observed by the method of ultrasonic localization.

In Fig. 8 are shown the diffraction spectra obtained from a quartz plate with simultaneously excited oscillations of two types.

For the investigation of the diffraction of light in a liquid medium, the liquid under study was poured into a cuvette with transparent walls. The following were investigated: alcohol, glycerin, water, turpentine, etc.

The clearest picture of light diffraction was obtained in turpentine, as a result of which, in subsequent experiments, the investigation was carried out with turpentine.

If three quartz plates emit plane waves at one frequency in three mutually perpendicular directions, then, under the action of ultrasonic vibrations, condensations are formed in the medium, i.e., scattering centers, which will be distributed in space at the vertices of elementary cubes. Spatial diffraction gratings can also be obtained in a solid transparent medium, for example in quartz. For this purpose the excitation of the quartz is carried out by the corresponding arrangement of electrodes on the surface of the quartz cube.

Fig. 8. Diffraction spectra obtained with simultaneous excitation of vibrations of two types.

The phenomenon of diffraction of light by ultrasound has numerous applications both in physics and in technology. One of them appears to be especially important, namely the use of the phenomenon of diffraction of light by ultrasound as a method of modulating light. This method was proposed and developed by the author as early as 1933.¹⁸

The idea of the method is as follows: a powerful beam of ultrasonic rays from a quartz plate is emitted into a liquid medium (kerosene). An intense beam of parallel light rays passes through the liquid medium in a direction perpendicular to the propagation of the ultrasonic vibrations. As in an ordinary diffraction setup, spectra of higher orders are obtained. If a modulated electrical voltage is applied to the quartz plate

\[ E = E_0 (1 + k \cos \Omega t)\cos \omega_0 t, \tag{2.11} \]

where \(\omega_0\) is the vibration frequency of the quartz, \(\Omega\) is the modulating frequency, and \(k\) is the coefficient of electrical modulation, then the intensity of the zero-order spectrum and the intensity of the diffraction spectra will oscillate with the modulating frequency \(\Omega\).

Let us denote by \(I\) the intensity of the total light flux passing through the modulator, by \(I_0\) the intensity of the zero-order spectrum, and by

\[ \sum_{i=\pm 1}^{i=\pm n} I_i \]

the intensity of the spectra of higher orders \((i = 1, 2, \ldots)\). Since

\[ I = I_0 + \sum_{i=\pm 1}^{i=\pm n} I_i, \]

an increase in the intensity of the diffraction spectra causes a corresponding decrease in the intensity of the zero-order spectrum \(I_0\), and conversely. For the purposes of light modulation one may use either the spectra of higher orders or the zero-order spectrum. In our investigations the zero-order spectrum was used.

To ensure a wide band of modulated oscillations, the damping decrement of the quartz vibrator must be large. For purposes of sound recording it is sufficient to confine oneself to a bandwidth of the order of \(15 \cdot 10^3\) cycles. For television purposes the bandwidth must be larger. At a large amplitude of oscillation of the quartz plate, the phenomenon of impact of the quartz surface against the liquid is observed. During the process of oscillation, the quartz is in contact with the liquid not throughout the entire period, but only during some part of it. This circumstance entails nonlinearity of the oscillations. In addition, in liquids under the action of ultrasonic waves, convection currents are observed, which also distort the diffraction pattern.

To avoid these shortcomings, it is advisable to use the vibrating quartz plate itself as the light modulator. This type of modulator provides the necessary intensity of the modulated light, reliability in operation, and absence of nonlinear distortions. If the excitation frequency of the quartz and the decrement are sufficiently large, then such a modulator provides modulation with a passband of several tens of kilocycles.

3. ULTRASONIC MICROSCOPE

In connection with the successful development of ultraacoustics and the production of very short ultrasonic waves, of the order of the wavelengths of visible light, it appears possible to create an ultrasonic microscope with which one will be able to see, on an enlarged scale, images of objects located both in media transparent to light and in media opaque to light. Since almost all bodies in nature are transparent to ultrasonic waves, the ultrasonic microscope may find a very wide field of application. The principle of operation of the ultrasonic microscope was proposed by the author as early as 1936.^19,20,21

A narrow beam of ultrasonic rays (Fig. 9), emitted by a piezoelectric quartz plate 1, “illuminates” the object under consideration 2. The ultrasonic rays reflected from the object fall on an acoustic collecting lens 3, at the focus of which is placed a receiver 4, consisting of a piezoelectric (for example, quartz) plate.

The receiving plate serves as the base (bottom) of the cathode tube 8. A narrow beam of cathode rays 7 inside the cathode tube falls on the inner surface of the receiving plate and knocks secondary electrons from its surface, which are collected at the anode 9.

Fig. 9. Principle of the design of an ultrasonic microscope.

Under the action of the charges formed on the inner surface of the receiving plate as a result of its irradiation by ultrasound, the secondary electron emission from the surface of the plate will undergo changes. These changes in secondary emission, reflected in the magnitude of the current entering the anode 9, can be amplified by means of a special amplifier and transmitted to the modulating device of the cathode tube 6 (the transmitting one). Then the intensity of the cathode ray in tube 6 will change in accordance with the change in the secondary emission of receiver 4. If, by the usual methods used in television, synchronous movement along lines and frames of the cathode rays of tubes 6 and 8 is carried out, then on the screen of cathode tube 6 a visible image will be obtained of the distribution of electric charges on the receiving plate 4.

Piezoelectric charges appear on the surface of the quartz plate at exactly those points where deformation of the plate takes place. Therefore the picture of the distribution of piezoelectric charges on the surface of the quartz plate corresponds exactly to the ultrasonic field in the focal plane of lens 3 acting on the quartz plate.

Since the configuration of the ultrasonic field in the focal plane in turn corresponds to the image of the object under consideration, on the screen of tube 6 we shall see directly the image of the object. Displacement of the object will, of course, cause displacement of its image on the screen.

The magnification of the image given by the system described is determined by the ratio of the linear dimensions of the frames of tubes 6 and 8.

Calculations show that magnifications of the order of tens of thousands of times are attainable in the ultrasonic microscope.

The resolving power depends on the cross-sectional area of the cathode beam in tube 8, on the parameters of the piezoelectric plate, and on the wavelength of the ultrasound.

Experiments show that a frequency \(f \simeq 10^9\) cycles is obtained without special difficulties, and there is hope of obtaining a frequency \(f \simeq 10^{10}\) cycles. In water, the wavelength of ultrasound at the frequency \(f = 3 \cdot 10^9\) cycles is equal to

\[ \lambda = \frac{c}{f} = \frac{1.5 \cdot 10^5}{3 \cdot 10^9} = 5 \cdot 10^{-5}\ \text{cm}, \]

i.e., to the wavelength of visible light.

At these frequencies the resolving power of the ultrasonic microscope can reach a value close to the resolving power of an optical microscope.

For capillary waves the propagation velocity is considerably smaller, and the wavelengths are correspondingly much smaller than the wavelengths of visible light. Therefore, by subsequently using radiation of the capillary-wave type at high frequency, we have the possibility of increasing the resolving power of the ultrasonic microscope by one or two orders of magnitude in comparison with the most perfect optical microscopes.

The objects under consideration may be “illuminated” both by continuous ultrasonic rays and by separate pulses.

To increase secondary emission, it is advisable to coat the inner surface of the receiving plate with a special layer possessing high secondary emission.

The method of obtaining a visible image may be modified, as shown in Fig. 10, a. The piezoelectric quartz plate 1 serves as the bottom of the vacuum tube 2. Ultrasonic rays fall on the outer surface of the piezoelectric plate 1, the inner surface of which is coated with a photosensitive layer. Under the action of ultraviolet rays 3, uniformly illuminating the inner surface of the plate, photoelectrons are emitted which, being accelerated by the applied electric field, pass through a system of magnetic and electric lenses 4 and fall on the fluorescent screen 5. On the screen, as in an ordinary electron microscope, we should see an image of the electron source, i.e., in our case, an image of the distribution of photoelectron emission over the surface of the piezoelectric plate 1. The distribution of photoemission over the surface of the plate must exactly correspond to the distribution of piezoelectric charges, which in turn reproduces the configuration of the ultrasonic field. Thus, on screen 5 we shall see an image of the ultrasonic field, and

therefore, an image of the object or of inhomogeneities placed in the ultrasonic field, on a correspondingly enlarged scale.

The resolving power in this case will depend on the wavelength of the ultrasound, on the thickness and dielectric properties of the piezoelectric plate used, and on the design of the lens system.

The ultraviolet radiation illuminating the quartz plate may be replaced by a homogeneous beam of electrons.

Another modification of the ultrasonic microscope is shown in Fig. 10, b. As in the preceding case, the image of the object

Fig. 10. Modifications of the design of the ultrasonic microscope.

is obtained on screen 5 on an enlarged scale. However, in this scheme screen 5 is a thin plate on which a photosensitive mosaic layer is deposited; under the action of the incident electrons it emits secondary electrons, which are collected on the annular anode 6. The electron beam 7 falls on screen 5 and, as in an ordinary television tube, moves along rows and columns, thereby equalizing on screen 5 the electric potential formed from the image of the object. Variations in the secondary electron emission are amplified and transmitted to a second tube, in which the cathode ray moves synchronously with cathode ray 7. In this case the image of the object is obtained on the screen of the second tube.

It should be noted that the resolving power is determined not only by the factors indicated above, but also by a number of additional causes of another kind, chiefly by the complexity

vibrations of a quartz plate excited by a nonuniform ultrasonic field, under whose action not only longitudinal elastic waves may arise in it, but also transverse and surface waves, which leads to distortion of the image. By using quartz plates of special cuts and choosing suitable methods of mounting (boundary conditions), the transverse and surface elastic waves in the quartz plate can be reduced almost to zero, and thereby the sharpness of the image can be increased.

Fig. 11. Image of a metal loop immersed in an opaque liquid (obtained with an ultrasonic microscope).

The field of application of the ultrasonic microscope will evidently be extremely varied and will expand as its resolving power increases.

We shall give a description of several experiments carried out with an ultrasonic microscope in our laboratory.

In Fig. 11 an image is shown of a metal object immersed in an opaque liquid (magnification 10 times).

In Fig. 12a are shown images of a glass rod and a glass tube of identical dimensions. Along the diameter of the rod a lightened band is observed, owing to the partial passage of ultrasonic waves. From the tube an even shadow is observed, since the ultrasonic rays do not pass through the tube. Thus

In this way, by means of an ultrasonic microscope it is possible to recognize the presence of fine capillaries.

a

b

Fig. 12. Images of a glass rod (left) and a tube (right) in a homogeneous (a) and nonhomogeneous (b) ultrasonic field.

In Fig. 12, b is shown the image of the same rod and tube, illuminated by a nonhomogeneous ultrasonic beam. Different

parts are illuminated with different intensity, and therefore the images are distorted.

With the aid of the ultrasonic microscope it is possible to observe the structure of the ultrasonic field especially well. It should be noted that the structure of the ultrasonic field accurately conveys all types of deformation to which the radiating plate is subjected (Chladni figures). Figure 13 shows a homogeneous ultrasonic field in the form of a bright, even spot—the radiating quartz plate vibrates in the fundamental tone.

Fig. 13. Homogeneous ultrasonic field excited by a plate vibrating in the fundamental tone.

Fig. 14. Inhomogeneous ultrasonic field excited by a plate vibrating in higher overtones.

An image of the inhomogeneous ultrasonic field from the same quartz plate vibrating in higher overtones is shown in Fig. 14. Fig. 15 gives an image of an ultrasonic field propagating in a medium in which thermal currents are formed by a heated wire. The thermal currents stand out clearly against the background of the ultrasonic field.

Drawing an analogy between the optical and ultrasonic microscope, it should be pointed out that in the ultrasonic microscope the objective corresponds to the tube associated with the ultrasonic field, while the eyepiece corresponds to the transmitting tube, on whose screen we see the image. The objective and eyepiece of the ultrasonic microscope may be placed in different locations at a great distance from one another and electrically connected with each other. The general appearance of the ultrasonic microscope is shown in Fig. 16.

Fig. 15. Ultrasonic field in a medium with thermal “flows” from a heated wire.

Fig. 16. General view of the ultrasonic microscope.

4. APPLICATION OF ULTRASONIC WAVES FOR OBSERVING PHYSICOCHEMICAL PROCESSES

Ultrasonic waves can also be used to study the kinetics of various physicochemical processes occurring in solid, liquid, and gaseous media, both transparent and opaque to light. The method described below makes it possible to measure, with high accuracy, the rate of development of reactions regardless of how long the reaction lasts (from several hours to microseconds)²².

The idea of the method is as follows: the development of physicochemical processes is usually accompanied by a change in the elastic properties of the medium and, at the same time, by a change in the velocity of propagation of ultrasound \(c\) and its absorption coefficient \(\alpha\). Consequently, knowledge of the dependence of these quantities on time (determined by direct measurements during the process) makes it possible to judge the course of development of the individual stages of the process.

This method should be especially effective in the case of polymerization reactions, where the changes in \(c\) and \(\alpha\) are sufficiently large. It may also be useful for studying the scheme of development of chains in chemical reactions. Existing schemes for the development of chains are not always entirely reliable, since in chemistry there are as yet no direct methods for determining labile intermediate products by means of which chain development proceeds, especially in cases where the intermediate products have a short lifetime. For example, in the reaction of oxidation of phosphorus by free oxygen, two paths of chain development are possible:

\[ \text{a) } P_4O + O_2 = P_4O_2 + O; \quad P_4 + O = P_4O; \quad P_4O + O_2 = P_4O_2 + O \]

and

\[ \text{b) } P_4O + O_2 = P_4O_3; \quad P_4O_3 + P_4 = P_4O_2 + P_4O; \quad P_4O + O_2 = P_4O_3. \]

For both possible paths of chain development, the velocities of propagation of ultrasound and the coefficients of its absorption will be different, and the corresponding measurements may serve as a basis for choosing between these possibilities.

The method described is carried out as follows²³ (see Fig. 17, a). A piezoelectric quartz or magnetostrictive ultrasonic emitter, excited by an electric high-frequency generator, is applied from the outside to the wall of the vessel in which the process under study is taking place. The intensity of the radiation should not be great, in order to avoid the influence of ultrasound on the course of the process itself. A second quartz plate (the ultrasonic receiver) is applied to the opposite wall of the vessel and is connected to an electric amplifier and a device recording the amplitude of the ultrasound, its frequency, and the velocity of its propa-

...propagation. The speed of propagation of ultrasound can be measured by various methods, for example by the standing-wave method, the location method, the light-diffraction method, or the quasi-modulated-frequency method.

Let us briefly describe the methods used in our practice. The ultrasonic location method, described above, consists in the following: an ultrasonic pulse of duration \(0.6\ \mu\text{sec}\) from a special quartz generator is emitted into the medium under investigation. The oscillation frequency is chosen to be of the order of several megacycles. A cathode-ray oscillograph with a rapid sweep records the reflected or transmitted pulse in the form of a sinusoid visible on the screen of the oscillograph (Fig. 17, b). When the speed of sound propagation changes, the pulse on the oscillograph screen is displaced. The displacement of the pulse can be measured with an accuracy up to \(1/4\) of a wavelength, which corresponds to a relative change in the speed of sound propagation of \(2.5 \cdot 10^{-8}\) at a frequency \(f = 10^7\ \text{cps}\). Such a relative change in the speed of sound propagation corresponds to a relative change in the density of the medium of approximately \(10^{-8}\).

Fig. 17. \(a\)—apparatus for studying the kinetics of physicochemical reactions: 1—generator of electrical oscillations, 2—quartz plate (emitter), 3—vessel in which the reaction is taking place, 4—receiving quartz plate, 5—amplifier, 6—recording device; \(b\)—sweep of the ultrasonic pulse.

The quasi-modulated-frequency method consists in the following23: the frequency of the high-frequency electrical generator exciting the quartz is periodically varied by 5–10% by changing the capacitance or self-inductance of the generator circuit. The generator is inductively coupled to a receiver of electrical oscillations. Thus the receiver simultaneously perceives two oscillations: the frequency \(f_1\), excited by the ultrasonic wave that has reached the receiver at a given moment (and therefore emitted earlier, when the generator had a different frequency), and the frequency \(f_2\), excited at the given moment directly by the generator. After amplification and detection, the difference frequency

\[ \Omega = f_1 - f_2, \]

is separated out and fed to the oscillograph.

It is easy to see that \(\Omega\) is proportional to the path length of the ultrasonic beam \(l\) and to the velocity \(c\) of sound propagation in the medium under investigation. If the path length of the ultrasonic beam \(l\) is given, then \(\Omega\) will be directly proportional to \(c\), and changes in \(\Omega\) will strictly follow changes in the velocity of sound propagation. This makes it possible to record the smallest changes in the velocity of sound propagation in a medium whose elastic properties change in the course of the development of a chemical reaction.

For measuring very small changes \(\Delta c\), it is expedient to pass the ultrasonic oscillations through two channels, which are vessels containing the medium under investigation.

In this case, changes in the density of the medium occur in one vessel, but not in the other. In this case we measure only the difference \(c_0 - c_1 = \Delta c\).

A method that makes it possible, with sufficient accuracy, to determine the velocity of sound propagation and its absorption coefficient may also be based on the use of the phenomenon of diffraction of light in an ultrasonic field, namely on knowledge of the dependence of the distances between the diffraction spectra and of the intensities of the spectra themselves on these quantities. However, the applicability of this method is limited by the transparency of the medium to light.

By illuminating the medium under investigation with ultrasonic beams in three mutually perpendicular directions, one can obtain on a screen diffraction spectra which also give an idea of the development of the chemical reaction not only in time, but also in space.

Fig. 18. Changes in the velocity of ultrasound in the course of a reaction:
1 — polymerization of methacrylic ester;
2 — inversion of cane sugar.

In this way we studied the following reactions:

1) polymerization of methacrylic ester under the action of a catalyst (benzoyl peroxide) (the reaction proceeded at a temperature of \(50^\circ\mathrm{C}\); the amount of polymerizing substance taken was \(100\ \mathrm{cm}^3\));

2) inversion of cane sugar.

In Fig. 18 (curves 1 and 2) the changes in the velocity of sound propagation in the first and second reactions are given. From these curves one can determine the rate at which the reaction proceeds.

Since the medium under investigation, in the course of the development of the reaction, is all the time under the action of ultrasonic oscillations, the question naturally arises: what influence do ultrasonic waves exert on the course of chemical reactions?

The question of the influence of ultrasonic oscillations on the development of chemical reactions was experimentally investigated by the author in earlier years. It was established that ultrasonic waves of low intensity do not exert any substantial influence on the chemical process that would be of practical significance. As the intensity of the ultrasonic rays is increased, a number of additional phenomena arise, for example the formation of cavitation phenomena and the formation, in bundles of oscillations, of local points with a sharp increase in temperature. These secondary phenomena can, of course, exert some influence on the development of the reaction.

Calculations show that the influence of ultrasonic waves on the course of chemical reactions may be neglected if the frequency of the ultrasonic field is small and the intensity does not exceed \(10^6—10^7\) ergs.

5. APPLICATION OF ULTRASONIC WAVES FOR THE PURPOSES OF INVESTIGATING THE DEGREE OF HOMOGENEITY AND THE STRUCTURE OF METALS

The ability of ultrasonic rays to “transilluminate” practically unlimited thicknesses of various metals (on the order of ten meters) is remarkable. It has now become the basis for the creation of a new technology—the technology of ultrasonic flaw detection.

The birthplace of ultrasonic flaw detection is the Soviet Union, where in 1927 the author first discovered the ability of ultrasonic rays to penetrate through metals\(^{24}\), and in 1928 created the first model of an ultrasonic flaw detector\(^{25}\). The possibility of rapidly detecting, with the aid of ultrasonic flaw detectors, the smallest defects, cavities, cracks, inclusions, etc., makes it possible to improve production technology, to raise substantially the quality of products, and thereby to place technology on a higher level.

At the present time, ultrasonic flaw detectors in our country have reached a high degree of perfection and have found wide application not only in the flaw detection of metals, but also for the study of a broad range of physical phenomena. At the same time, the possibility of ultrasonic transillumination of metals has opened the way to the study of their physicochemical properties both in the solid and in the liquid phases.

If the elastic medium in which ultrasonic waves propagate is unbounded and homogeneous, then ultrasound from a quartz plate of radius \(R\) propagates in the form of narrow bundles of rays, the directionality of which will depend on the dimensions of the radiator, on the frequency of the emitted oscillations, and on the velocity of propagation of sound in the medium. The angular width of the bundle for a homogeneous medium is determined by the well-known expression

\[ \sin \alpha = 0.61\,\frac{\lambda}{R}. \tag{5.1} \]

The presence of inhomogeneities and bounding surfaces considerably complicates the law of wave propagation. As already indicated, the ultrasonic properties of a metal depend on the size of the grains, their orientation, and on the inclusions between them. When propagating in an inhomogeneous metallic medium, ultrasonic waves are scattered, undergoing multiple reflection from the faces of the inhomogeneities.

The coefficient of reflection from the interface between two media with different elastic properties, for normal incidence of the wave, may be calculated from the formula

\[ r = \frac{ \left( \frac{\rho_1 c_1}{\rho_2 c_2} - \frac{\rho_2 c_2}{\rho_1 c_1} \right)^2 }{ 4\operatorname{ctg}^2 \frac{2\pi d}{\lambda} + \left( \frac{\rho_1 c_1}{\rho_2 c_2} + \frac{\rho_2 c_2}{\rho_1 c_1} \right)^2 }, \tag{5.2} \]

where \(c_1, \rho_1, c_2\), and \(\rho_2\) are the velocities of propagation of ultrasound and the densities in the first and second media, respectively; \(d\) is the thickness of the metal layer; \(\lambda\) is the wavelength in the metal.

The magnitude of the reflection coefficient must be taken especially into account when ultrasonic vibrations pass from a liquid medium into a solid one. In this case, in order to reduce the reflection coefficient and thereby increase the coefficient of their penetration into the solid, it is advisable to excite vibrations in a liquid in which the value \(c\rho\) (the acoustic stiffness) is as close as possible to its value in the metal.

It is known that in a liquid medium only longitudinal waves propagate, whereas in a solid body both longitudinal and transverse waves occur, and in some cases also surface waves. Only in one case, namely in the case of perpendicular incidence on the surface, do only longitudinal waves propagate in the metal. The occurrence of transverse waves is mainly associated with reflections from the faces of the metal, or from the faces of inhomogeneities located inside the metal. As a result of interference in a metallic plate of given thickness \(d\), under perpendicular incidence, the maximum intensity of the transmitted waves will occur in those cases when the thickness of the plate satisfies the following relation:

\[ d = \frac{(2n - 1)\lambda}{4}, \qquad n = 1, 2, 3, \ldots, \tag{5.3} \]

where \(d\) is the thickness of the plate, \(\lambda\) is the wavelength, and \(n\) is an integer. Thus, by observing the maximum intensity of transmitted ultrasonic vibrations under perpendicular incidence on a metallic plate, it is possible to measure the wavelength of ultrasonic waves in the metal, and consequently also the velocity of their propagation, if the frequency of the vibrations is known. The intensity of the transmitted waves depends on the angle of incidence of the wave on the metal surface. Since

if the velocity of propagation of longitudinal waves is greater than that of transverse waves, then it is possible to choose such an angle of incidence at which the longitudinal waves are completely reflected from the surface of the metal, and only transverse waves will propagate inside it.

As has already been indicated, owing to multiple reflections, in any region inside the metal there simultaneously propagates a large number of random waves of the same frequency, differing in amplitude and phase. In this case the problem should be reduced to calculating the most probable amplitude acting on the receiving quartz plate, assuming the independence of the individual random waves acting on the surface element, and the phases of the oscillations to be equally probable.

The phenomenon of multiple reflection becomes especially noticeable when oscillations are excited in metal articles of small dimensions. In this case the phenomenon may continue for a long time and resembles the reverberation phenomenon known in the acoustics of closed rooms.

To excite ultrasonic oscillations in a metal, piezoelectric oscillations are used.^26 The ultrasonic radiator is a quartz plate of suitable dimensions, set into a special holder and immersed in transformer oil. Depending on the design, the quartz plate radiates oscillations either from one side, facing the metal, or from both sides. Such a plate may serve both as a radiator of ultrasonic oscillations and as a receiver of them.

The first industrial model of an ultrasonic flaw detector, based on the principle of through “transillumination” of metals, was, as already indicated, developed by the author in 1928. However, our industry, developing rapidly, put forward new, higher requirements for ultrasonic flaw detection: flaw detectors with greater resolving power were required. To accomplish this task, in 1935 the author developed^26 a flaw detector of a new type (a “reflectoscope”), based on the principle of ultrasonic location. Although the technology of that time made it possible to obtain ultrasonic pulses of a duration on the order of 10 microseconds, nevertheless the resolving power of flaw detectors constructed on this principle proved rather high, and they were successfully used alongside flaw detectors of the earlier type.^27 Subsequently the pulse method was improved; the resolving power increased through a reduction in the duration of the ultrasonic pulses. In 1941 our flaw detectors of this type, in connection with the appearance of radar, operated with pulses on the order of 2–3 μsec. In recent years we have obtained ultrasonic pulses of a duration of fractions of a microsecond. This increased the resolving power of the flaw detector so much that it became possible to detect defects with dimensions of fractions of a millimeter, occurring at great ...

in depth. During the war years the pulse flaw detector (reflectoscope) was also improved in other laboratories^88.

Fig. 19. Block diagram of a pulse flaw detector.

The principle of operation of the pulsed ultrasonic flaw detector is as follows: a quartz plate emits a short-duration high-frequency ultrasonic pulse. This pulse, propagating in the metal, is reflected from defects encountered and returns to the same quartz plate. Piezoelectric

Fig. 20. Flaw detector in operation.

charges arising on the receiving plate under the action of an ultrasonic pulse are amplified and transmitted to the scanning device (a cathode-ray oscilloscope), where they are recorded in the form of peaks.

a

b

Fig. 21. a—a typical oscillogram; b—the corresponding defects.

The sweep of the cathode-ray oscilloscope acts synchronously with the propagation of the ultrasonic pulse in the metal in such a way that the pulse reflected from the opposite face of the metal

the pulse was not recorded by the oscillograph at all, or was recorded only at the end of the sweep. Thus, a defect located inside the metal and reflecting the ultrasound will be registered on the screen of the oscillograph in the form of a clearly expressed pulse, the magnitude of which is to some extent a measure of the size of the defect. The distance, on the oscillograph scale, between the initial pulse and the pulse reflected from the defect is proportional to the depth at which the defect lies. The frequency of the carrier oscillations of the ultrasonic pulses in flaw detectors lies within the range from \(f = 0.5 \times 10^6\) cycles to \(f = 15 \cdot 10^6\) cycles.

By selecting the appropriate frequency and intensity of the ultrasound, we can sound metals to a great depth (on the order of 10 m) and detect the smallest defects inside the metal. Fig. 19 gives a block diagram of a pulsed flaw detector. Fig. 20 shows the general appearance of the flaw detector in operation. The photographs in Fig. 21 give an idea of the oscillograms obtained (a) and the corresponding defects (b).

Fig. 22. Reflection from structural inhomogeneities of the metal.

If several defects at different depths lie in the path of the ultrasonic beam, then all of them are recorded in the order of their arrangement on one and the same scale. It should be noted that ultrasonic pulses are reflected not only from obvious defects in the metal, but also from looseness, regions of recrystallization, inclusions, etc. In this respect ultrasonic flaw detection is an unsurpassed method in terms of sensitivity, making it possible to detect the smallest inhomogeneities inside the metal. In cases where there are no obvious defects in the metal, but only small loosenesses or regions of recrystallization are present, it is advisable to set the sweep of the cathode ray in such a way that the pulse multiply reflected from the bottom is recorded several times (for example, five). Then, against the background of regularly spaced pulses, one can clearly notice reflections from disturbances of the metal structure (Fig. 22).

The high sensitivity of the ultrasonic flaw detector to the smallest disturbances of uniformity makes it possible to use the ultrasonic flaw detector for determining the depth of the hardened layer. In this case the ultrasonic beam is directed at a small angle into the metal, reaches the boundary between the hardened and unhardened regions, is reflected, and is registered on the oscillograph. In this way it is possible to judge, to a certain extent, also the quality of hardening, by comparing the magnitude of the reflected pulses from

different portions of the hardened layer^20. In this case the construction of the transmitting and receiving probes must be somewhat beveled, in order to ensure the direction of the ultrasonic beam at any desired angle to the surface of the hardened layer. It should be noted that the velocities of propagation of ultrasound in the hardened and unhardened regions of the metal differ very little from one another (on the order of a fraction of a percent).

Let us point out one more very useful application of the ultrasonic flaw detector, namely, the determination of the dimensions of products. If, under perpendicular incidence, the pulse reflected from the opposite face of the product is recorded, then in this way we can measure the thickness of the product with great accuracy. To increase the accuracy of the measurements, the ultrasonic pulse should be expanded to such an extent that it becomes possible to observe the individual oscillations of which it consists.

This makes it possible to measure the thickness of the product with an accuracy down to fractions of a percent.

The indicated method is extremely convenient, simple, and absolutely necessary in those cases where the opposite face of the product is inaccessible to ordinary measuring instruments.

One could indicate a whole series of very interesting applications of ultrasonic flaw detection. However, a detailed description of ultrasonic flaw detection is not among the tasks of this article. We shall point out only one more application in geophysics, namely the possibility of studying the propagation of seismic waves in the Earth’s crust by means of modeling. It is necessary to note that, when ultrasonic pulses propagate not only in metal but in any solid body, transverse and surface waves also arise along with longitudinal waves, propagating with the corresponding velocities. Transverse and surface waves are especially easily excited when an ultrasonic pulse is incident obliquely on a surface (“ultrasonic earthquake”), which has an extremely harmful effect on the operation of the flaw detector. Therefore, in ultrasonic flaw detection the main task is to develop such a probe design as would not allow the appearance of transverse and surface waves. On the screen of the oscillograph all the indicated types of waves are recorded in the form of separate pulses, spaced from one another by distances corresponding to the velocities of propagation of the waves. In Fig. 23, a is shown a photograph of pulses corresponding to the simultaneous excitation of all three types of waves.

Let us imagine a model of the terrestrial globe, made on a reasonable scale from materials in accordance with the data of geophysics on the structure of the Earth (Fig. 23, b). The ultrasonic waves propagating in this model should, on the same scale, be shorter than the seismic waves propagating in the Earth’s crust.

The main part of the spectrum of seismic waves can be covered in an ultrasonic model by the spectrum of ultrasonic waves with frequencies of approximately from \(10^5\) to \(3 \cdot 10^7\) Hz. (The propagation velocity of surface ultrasonic waves in the model should be approximately equal to the propagation velocity of seismic waves in the earth’s crust.)

Fig. 23. \(a\)—pulses corresponding to the simultaneous excitation of longitudinal, transverse, and surface waves; \(b\)—a model of a section of the earth’s surface for ultrasonic modeling of seismic phenomena.

By introducing inhomogeneities on the surface of the model corresponding to the earth’s relief, we can, by studying at various points of the model ultrasonic pulses representing the superposition of many frequencies in the indicated interval, obtain an idea of the character of the propagation of seismic waves in different regions of the earth’s crust.

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