Practical Applications of the Piezoelectric Properties of Crystals

P. N. Belikov, Moscow.

Many works by the greatest physicists of the last century have been devoted to the study of piezoelectric phenomena (Curie, Röntgen, Voigt, Pockels, Lippmann, Thomson, Riecke). In recent times these phenomena have acquired new interest thanks to the very fruitful applications of the piezoelectric properties of quartz in radio engineering and in acoustics.

The first observations of the piezoelectricity of Iceland spar were made in 1817 by Haüy and then by Becquerel (E. Becquerel). But at that time these new phenomena did not arouse great interest and did not become the subject of study; attention was again drawn to the appearance of charges on the faces of a crystal under the influence of applied pressure in 1880 by the Curie brothers¹*) (P. and J. Curie), and this effect was first subjected by them to detailed study on tourmaline and on certain other crystals. The scheme of Curie’s initial experiments was as follows: the bases of a prism cut from tourmaline so that its edges are parallel to the axis of the crystal are provided with metallic plates, which are connected to the quadrants of an electrometer. Pressure applied to the bases of the prism causes a deflection of the electrometer, and when the pressure is removed the electrometer returns to its initial position; if, however, after subjecting the crystal to compression, the electrometer is discharged and the pressure is then begun to be decreased, the electrometer shows a deflection in the opposite direction.

*) References designated by numerals refer to the bibliography on p. 325.

By such initial qualitative observations, Curie established that when a prism is subjected to compression along its axis, unlike charges arise on its opposite faces; these change to the opposite ones when compression is replaced by tension, and the piezoelectric effect proves to be proportional to the pressure.

Further study of piezoelectric phenomena under more complex deformations was carried out by Röntgen²) and Kundt³), and in order to determine the sign of the charges arising under mechanical actions Kundt used the same experimental method that he had used in studying pyroelectric phenomena: for this purpose the crystal is dusted from a pulverizer with a mixture of fine powder of red lead and sulfur. Owing to friction during spraying, the sulfur becomes negatively electrified and the red lead positively, so that the places of the crystal which have received negative charges prove to be covered with a red coating of red lead, while those where positive charges have arisen are covered with a white coating of sulfur.

Lippmann, proceeding from thermodynamic considerations, predicted the inverse piezoelectric effect. And indeed, experiment confirmed that if two faces of a crystal, perpendicular to its electric axis, are provided with metallic coatings and a certain potential difference is applied to these coatings, then the crystal expands or contracts depending on how the potential difference is applied to its ends.

If that end of the crystalline prism which, under compression, becomes positively charged is charged negatively, and the opposite end positively, then the crystal contracts; conversely, if a positive charge is imparted to that face of the crystalline prism which under compression is likewise positively electrified, then the crystal undergoes expansion.

As already stated, many major physicists have dealt with the theory of piezoelectricity. Without touching here on the theories of the phenomenon⁴), we shall give only the final equations of Voigt’s theory, by which the connection is established between mechanical deformations and the polarization arising in the crystal in piezoelectric phenomena.

Denoting by \(P_1, P_2, P_3\) the components of the piezoelectric moment referred to a unit volume of the crystal subjected to deformation, and by \(x_x, y_y, z_z\) the displacements along the corresponding axes, and by \(y_z, z_x, x_y\) the changes of angle occurring upon rotation about the corresponding axis, Voigt obtains the components of the vector \(P\) in the form

\[ \begin{aligned} P_1 &= E_{11}x_x + E_{12}y_y + E_{13}z_z + E_{14}y_z + E_{15}z_x + E_{16}x_y,\\ P_2 &= E_{21}x_x + E_{22}y_y + E_{23}z_z + E_{24}y_z + E_{25}z_x + E_{26}x_y,\\ P_3 &= E_{31}x_x + E_{32}y_y + E_{33}z_z + E_{34}y_z + E_{35}z_x + E_{36}x_y. \end{aligned} \]

where \(E\) are the piezoelectric constants of the crystal. If, instead of the displacement components \(x, y, z\), one uses the experimentally measured components of pressure \(X, Y, Z\), then an analogous system of equations is obtained

\[ \begin{aligned} - P_1 &= \delta_{11}X_x + \delta_{12}Y_y + \delta_{13}Z_z + \delta_{14}Y_z + \delta_{15}Z_x + \delta_{16}X_y,\\ - P_2 &= \delta_{21}X_x + \delta_{22}Y_y + \delta_{23}Z_z + \delta_{24}Y_z + \delta_{25}Z_x + \delta_{26}X_y,\\ - P_3 &= \delta_{31}X_x + \delta_{32}Y_y + \delta_{33}Z_z + \delta_{34}Y_z + \delta_{35}Z_x + \delta_{36}X_y. \end{aligned} \]

The quantities \(\delta\) are called the piezoelectric moduli. The piezoelectric moduli are connected with the piezoelectric constants by the relations

\[ \delta_{ih} = \sum_k E_{ik}\cdot s_{hk} \quad \text{and} \quad E_{ih} = \sum_k \delta_{ik}\cdot c_{hk}, \]

where \(k\) are integers from 1 to 6, while \(c\) and \(s\) are the elastic constants and moduli determined from the equations of the theory of elasticity

\[ - X_x = c_{11}x_x + c_{12}y_y + c_{13}z_z + c_{14}y_z + c_{15}z_x + c_{16}x_y \]

and

\[ - x_x = s_{11}X_x + s_{12}Y_y + s_{13}Z_z + s_{14}Y_z + s_{15}Z_x + s_{16}X_y. \]

Of all piezoelectric crystals, only quartz \((\mathrm{SiO_2})\) has found broad practical application. This is due, on the one hand, to its considerable piezoelectric properties, and, on the other, to its great mechanical strength.

Belonging to the crystals of the hexagonal system, quartz is a member of the trapezohedral tetartohedral group,

having one triple optical axis and three double (electric) axes perpendicular to it, making angles of \(120^\circ\) with one another. Its crystals are a hexagonal prism bounded by two pyramids (Fig. 1). When compressed in the direction of one of the electric axes (i.e., in the direction \(LM, NP, RS\)), piezoelectric charges arise at the ends of these axes; but when compressed in the direction of the optical axis \((AB)\), no charges are obtained.

The structure of quartz (\(\alpha\)-quartz) can be depicted as in Fig. 2 (left); here the black circles, white circles, and crosses represent Si atoms lying in different horizontal planes. Between the Si atoms lie O atoms, so that each individual cell of the crystalline structure has the form shown by its model (Fig. 3), where the large black spheres represent Si atoms and the small white ones represent O atoms. Left- and right-rotating quartzes differ only in the difference in the course of the helix (right and left) corresponding to the arrangement of the Si atoms.

Fig. 1.

At \(573^\circ\), \(\alpha\)-quartz, which has an asymmetric atomic structure, transforms into \(\beta\)-quartz, which possesses a symmetric structure and is not piezoelectric. Its structure is shown in Fig. 2 on the right. If, however, by cooling, \(\beta\)-quartz is converted into the \(\alpha\) form, then its piezoelectric properties are again fully restored.

It should be noted that among \(\alpha\)-quartzes there is also encountered a large number that do not possess piezoelectric properties, which is evidently explained by simultaneous

by the existence, throughout the entire mass of crystals, of left and right quartz (Kolenko^5).

For practical purposes, a plate is cut from quartz in such a way that its broad faces are perpendicular to one of the electrical axes \((E)\), while the optical axis \((O)\) is perpendicular to the plane bounded by the longest and shortest edges of the plate (Fig. 4). Then, under compression along the axis \(E\), charges of different names arise on the faces \(ABCD\) and \(EFGH\), which are perpendicular to the axis \(E\), changing their sign when the sign of the deformation is reversed (longitudinal effect). Under compression along the axis \(Y\), on the faces \(ABCD\) and \(EFGH\) there arise

Fig. 2.

charges the same as those obtained under tension along the axis \(E\), and, conversely, under tension along the axis \(Y\), on the faces \(ABCD\), \(EFGH\) the same charges are produced as were obtained under compression along the axis \(E\) (transverse effect). In addition to this direct piezoelectric effect, on the same quartz plate one may observe the inverse piezoelectric effect, consisting in the fact that if the faces \(ABCD\) and \(EFGH\) are charged with opposite charges, then this leads, first, to compression of the crystal in the direction of the electric field produced, i.e. along the axis \(E\) (longitudinal effect), and, second, to its elongation in the direction perpendicular to the optical and electrical axes, i.e. along the axis \(Y\) (transverse effect). It goes without saying that a reversal

a change of the sign of the charges also entails a change of the sign of the deformation.

According to Voigt, the crystalline group to which quartz belongs has only 5 piezoelectric moduli different from zero, and 5 piezoelectric constants not equal to zero. Their numerical values in CGS units are as follows: the piezoelectric constants

\[ E_{11}=-E_{12}'=-E_{26}'= \]

\[ =-4.77\cdot 10^4;\qquad E_{25}=-E_{14}= \]

\[ =1.23\cdot 10^4, \]

and the piezoelectric moduli

\[ \delta_{11}=-\delta_{12}=-\frac{1}{2}\delta_{26}'= \]

\[ =-6.36\cdot 10^{-8};\qquad \delta_{14}=-\delta_{25}= \]

\[ =1.69\cdot 10^{-8}. \]

Fig. 3.

It should be noted, however, that in measurements made by Dawson6 over thin quartz plates, it turned out that in different parts of one and the same plate the piezoelectric constant has different values. Thus, under pressures of 1 kg applied to different parts of a plate, the area on which the pressure was exerted being less than \(0.1\ \mathrm{mm}^2\), the electrometer gave readings according to which \(\delta_{11}\) on the negative side of the plate varied from \(5.8\cdot 10^{-8}\) to \(7.1\cdot 10^{-8}\), and on the positive side—from \(4.9\cdot 10^{-8}\) to \(6.4\cdot 10^{-8}\). Such a difference in the values of \(\delta\), determined on one and the same specimen of a crystalline plate, may be explained by the fact that, in the general mass of the crystal, there may exist small crystallites embedded in it, oriented differently from the whole crystal, as was discovered radiographically by Bragg, Darwin, and James7 (Bragg, Darwin, James).

Since, of all the moduli and constants, only 5 are nonzero, for quartz the fundamental equations will be written as follows:

\[ \begin{aligned} P_1&=E_{11}x_x+E_{12}y_y+E_{14}y_z,\\ P_2&=E_{25}z_x+E_{26}x_y,\\ P_3&=0 \end{aligned} \]

or else

\[ \begin{aligned} -P_1&=\delta_{11}X_x+\delta_{12}Y_y+\delta_{14}Y_z,\\ -P_2&=\delta_{25}Z_x+\delta_{26}X_y. \end{aligned} \]

But since under experimental conditions only the deformations of compression and elongation are of importance, these equations may be simplified, writing only

Fig. 4.

\[ P_1=E_{11}x_x+E_{12}y_y \quad\text{and}\quad -P_1=\delta_{11}X_x+\delta_{12}Y_y. \]

In these two equations the first terms refer to the longitudinal piezoelectric effect (deformation or pressure in the direction of the electric axis), and the second terms to the transverse effect (deformation or pressure in a direction perpendicular to the electric and optical axes). The quantity of electricity arising on the face \(ABCD\) (Fig. 4) in the longitudinal effect is \(q=-\delta_{11}\Gamma\) (\(\Gamma\) is the force acting on the area \(ABCD\)); in the transverse effect, on the face \(ABCD\) there arises a quantity of electricity

\[ q'=-\delta_{12}\frac{L}{d}\cdot\Gamma \]

(\(L\) is the length of the plate, \(d\) its thickness, \(\Gamma\) the force applied to the face \(ABFE\)). Likewise, in the converse piezoelectric effect the displacement for the longitudinal effect is \(x=v\cdot\delta_{11}\), and for the transverse effect \(y=v\cdot\delta_{12}\dfrac{L}{d}\), where \(v\) is the potential difference; calculation shows that with a potential difference of hundreds of volts a displacement of the order of \(10^{-7}\,\mathrm{cm}\) is produced.

If a quartz plate, cut as was shown in Fig. 4, is provided with metallic electrodes and an alternating voltage is applied to them, then, owing to the inverse piezoelectric effect, the plate enters into elastic vibrations. Since it has a natural frequency of mechanical vibrations, depending on the dimensions and elastic properties of quartz, its elastic vibrations prove to be most intense when the frequency of the alternating current is equal to the natural frequency of the crystal’s elastic vibrations. In essence, all practical applications of quartz are based on the phenomenon of resonance between electrical and mechanical vibrations; moreover, it turns out that, in the transverse effect, the displacement of the end of the rod at resonance exceeds by 4,000 times the displacement produced by a static field. The excitation of quartz by a high-voltage alternating current was first carried out by Langevin⁸) (Langevin), who in this way constructed a powerful emitter of high-frequency acoustic vibrations; subsequently Cady⁹) (Cady), proceeding from the equations given above, developed, using a graphical method, the theory of vibrations of a quartz rod and indicated possible applications of quartz in radio engineering. These works laid the foundation for the practical use of the piezoelectric properties of quartz.

The natural frequency of elastic vibrations of a quartz plate can be calculated from its dimensions, from the density of quartz \((d = 2.65\ \mathrm{g/cm^3})\), and from its modulus of elasticity \((—7.85 \cdot 10^{11}\ \mathrm{dyn/cm^2})\). From these quantities the speed of sound in quartz is

\[ = \sqrt{\frac{7.85 \cdot 10^{11}}{2.65}} = 545 \cdot 10^3\ \mathrm{cm/sec}. \]

Obviously, for vibrations at the natural frequency, the dimension of the rod \((l)\) is equal to half the length of the standing wave in it, and the natural frequency of the vibrations is

\[ n = \frac{545{,}000}{2l}\ \mathrm{sec}^{-1}. \]

It is therefore evident that, in the case of electromechanical resonance, the wavelength of the closed circuit producing the electrical vibrations must be equal to

\[ \lambda = \frac{3 \cdot 10^{10} \cdot 2l}{545{,}000} \]

or \(\lambda_{\mathrm{m}} \simeq 110\,l_{\mathrm{mm}}\). A plate having the form

of a parallelepiped, has three fundamental natural frequencies and a large number (up to 50) of overtones corresponding to each of these frequencies. Since the plates are usually cut so that their linear dimensions differ noticeably from one another, the resonance frequencies are usually also sufficiently far from one another. Round quartz plates, cut perpendicular to the electrical axis so that the optical axis of the crystal is one of the diameters of the disk, also have, as Hund[^10] found, three natural frequencies, determined experimentally as

\[ f=\frac{2870}{d},\quad f_1=\frac{2715}{D},\quad f_2=\frac{3830}{D}, \]

where \(f\) is the frequency in kilocycles, \(d\) is the thickness of the disk, and \(D\) is its diameter in mm.

The overtones of the mechanical oscillations of a plate can conveniently be detected by sprinkling a fine powder on the quartz plate, as was done by Wachsmuth and Auer[^30]. In oscillations with frequencies higher than the fundamental frequency of the plate, the powder collects along the nodal lines. Then one can directly measure the length of the elastic waves in quartz and, from them, the speed of sound in it. According to the experiments of these authors, it turned out that the speed of sound in quartz changes with the frequency of oscillation, increasing as it increases.

Fig. 5.

Finally, a quartz plate possesses, in addition, natural frequencies much lower than those which depend on the length of the standing acoustic waves in it, and which are caused by transverse oscillations of the plate, similar to the oscillations of a string. Harrison[^11] obtained such oscillations in quartz by using for this purpose electrodes, one of which covers not the whole plate, but only a certain part of it; then on the plate one can mark

a series of nodal points at which powder poured onto the plate is retained (Fig. 5).

Since all practical applications of quartz are based precisely on the phenomenon of electromechanical resonance, for practical purposes it proves extremely important to have a method for accurately determining the moment of resonance. Cady used for this purpose the determination of the current strength passing through an oscillatory circuit, parallel to whose capacitance the quartz is connected, the natural frequency of the quartz being approximately equal to the frequency of the circuit. In

Fig. 6.

Fig. 7.

Fig. 6 shows the arrangement for such a measurement. To measure the current strength, two thermoelements \(T_1\) and \(T_2\) are introduced into the circuit \(LC\) and into the circuit of the quartz \(K\). When oscillations are transferred from the circuit \(L_1\) to the circuit \(LC\), then, as resonance is approached, the current in the circuit \(LC\) increases; but at the moment of resonance between the circuit \(LC\) and the mechanical vibrations of the quartz, i.e., when the vigorously vibrating quartz draws much energy from the circuit, the current in the \(LC\) circuit drops sharply; therefore a dip is obtained on the resonance curve, which can be determined by a galvanometer connected with \(T_1\) (Fig. 7). At the same time, the current passing through the quartz and measured by thermoelement \(T_2\) increases sharply at resonance.

Since the constancy of the natural frequency of the mechanical vibrations of a quartz plate is very great and, as is evident from Fig. 7, the resonance curve of quartz is very sharp, a quartz plate can conveniently be used for

control of the constancy of the frequency in an oscillatory circuit. Thus, for example, control of the constancy of the frequency can be carried out according to the scheme of Fig. 8. The controlled waves act on the circuit \(LC\), in parallel with whose capacitance a quartz is connected. A small incandescent lamp is coupled with the circuit; it lights up as one approaches resonance between the frequency of the incoming oscillations and the frequency of the \(LC\) circuit. But at the moment when resonance is reached between \(LC\) and the vibration frequency of the quartz, the lamp goes out. In this way tuning of the circuit to a definite wavelength is achieved with an accuracy up to \(1/100\,000\).

Fig. 8.

An even simpler method for determining the moment of resonance of the quartz with the oscillatory circuit is the acoustic method proposed by Cady (Fig. 9). A tube generator, to which the quartz is connected, acts on the receiving circuit of the amplifier \(V\); if the frequency in the generator is varied smoothly, then at the moment of resonance of the oscillatory circuit with the quartz a click is heard in the telephone of the receiving device.

Fig. 9.

This method proved very convenient and sensitive for recognizing piezoelectric crystals. Giebe and Scheibe\(^{12}\) thus investigated a large number of different substances, the test for piezoelectricity being carried out not on large specimens of crys-

crystals, but on crystalline powders poured between the plates of a capacitor connected in parallel with the capacitance of the oscillatory circuit of the generator (Fig. 9). With a smooth change of the wavelength of the circuit (\(\lambda\) from 50 to 1,000 m), at certain positions of the variable capacitor, in the telephone

Fig. 10.

of the amplifier a noise is heard, arising from the fact that the frequencies of some of the crystals turn out to be in resonance with the frequency of the circuit. This method is very convenient for qualitative tests, but does not provide the possibility of quantitative measurements.

An even more accurate method for determining resonance was proposed by Giebe and Scheibe \(^{13}\) from the optical effect, observed

given at the moment of resonance to a quartz plate, placed in a vacuum (10–15 mm of mercury) and set freely between the electrodes so that the distance between it and the upper electrode would be 0.5 mm or somewhat more. Under the influence of the alternating field, the quartz enters into intense oscillations, and the secondary direct effect, produced by the compressions and expansions of the plate, creates so strong a field between the quartz and the electrodes that a glow arises, photographs of which are given in Fig. 10. As can be seen from the photographs, by selecting the frequency of the exciting field one can obtain glow patterns corresponding to various overtones of the mechanical oscillations of the quartz.

Fig. 11.

Using several harmonics of the mechanical oscillations, it is possible to employ the quartz plate as a monitoring device for several frequencies. A somewhat modified type of such a device, developed by the same authors[^14], in which small electrodes are applied only to the middle part of the quartz and the luminous spots are obtained along the entire rod, not touching the electrodes, is at present being offered for sale by the Berlin firm Radio-Frequenz for frequency monitoring.

In a later work, Giebe and Scheibe[^31] applied the same optical method for detecting mechanical oscillations arising not only during elongations of a quartz rod (longitudinal waves), but also during its periodic bendings

(transverse waves) or by its twisting. Oscillations of this kind are produced by a nonuniform alternating field, which can be created in quartz with the aid of two pairs of small electrodes, applied in the proper manner in the middle part of the rod. By changing the frequency of the voltage supplied to the electrodes, intense oscillations corresponding to its overtone frequencies can be produced in the quartz rod. In this case the whole rod, placed in a vacuum of 0.3–0.5 mm of mercury, is divided into sharply separated light and dark regions, by which the places of maximum deformations can be recognized*).

The influence of temperature on the oscillation frequency of quartz is not very strong; when the temperature changes by 1° a plate having a frequency of \(10^6\) changes the number of its oscillations by only 25 osc./sec. for the longitudinal effect and by 50 osc./sec. for the transverse effect \(^{15}\). The constancy of quartz’s natural frequency and the tuning accuracy attainable with it at the present time make piezoquartz an absolutely necessary instrument in the standard graduation and verification of wavemeters.

Thanks to these same properties, quartz has yet another very important significance in radio engineering—as a standard generator of oscillations. At the present time there already exists a large number of different generator circuits in which quartz brought into oscillation serves as a frequency regulator. One of the initial circuits of this kind is shown in Fig. 11. Here the quartz is placed in the grid circuit of the generator tube in parallel with a resistance. The frequency of the longitudinal or transverse oscillations of the quartz must be the same as the frequency of the oscillatory circuit located in the anode circuit of the generator tube. The moment of resonance between the quartz and the oscillatory circuit can be determined by the sharp drop of current in the anode circuit. Such a generator operates with an unchanging frequency, and the tuning accuracy of the quartz generator can be brought to \(10^{-4}\%\).

*) The excellent photographs of Giebe and Scheibe are not reproduced here, since the work mentioned appeared after the present article had been submitted for printing.

Fig. 12.

It goes without saying that such standard generators must play an especially important role in the region of short waves, which in recent years has been winning an ever firmer place in radio. However, the practical frequency limits within which a quartz generator can operate are restricted by the dimensions of the quartz plates. For long waves, excessively large plates are required, while plates less than 1 mm thick (which corresponds approximately to a wavelength of about 100 m) prove fragile and cannot withstand high voltages. Nevertheless, it is possible to use standard quartz generators for transmission by short waves, provided that the frequency is artificially increased, as is done, for example, at the Nauen station. The circuit of the Nauen transmitter is shown in Fig. 12. A quartz generator with a power of 2 W produces waves 100 m long; subsequently the power is increased to 20 kW and the frequency is quadrupled to a wavelength of 25 m.

Finally, mention must also be made of another property of quartz, likewise now widely used in radio engineering for the same purpose—to achieve as great a po-

constancy of the frequency of oscillations in the generating circuit. Cady, in his first paper\(^{9}\) on the oscillations of a piezoelectric crystal, theoretically investigated the question of the reverse action of quartz on an oscillatory circuit. He showed that the capacitance of a quartz capacitor, connected in parallel with the capacitor of the oscillatory circuit, as was depicted in Fig. 6, does not remain constant as resonance is approached: as the frequency is increased it first rises rapidly, then drops sharply, taking on negative values, and then, as one moves away from the resonance position, it increases again, once more attaining the value of the static capacitance of the quartz capacitor (Fig. 13).

Fig. 13.

Later the same questions were analyzed theoretically by Laue\(^{16}\). The presence of such a sharp jump in the capacitance of the quartz resonator at the moment of resonance makes it possible to use quartz as a stabilizer of oscillations in a circuit. Indeed, if the capacitance of the circuit for some reason decreases, this will entail an increase in the capacitance of the quartz, and conversely—an increase in the capacitance of the circuit will cause a compensating decrease in the capacitance of the quartz capacitor. The region in which quartz acts as a stabilizer is, of course, very narrow; it is determined by the resonance curve of the quartz plate. Thus quartz, in its various applications, makes it possible to solve one of the very important problems in the present state of radio engineering—the question of the constancy of the frequency and of the radiated wave; and in the last 2–3 years an extensive, predominantly American literature has already arisen devoted to the question of the use of quartz in radio\(^{17}\).

Despite the fact that quartz can predominantly serve the region of high frequencies, it can also be used to create oscillations of audio frequency. Two quartz plates having natural frequencies close to one another, when placed in a common generator circuit, produce beats in the generator, the frequency of which may be arbitrarily low. The same low-frequency beats may also be obtained when two quartz plates are in different generator circuits, or else with the aid of a single plate having the shape shown in Fig. 14 and possessing two different frequencies[^10]. Thus the piezoelectric properties of quartz can also be used for acoustic purposes. But quartz is of chief importance for acoustics as an emitter of powerful high-frequency oscillations lying far beyond the limits of audibility—in the region of the so-called ultrasonic frequencies.

Fig. 14.

For the purposes of practical acoustics, quartz was first used, as has already been said, by Langevin, who constructed an underwater ultrasonic transmitter originally intended for determining sea depths*) (echo sounder). This was also the first technical application of piezoelectricity, because Langevin was the first to use, for obtaining powerful mechanical oscillations, the resonance phenomena of elastic and electric oscillations of a piezoelectric crystal provided with the corresponding armature. The quartz plates initially used for this purpose by Langevin, measuring \(10 \times 10 \times 1.6\ \text{cm}\), were subsequently replaced by a device consisting of a multitude of quartz plates laid like a mosaic between two massive

) See UFN*, vol. 5, 240, 1925.

steel disks, which served as electrodes; one of the disks, being movable, is the source of acoustic waves. The alternating voltage in Langevin’s apparatus was supplied by an arc generator with a frequency of about 40,000, which corresponded to the resonant frequency of the device he used. The transition to the region of ultrasonic frequencies made it possible to have an emitter whose dimensions are greater than the length of the sound wave it emits, and thus it became possible to obtain in water a directed beam of acoustic waves emitted in a direction perpendicular to the plane of the electrode. With an expended power of about 1 kW (with radiated power of several hundred watts), a propagation range of the beam of ultrasonic waves of several tens of kilometers is achieved. Subsequently Langevin’s ultrasonic transmitter served not only as an echo sounder, but was also used for communication between ships; in this case the reverse conversion of ultrasonic waves into electrical oscillations can be carried out by means of a similarly mounted quartz receiver of appropriate dimensions, on the electrodes of which voltage oscillations of a strictly definite frequency arise; after amplification and transmission to a radio receiving device, the electrical oscillations arising on the quartz electrodes are detected by ordinary methods.

Langevin’s quartz transmitter, with a voltage on the electrodes of 30,000–40,000 V, creates in water such powerful acoustic radiation that small fish entering the zone of the ultrasonic beam die, and if one places a hand in the water in the path of the sound beam issuing from this transmitter, a sharp pain is felt. This method of producing powerful acoustic oscillations of very high frequencies made possible new acoustic investigations. In 1927 an interesting work by Wood and Loomis[^18] (R. Wood and A. Loomis) was published; they discovered certain very curious phenomena accompanying the propagation of short sound waves.

To study the properties of plane acoustic waves of ultrasonic frequency and high power, Wood and Loomis

they used a cathode generator consisting of two tubes, each of 1 kW power, which gave frequencies from 100,000 to 700,000. To the oscillatory circuit of the generator, through a transformer bringing the voltage up to approximately 50,000 V, were connected the metallic plates of a quartz plate: one of these plates was a massive lead one, the other of thin copper. The quartz plates used were disks 10 cm in diameter and from 7 to 14 mm thick. The quartz with its fittings was placed at the bottom of a glass vessel filled with transformer oil. From the thin copper electrode, acoustic waves of very great power propagate in the oil, despite the fact that Wood and Loomis did not work under conditions of electro-mechanical resonance. First of all, it turned out that these waves exert an extraordinarily great pressure on an obstacle placed in their path. Thus a glass disk 8 cm in diameter, upon which the sound waves exert pressure from below, can, without falling, be loaded with weights of 150 g. The waves exert the greatest pressure on the disk when the distance between the sound source and the reflecting disk is equal to an integral number of half-waves. If, in the presence of sound pressure, the disk is lowered, holding it by hand by a small rod glued to its center, then the hand periodically feels, after each quarter-wave traversed, increases and decreases in the resistance to the applied force. In this way one can determine the wavelength of the sound wave in the liquid, and consequently also the velocity of sound in it. This method of determining the velocity of sound was developed in detail by Hubbard and Loomis ^19) (Habbard a. Loomis). When the distance between the reflecting plate and the quartz radiator is equal to an integral number of half-waves, the back action of the quartz on the transmitter becomes most intense, which is recognized by the glow of a neon lamp connected with the transmitter.

By moving the reflecting disk with a micrometer screw, one can read off the position of the nodes with an accuracy of up to 0.01 mm. This method makes it possible to determine accurately the velocity of sound in any liquid, using a very small quanti-

of its quality; for this purpose a small vessel with liquid is placed directly on the oscillating quartz, and into this vessel is lowered a disk connected with the micrometric screw that lowers it. Boyle \(^{20}\), by the same method, demonstrates standing ultrasonic waves in liquids: the nodal planes in the liquid are sharply visible from the small gas bubbles that collect in them.

Fig. 15.

How great the sound pressure is in these experiments can be seen from the photograph, Fig. 15, which shows the surface of oil in which a quartz vibrator is located. Since the waves traveling from the vibrator also exert pressure on the surface of the liquid, it is at first covered with ripples; then, as the frequency of the generator approaches the region of resonance of the quartz, the surface of the liquid rises upward, and individual drops begin to fly off from it. At resonance, in Wood’s experiments, the surface of the oil rose by \(7\ \mathrm{cm}\), and with increased power even by \(10\ \mathrm{cm}\).

The results of experiments on obtaining standing waves in glass tubes also proved extremely interesting. For this purpose a tube sealed at one end is immersed with its end in oil, where rapid oscillations have been excited. If

if the outer side of the tube is coated with oil or liquid paraffin, then this liquid material gathers along the nodal lines, forming a system of rings. In exactly the same way, standing waves may be observed on a glass disk placed on the surface of oil, to the center of which a glass rod supporting it is glued. In this case the system of standing waves is formed owing to reflection from

Fig. 16.

the edge of the disk. In Fig. 16 (negative) a system of bands is visible, formed by lycopodium sprinkled on a glass disk, to which the supporting rod is attached eccentrically. The point of its attachment is visible in the system of bands; moreover, symmetrically to the point of attachment there has formed a focus of waves reflected from the edge of the disk; this focus itself is the source of secondary waves, which have produced a complex system of interference bands. Experiments with a glass disk having different thickness at the center and at the periphery

(bottom of a bottle), led to the conclusion that in this case transverse waves propagate in the glass, since the distances between the nodal lines, which have the form of circles, are in this case not the same: at the center, where the glass is thicker, the distances between the nodes are greater than at the edge of the disk. The same effect—the difference in the wavelength propagating in such glass rods of different diameters at one and the same frequency of oscillation—is illustrated by Fig. 17.

It shows microphotographs of glass rods with diameters of 0.15, 0.5, and 1 mm, on which, by the method mentioned above, marks of nodal lines were obtained, formed at the same frequency of oscillation. The smaller the diameter of the rod, the shorter the sound wavelength in it. This also confirms the authors’ conclusion as to the transverse character of the sound oscillations they observed in glass. The speed of sound in glass rods, determined from the data obtained, proved in these cases to depend on two quantities—the diameter of the rod and the frequency of oscillation; the speed of sound turns out to be the greater, the thicker the rod and the greater the frequency, while the speed determined in this way is much less than the ordinary speed of sound in glass—it varied under different experimental conditions from 400 to 2600 m/sec.

Fig. 17.

Through such thin glass rods one can transmit energy at high density. Thus, for example, a glass tube with a sealed end, terminating in a thin glass thread a meter or more in length, may serve as a convenient collector for sound energy, which through the thin end of the glass thread can be brought, for example, to living organisms being studied under a microscope, or to some separate organ of an animal. If the end of such

if the thread is taken between the fingers, a severe burn results from the heat released at the point of contact; it is also curious, for example, that a thermometer immersed in oil and indicating only \(25^\circ\) cannot be taken in the hand, since at the point of contact so large an amount of heat is released that a burn remains on the skin. The sharpened end of a glass rod, to which the energy is transmitted, passes freely through wood, charring it, and even through glass, drilling a little hole in it.

When these powerful waves are absorbed, so large an amount of heat is developed that \(50\ \mathrm{cm}^3\) of water acquire 430 calories per minute, and the temperature of the water placed in a test tube in a medium through which the ultrasonic waves pass rises very rapidly, despite the fact that the surrounding medium is maintained at \(0^\circ\). Alcohol in an amount of \(45\ \mathrm{cm}^3\) under the same conditions showed a temperature increase of \(4^\circ\) after 20 seconds. In exactly the same way, ice, absorbing sound waves, converts them into heat and melts.

Hardly the most interesting experiment among those performed by Wood and Loomis with ultrasonic waves is the formation, by means of these waves, of very fine emulsions. Oil and water, under the action of powerful oscillations of high frequency, give a stable emulsion. Water with mercury gives an emulsion that is at first white in color, then brownish, and finally black; even 24 hours after the formation of such an emulsion, large quantities of mercury remain in the water in the form of a suspension. Thus ultrasonic waves, as it turns out, can be used for the preparation of colloidal solutions. Benzene, subjected to the action of ultrasonic waves, is atomized and forms a mist; a photograph of the mist thus formed is given in Fig. 18. The same kind of mist, but with larger droplets, can also be obtained from water.

If a glass tube, narrowed in its middle part, is coated with oil and then, through the liquid, brought into contact with vibrating quartz, then on the narrowed part of the tube there is also formed an extremely fine mist of oil, as can be seen in Fig. 19, where in some

...points (nodal points of standing oscillations) separate foci of fog are visible. If a match is slowly brought up to the fog formed in this way, at first a large number of flashes of individual droplets is noticeable, and then the entire tube surrounded by fog catches fire like a torch.

Further, Wood and Loomis drew attention to certain properties of short sound waves. Under the action of these waves, small particles suspended in a liquid unite into larger formations, the course of certain chemical reactions is accelerated, and under the action of these waves the process of crystallization is accelerated.

Fig. 18.

The chemical actions of powerful ultrasonic waves were studied in greater detail by Richards and Loomis1 (Richards a. Loomis), who discovered the acceleration of certain chemical reactions and the decomposition, under the action of these waves, of certain metastable chemical compounds; they also noted that the boiling point of a liquid subjected to ultrasonic waves is somewhat increased—

decreases, and in those cases where gas is present in the liquid, ultrasonic waves promote the removal of gas from the liquid.

No less interesting are the results concerning the biological action of waves, discovered by Wood and Loomis. Small organisms,

Fig. 19.

such as, for example, paramecia, under the action of ultrasonic waves quickly lose the ability to move and then die. Red blood corpuscles in a physiological solution are rapidly destroyed. Small fish and frogs, under the action of powerful ultrasonic waves, die after one or two minutes; mice prove less

sensitive to sound waves and merely lose the ability to move.

Thus the piezoelectric properties of quartz can serve as a convenient method for acoustic investigations. Using this method, Abello^22) measured the absorption of sound at \(f = 612\,000\) in hydrogen and \(CO_2\); Boyle applied the same method to the study of the passage of short sound waves through various obstacles^23).

Speaking of acoustic phenomena accompanying piezoelectric processes, one should mention one interesting phenomenon observed by Meissner^24). If a quartz plate, cut in the usual way, is placed freely between the plates of a capacitor, fastened at its center, then, when an alternating field of a frequency corresponding to electromechanical resonance is applied to its plates, the quartz plate begins to rotate rapidly.

Fig. 20.

It is especially interesting that if two identical plates are taken, one cut from right-handed and the other from left-handed quartz, and they are placed in the capacitor so that, for both, the planes which become negatively charged under compression are on top, then the right-handed quartz begins to rotate to the right, and the left-handed quartz to the left. Studying these rotations, Meissner found that when, during periodic elongations and shortenings of a quartz plate along its long axis (the transverse effect), acoustic waves are produced in the air, then wind issues from the corresponding sides of the plate. This wind deflects the flame of a candle and can rotate a small windmill. In cases where a plate is taken with equal longitudinal and transverse dimensions, the wind arises

does not arise along the entire side of the plate, but only from one of its edges, as is seen in Fig. 20.

As a result of this the plate receives a torque, producing this curious effect. It further turned out that right- and left-handed quartz give rise to wind directed differently, which is what accounts for the rotation of right- and left-handed quartz in opposite directions. In Fig. 20 A the onset of rotation of right-handed quartz is shown, and in Fig. 20 B that of left-handed quartz. The circumstance that the wind arises along the edges of the plate is explained by Meissner by the fact that the quartz plate has certain directions in which the concentration of molecules is not the same; because of this, unequal conditions for the propagation of elastic waves are created in it; the author points out that these piezoacoustic phenomena may serve for further investigations of the structure of quartz.

For acoustic purposes the piezoelectric properties of crystals may be used not only for producing sound waves. It has already been mentioned above that the same device which Langevin used as a transmitter of sound waves under water can also serve as a receiving apparatus. On the same principle both piezoelectric telephones or loudspeakers and microphones can be constructed. In 1919 Nicholson^25) (Nicolson), and then Russel and Cotton^26) (Russel a. Cotton), constructed a piezoelectric emitter and receiver of low-frequency acoustic waves from Rochelle-salt crystals.

Rochelle salt (sodium potassium tartrate—NaKC₄H₄O₆·6H₂O) possesses much stronger piezoelectric properties than quartz, and fails to find practical application only because of its brittleness and instability.

Its crystals belong to the rhombic system, and according to Pockels its piezoelectric moduli (in CGS units) have the values $\delta_{14} \sim 1\,000 \cdot 10^{-8}$; $\delta_{25} = -165 \cdot 10^{-8}$; $\delta_{36} = 35.4 \cdot 10^{-8}$.

As is seen from the numbers given, Rochelle salt exhibits strong piezoelectric properties under torsion.

PRACTICAL APPLICATION OF CRYSTALS

Valašek discovered certain interesting features in the piezoelectric properties of Rochelle salt. Thus, for example, it turns out that if a Rochelle-salt crystal serves as the insulator in a capacitor, then the amount of electricity arising on the plate of the capacitor depends on the voltage to which this capacitor had previously been subjected, so that the graph relating voltage to the amount of electricity has the form of a hysteresis loop.

At \(-30^\circ\) C Rochelle salt is not piezoelectric. With increasing temperature its piezoelectricity increases, reaches a maximum at \(-5^\circ\), and thereafter begins to decrease, disappearing again at \(50^\circ\), a few degrees short of its melting temperature \((56^\circ)\).

Fig. 21.

Crystals artificially obtained from a supersaturated solution under definite conditions of growth have the appearance shown in Fig. 21. They are composite crystals and consist of pyramids turned with their vertices toward the center. This type of crystal is convenient for work with low-frequency currents. Nicolson used, for crystals of this type, mutually perpendicular electrodes, the arrangement of which is shown in Fig. 22.

Fig. 22.

Russell and Cotton, in their microphone, allowed sound waves to act directly on the crystal,

one electrode of which is connected to the cathode, and the other to the grid of a cathode amplifier. But since the piezoelectric properties of Rochelle salt are strongly affected by humidity, microphones of this kind change their properties with time, although Russell and Cotton indicate that several weeks after manufacture their microphone retained constancy.

Rochelle salt cannot withstand high voltages; therefore it also cannot be used as a powerful transmitter, and for the same reason it finds no application in radio engineering.

A quite special application of these crystals was given by Winn-Williams27 (Winn-Williams). A Rochelle-salt crystal, with dimensions along the axes \(b\) and \(c\) of \(2.5\ \mathrm{cm}\) and in the direction of the axis \(a\) of \(1\ \mathrm{cm}\) (see Fig. 21), provided with such electrodes as are shown in Fig. 22, has a light aluminum pointer \(3\ \mathrm{cm}\) long fastened to the plane \(ab\). This pointer indicates rotation about the axis \(c\), for which purpose it is furnished with a small mirror. The Rochelle-salt crystal mounted in this way can serve as an oscillograph suitable for frequencies from 0 to 600. For higher frequencies this oscillograph proves of little use, since all sorts of extraneous factors—humidity, temperature, the age of the crystal—have too strong an effect on it.

Fig. 23.

Analogous piezoelectric oscillographs were constructed by Wood28 (A. Wood) from quartz, despite its relatively small piezoelectricity. A quartz rod, fixed at one end, elongates in proportion to the voltage applied to the plates serving as the quartz electrodes (Fig. 23). The elongation is the greater, the longer the rod and the smaller its dimension in the direction between the plates. If the movable end of the quartz is connected to a rotating mirror, then with a rod length of \(5\ \mathrm{cm}\) and

thickness of \(0.01\ \text{cm}\), on a scale placed \(1\ \text{m}\) from the mirror, a displacement of \(1\ \text{cm}\) can be obtained at \(935\ \text{V}\).

A similar construction of an oscilloscope made of Rochelle salt, in which the direct elongation of the crystal was used, was carried out by Scheibe and proved to be approximately 4,000 times more sensitive.

An even more sensitive oscilloscope was constructed by A. Wood from two quartz plates put together. The plates are chosen so that when one lengthens, the other must shorten. By fastening one end of the rod, he obtained a sensitive oscilloscope in which the free end of the quartz plates put together, mounted like the oscilloscope shown in Fig. 23, moves up and down with changes in voltage and rotates the movable little mirror. From such an oscilloscope, on a scale standing at a distance of \(1\ \text{m}\) from the mirror, one can obtain a displacement of \(1\ \text{cm}\) with a voltage of only \(2.5\ \text{V}\).

Finally, one should also mention another possible practical use of the properties of piezoquartz. Kerr Grant\(^{29}\) (Kerr Grant) used quartz as the insulator in a Kerr condenser. When quartz is placed between crossed nicols and is excited by an alternating electric field of its resonant frequency, a beam of light passing through it in the direction of the optical axis gives periodic darkenings and flashes with a frequency corresponding to twice the frequency of the electric field. Thus, at a field frequency of 144,000, the corresponding number of passages of a light beam through the Kerr condenser was observed with the aid of a rotating mirror. It is evident that the number of light interruptions can be made much larger and brought up to several million per second. This method may in many cases be more perfect than, for example, the methods of Fizeau and Foucault, and may be applied, for example, to determine the speed of light, to count small intervals of time on moving films, or it may be used in that system of transmitting images over a distance which was developed by Karolus and which has now already entered into practice.

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1. Richards a. Loomis. ↩