V. D. Kuznetsov.

Piezoelectric Quartz and Its Application for Measuring Very Weak Electric Currents.

(To Article I, p. drawings).

The instrument known as Curie’s piezo-quartz consists of a crystalline quartz plate about 10 cm long, 1.5–2 cm wide, and 0.05–0.07 cm thick, cut so that the optical axis of the crystal (Fig. 1) is parallel to its width and perpendicular to its length, while one of the binary, or electrical, axes is perpendicular to the plate. When such a plate is stretched, equal but opposite quantities of electricity appear on its broad faces; these are collected by tinfoil leaves pasted onto the quartz plate. Therefore piezo-quartz may be called a standard of quantity of electricity. It is used to measure very weak electric currents of the order of \(10^{-14}\)—\(10^{-17}\) amperes.

Fig. 2 shows piezo-quartz in the construction of the firm “Société Centrale de produits chimiques. Paris,” which I used in my investigations. The piezo-quartz plate \(PK\) is set at its ends into metal clips \(OB\). The plate is suspended from the hook \(K\), and to its lower end is attached the rod \(C\) with the cup \(Ch\), on which weights (up to 5 kg) are placed for stretching. The charges appearing during stretching are captured by tinfoil or silver coatings covering both sides of the plate. Each coating has two narrow (0.1–0.2 mm) slots \(Shch\), separating the central part of the coating from its ends. To the central parts, which together with the quartz plate form a flat capacitor, small metal circles are glued, connected by spiral copper springs to the terminals \(Z\) with amber insulation. One of the coatings can be connected to earth by means of a special device consisting of the cam \(KL\), the lever \(P\), and a horizontal rotating rod provided with the handle \(RK\). The other coating is ordinarily always connected to earth. The lower part of the brass case \(F\) has a removable bottom \(D\), which is fastened by means of two pins. To remove the bottom, it must be turned as far as it will go and then, while turning slightly, pulled downward. On the bottom of the case lies an annular glass cup \(SCh\), into which pure sulfuric acid with a small amount of fuming Nordhausen acid is poured, to about one third, for absorbing water vapor, since only in the absence of moisture inside the case do the slots \(Shch\) insulate well and the instrument function properly. Through the brass tube \(T\) (see also Fig. 2-a) passes the rod \(C\) with the cup. The metal plugs \(PR\) serve to reduce the openings and, consequently, to hinder the access of moisture and to eliminate oscillations of the rod that arise when weights are placed on the cup. From above the instrument is closed by a brass cap \(KP\) (Fig. 2-b). The terminals \(Z\) pass through movable metal plugs, which during pauses in the experiments are moved tightly up against the walls of the cap and only during the experiments, for insulating the terminals, are moved away.

A quartz plate should be kept very clean. In particular, attention must be paid to the insulating slits and to the already open faces of the plate. Under no circumstances may these be touched with the fingers. If the insulation of the open faces and slits is not sufficiently perfect, they should be washed with a piece of clean paper moistened first with distilled water, then with pure alcohol, and finally again with water. After washing, the instrument must not be used for several hours.

J. and P. Curie¹ showed that the quantity of electricity \(Q\), expressed in electrostatic units, which appears on each plate of piezo-quartz when it is stretched or compressed, is expressed by:

\[ Q = k \frac{L}{D} P, \]

where \(L\) cm is the length of the active part of the quartz plate, i.e. the length of the plate, \(D\) cm is the thickness of the plate, \(P\) dynes is the load stretching or compressing the plate, and \(k\) is the so-called piezo-electric constant, numerically equal to the quantity of electricity that appears on the plate of a quartz condenser having a length and thickness of 1 cm under the action of a force of one dyne. The investigators who studied the piezo-electric properties of quartz obtained the following values of the constant \(k\):

J. and P. Curie² \(k = 6.32 \cdot 10^{-8}\) per one dyne, J. Curie³ \(k = 6.90\), P. Czermak⁴ — \(6.26\), E. Riecke and W. Voigt⁵ — \(6.45\), F. Pockels⁶ — \(6.27\), and W. Röntgen⁷ — \(6.94 \cdot 10^{-8}\).

The last number, obtained by Röntgen, differs quite considerably from the other numbers, except for J. Curie’s number. The constant \(k\), referred to a kilogram, according to Röntgen is equal to \(0.0681\), and according to J. Curie \(k = 0.0677\). Röntgen sees the reason for the discrepancy between his number and those of other investigators in a whole series of circumstances not fully taken into account in earlier investigations. The number \(k\) may come out smaller than the true one: 1) when the optical and electrical axes are incorrectly situated relative to the face of the plate; 2) when the stress in the crystal is insufficiently homogeneous; 3) when there are impurities in the crystal; 4) when the capacity of the absolute condenser used in determining \(k\) is underestimated; 5) when the values of the electromotive forces of normal cells are underestimated, and, finally, 6) when the insulation is insufficiently perfect.

In Fig. 3 is shown the diagram of the connection of the instruments in determining the constant \(k\). One of the plates of the quartz plate is connected to earth; the other is connected with an insulated pair of quadrants of the quadrant electrometer \(E\). With this same pair of quadrants is connected one of the plates of a flat normal condenser \(C\) with a guard ring, the other plate of which, by means of the switch \(PR\), can be connected either to earth or to the pole of the battery \(B_2\) of normal cells.

The experiment consists in the following: first, by opening the key \(K'L\), the pair of quadrants is insulated; then, by throwing the switch \(PR\), the plate of the condenser is charged to the potential \(V\), and at the same time a suitable weight \(P\), selected so that—

so that the quantity of electricity \(Q\) appearing on the quartz plate is exactly compensated by a charge of the opposite sign on the plate of the condenser. When these charges are equal, the needle of the electrometer remains at rest, and the constant \(k\) is determined from the equality:

\[ Q = CV = k \frac{L}{D} P, \]

where \(C\) is the capacitance of the absolute condenser. In practice one may proceed differently, namely: measure \(L\) and \(D\) and use the ready value of \(k\).

In 1881 the brothers P. and J. Curie¹ proposed a special compensation method for measuring very weak electric currents, which became rather widely used, especially after the work of the Curies² on radioactive substances. Fig. 4 shows the connection diagram of the instruments in this method.

The plate \(A\) of the measuring condenser \(IK\), through which the current to be measured flows from the battery \(B_2\), may be connected by means of the switch \(P\) either to earth or to the insulated pair of quadrants of the quadrant electrometer \(E\), which is in permanent connection with one of the plates of the piezo-quartz \(PK\). The second pair of quadrants and the second plate of the piezo-quartz are always connected to earth. The needle of the electrometer is connected to one pole of the battery \(B_1\), the other pole of which is earthed.

The electric current flowing through the measuring condenser goes to earth. To measure it, at a certain moment the switch \(P\) is thrown over and at the same time the quartz is stretched, increasing the load so that the needle of the electrometer remains at zero the whole time. At the moment the switch is thrown, a stopwatch is started, and it is stopped after such an interval of time \(T\) when the stretching force \(P\) reaches a definite value. The current strength is determined by the formula:

\[ i = k \frac{L}{D} \cdot \frac{P}{T} \ \text{el.-st. units}. \]

To obtain the current strength in amperes, the value obtained should be divided by \(3 \cdot 10^9\). Instead of gradually increasing the stretching of the quartz, one may, conversely, decrease the stretching load from some value \(P\) to zero; only in this case the other plate of the quartz must be connected to earth.

The most important role in this method is played by the gradual, smooth change of the load. J. Curie indicates two ways of effecting such a change.

The first method consists in placing on the pan of the piezo-quartz a vessel into which mercury is poured through a stopcock. The outflow can be regulated so that exact compensation is obtained. The quantity of mercury that has flowed into the vessel during the time \(T\) is determined by weighing. This method gives great accuracy and is convenient only with an unchanging current strength. Having adjusted the inflow of mercury for a constant current, observations can be continued for a long interval of time. However, this method is inapplicable with a varying current, which often has to be dealt with in studying the conductivity of dielectrics.

The second, simpler, method consists in gradually placing weights on the pan during compensation and, supporting it all the time by hand, regulating the load so that the needle does not deviate from zero, with

Then the time is noted from the moment the stretching begins until the removal of the hand supporting the cup. One may simply place a suitable load \(P\) on the cup and, at the beginning of the compensation, support it by the effort of the hand, which, to avoid fatigue, should be placed on a support of suitable height. With some practice, good measurements can be made by this method. The hand gradually becomes accustomed to the adjustment and instinctively supports or lowers the load.

The advantage of the second method over the first lies, above all, in its simplicity. Further, the second method is applicable with a varying current, when it is necessary to perform compensation over small intervals of time—of a few seconds—rapidly following one another. Working by hand and passing without interruption from one load to the next, it is necessary only to mark the moments of each change in load. The firm “Societe centrale de produits chimique. Paris” manufactures a special device for more convenient support of the loads, but the instrument which I used had no such device.

I devoted a rather long time to mastering this method well, and in practice became convinced that it has substantial shortcomings. First of all, it is very difficult to relax smoothly the effort of the hand supporting the cup with the loads: jolts occur, causing a displacement of the electrometer needle, which can only with difficulty be annulled by subsequent compensation. When one has to work for several hours, the hand becomes so tired from the tension that, in the end, the compensation obtained is poor. The observer’s restless state has a strong effect on the accuracy of the measurements. To eliminate the jolts I tried fastening spiral springs to the cup, which I held stretched by hand and gradually released. This brought some improvement in smoothing out the jolts; but the hand, as before, quickly became tired.

The second major shortcoming of this method is the low accuracy in determining the moment when the hand ceases to support the load.

After a whole series of attempts to improve the compensation method, I apparently succeeded in attaining the goal and in developing a more convenient and accurate method. The essence of this third method is as follows. To the lower frame of the piezo-quartz, \(PK\) (Fig. 5), a steel spiral spring \(PR\) of suitable elasticity is suspended on a thread; to the lower end of the spring is fastened an iron ball \(ZhSh\) of a weight appropriate to the observed current strength. The ball can be made hollow and its weight varied for different series of experiments by means of shot or mercury. The glass beaker \(SS\) is filled with such an amount of mercury that, when it is raised, the ball can float. From the upper part of the ball and from the mercury run two flexible, thin, spiral-shaped conductors to the electromagnet of an electric chronograph, with an accumulator \(AK\) placed in the circuit. Before the observation, the beaker is raised by hand to such a height that the ball floats freely on the mercury and the spring is relaxed. In this position the circuit is closed and the armature with pen \(P\) is attracted to the core of the electromagnet. After this, the electrometer and the piezo-quartz are insulated from the ground by means of a switch with mercury contacts; this moment of insulation is marked by the second pen of the chronograph¹. Gradually lowering the beaker, the electrometer needle is kept at zero. At the moment the iron ball breaks away from the mercury, the pen springs back from the electromagnet and

makes a mark on the tape of the chronograph. Thus the chronograph makes two marks, from which one can determine the interval of time \(T\) required for the stretching force to increase from zero to a value equal to the weight of the ball with the spring. This interval of time is easy to determine with an accuracy of a tenth of a second, since the third pen of the chronograph marks the seconds.

The method described has great practical advantages. First of all, the observer has no need whatever to keep track of the time, since it is determined automatically. Consequently, the entire attention of the operator can be concentrated exclusively on the accuracy of the compensation, i.e., on keeping the needle of the electrometer at zero. Further, thanks to the spring on which the load hangs, the very process of compensation is considerably facilitated. The spring smooths out the jolts unavoidable when lowering the load, and makes the lowering soft and smooth. This is also promoted by the very method of gradually increasing the load by reducing the volume of mercury displaced by the ball. I had to work a great deal with this method, and I found no substantial shortcomings in it. On the contrary, by comparison I became convinced that this method has many advantages over Curie’s methods. In this method the hand becomes incomparably less tired than in the second method, since, thanks to the spring and the mercury, during the observation it is under less strain. True, this method too has one drawback, but it depends entirely on the chronograph and consists in the fact that sometimes the markers of the chronograph, owing to friction against the paper, begin to lag a little and thereby introduce an error into the determination of the time interval; but with careful attention to their action, by means of appropriate adjustment, this defect is easily eliminated.

At first I had wished to confine myself to the use only of mercury and a ball without a spring, but this proved insufficiently convenient and was not a significant improvement of the method. The use of cylindrical iron weights with a spherical base likewise proved of little suitability.

In the first experiments it seemed to me that the spring, while the cup was being lowered, might oscillate and thereby make the moment of detachment indefinite; but special experiments removed this doubt.

To the article by V. D. Kuznetsov, “Piezoelectric Quartz and Its Application for Measuring Very Weak Electric Currents.”

Fig. 1.

Fig. 2.

Fig. 2-a.

Fig. 2-b.

Fig. 3.

Fig. 4.

Fig. 5.

1. I used a chronograph with three electromagnetic markers writing on a paper tape moved by an electric motor. This very convenient and excellently operating chronograph was purchased from the firm “The Cambridge Scientific Instrument Co., Cambridge England” [Catalogue No. 52, p. 15 (1908)]. ↩↩↩

2. Mme S. K. Curie. Recherches sur les substances radioactives. Paris, 1903. ↩↩

3. J. Curie. l. c.; ↩

4. P. Czermak, Wien. Sitzungsber. 96, 1217 (1887); ↩

5. E. Riecke and W. Voigt, W. A. 45, 549 (1892); ↩

6. F. Pockels. Abh. d. Ges. d. Wiss. Göttingen. 39 (1894); ↩

7. W. Röntgen. Ann. d. Phys. 41, 449 (1913). ↩