Lecture Demonstrations on Ferroelectricity in a General Physics Course

K. N. Karmen

The growing interest in ferroelectrics has still not found due reflection in university courses of general physics[^1],[^2]. The existing monographs and the large number of articles on this question are not readily accessible to the broad circle of students in the junior years who study general physics. The proposed demonstrations should contribute to a deeper understanding of ferroelectric phenomena.

Among the ferroelectrics known at present, Rochelle salt is the most suitable for lecture demonstrations. The sharply expressed nonlinearity of the dependence of polarization on the electric or mechanical stress in the ferroelectric region, the transition—easily attainable in terms of heating duration—to the non-ferroelectric state, and the high value of the dielectric constant $\varepsilon_x$ and of the piezoelectric modulus $d_{14}$ make this ferroelectric indispensable for the indicated purposes.

In connection with the fact that knowledge of the laws of alternating current is required for an understanding of the demonstrations, it is desirable to carry out a detailed study of ferroelectrics at the end of the section “Electricity,” after a preliminary cursory consideration of this question in electrostatics.

The specimens used in carrying out the demonstrations have the form of rectangular parallelepipeds. The side surface normal to the crystallographic axis $x$ should have dimensions $2 \times 2\ \text{cm}$ and a thickness of $3$–$5\ \text{mm}$. The plate is cut from a single crystal so that its smaller faces are perpendicular to the bisector of the angle between the $y$ and $z$ axes. As electrodes, a layer of graphite is applied to the large faces with a soft pencil. Fairly good results are also obtained with electrodes of colloidal gold. Rochelle-salt samples may be stored without special precautions so long as the relative humidity does not exceed 60–70%. The most favorable humidity for carrying out the demonstrations is 40–50%. Drying the samples in closed vessels containing a desiccant should not be prolonged, since the loss of crystallization water caused by excessive drying entails a considerable weakening of the ferroelectric effects.

As a universal holder it is proposed to use the device shown in Fig. 1a. As is clear from the drawing, the sample being demonstrated is placed on the lower platform, which is rigidly connected with the upper one. Electrodes well pressed to the faces provide for maintaining the desired humidity inside the vessel. For this purpose, after the sample has come into contact with moist air in the beaker, a small glass vessel containing powdered calcium chloride is placed on the lower platform near the sample. After a time, which is not difficult to determine from the change in the surface conductivity of the sample, the vessel with the calcium chloride is quickly removed from the beaker. To observe the change in surface conductivity, the sample placed in the holder with the desiccant is connected through a mirror galvanometer of sensitivity about $10^{-9}\ \text{A/mm}$ to a battery of cells whose emf is of the order of 200–300 V. The galvanometer must first be shunted, since for a “damp” sample the effective conductivity may prove considerable. The next step should be considered complete after the current has decreased to $10^{-2}$–$10^{-3}$ microampere. The amount of calcium chloride required for this purpose is several tenths of a gram. Drying under these conditions takes 10–15 min.

Fig. 1a. Universal holder with press. \(A\) — brass cup into which the holder is placed. In demonstrations that do not require constant mechanical stress, the steel press \(Б\) is removed; a coupling \(Г\), preventing contact of the rod with the crystal, is put on the rod \(B\), made of high-quality steel. In the latter case the specimen, lightly clamped between the springs \(Д\), is practically not subjected to external mechanical stresses.

Fig. 1b. Section of the universal holder with cup, at \(1/2\) natural size. \(П_1\) and \(П_2\) — ebonite platforms rigidly connected with one another. Platform \(П_2\) in its upper part is well fitted to cup \(A\). In the middle of the lower platform \(П_1\) a steel backing plate \(П_3\) is “sunk” into the ebonite, above which the specimen is mounted. To avoid short-circuiting the press to the side of the crystal facing it, it is glued to a thin ebonite plate. For more reliable contact between \(Д\) and the specimen electrodes there are lead plates of size \(4 \times 4 \times 1\ \mathrm{mm}\), fastened to the springs \(Д\). The rod \(B\) is passed through the bushing \(К\), set into the ebonite platform \(П_2\). To obtain the desired mechanical stresses, iron cylinders of various masses are placed on \(M\). One of these cylinders is shown in Fig. 1a.

Fig. 2. Circuit diagram of the apparatus for demonstrating ferroelectric phenomena. \(Б\) — battery, \(V_1\) and \(V_2\) — voltmeters. \(M.\ E.\) — capacitance box, \(З.\ Г.\) — audio generator, \(Э.\ О.\) — electronic oscilloscope, \(П_1\) and \(П_2\) — switches, \(C_1\) — ferroelectric capacitor, \(C_2\) — capacitor of capacitance \(5\ \mu F\), \(R_1,\ R_2,\ R_3\) — resistances.

The demonstration of hysteresis is carried out according to the circuit shown in Fig. 2. The vector diagram of this circuit is shown in Fig. 3. As is evident from the diagram, the distortion of the hysteresis loop caused by the phase shift of the voltages applied to the oscilloscope inputs can be reduced to a minimum if the equality is satisfied:

\[ \frac{C_1}{C_2}=\frac{R_2}{R_1}, \tag{1} \]

where \(C_1\) is the capacitance of the ferroelectric capacitor, \(R_1\) is its active resistance, \(C_2\) is the capacitance of the second capacitor, connected in series with the ferroelectric one, and \(R_2\) is the variable shunting resistance. The minimum phase shift is most easily achieved by increasing \(C_2\), insofar as this is allowed by the gain coefficient of the oscillographic amplifier. Since the active resistance \(R_1\) is practically due to surface conductivity and hysteresis losses, changes in voltage, frequency, and humidity may produce a distortion that was not initially present under other conditions. The presence of the variable shunting resistance \(R_2\) makes it possible to eliminate these distortions easily.

Fig. 3. Vector diagram. \(J_{c1}\)—reactive current through the ferroelectric capacitor, \(J_{c2}\)—reactive current through the linear capacitor, \(J_{R1}\)—active current of the ferroelectric capacitor, \(J_{R2}\)—current in the shunting resistance, \(v_1\) and \(v_2\)—voltages across the capacitors \(C_1\) and \(C_2\), \(v\)—voltage at the generator terminals, \(a_0\)—phase shift between the voltages applied to the oscilloscope inputs.

Fig. 4. Hysteresis curves at different voltages:
\(a\)—50, \(b\)—100, \(v\)—150 and \(g\)—185 V, \(\nu=50\) Hz, \(t=18^\circ\)C.

The series of curves in Fig. 4, in addition to the hysteresis itself, illustrates the basic dielectric properties of ferroelectrics, in particular nonlinearity. To estimate the capacitance of the ferroelectric capacitor and for comparison, a mica capacitance box is connected in place of the first capacitor.

The existence of the upper Curie point can easily be shown by removing the holder from the stand and positioning it so that the middle of a smaller face is parallel to the filament of a 75-W lamp mounted on a stand 5–8 cm from the specimen. (In this case, owing to heating, humidity has no significant effect.) Heating by this method ensures within a few minutes a complete transition to the non-ferroelectric state, marked by the appearance of a straight line on the oscilloscope screen. After the lamp is switched off, approximately over the same interval of time the hysteresis curve gradually reappears.

To demonstrate the influence of a constant biasing field on the polarization process, the same circuit is used; switch \(P_1\) and slider \(D\) (Fig. 2) make it possible to change the sign and magnitude of the constant voltage applied to the ferroelectric capacitor. The characteristic curves obtained are shown in Fig. 5. Replacing the ferroelectric capacitor by a capacitance box, for which any value of the biasing field produces no changes in the straight line on the oscilloscope screen, convincingly emphasizes the profound difference between a dielectric and a ferroelectric.

All the experiments described are carried out at the usual frequency for studying ferroelectrics, 50 Hz. Increasing the frequency to \(10^4\) Hz at an effective voltage of 130–150 V produces the following: 1) at first the loop, while simultaneously shortening and widening, takes the form shown in Fig. 6; 2) after some time

narrowing begins, ending with the degeneration of the loop into a straight line; 3) the transition to a frequency of 50 cps at first does not cause a change in the straight line on the oscilloscope screen, but with time a loop again appears, gradually assuming its original form. The phenomena described, caused by heating of the specimen at the expense of losses, can be explained without particular difficulty with the aid of the vector diagram described earlier.

The presence of the direct piezoeffect in the static regime can be demonstrated by means of a setup consisting of a specimen with a holder, the terminals of which are connected directly to a ballistic galvanometer short-circuited through its critical resistance. When a load is placed on platform $M$ an initial throw in one direction is observed, and when it is removed a throw in the opposite direction occurs. Because of hysteresis these throws are, generally speaking, not equal to one another. Successive application of loads from 0.5 to 5.0 kg makes it possible to observe saturation of the piezoelectric polarization. Comparison of the throws when one and the same load is applied before and after rotating it by 90° about the $xx$ axis gives a visual representation of the unipolarity of the specimen. It should be noted that, for the indicated dimensions, most specimens are unipolar; nevertheless, in those cases when it is desired to demonstrate appreciable unipolarity, the specimen must first be polarized by a field of strength 200–300 V/cm over the course of an entire week. In such prepolarized specimens the unipolarity manifests itself very sharply. It must be noted that for most of the demonstrations described one should use a specimen with minimal unipolarity. If by chance no such specimen is available, then its almost complete disappearance can always be achieved in several days by an electric

Fig. 5. Hysteresis curves distorted by a constant biasing field $V = 80$ V, for different values of the alternating voltage: $a$—50, $b$—100, $v$—185 V, $\nu = 50$ cps, $t = 18^\circ$C.

Fig. 6. Increase of hysteresis losses when the frequency is changed from 50 to $10^4$ cps: $a$—initial state, $\nu = 50$ cps; $b$—hysteresis loop 30 sec after the transition to a frequency of $10^4$ cps; $v$ and $g$—the same, respectively, 2 and 5 minutes after the moment of switching to the frequency $10^4$ cps.

field of the same strength but of opposite sign (relative to the sign of the field that causes enhancement of the unipolarity). The presence of the direct piezoeffect can also be demonstrated without using a galvanometer. For this purpose one uses the setup shown in Fig. 2; with a constant field $E = 0$ such a value of the alternating field is chosen that the amplitude $E_0$ reaches the value required for saturation. Then loads from 0.5 to 5 kg are successively placed on and removed from platform $M$. The identity of the oscillograms observed upon application of constant electrical and mechanical stresses convinces one of the presence of the effect itself and makes it possible to establish the relation between the electrical and mechanical stresses that cause one and the same polarization. For this purpose, after application of the constant field, the specimen is deformed by a load whose magnitude is selected so that the characteristic asymmetric curve assumes its usual form of a hysteresis loop.

The piezoeffect in the dynamic regime is conveniently demonstrated by directly connecting the terminals of the holder to the oscilloscope. By selecting a constant load (about

1.5–2 kg), it is possible to reach the region of the steepest increase of the piezoelectric polarization. Blows of a wooden hammer on the platform on which the load is placed produce vibrations that cause periodic changes in the piezoelectric polarization. With some skill, one can obtain on the oscilloscope screen a sinusoid with an amplitude slowly decreasing as a result of damping. With additional shielding of the holder (which makes it possible to use considerable amplification of the oscilloscope amplifier), this circuit is very sensitive and makes it possible, on the oscilloscope screen, to record vibrations caused by light blows on the experimental table, by footsteps of a person passing nearby, etc.

Fig. 7. Hysteresis curve under unilateral compression, which, by analogy with the curve $\varepsilon$ in Fig. 5, makes it possible to demonstrate the presence of piezoelectric polarization—the direct piezoelectric effect.

The inverse effect is demonstrated by switching the specimen with the same constant load to the input of an audio generator. A distinct sound is already noticeable at a frequency of 200–400 Hz. This sound is especially sharply intensified at resonance. A smooth change of frequency over the entire range of the audio generator makes it possible to distinguish the values of certain harmonics of the specimen. By shifting the specimen somewhat away from the center of the lower platform, one can obtain a noticeable displacement of it, due to the inverse piezoelectric effect.

Fig. 8. Dependence of the voltage on the plates of a vibrating ferroelectric plate on time.

The number of possible demonstrations can, if desired, be considerably increased. However, even the demonstrations described make it possible to reveal the principal areas of the varied applications of ferroelectrics: miniature capacitors, transducers, sensors, etc.

CITED LITERATURE

1. K. A. Putilov, Course of Physics, Vol. II, Gostekhizdat, Moscow, 1954.
2. S. E. Frish and A. V. Timoreva, Course of General Physics, Vol. II, Gostekhizdat, Moscow–Leningrad, 1956.
3. W. Cady, Piezoelectricity, IL, Moscow, 1949.