PIEZOELECTRIC VOLTAGE OF BARIUM TITANATE WITH STABILIZED DOMAINS A. JA~KIEWICZ

Institute of Physics, Wroclaw University, Wroclaw*) I n BaTiO 3 with unidirectional stabilized domains mechanical excitation causes a piezoelectric stress that is strongly asymmetrical with respect to the orientation of the electric field applied to the sample. The magnitude of the piezoelectric stress measured in the direction of polarization of the stabilized domains is usually greater t h a n in the opposite direction. At a cyclic change in the weak electric field the dependence of the piezoelectric stress on this field is reflected in the shape of the asymmetric hysteresis loop.

1. I N T R O D U C T I O N In a paper on stabilized domains in ferroelectrics [11 the author showed that the electric charges deposited on domain walls compensate the depolarization field and thus change the reversibility of the domains in an externally applied electric field. The deposition of charges on the d o m a i n walls. takes p l a c e i n every ferroelectric, though to a different extent. The effect caused by the accumulated charges can be exaggerated if, due to some external agent, the n u m b e r of free electric charges is increased. Domains with large compensation charges do not share in the direct change in polarization of the crystal when in a n electric field. The stabilized domains i n a partly stabilized specimen would have their share, however, in the indirect influence on the polarizability of the crystal. First, the stabilized domains diminish the total amount of the reversible volume of the specimen in question, since some reversible domains are transformed into irreversible ones. Second, they can change the distribution of polarization vector of switchable domains. The change in volume is readily observed when the hysteresis loop is taken for an irradiated ferroelectric; then a decrease in polarization of the sample is observed. W h e n a crystal is polarized by a steady electric field and then stabilized by irradiation, the asymmetric distribution of the remaining unstabilized domains can be expected. In this paper we show the results of investigating polycrystalline barium titanate polarized by a d.c. field and t h e n irradiated. /

2. E X P R E S S I O N O F A L T E R N A T I N G P I E Z O E L E C T R I C V O L T A G E These investigations are carried out using the ultrasonic method devised by H u s i m i [2]. Mechanical excitation applied to a specimen liberates free electric charges due to the piezoelectric effect. The total a m o u n t of charges is proportional to the macroscopic polarization of the specimen. if the effect is a n electrostrictive one. Thus we can use the piezoelectric constant of such a ferroelectric as a measure of the polarization state. The dependence of the piezoelectric constant on the polarization is given [3] as (1)

d33 = 2XcQ333 P ,

where Zc is the susceptibility of the crystal along the c axis at constant stress, Q333 the electrostrictive coefficient and P the macroscopic polarization of the specimen.

*) ul. Partyzant6w 71 m 3, Wroetaw 9, Poland. 396

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Piezoelectric Voltage o f Barium Titanate with Stabilized Domains

Applying an alternating mechanical excitation X sin tot to the crystal we get the alternating piezoelectric voltage (2)

U = 2zcQa33PlX33 sin tot

where l is the thickness of the crystal. For constant mechanical excitation the piezoelectric voltage developed across the specimen is a measure of macroscopic polarization. It should, however, be borne in mind that the proportionality factor between this voltage and the polarization is unchanged if the stabilization state of the crystal is unchanged, since the susceptibility may vary. 3. EXPERIMENTAL RESULTS AND INTERPRETATIONS The m e a s u r e m e n t s were carried out for polycrystalline b a r i u m titanate. The s a m p l e was p o l a r i z e d by a strong d.c. electric field a n d then i r r a d i a t e d ; i n some instances the s a m p l e was p o l a r i z e d by a strong d.c. field at a t e m p e r a t u r e in the vicinity of the Curie p o i n t w i t h o u t being i r r a d i a t e d . I n o r d e r to achieve r e p r o d u c i b l e results the sample was d e p o l a r i z e d b y an a l t e r n a t i n g field o f 1 k V / c m a m p l i t u d e before every m e a s u r e m e n t was m a d e . T h e m e a s u r i n g a r r a n g e m e n t is s h o w n in Fig. 1. T h e b l o c k d i a g r a m is given in Fig. 2.

Fig. I. Measuring apparatus. 1 -- ferroelectric sample, 2 -- quartz crystal, 3 -- aluminium screen, 4 -- brass base, 5 -- insulating layer.

Fig. 2. Block diagram. 1 -- h.f. generator, 2 -- measuring device shown in Fig. 1,3 - h.f. band filter, 4 -- voltmeter.

c,L t / /

Fig. 3. Piezoelectric voltage of polarized and' stabilized polycrystalline barium titanate versus applied d.c. electric field.

The first series o f m e a s u r e m e n t s were carried out using a w e a k steady electric m e a s u r i n g field. The results are shown in Fig. 3. The positive direction is the same as that o f the strong poling field. The p o l a r i z a b i l i t y o f the specimen is a s y m m e t r i c ; it is larger in the direction o f the strong p o l i n g field t h a n in the o p p o s i t e direction. T h e a s y m m e t r y d e p e n d s o n the strength o f the p o l i n g field a n d on the p o l i n g time. Czech. J. Phys. B 16 (1966)

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A. Jagkiewicz

Before any change was made in the direction of the measuring field the specimen was depolarized by an alternating field. The polarizability measured after annealing for about 24 hours at a temperature of 200~ was nearly symmetric. The asymmetric polarization o f a ferroelectric had already been observed [4] but it was field irreversible. The second series of measurements were carried out for a sample prepared as before. A weak alternating field of low frequency was used as measuring field; the results are shown in Fig. 4. The resulting polarization of the sample is the polarization

I

I

i

U

i

[mVl

U

10

[mV2

8 6

-2oo J

100

0

I

I

I

100

200

300

I

I

200 E [ V/cm 2

I

400 500 E IV/era2

Fig. 4 . Piezoelectric voltage of polarized and

stabilized polycrystalline barium titanate versus applied a.c. electric field.

Fig. 5. Hysteresis loop of polarized and stabilized polycrystalline barium titanate.

averaged over one cycle of the alternating field. For a poled specimen an increase of the averaged polarization is always observed when the amplitude of the measuring field is increased. The resulting polarization assumes zero value for any value of the applied alternating field if the specimen is annealed at a temperature high above the Curie point. Using the same measuring apparatus and samples as before, the hysteresis loop was taken at room temperature in a slowly cycling field of 0.9 kV/cm amplitude. The results are shown in Fig. 5. All the results of the measurements showed asymmetric hysteresis loops characterized not only by the shift usually observed along the axes for irradiated ferroelectrics but also by the lack of a symmetry point. The symmetry point appears, however, when the hysteresis loop is taken in fields inducing saturation polarization. Figure 5 clearly shows that the descending and ascending branches of the loop differ quite largely. The branches can be described by the equations

(3a)

Ua = ao + a l E + a2 E2 ,

(3b)

Ua = bo + b l E + b2 E2 ,

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Piezoelectric Voltage o f Barium Titanate with Stabilized Domains

for the descending and ascending branches respectively. In the case of the symmetric loops observed so far, the coefficients appearing in Eqs. (3) satisfy the relation: b~/a 1 = 1, b2/a2 = - 1 . For the asymmetric loop shown in Fig. 5, we get for the ratio of the coefficients: bl/a~ = 1, b2/a 2 = - 4 . 2 (the coefficients were determined by the least squares method). The value of the ratio of the coefficients at the squared term in Eqs. (3) depends on the stabilization state of the specimen induced by the strong d.c. field. For specimens depolarized by a high a.c. field, the value of the asymmetry coefficients decreases. For the totally annealed samples the value is equal to minus one. 4. C O N C L U S I O N

All the measurements show that after prolonged polarization by a strong steady electric field a ferroelectric specimen reveals asymmetric polarizability. The polarizability is always larger in the direction of the poling field applied previously. The results show that the reversible domains are probably distributed in such a way as to make the total electric moment that was disturbed by the creation of irreversible stabilized domains equal to zero. The polarizability or piezoelectric voltage of a specimen polarized by a d.c. field without irradiation is symmetrical, thus the observed effect is caused by the stabilized domains. Received 21.10. 1965.

References [1] [2] [3] [4]

Jagkiewicz H u s i m i K.: C a s p a r i M. Chynoweth

A.: Acta Phys. Polon. 27 (1965), 637. J. Phys. Soc. Japan 12 (1957), 432. E., M e r z W. J.: Phys. Rev. 80 (1950), 1082. A. G.: J. Appl. Phys. 27 (1956), 78.

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