MEASUREMENTS OF COMPLEX PIEZOELECTRIC CONSTANTS IN FERROELECTRIC CRYSTALS

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MEASUREMENTS OF COMPLEX PIEZOELECTRIC CONSTANTS IN FERROELECTRIC CRYSTALS

H. Müser, H. Schmitt

To cite this version:

H. Müser, H. Schmitt. MEASUREMENTS OF COMPLEX PIEZOELECTRIC CONSTANTS IN FERROELECTRIC CRYSTALS. Journal de Physique Colloques, 1972, 33 (C2), pp.C2-103-C2-104.

�10.1051/jphyscol:1972232�. �jpa-00214968�

JOURNAL DE PHYSIQUE Colloque C2, supplkment au no 4, Tome 33, Avril 1972, page C2-103

MEASUREMENTS OF COMPLEX PIEZOELECTRIC CONSTANTS IN FERROELECTRIC CRYSTALS

H. E. MUSER and H. SCHMITT

Institut fiir Experimentalphysik 11, Universitat des Saarlandes, D-66 Saarbriicken RBsumB.

Nous avons determink les contraintes et le champ Clectrique dans le cas du Sel de la Rochelle

l'aide d'un dilatometre dynamique

effet capacitif. Ces deux mesures ont ete faites simultanement dans la region des audio-frequences juste au-dessus du point de Curie. Nous avons sensiblement observk la m&me dispersion pour la constante piezoklectrique

et pour la cons- tante dielectrique

l'etat libre.

Nous avons conclu du point de vue analyse thermodynamique que la constante dielectrique pour un cristal clampe

et les coefficients piezoklectriques

et

ne presentent pratiquement pas de dispersion.

Abstract.

With a dynamical capacitive dilatometer strain and electric field strength of Rochelle salt crystals were determined simultaneously in the audio frequency region near the upper Curie point. Nearly the same relative dispersion step was observed both in the piezoelectric constant

and in the free dielectric constant

It is concluded from a thermodynamical analysis that the clamped dielectric constant and the piezoelectric coefficients

and

are nearly free of dispersion.

1. Method. -

Several years ago a dielectric disper- sion in the audio frequency region was found in the ferroelectric a-direction of Rochelle salt (RS). It is nearly a Debye type relaxation. The relative dispersion step is proportional to the dielectric constant

The relaxation is caused by jumping point defects and can phenomenologically be described by means of an intrinsic electric field, which in equilibrium is propor- tional to the dielectric displacement [I],

The defects effect a slight dielectric relaxation also in the b-direction, whilst

remains constantly at audio frequencies

We looked for an influence of the defects on the piezoelectric behaviour of RS.

The measurement of the strain was carried out in a capacitive dilatometer [3]. At the end of an X-450-cut RS bar a small metallic plate was cemented, forming a capacitance to the electrode of an X-cut quartz, which is adjusted with a very small gap. This capacitance determines the frequency of an hf-oscillator circuit (about 100 MHz). If now the RS crystal is excited by a low frequency voltage, due to the inverse piezoelec- tric effect the gap width and thus the capacity and the frequency of the hf circuit are changed periodically.

Now such a If voltage is applied to the quartz, that the modulation of the hf voltage vanishes. In this case the elongations of RS crystal and quartz are equal in amplitude and phase. From a comparison of the voltages exciting RS and quartz, with use of the well known piezoelectric data of quartz and the dimensions of the samples, the piezoelectric coefficient d;z in the rotated system and the phase shift between electrical and mechanical state in RS can be calculated. As well known is dl4

2 di2. Furthermore,

was determined by capacitance measurements with a GR bridge.

2.

- The frequency dependence of the piezoelectric consfant d,, at 25 OC is shown in figure 1.

FIG. 1. -

Debye circle for

complex plane.

dl4 gives the ratio of the amplitudes of deformation

to applied field or of dielectric displacement to applied stress.

indicates the phase shift in the same way as it is usual in the description of dielectric properties, i. e., tg

d;4/d14. From a comparison with figure 2,

FIG. 2. -

Debye circle

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972232

C2-104 H. E. MUSER AND H. SCHMITT

giving the dielectric behaviour of the free crystal at

the same temperature, it can be seen, that the relative dispersion steps are equal within the accuracy of the measurements. Taking into account further measurements in the whole temperature range of our investigations (24-27 0C) it seems, that the relative step in di4 is very slightly larger than the step in

Measurements below the Curie point were not yet evaluated, because domain effects play an important role in this region [2] making a precise analysis very difficulty. Measurements of the dispersion of dl4 at higher temperatures were not possible because the accuracy was not high enough. An overlook on the whole temperature range of our present investigations is given in figure 3 of the following section.

FIG. 3. - e14, e14

as function

temperature.

3. Thermodynamical treatment.

- As well known, for small deviations from a reference state thermodyna- mic potential functions with second order terms only are sufficient for a description of the phenomenological behaviour 141. Furthermore, variables which are constant for all processes under investigation can be omitted. Thus we can restrict ourselves to the shear components

and

of strain and stress and the x-component El and D l of the field and displacement, resp. Having regard to the observed relaxation, we need an additional internal variable [5]. Considering adiabatic processes we have the potentials

In these equations the physical meaning of the internal variable is not fixed, i. e., one factor can be choosen arbitrarily. If we choose

1, 5 is identical with the well known intrinsic field of earlier papers [I], [2].

In quick changes of state, 5 remains constantly. Thus, all elastic, dielectric, and piezoelectric constants of eq. (I) to (4) are the values of the high frequency end of the dispersion step. The material constants for equilibrium can be calculated from the condition, that the deviation of the appropriate potential function with respect to the internal variable vanishes. From this condition we find, e. g.,

the material constants for clamped isolated changes of state in equilibrium, that is, at the low frequency end of the dispersion step.

If one set of material constants is known, all other sets can be calculated by Legendre transformations [5].

In our measurements we have determined the inde-

T T s

pendent constants

i , dl4, _and di4. Furthermore

is a well known constant [6]. Together with

1, all constans of eq. (1) to (4) can be calculated.

The result is, that

pY1, h14, and e14 are within the accuracy of our present measurement free of dispersion. As an example,

is plotted in figure

Therefore it can be concluded, that the energy diffe- rence of the two places, which can be occupied by the jumping point defects, is caused by the deformation of the lattice and not directly by the polarization. The same law is true for other point defects, which cause a relaxation in the MHz-region [7], [8].

-

h14

S4

S4 5

5 (1)

H =

+ & T l ~ : + + , t 2 -

We are indebted to the Deutsche Forschungsgemeinschaft for a support of

- dl,

E l T4 -

T4 5 - qi ^{E l t (2)} our investigations.

References

[I] UNRUH (H.

and M ~ S E R (H.

MUSER (H.

and PETERSSON

Fortschritte der

1962, 14, 121. Physik, 1971,

[2] UNRUH (H.

1963, 16, 315.

LANDOLT-BORNSTEIN, v01. III/l, Springer, Berlin, 1966,

EHSES

H.), Proc. European Meeting on Ferroelec- 63.

tricity, Wiss. Verlagsges., Stuttgart, 1970, 195. [7] UNRUH (H. G.), and SAILER (E.),

1969,224,45.

[4]

FORSBERGH jr

Handbuch der Physik, vol. 17,

KLEIN

and LUTHER (G.),

25a,

Springer-Verlag, Berlin, 1956, 264. 1970,1159.