Short Notes K95

phys. stat. sol. (b) 53, K95 (1972)

Subject classification: 14.4 .1; 22 .8 .1

Sektion Physik der Martin-Luther-Universitat Halle

Piezoelectric d Coefficient of Gadolinium Molybdate 36

BY C. SCHEIDING and G. SCHMIDT

The unusual ferroelectric properties of gadolinium molybdate (1) (Gd (MOO ) 2 4 3 '

GMO) have nowadays been understood since Levanyuk and Sannikov showed that the

basic macroscopic properties qualitatively can be described by a free energy ex-

pansion in terms of two nonhomogeneous transition parameters (2). An exact ex-

pression for the free energy, compatible with the symmetry change of GMO at the

159 OC transition point, has been given by Dvol%k (3). Thus it has been possible to

express the elastic, piezoelectric, and dielectric coefficients of the polar crystal

by the corresponding material constants and the coefficients of the free energy ex-

pansion of the nonpolar phase. Unfortunately not very much conclusions can be drawn

from this theory up to now. Too few macroscopic parameters a re known with due

accuracy. It can be taken as sure that the clamped dielectric susceptibility exhibits

no anomaly at the phase transition point (1). There also exist some data on the

elastic properties of GMO (4). But only the room temperature value of d

given by Aim et al. (5), which i s the only known piezoelectric coefficient. Therefore

we intended to determine the electromechanical properties of GMO within the temper-

ature interval from RT to well above the transition point. The crystals used for our

investigations have been grown by Bohm and Kursten (8). Up to now conclusive re-

sults bave been obtained for the d

two different methods. For the dynamic resonance-antiresonance method lengthwise

vibrations of 45 Z-cut bars (relative to the a-axis of the tetragonal high temperature

phase) have been investigated (6). Quasi-static measurements have been performed

by measuring the'piezoelectric strain in [ l lO] direction after applying a' low-fre-

quency alternating voltage to the electrodes of a Z-cut GMO plate (7).

has been 36

coefficient. This quantity was determined by 36

0

The results obtained above the transition point by these two methods a re in good

agreement, as can be seen from Fig. 1. A steep increase of d

close to the phase transition point.

can be observed 36

K96 physica status solidi (b) 53

TIV - Fig. 1 Fig. 2

Fig. 1. Temperature dependence of the piezoelectric d coefficient ( 0 determined 36 by dynamic measurements, 0 by quasi-static measurements)

vibrations of a [loo] bar; 0 E - < 0, A E - 7 0 Fig. 2 . Temperature dependence of the d coefficient determined by shear mode

36 - -

From earlier experience obtained by investigations at the 110 K transition point

of SrTiO (9) we know that the temperature of the peaks of a material coefficient

must not coincide with the transition point. In order to answer this question for the

case of GMO resonance and optical investigations have simultaneously been made

using the same sample. It could be seen that the minimum of the resonance frequency

(corresponding to the maximum of d

electric domains. (The domains appeared suddenly as it i s typical for a first-order

transition. )

3

) coincided with the appearence of ferro- 36

The d36 coefficient could also be determined by exciting a shear mode of a

[ l l O ] bar (6). The results of these measurements which could also be made at

temperatures below the transition point, a r e shown in Fig. 2. In order to avoid

domain effects in the polar phase a biasing dc field was applied. In some cases

somewhat different results were obtained for. opposite directions of the bias. W e

assume that this is caused by the fact that for one direction the crystal was not

made single domain by the applied field.

From the resonance frequencies of the shear mode of these bars the elastic

compliance s 66 ature in Fig. 3 .

was determined. The results a r e plotted as a function of temper-

Short Notes K97

Fig. 3 Fig. 4

Fig. 3. Temperature dependence of the elastic compliance s

Fig. 4. Temperature dependence of the piezoelectric h

; 66 O E > O , A E - < O - - - coefficient

36

It should be pointed out that d increases from the high temperature value 36

2 ~ 1 0 - l ~ m/V by a factor of about 8 to more than 1 6 ~ 1 0 - l ~ m/V. In the same

temperature region the elastic compliance s

3. If we calculate the h coefficient from d and s (6)

increases only by a factor of about 66

36 36 66

E = ps d /s h36 33 36 66 '

we also obtain a quantity that depends noticeably on temperature (Fig. 4). This

piezoelectric coefficient corresponds to a

Dvor5k (3). We see that h36 shows nearly the same temperature dependence as

s

meability

in the free energy function given by 36

If we consider the relation between the free and the clamped dielectric imper- 66'

2 E ' - h s 2 D - h /c T p.33= p 3 3 36 66% p33 36 66 '

T we see that the peak of p has to be ascribed to the anomaly of sE6 as well a s to

that of h36.

a r e being made. First results have been obtained for d'

of 45 Z-cut bars (Fig. 5). This quantity has a very small value for negative bias.

In order to determine the morphic piezoelectric coefficients further investigations

from lengthwise vibrations 31 0

K98 physica status solidi @) 53

Fig. 5. Temperature dependence of d ' = +d +

+ 1 / 2 d36 for positive (d

biasing fields. (The broken curve corresponds to

t g 31 - 31 $ 8 I +

) and negative (d'il) 31 kc

Q @

$

@ 6

$ 4 d36/2) 'b

This corresponds to the observation by Cummins

that no detectable length-extensional mode could

be excited for ba r s with Ienghts along the ortho-

50 700 750 ZOO TPCJ -

rhombic b-axis (10). From this result it can be concluded that d

same value as d /2.

has nearly the 31

36 The results on further morphic coefficients of GMO will be published elsewhere.

References

(1) L.E. CROSS, A . FOUSKOVA, and S. E , CUMMINS, Phys. Rev. Letters 21, 812

(1968).

(2) A.P. LEVANYUK and D.G. SANNIKOV, .Fiz. tverd. TelaL2, 2997 (1970).

(3)V. D V O U K , phys. stat . sol. (b) 4 2 , 763 (1971).

(4) D.J. EPSTEIN, W . V . HERRICK, and R . F . TUREK, Solid State Commun. S , 1491 (1970).

( 5 ) K. AIZU, A. KUMADA, H. YUMOTO, and S. ASHIDA, J. Phys. SOC. Japan

- 27, 511 (1969).

(6) W.P . MASON, Piezoelectric Crystals and Their Application to Ultrasonics,

Van Nostrand Co., Toronto, New York, 'London 1950.

('7) G. SCHMIDT, Exper. Tech. Phys. 6 , 250 (1958).

(8) J. BOHM and H.D. KURSTEN, Kristall und Technik?, 213 (1971).

(9) G. SORGE, E. HEGENBARTH, and G. SCHMIDT, phys. stat . sol. 37, 599

(1970).

(10) S .E . CUMMINS, Ferroelectr ics 1, 11 (1970).

(Received August 7 , 1972)