Fifty Years of Ferroelectricity

œditor'$ Note' This is the seventeenth in a series of review and tutorial papers on various aspects of acoustics.

Received 10 June 1971 10.1, 10.3; 5.18

Fifty Years of Ferroelectricity

WARREN P. MASON

Columbia University, New York, New York 10027

Developments in the field of ferroelectricity are traced from the discovery of the ferroelectric effect by Joseph Valasek in 1921 to its use in a variety of modern applications. Its appearance and utilization in different substances is discussed.

INTRODUCTION

The occasion for this review paper is that this is the 50th anniversary of the discovery of the ferroelectric effect by Professor Joseph Valasek of the University of Minnesota. He first showed that the dielectric properties of Rochelle salt were similar in nature to the

ferromagnetic properties of iron in that there was a hysteresis effect in the field-polarization curve, that there were two Curie temperatures rather than a single one for iron and that there were very large dielectric and piezoelectric constants in the ferroelectric region.

I. ROCHELLE SALT DISCOVERY

Since all the original ferroelectric properties were associated with the crystal Rochelle salt--which is sodium potassium tartrate with 4 moles of water, NaKC4H406- 4H•.O--some account of its discovery and uses appear to be in order. Rochelle salt was first synthesized by an apothecary Elie Seignette about 1655 in the city of La Rochelle in France. Hence the material came to be

known as "Sel de Seignette" or "Sel de la Rochelle." The latter name became the recognized name although .. the anomalous dielectric properties were called for many years the "Seignette electric effect." Finally the name "ferroelectric effect" has become universally used in analogy with the ferromagnetic effect in iron and other materials. -

While the chemical and medicinal properties of the material became well known, it was not until 1880 that anything unusual was found in the physical properties. In that year the brothers Pierre and Jacques Curie [1-] included it in their studies of the piezoelectric effect. Apparently they missed the very large effect found along the ferroelectric axis. The first quantitative measurement was made in 1894 by P/Jckels [-2-], who also observed an anomalous dielectric behavior in the ferro-

electric direction. However, his findings were not

followed up and it was not until World War I that anything further was done on its physical properties. During the war, in France, Langevin showed that

in•erior

_ _

t

exterior steel place

FIa. 1. Langevin's apparatus for depth sounding.

The Journal of the Acoustical Society of America 1281

Copyright ̧ 1971 by the Acoustical Society of America.

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21:26:24

w. P. MASON

5OO

o 400

z - o

a:: Io 200

[ I HYSTERESIS LOOP ELECTRIC FIELD

lOO

o -4000 - 2000 o 2000 4000

ELECTRIC FIELD IN VOLTS PER CENTIMETER

(•)

;55O

HYSTERESIS LOOP ELECTRIC FIELD

VS CHARGE 280

z:• 210 =) o

z

--o t40

n,, I • o 70

o

o -4000 - 2000 o 2000 4 ooo

ELECTRIC FIELD IN VOLTS PER CENTIMETER

(b)

FIO. 2. Measurements of charge-polarization curves of Rochelle salt' (a) temperature, 20øC; (b) temperature, 8øC (after Valaseka).

piezoelectric crystals could be used to generate and de- tect sound waves in seawater and constructed the first

underwater sound transducer, as shown by Fig. 1. In this transducer, thin plates of quartz were cemented between steel plates which were used to bring the frequency of the transducer down to 50 kHz. This device was quite successful in locating submarines and mea-

•400 x/•-a

i•oo

-6O -40 -2O 0 20 4O "C.,

FIO. 3. Dependence of piezoelectric strain coefficients of Rochelle salt upon temperature (after Valaseka).

suring depths, but was not developed until after the war.

Under the auspices of the U.S. Navy, a similar study was made in the United States. J. A. Anderson of the Mount Wilson Observatory and Professor W. G. Cady from Wesleyan University and A.M. Nicolson of the Bell Laboratories experimented with Rochelle salt, since it was highly piezoelectric and was much more available than quartz. They were successful enough to cause Rochelle salt to be adopted by the U.S. Navy and it was the standard transducer crystal from !918 to World War II.

II. VALASEK'S MEASUREMENTS

In investigating the dielectric properties of the material, Cady and Anderson as well as Nicholson found indications of nonlinearity and dielectric hysteresis in the material, but it remained for the work of Professor J. Valasek to give a complete explanation for the effect. Starting with a paper in 1921, Valasek [-3-] measured hysteresis loops in the electric field-electric polarization as shown by Fig. 2. These were measured by using a ballistic galvanometer. Curve (a) shows the results at 20øC while curve (b) shows the hysteresis loop at 8øC

1282 Volume 50 Number 5 (Part 2) 1971


21:26:24

FIFTY YEARS OF FERROELECTRICITY

Fxo. 4. Dielectric constant of Rochelle salt for low and high field gradients (after H. Mueller4).

4500

4000

3500

• 3ooo

o 2500

._o & 2000

•5 1500

IOOO

5OO

o -30

500 V/cm

I

-2O

i

i i I I I I

-I0 0 I0 20 30 40 50

Temperature in degrees centigrade

that is intermediate to the two Curie temperatures. Valasek also measured the piezoelectric effect for Rochelle salt as shown by Fig. 3. This was measured by applying a large weight which saturates the dipole motion and gives a constant value in the ferroelectric region. The same result is obtained for the dielectric constant, as shown by later measurements of Mueller [-4] on Fig. 4. For low field strengths, the dielectric constant approaches large values at the Curie temperatures, but is flat for high field strengths.

1200

LI.I

rr 1000

800

'z 600 o

N

q: 400

o

o m 200

o

o• 0 -24

Valasek was the first to call the two limiting temperatures "the Curie temperatures" and to recognize the analogy between the ferroelectric effect and the ferromagnetic effect. If he had plotted the intercept of the hysteresis loops at zero field, he could have measured the spontaneous polarization which was later measured by Habliltzal as shown on Fig. 5. This figure also shows that, if the hydrogens are replaced by deuteriums, the spontaneous polarization is larger and the Curie temperatures are spread apart.

J HEAVY-WATER

/ ••,•HELLE SALT ROCHELLE SALT

-16 -8 0 8 16 24 :32 40

TEMPERATURE IN DEGREES CENTIGRADE

Fro. 5. Spontaneous polarization of Rochelle and heavy-water Rochelle salt as a function of the temperature (after Habliitzal•).



21:26:24

w. P. MASON

III. RUSSIAN MEASUREMENTS

Valasek's last paper appeared in 1927 and little more was done on the subject until 1929, when two Russians, Shulvas-Sorokina [6-] and rurchatov [7-] made many in- vestigations. Figure 6 is a graph taken from Kurchatov's book which gives measurements of the specific heat near the upper Curie temperature, showing that the transition was second order. Figure 7 shows the effect of introducing an isomorphoui substance in the crystal which causes the two Curie temperatures to approach each other. Kurchatov also produced the first theory of the ferroelectric effect. This was based on rotatable

dipoles and was quite similar to Langevin's theory of the ferromagnetic effect.

There is, however, a distinct difference between the ferromagnetic and the ferroelectric theories in that one

ß iT ---

• 0,1 ø

07

i i I ! I I 19 20 21 22 23 2zt 2,5 26 27 oc

Fro. 6. Specific heat of Rochelle salt near the upper Curie temperature (after Kurchatov7).

6OOO

i ,,.,

5OOO

4000

3000

2000

1000

can neglect mechanical coupling in the ferromagnetic case whereas this is not feasible in the ferroelectric case. This follows from the fact that the strains associated

with the ferroelectric effect are 1% or larger whereas the magnetostrictive effect is only 30 parts/million for nickel, the most magnetostrictive of all the materials. For example, Fig. 8 shows [8-] the resonance frequency of a Rochelle salt crystal as a function of the temperature. The top curve, C, shows the resonance frequency of an unplated crystal in which there is no coupling between the mechanical properties and the dielectric properties and it is seen that the crystal stiffness modulus is nearly independent of the temperature. For a fully plated crystal, for which the mechanical properties are coupled to the dielectric properties, a very large dip occurs in the resonance frequency at the upper Curie temperature and there is also a dip at the lower Curie temperature at --16øC. The middle curve represents the antiresonance frequency of a plated crystal--that is, the frequency for which the electrical impedance becomes very high. From the ratio of these two frequencies, one can obtain the electromechanical coupling factor which determines how much electrical energy can appear in mechanical form or vice versa. Figure 9 shows this factor for Rochelle salt [-8-], and at the Curie temperature it is found that over 90% of the electrical energy can appear in mechanical form. If one changes the temperature very slowly, the coupling becomes 100% and a phase change from orthorhombic to a monoclinic structure occurs at the

Curie temperature. The change in the crystal axes is determined by the spontaneous polarization acting on the shear piezoelectric constant.

48OO

4000

3200

2400

1600

800

-30 -20 -10 0 10 20 30 -20 -10 0 10

TEMP. (øC) TEMP. (øC)

(a) (b)

20

Fro. 7. Dielectric constant of Rochelle salt at low field gradients. (a) Effect of introducing isomorphous ammonium tartrate on the Curie temperatures; (b) (after Kurchatov7).



21:26:24


Fro. 8. Resonances of a Rochelle salt crystal as a function of temperature. Curve A: resonance frequency of a plated crystal. Curve B: antiresonance frequency of a plated crystal. Curve C: resonance frequency of an unplated crystal in an air gap holder (after MasonS).

220

,_200

E -.•_

• 180

• 160

'- 140

u' 120

I00

A

i I I I I I I I I I I I

0 8 16 24 32 40 48

Temperoture in degrees centigrode

IV. APPLICATION OF ROCHELLE SALT

About the same time as this work was proceeding in Russia, considerable work was being done in the United States, mostly on the applications side. Dr. C. D. Sawyer and his associates at the Brush Development Company grew some large-sized and excellent Rochelle salt crystals of the form shown by Fig. 10. The figure also shows the crystal cuts that have been used in phonograph pickups E9] and other devices for responding to dis- placement changes. Sawyer and Tower [10] also measured hysteresis loops for Rochelle salt by using a cathode-ray oscillograph. The results are shown on

Fig. 11 and give a good indication of the variation of the loops with temperature.

At this point, one wonders how a phonograph pickup can operate in the room-temperature range and higher with the large variation of the piezoelectric constant shown previously. An answer to the question was supplied by the writer Es], who measured the ratio of the charge generated to the applied stress;as shown by Fig. 12, this ratio is nearly independent of the temperature. Hence, if the pickup is worked into a high- impedance device such as the grid of a vacuum tube, an output independent of the temperature is obtained.

FIO. 9. Curve A represents the electromechanical coupling constant of a Rochelle salt crystal. Curve B represents the dielectric constant of the crystal clamped (after MasonS).

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21:26:24

w. P. MASON

V. APPLICATION OF THERMODYNAMICS TO ROCHELLE SALT AND ATOMIC THEORIES

Professor Hans Mueller Eli] was the first to apply thermodynamics to the ferroelectric Rochelle salt. Starting with the relation of Fig. 12, Mueller writes the free energy in the form

G=•C44P(S4--S4ø)2-q-•xlP2-q-•-Bp4-q- f14PS4, (1)

where C44 P is the elastic shearing constant measured at constant polarization, P is the applied and spontaneous polarization, xx is the clamped electric susceptibility, and B and fx4 are nonlinear constants. Since all the constants except xx were shown experimentally to be independent of the temperature, Mueller succeeded in reducing all the anomalies to one parameter, the clamped dielectric constant.

This could be measured from the properties of the free energy and its derivatives, and is shown in Fig. 13

X- CUT • y CFtYSTAL

A

B

Fxo. 10. Rochelle salt crystal and principal cuts.

by a dashed line. All of the anomalies can be reduced to the anomaly in the clamped dielectric constant, but this requires an atomic theory to account for the properties. Although a number of theories involving the orientation of free dipoles were proposed by Kurchatov, Mueller, Busch, and others, it appears that the best agreement with experiment is obtained by employing the motions of hydrogens in the bonds proposed by the writer [12-]. If the bond is symmetrical, as shown by the top portion of Fig. 14, only a single Curie temperature results (as demonstrated by the theory of Slater on KDP); but, if there are two nearly equivalent positions as shown by the bottom, then there are two Curie points and a ferroelectric region which occurs when the cooperative effect gets large enough to produce the lower Curie temperature while the upper one occurs when thermal agitation destroys the effect. A calculation of the clamped dielectric constant is shown in Fig. 14.

VI. NEW FERROELECTRICS KDP AND ANTI-

FERROELECTRICS (ADP)

In 1935, a new series of ferroelectric crystals was produced by Busch and Scherrer [13-] in Zurich. These materials were phosphates and arsenates of which potassium dihydrogen phosphate and ammonium dihydrogen phosphate were the principal examples. The potassium salt had a single Curie temperature at 122øK while the ammonium salt turned out to be the first

antiferroelectric crystal with a critical temperature of 147.9øK. When the hydrogens are replaced by deu-

26 ø 23.3 ø 21.8"C

15' 0* -8'C

Fxo. 11. Rochelle salt hysteresis curves, 60 cycles ac (after Sawyer and TowerXø).

O I0

•O 5

-8 0 8 16 24 32 40 48 TEMPERATURE IN DEGREE5 CENTIGRADE

Fxo. 12. A plot of the piezoelectric constant as a function of the temperature (after MasonS).



21:26:24


Fxo. 13. Measured and calculated

values of the clamped dielectric constant of Rochelle salt for low field strengths plotted as a function of the temperature (after MasonS).

300

LCUI_ATE D

MEASURED

Z

• 250

o o 200

o 1.50

0

_1 50

0 -50 -40 -.30 -20 -10 0 10 :•0 30 40 50


terium, a large increase in the critical temperatures occurs. These are 213øK for potassium dideuterium phosphate and 235øK for ammonium dideuterium phosphate. The ferroelectric nature of potassium dihydrogen phosphate, which has the abbreviation KDP, is shown [-14-] by Fig. 15, which shows the resonance frequency for plated and unplated crystals. For ADP, the two frequencies are also shown by Fig. 15. At the critical temperature, the crystal fractures into small pieces. The larger separation between the unplated and plated frequencies in ADP indicates a larger electromechanical coupling with the values [14] shown in Fig. 16. With a 30% coupling at room temperature, the crystal became the principle underwater sound transducer in World War II, replacing the very temperature-sensitive Ro-

chelle salt. Figure 17 shows an underwater sound transducer [15-] with the face plate consisting of ADP crystals attached to a backing plate. The arrangement of four crystals per unit block on the inside and two on the outside produced the directional pattern shown by the bottom portion of the figure. The whole transducer was mounted in a case filled with castor oil and the

acoustic energy was transmitted to the sea water through a rubber face plate. This type of transducer worked at about 25 kHz and was capable of delivering several kilowatts of power. It was used successfully in World War II in detecting submarines.

Several theories of the ferroelectric effect in KDP

have been given, the most successful one being due to Slater [-16-]. Figure 18 shows the structure of KDP. The

FID. 14. Possible potential well distributions of (OH)s hydroxyl group of the tartrate molecule: (a) for symmetric bond; (b) for dissymmetric bonds (after MasonS).

,,/,,,/,," //

SEPARATION • OXYGEN MOLECULES

(a)

(b)

Ol 2



21:26:24

W. P. MASON

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120

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I' -200

, ., i , , i,, .,* ß .. .

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TEMPERATURE IN DEGREES CE•qTIGRADE

180

,,_PLATE D

u 175 i

z - 17o

z

v• 165 z o

>. 16o u z

0 155

150 120 -I00 -80 -60 -40 -20 0 20 40 60 80 I00

TEMPERATURE IN DEGREE,% CENTIGRADE

FiG. 15. Top: resonance frequencies of plated and unplated KDP crystal. Bottom: resonance frequencies of unplated and plated ADP crystal (after MasonS).

structure contains phosphate groups connected by hydrogen bonds, and it is assumed that the hydrogens are capable of taking up one of two different positions. Different possible arrangements of the hydrogens result in different orientations of the (H•PO4)- dipoles. At high

temperatures the dipoles are randomly arranged, but at low temperatures the energy is the lowest if the dipoles point along the ferroelectric (c) axis. Slater calculated the free energy for various arrangements and showed that the function determining the distribution was given

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u_ o.e

o

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0 !,)o .4

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FiG. 16. Coefficient of coupling of ADP and KDP as a function of temperature; both measurements are for 45 ø Z-cut crystals (after MasonS).



21:26:24


"• ...::•';-;::;-•..: .:-.-.". i . ' ..... I . .;..:/L. ;.

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i• --;:; 3 •':' ;-"i--:--:::':::, ':.'-"---•-'; :::'"'

Fxo. 17. Use of ADP crystals as underwater sound transducer. Top left: crystal array for QJA underwater sound transducer. Bottom left: theoretical and measured directional pattern of QJA transducer. Right: case and pc rubber transparent window for QJA transducer.

by the curves of Fig. 19. Below the Curie temperature 0, the energy is lowest if the polarization is q- or -- unity times the sum of all the dipole moments. Above the Curie temperature, the most probable position is zero unless a field is applied when a positive polarization results. If the dielectric constant resulting from this

model is used as the clamped dielectric constant, a good agreement with experiment is obtained.

An improvement in the statistics was made by Shirane and Oguchi !-17-1 and Takagi !-18-1, who allowed for the probability of the existence of two or no hydrogens and three and one hydrogens in the bonds. The principal

OK

C .- --ø" ø H

KHzPO• , o.=b=7.43A

C=•.g7A

O(-z)

Fzo. 18. Structure of KDP. (a) Unit cell. (b) Hydrogen bonds near PO4 tetrahedron.



21:26:24

W. P. MASON

-0.1

-0.2

A/nk e ,

-i o

Fro. 19. Slater's free energy curves for KDP. Dotted lines show effect of electriC' field,

stumbling block with Slater's theory is the difficulty of explaining the large shift in the Curie temperature caused by the substitution of deuterium for hydrogen. Several theories [-19-] have been proposed based on the use of long-range forces as well as the short-range forces used by Slater, but it appears that no completely satisfactory theory has been obtained.

For ADP, a different type of dielectric constant results, as shown by Fig. 20. As the temperature is lowered, as indicated by the measurements of Mason and Matthias [-20-], a temperature is reached at which a sudden drop in the dielectric constant occurs, usually with fatal results. The difference between the two types of behavior is due to the fact that the energy is lowest when dipoles lie in alternate layers, as shown by Fig. 21. This arrangement was first suggested by Professor

95

lit

-•"C

90

85

80

75

70

65

60

z

z

0 50

• 45

-J 40

35

30

15

10

5

0 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70


Fro. 20. Dielectric constant of deuterated ADP (after Mason and Matthias•ø).



21:26:24


Fxo. 21. Arrangement of hydrogen nuclei to produce an antiferroelectric condition (after Mason and Matthias•0).

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0 t20 80 •10 0 40 80 120 TEMPERA'TURE IN DEGREES CENTIGRADE

Fxo. 22. Dielectric constant and dissipative function tan8 for an unpolarized barium titanate ceramic (after Von Hippel ½t a/.•9.



21:26:24

W. P. MASON

XlO 3 16•

14

i--. I0

z 0

u 8

•j 6

0 70 80 90 I00 I I0 120 130 140 150


xlO-5 ,4O

30

20

0 160

I0

Fro. 23. Dielectric constant along the c axis as function of the temperature. •p=Aq-B/(T--T?'), for T>T• •' (after Merz•4).

Nageyama of Osaka University. This arrangement represents the condition for an antiferroelectric crystal,

and AD P was the first crystal for which such a condition was observed.

VII. BARIUM TITANATE FERROELECTRICS

In 1945, a new ferroelectric material, barium titanate, was discovered and this and similar structures have

turned out to be the most useful and interesting ferroelectrics. Barium titanate was discovered at approxi- mately the same time by Von Hippel, Breckenridge, Chesley, and Tisza at M.I.T. [-21-] and Vul and Gold- man [-22-] in Russia. It can be produced in ceramic form and given its ferroelectric properties by a polari-

zation process. Figure 22 shows a measurement of the dielectric constant and the dissipative function tan•i for an unpolarized ceramic over a wide temperature range. It is obvious that there are three temperatures for which a transition occurs from one dielectric constant value to another, with a change also in the tan•i function which indicates the dissipa- tire properties.

10x103

9-

Z 6- 0 U

5- U

I- 4- U

J3

a 2

AXIS

Fro. 24. Complete measurements of dielectric constants along the a and c axes as a function of the temperature (after Metz'4).

1 c AXIS

-120 -t50 -40 0 40 80

TEMPERATURE IN DEGREES C

120



21:26:24


P$ COUL/CM 2 , ,

16

14---

12-"

I0--

8'--

6--

4--

o - 180 -150 -I1•0 -90 -60 - 50 0

T*G

Fro. 25. Spontaneous polarization of barium titanate, along one axis, over a temperature range (after Merz•).

150

Single crystals of barium titanate have been grown mostly by the Remeika method [23-]. These allow a better determination of the properties than can be obtained from the ceramic. Figure 23 shows the measurements of the dielectric constant along the ferroelectric axis made by Merz [24-]. Above a critical temperature designated To v, the dielectric constant follows the Curie-Weiss law that the inverse of the dielectric con-

stant is proportional to the temperature. If we extrapo-

late to a zero value of 1/•o, the temperature To is about 10øC lower than To v. This difference is a measure of the effect of the electromechanical coupling on the dielectric constant.

The next illustration, Fig. 24, is a measure of the dielectric constant along the c ferroelectric axis and the a axis at right angles, as measured by Merz [24-]. The three transition temperatures are obvious from the measurement. Merz also measured the spontaneous

Fro. 26. Hysteresis loop of single crystal of barium titanate.



21:26:24

w. P. MASON

4.030

4.020

4.010

4.000

3.990

3.980

Rhombohedral Orthorhombic Tetragonal Cubic

:3.970 , , • I , , , , I , , , , I I I , , I -I 50 -I00 -50 0 50 I00 150

Temperature øC

FIO. 27. Unit cell parameters of barium titanate as a function of the temperature (after Kay and Voudsen•5).

polarization, as shown by Fig. 25. It will be noted that the polarization along the c axis drops by l/x/2 in the second region and 1/VJ in the third region. It is also obvious that, if the polarization in the highest region is reversed in a millionth of a second, which is possible, about 30 A/cm 2 are obtained from the process. Hence considerable electrical energy can be obtained from a mechanical reversal or destruction of the polarization in a short time.

Figure 26 shows the hysteresis loop of a barium titanate crystal. With the square corners, one might expect that such crystals could be used in information storage, as is common with ferromagnetic cores. How- ever, it was found that, after a number of reversals, the height of the loop declines and the corners become less square. Hence, this use did not become practical.

Devonshire [19]] first applied thermodynamics to the properties of barium titanate. By writing the free energy of the crystal in the form of an expansion in even powers of the polarization along the three axes, as shown by Eq. 2,

G • = 2a'C-• ( r -- To) ( P • q- Pv a q- P? ) -+-l-Bva g 4 X (P•4+Pv4+pz4)+•B'vSg6(P•,6+Pv6+P•6)

q-«B"vag4(p?Pv=-kP2P,2q-Pv•P?), (2)

he showed that there was a possibility of four solutions for the spontaneous polarizations along the three axes. The solutions obtained are

P•,=Pv= P•=O, above Curie temperature, P•=Pv=O; Pz•O, at 120øC to 10øC, P•=O; Pv=P•O, at --90øC to 10øC, P•= Pv= P•O, below --90øC.

(3)

To agree with the polarizations observed in Fig. 25, the coefficient for the /m term has to vanish at the Curie

temperature and follow the form shown by the first term, where C is the Curie dielectric constant. The terms involving the fourth power have to be negative, while the terms involving the sixth power of the polarization have to be positive. The values of the constants can be evaluated from the transition temperatures.

If one wishes to study the strains accompanying the phase changes, it is necessary to introduce terms in the free energy involving products of the strains times the squares and products of the polarization. However, one can regard the distortion associated with the three phases as slight distortions of the cubic phase associated with the products of the square of the polarizations by the electrostrictive constants, of which there are three for a cubic crystal. These constants can be evaluated by using the unit cell parameters determined by Kay and Voudsen 1-25• and shown in Fig. 27 plotted as a function of the temperature. In the cubic phase existing above 120øC, all axes are equal. Below 120øC, one axis--the ferroelectric axis--becomes about 1% larger than the other two. In fact, the axis dimensions together with the spontaneous polarizations can be used to evaluate the electrostrictive constants of the crystal, of which there are three. The two longitudinal constants can be evaluated in the tetragonal range while the shear constant can be evaluated from the three unit cell dimensions in the orthorhombic phase.

Knowing these values, one can account for the changes in the unit cell dimensions for the three axes as shown by Fig. 28. For the tetragonal phase, the polarization is along a cube axis, and this results in an expansion along the polarization direction and a contraction along the other two. For the orthorhombic phase, the polarization is along a face diagonal. This results in an expansion of two of the axes, a contraction of the third, and a



21:26:24


Fzo. 28. Electrostriction dimensional

changes in barium titanate for three phases (after MasonS).

T ET RAGO NAL

PHASE

lOøC TO 120 øc

ORTHORHOMBIC PHASE

-80 øC TO +10 øC

TRIGONAL

TRIGONAL PHASE

-273 øc TO -80 øC

shearing strain in the plane of the polarization. All of these strains are shown on the right-hand figure. To get the orthorhombic structure we have to take axes at 45 ø

to the cubic axes, in which case the unit cell will have three different values. Finally, when the polarization is along a cube diagonal, the spontaneous strains are all shearing modes. When these are added together, a

2.00 Ao•Tlt. 86 A 2.17 A

0o

BoTi0$ PbTi0$

Fro. 29. Neutron diffraction determination of displacements of atoms in unit cell for barium titanate and lead titanate (after Fraser, Danner, and Pepinsk?'ø).

trigonal phase results with the trigonal axis along a cube diagonal.

Barium titanate is a displacive ferroelectric, as can be seen from the neutron diffraction determination of

Pepinsky and associates E26-] shown on Fig. 29 for the tetragonal phase. For BaTiO3 on the left, the titanium is displaced upward by 0.12 3. and the bariums upward by 0.06 3., while the oxygen cage is displaced downward by 0.03 3.. For lead titanate, the effect is considerably larger and results in a higher spontaneous polarization and a higher Curie temperature. A number of theories of the action of barium titanate have been proposed. Slater E27] has extended his theory for KDP by calculating the local field on all the atoms and showing that it is much enhanced in the direction of the titanium

displacements. Ferroelectricity results from the polarization catastrophe, as in KDP.

A different type of theory has been proposed by Cochran E28-1 which connects ferroelectricity with an instability in the transverse optical mode in lattice dynamics. Starting with the Lydane-Sachs-Teller relation E29]

(4)

where cog is the longitudinal optical frequency, cot is the transverse optical frequency, •s is the static value of the dielectric constant, and •e is equal to the square of the refractive index, Cochran shows that if the static value



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W. P. MASON

DIRECTION OF

I ELECTRIC FIELD 7

REMANENT POLARIZATION

Fro. 30. Modes of motion generated in a polarized ferroelectric ceramic.

is very large the transverse, optical frequency is very small. Infrared and neutron diffraction measurements

show that the transverse optical frequency is low near the Curie temperature. By studying the vibrations

which contribute to the static dielectric constant

Cochran was able to derive the expression for the free energy of barium titanate--which was assumed by Devonshire--from atomic considerations.

7000 -

i- 6000- z

z 5ooo- o

_o 4000

J 3000

02000

D

>• tooo

o

300 I-z uo

-mu-.U 2oo

,oo o

u.I -40 0 40 80 120 160 200 TEMPERATURE IN DEGREE3 CENTIGRADE

1.4

1.3

D J D

1.2

u

1.1

1.0 >'Z

0.9 •Z

•o.•

0.7 24O

Fro. 31. Dielectric constant, piezoelectric constant, and Young's modulus of a polarized barium titanate ceramic (after MasonS).



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All the applications of barium titanate and related c'ompounds involve the ceramic rather than the single crystal. On account of the high dielectric constant, small-sized condensers have been used in most television

sets. However, the largest application is in connection with polarized ceramics used in electromechanical transducers. Figure 30 shows the modes of motion that can be generated in a polarized ceramic. By flipping over domains in the direction of the applied field and by squeezing domains at right angles to the applied field, the ceramic acquires a permanent polarization. If now an alternating field is superposed on this permanent polarization, it generates an expansion in the direction of the applied field and a radial contraction at right angles to the applied field. A third mode of motion can be generated by polarizing in one direction and applying the field in a perpendicular direction. This generates a thickness shear mode that has been used in sending shear waves in delay lines.

The constants of barium titanate alone are not too

satisfactory, as shown by the data of Fig. 31. The Young's modulus shows big dips at the Curie temperature and at the tetragonal-orthorhombic transition temperature. The same is true of the dielectric constant and the piezoelectric constant d3• which determines the value of the radial coupling constant to be kr=0.36. The thickness longitudinal mode has a value of 0.50, while the face shear mode has a coupling of 0.48.

One method for stabilizing the ceramic is to introduce a certain amount of calcium titanate or lead titanate, which lowers the second transition temperature and raises the Curie temperature. However, this occurs at the expense of the coupling coefficient. A better method is to employ the solid solution of lead zirconate and lead titanate first proposed by Bernard Jaffe [30•, Hans Jaffe [31•, and their associates at the Clevite Company. When the ratio is about 50-50, as shown by Fig. 32, the piezoelectric constants increase markedly and the radial coupling constant approaches 400-/0. Furthermore, all the properties are reasonably constant from --100øC to 200øC. This composition and related compositions with certain additions to stabilize certain of the properties have been given the trade name of PZT. There are eight such combinations, the final one, PZT8, being the one that produces the highest acoustic power output.

These combinations are the most widely used electromechanical converters. Probably the largest use is for underwater sound transducers. These have gone down in frequency and consequently have a much larger radiating face in order to maintain a directivity. With such radiators, the power output for a pulse runs into megawatts as compared to the kilowatt outputs of the World War II period.

The converse effect of converting a short mechanical pulse into electrical energy is also widely used. A trivial

0A

o

"iQ2 -

• 0.1 -

o

rhc•tx/•,dml '- tetrogonal

-

, ,,\ /

! I. I I I I !

( mole percent) PbTiO$ (increasing PbTiO$ content •)

Pb Zr 05

xKy 'e

i•o

Fro. 32. Dependence of electromechanical properties of PbZrOa- PbTiOa solid-solution ceramics on composition (after JaffeaX).

example is of a cigarette lighter, which has been used in Japan for some time and has recently been advertised here. Here, a sharp mechanical pulse generates a high enough voltage by the piezoelectric effect to light the lighter fluid.

Recently, there has been considerable work on the electro-optic effect, which is larger in a ferroelectric than in ordinary piezoelectric crystals. In this effect, a birefringence is generated in light shining through the crystal that can be used to modulate laser beams and other sources of light. The first crystal used for this purpose was KDP. This has the disadvantage that the light direction and the applied field directions are the same. Two cubic ferroelectric crystals, LiTaO3 and LiNiOs, have the advantage that the electric field can be applied perpendicularly to the light direction. The most sensitive crystal so far obtained is the ferroelectric crystal Ba•NaNb50•5 E32•. By using the electro-optic effect in ferroelectric crystals, a billion bits per second have been impressed on laser beams.

Another possible use for ferroelectric ceramics is in image storage and display devices [33•. These make use of fine-grained lead zirconate-lead titanate ceramics, sometimes doped with lanthanum (abbreviation PLZT). A discussion of methods for using these ceramics as storage devices has been given by Maldonado and Meitzler E34•.

In summary then, the ferroelectric effect has been found in over a hundred crystals since the work of Valasek. The applications are somewhat different than for a ferromagnetic material, in that high dielectric constant ceramics and polarized ceramics used as electromechanical transducers are the principal applications. Potential applications in the optic field and for information storage are also possibilities.

BIBLoGRAPHY

1. J. Curie and P. Curie, Bull. Soc.. Mineral. de France 3, 2. F. Piickels, Abhandl. G6ttingen 39, 1-204 (1894)' also, in 90-93 (1880). Uber den Einfluss des Electrostatischen Felds auf das



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W. P. MASON

8e 9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

optische Verhalten piezoelektrischer Krystalle (Dieterische Verlagsbuchhandlung, G6ttingen, 1894). J. ¾alasek, Phys. Rev. 17, 475-481 (1921); Phys. Rev. 19, 639-664 (1922); Phys. Rev. 24, 560-568 (1924). 20. H. Mueller, Phys. Rev. 4?, 175-191 (1935). J. I-Iabliitzal, Heir. Phys. Acta 12, 489-510 (1931). 21. R. D. Shulvas-Sorokina, Phys. Rev./t4, 1448-1450 (1929), and many others. 22ø I. V. Kurchatov, Seignette Electricity (Moscow, 1933), 104 pp.; French transl. Le Champ Mol•culaire dans les die 23. lectriques (Hermann and Cie, Paris, 1936), 47 pp. 24. W. P. Mason, Phys. Rev. 55, 775-789 (1939). 25. C. B. Sawyer, Proc. IRE 19, 2020-2029 (1931). 26. C. B. Sawyer and C. H. Tower, Phys. Rev. 35, 269-273 (1930). tt. Mueller, Phys. Rev. 57, 829-839 (1940); Phys. Rev. 27. 58, 805-811 (1940). 28. W. P. Mason, Phys. Rev. 72, 854-865 (1947). 29. G. Busch and P. Scherrer, Naturwiss. 23, 737 (1935). W. P. Mason, Phys. Rev. 69, 173-194 (1946). 30. W. P. Mason, Piezoelectric Crystals and their Applications to Ultrasonics (D. Van Nostrand, Princeton, N.J., 1950), pp. 158-160. J. c. Slater, J. Chem. Phys. 9, 16-33 (1941). 31. G. Shirane and T. Oguchi, J. Phys. Soc. Japan 4, 172 32. (1949). Y. Takagi, J. Phys. Soc. Japan 3, 271 (1948). 33. For example, J. Pirenne, Heir. Phys. Acta. 22,479 (1949); W. P. Mason, Piezoelectric Crystals and their A pplication to 34. Ultrasonics (Van Nostrand, Princeton, N.J., 1950); A. F.

Devonshire, "Theory of Ferroelectrics," Phil. Mag. Suppl. 3, 85 (1954); R. Blinc and D. Hadzi, Molec. Phys. 1,391 (1958). W. P. Mason and B. T. Matthias, Phys. Rev. 88, 477-479 (1952). A. Von Hippel, R. G. Breckenridge, F. G. Chesley, and L. Tisza, Ind. Eng. Chem. 38, 1097 (1946). B. Wul and I. M. Goldman, Compt. Rend. Acad. Sci. USSR 46, 139 (1945); 49, 177 (1945); 51, 21 (1946). J.P. Remeika, J. Amer. Chem. Soc. ?6, 940 (1954). W. J. Metz, Phys. Rev. 76, 1221 (1949). H. F. Kay and P. Vousden, Phil. Mag. 40, 1019 (1949). B.C. Fraser, H. Danner, and R. Pepinsky, Phys. Rev. 100, 745 (1955); for orthorhombic phase, see G. Shirane, H. Danner, and R. Pepinsky, Phys. Rev. 105, 856 (1957). J. C. Slater, Phys. Rev. ?8, 748 (1950). W. Cochran, Advan. Phys. 9, 387 (1960); 10, 401 (1961). R. H. Lyddane, R. G. Sachs, and E. Teller, Phys. Rev. 59, 673 (1941). B. Jaffe, R. S. Roth, and S. Marzullo, J. Appl. Phys. 25, 809 (1954). A complete description of all the solid-state Perovskite-type oxides is given by F. Jona and G. Shirane, Ferroelectric Crystals (Macmillan, New York, 1962), Chap. V. H. Jaffe, J. Amer. Ceram. Soc. 41,494 (1958). J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, Appl. Phys. Lett. 11, 269 (1967). C. E. Land and P. D. Thatcher, Proc. IEEE 57, 751-768 (1969). J. R. Maldonado and A. tt. Meitzler, Proc. IEEE 59, 368-389 (1971 ).



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Fifty Years of Ferroelectricity