PROCEEDINGS OF THE IEEE VOL. 53, NO.

10 OCTOBER, 1965

Piezoelectric Transducer Materials

H.JAFFE, FELLOW, IEEE, AND D. A. BERLINCOURT, MEMBER, IEEE

Abstract-Properties of piezoelectric crystals and ceramics are els of piezoelectric coupling with low dielectric constant.
reviewed as they affect use of suchmaterials in electroacoustic These compounds are also semiconductors and photo-
transducers. Extensive data on lead titanate-zirconate ceramics are
presented to helpin selection of the appropriate material for a variety
conductors. Moreover, someof them retain piezoelectric
of applications in thelowerand medium frequencyrange, up to properties as a result of preferred orientation in vapor-
severalmegacycles per second. Quartz and severalrecently dis- depositedpolycrystallinelayers.Noveldevicesbased
covered piezoelectric crystals wil share the higher megacycle range. onthesecombinations of propertiesarediscussedby
Foster, this issue, page 1400.

P IEZOELECTRIC TRANSDUCER materials have

held a key position as electroacoustic transducers
in the sonic and ultrasonic range for some forty
years. There has been no serious challenge to this posi-
Improved high-temperature crystal-growthprocesses,
broughtaboutbytransistorandlaserdevelopments,
havealsobenefittedthepiezoelectricart.New
electriccrystalssuchaslithiumgallate[4],lithium
piezo-
tion for sonic transducers into dense media, or for ultra-
niobate [SI, and bismuth germanate [6] have recently
sonic transducers up to about a gigacycle. The frequency
been announced.Theyarelikelytocontributeim-
range from about 30 Mc/s up has, in fact, been opened
portantly to transducers in the 10 to 100 Mc/s range.
up broadly only in the last three years andoffers an at-
tractive field fornewpiezoelectricmaterialsand new RELATIONS OF PIEZOELECTRICITY
forms of piezoelectrics such as cadmium sulfide films.
Properties of currently or
potentially
important
Untilthelate 1940’spiezoelectrictransducerscon-
piezoelectric materials will be presented here. The no-
sisted of a handful of piezoelectricsinglecrystals,
menclatureandunits used will be those of the IRE
notablyquartz,Rochellesalt,tourmaline,ammonium
Standards on Piezoelectric Crystals 1958 [7] and 1961
dihydrogen phosphate(ADP),and
lithium
sulfate
[8]. For a more complete and rigorous presentation of
monohydrate. In 1947 the first piezoelectric transducer
piezoelectric relations than given in this paper, and for
employingpolarizedferroelectricbarium titanate ce-
data on the older established piezoelectric crystals, the
ramics appeared. The art of producingandapplying
reader is referred to several treatises [9]-[14], a review
bariumtitanateceramictransducerswasdeveloped
article [15], and a pamphlet [la].
broadly in the following ten years. Since 1957 barium
Inthe 1961Standards,emphasisisplacedonthe
titanate has been increasingly replaced by leadtitanate-
piezoelectric strain constants (d constants) and elastic
zirconate solid-solution ceramics offering higher piezo-
compliance constants (s constants), which are directly
electriccoupling,wideroperatingtemperaturerange,
applicable to bodiesvibratingunderlaterallyuncon-
and a choice of useful variations in engineering param-
strained condition. This condition is usually fulfilled at
eters to be discussed later in this paper. The key physi-
frequencies below or near fundamental resonance of the
calproperty of bariumtitanate,the leadzirconates,
body(determinedbyitslargestdimensions);these
and other piezoelectric ceramics is ferroelectricity. Fer-
constants will therefore be used here preferentially for
roelectricshave
electronic
and ionic displacements
the materials serving in the sonic or low-frequency-ultra-
producing net spontanews polarization, which can be
sonic applications. In discussing materials for high-fre-
preferentiallyorientedbyanapplied“poling” field.
quencyapplications,notablythenewerpiezoelectric
Within the unit cell, there are certain discrete directions
single crystals, we will emphasize the constants relating
that the polarizationcantake,dependentoncrystal
to laterally restrained bodies. These are the piezoelec-
symmetry; a region in which the polarization is uniform
tric stress constants (e constants) and elastic stiffness
is calledadomain.Ferroelectricity is generallycon-
constants (c c,onstants) which are directly observed by
nected with a high level of dielectric constant. This leads
study of thickness resonance. Two further piezoelectric
to relatively low electrical impedance, usually desirable
constants, g and it, are obtained by dividing thed and e
in the sonic and lower ultrasonic field up to abouta few
constants by the appropriate permittivity, and apply
megacycles per second. At higher frequencies ferroelec-
when electricdisplacementistakenasindependent
tricceramicshaveinconveniently low impedance.In
variable.’ Constants g and h vary much less from one
this field quartz has retained an important place in spite
piezoelectric crystal to another thand and e, and do not
of its low piezoelectric coupling.
show the extreme temperature dependence found for the
About 1960 it wasdiscovered[1]-[3] that simple
latter constants in ferroelectric materials. The g con-
compoundshavingwurtzitestructure,includingzinc
stants, with appropriate geometric factors, give open-
oxide and cadmium sulfide, combine intermediate lev-
Manuscript received June 8, 1965. 1 The g constants, like the d constants, are directly applicable to
The authors are with Clevite Corp., Electronic Research Div., bodies vibrating without lateral constraint. The k constants, like
Cleveland, Ohio. the e constants, are directly applicable to laterally restrained bodies.
1372
 JAFFE AND BERLIKCOC'RT: PIEZOELECTRIC TRANSDUCER MATERIALS 1373

circuit voltage output per unit force input. The follow- TABLE I
ing equations define the basic piezoelectric relations in AND UNITSFOR ELECTROELASTIC
SYMBOLS CONSTANTS
four different ways:
1 Symbol I Unit
D = eTE 4- dT. Stress N/m*
S = dtE 4- s'T. Strain
Electric field strength
D = @E +- RS, Electric displacement S D

T = - etE +- cES. Elastic compliance

Elastic stiffness
E = BTE - gT, Permittivity
Dielectric impermeability , fl
Piezoelectric strain
constant 1 d
Piezoelectric stress
constant j e C/m2 or N/Vm
Piezoektric strain constant
Piezoelectric stress
constant ~ h \'/m or S/C
Piezoelectric coupling factor , k
Mechanical quality factor
The meanings of the symbols and their units in the Electrical qualityfactor
Qu
~

Q E= l / t a n 6
I
MKS system are given in Table I. In data tabulations, fa.l for LEt mode Cycle m/s
f.t for T E mode
dielectricconstants K = € / E O arecustomarily given Elastic -velocity
rather than the permittivities (EO = 8.85. 10-l2 F/m). Density I k/m3
Equations (la)-(ld) are matrix equations relating the
three components of the electric field or displacement TABLE I1
vectors with the six components of the stress or strain ELECTROELASTIC MATRIXFOR CRYSTAL CLASS2"
tensor.The piezoelectric constantmatriceshave six
columns and three rows; the transposed matrices identi-
fied bythesubscript t have rows andcolumnsinter-
changed. See Table 11. Fortunatelythematerials of
greatest technical interest have high symmetry, which
simplifies thematrices of the coefficients. We begin
with the crystal class of lithium gallate, orthorhombic
polar, 2rnm (C2,, in older notation). The symbol signifies
the presence of a two-fold axis of symmetry (the Z axis)
and two planes of symmetry (normal to the X and Y
axes). The electroelastic relations of (la) then reduce to
those shown in the matrix Table 11. The effect of sym-
metry 2mm on (lb), (IC), and (Id)is exactly the same.
Thestress
components TI, T2, T3 represent axial
stresses (tension positive, compression negative), while
components T4, T5, T6 representshearstresses in the
planes normal to the X, Y,and Z axes, respectively. As
an example for the use of Table 11, note that electric
displacement D3 parallel to the 2 axis (charge density
on face normal to Z ) is caused by axial stress along any
of the coordinate axes, aswell as by a field parallel to 2 :
D3 = e u T E 3 + d31T1 + d32T2 + d33T3. (2)
Theveryimportantcrystal class6mm (&), con-
taining the wurtzite-type crystals CdS and ZnO, results
when we increase the order of the symmetry ( Z ) axis to
6 . The X and Y axes then become equivalent, and the
following equalities are introduced in the matrix con-
electric field in the polar ( 2 ) direction and axial strain
stituting Table I1 :
in the same direction, while dS1relates the same field to
€11 = €22; d31 = d 3 z ; d 2 4 = d15; extensional strain in any direction normal to the polar
(3) direction. The coefficient dl5 relates an electricfield nor-
s11 = SZZ; s13 = s23; s66 = 2(sll - sl2); s44 = s55.
mal to the polar axis with a shear strain in the plane
Identical relations hold for the other forms of ( l ) , ex- containing the polar axis and signal field; in a plate with
cept that CE6 =4(c11-c12). The number of independent signal field along the short edge this will be a thickness
piezoelectric constants is thus reduced to three, elastic shear mode, used to generate or detect shear waves.
constants to five, and dielectric constants to two. The A body composed of many polar crystallites, which
piezoelectric constant dsadescribes interaction between have been given a preferred orientation by a unidirec-
1374 IEEE PROCEEDIXGS OF THE OCTOBER

tional polar effect, has a symmetry which is equivalent ing waves exist and in general not all elastic energy is
to 6mm in electroelastic properties.
Relations (3) dielectrically coupled. With the former, the elastic en-
therefore apply to ferroelectric ceramics made polar by ergy density is uniform. The effective coupling facto?
treafment in a high electricfield,as well as films of is defined as follows, in terms of the characteristic fre-
CdS, ZnO, and even cubic ZnS having preferential polar- quencies fp and fa:
crystalgrowthtendencies.
fP2 -f a 2
Anotherpolarcrystalclasslikelytobecome of in- kefff = ~ 3
(4)
creasing interest is the trigonal class 3mm (&) repre- fP2
sented by the mineral tourmaline and thenew ferroelec- This definition holds,for all resonant modes and their
tric crystal, lithium niobate. The loweringof symmetry overtones, and as mentioned, it is this coupling factor
compared to class 6mm introduces a fourth independent which determines filter or transducer bandwidths. Geo-
piezoelectric coefficient d22 or e22, and also ep1-=-e22 and metrical factors are required in the general case to relate
e16= -e22. As a result a field parallel to X will, in this an effective coupling factor to the appropriate material
class,causethicknessshears S5 and Se, while a field coupling factor and thus to the piezoelectric, dielectric,
parallel to Y causes thickness shear strain S4 and thick- and elastic constants. As an illustration, consider the
ness axial strain Sp. The elastic behavior of class 3mm thicknessextensionalmode of a piezoelectricceramic
is thesameasthat of the class of quartz, 32. I t is plate. The effective coupling factor is given by (4). The
complicated by elastic cross-couplings between strains material coupling factor, definedfor the same mechani-
Sz and Sd, as well as between S5 and Se. For the X cut cal boundary condition (one-dimensional strain parallel
of class 3mm, this means that two independent thick- to the thickness), but with uniform stress, is designated
nessshearwaves will be generated which havetheir k t and is relatedtothecharacteristicfrequenciesas
particlemotions in the ( Y , Z ) plane,inorientations follo\vs:
which depend on the specific values of the elastic con-
stants. In the Y cut, two impure modes will be excited,
of which one is predominantly longitudinal.
Piezoelectric materials may be characterized by a set
of dimensionless constants, the coupling factors, which For k t verysmallthecouplingfactors of (4) and ( 5 )
are a direct measure of the strength of the electrome- reduce, respectively, to
chanicaleffect.Thecouplingfactors of piezoelectric Af
materials with considerably different permittivity and keff2 2 - N

fP
compliance may be directly compared. The appropriate
effectivecouplingfactorlimitsthebandwidth of a and
filter or transducer.
A piezoelectric coupling factor may be defined as the
square root of the ratio of energy available in electric
form to total input mechanical energy (direct effect) or Thus for K very small
thesquareroot of theratio of energyavailable in
mechanical form to total input electric energy (converse
effect). The value of suchacouplingfactordepends
-
79
kt2 - ketf’.
8
(8)
upon the appropriate electric and mechanical boundary
conditions. Table I11 lists the material coupling factors Overtones f,(n) and fa(n)of the fundamental thickness
of major importance in piezoelectric ceramics and crys- extensional mode exist, withfp(n)forming an exact odd
tals of class 6mm and correlates each with the appropri- harmonicsequencewith n = 1, 3, 5, . . . . Forsmall
ate resonant element. All modes in Table I11 with the values of k t the effective coupling factors of the over-
exception of PE can be excited in all piezoelectric crys- tones decrease as l / n and the sum of the squares of the
tals, but in many cases rotated cuts must be used.2 The effective coupling factorsfor fundamental and overtones
PE moderequirescouplingbetweenexpansion in a equal the square of the appropriate material coupling
plane and electric field normal to the plane, and i t is factor,
free of undesirable coupling to other modes only when
isotropy exists in the plane. This mode is of considerable
practical importance as it allows ready evaluation of
the properties of piezoelectric ceramics, which are con- as before.
veniently fabricated as small thin disks.
Adistinctionmust be madebetween thematerial The older literature uses the ratio I of the clamped to motional
coupling factors of Table I11 and the effective coupling capacitance in the equivalent circuit; r = ( l -Ref?)/RefZ.The charac-
teristic frequencies f, and fa are generally termed the parallel and
factors of the resonant elements. With the latter, stand- series rewnance frequencies. They are never measured directly; the
frequencies actually measured are those of zero reactance (fa andf,) or
The simple relationships in Table I I I hold only when symmetry of maximum and minimum impedance (f,,and fm). For a lossless
is sufficient to exclude cross-coupling effects, which in the general resonator f p =fa =f. and f. =f, =fm. When losses are not negligible,
case exist in thickness modes. fp-f8 must be calculated fromf,,-f,, as in (2) of [8].
1%5 JAFFE AND BERLINCOURT: PIEZOELECTRIC TRASSDUCER MATERIALS 1375

T.4BLE 111
COUPLING FACTORS
IMPORTANT MATERIAL OF PIEZOELECTRIC CERAMICS OR CRYSTALSOF CLASS6" AND CORRESBONDING
ELASTIC
BOUNDARY CONDITIONS. THERESONANT ELEMENTS AND ELECTRIC BOUNDARYCONDITIONS
FOR THE EFFECTIVECOUPLING FACTOR AREA L S O LISTED

Material Coupling Elastic Boundav Electric Boundary Resonant

Factor Condition Resonant Element Condition Mode

All stress components zero Bar with length perpendicular to 2,thickness Constant-E a t f, LEt
except TI. parallel to Z;fundamental mode.
A l l stress components zero Bar with length parallel to Z ;fundamental Constant-D a t f, LE,
except T3. mode.
All stress components zero Disk with thickness parallel to Z,fundamen- Constant-E a t f. PE
except TI= T?. t a l mode.
-411 strain components zero Plate with thickness parallel to Z,thickness Constant-D a t f, TE
except S,. extensional mode.
All strain components zero Pfate with Z in plane of the plate, thickness Constant-D a t f p TS
except S5. shear mode.

L E t = longitudinal expander, transverse electric field;

LE, = longitudinal expander, parallel electric field;
PE =planarexpander;
TE-thickness expander; TS-thickness shear.

Fig. 1. The ratio k,.t/Lff is shown as a function of kerf for the PE

mode of a disk (k,) and the LEtandLE, modes of a' bar (kal and
k38). The ratiofor the T E and TS modes of plates (kt and kI5)cor-
responds to that for k33. The coupling factors are described in
Table 111.

Only in very special cases where there are no over-

tones of a given resonant mode does the effective cou-
plingfactorequaltheassociatedmaterialcoupling for k33 is equal to that for k t , but the related material
factor.Thecriterion is that the stress beuniform at couplingfactorisdifferent(Table 111). Theratio is
resonanceorantiresonance. An example is theradial equal also for theTS mode (k15, Table 111). The electric
mode of a ring in piezoelectric ceramics (poled radially boundary condition is constant D a t f, for k33, k t , and
oraxially)or in crystals of class6mm ; in thiscase kI5 (related to s3sD, c 3 P 1 and c44D, respectively) and con-
keff = k31. stant E a t f. for k~ (related to sIlE)and k, (related to
With low values of k the effective coupling factor and s1lE and ~ 1 2 ~ Figure
) . 2 shows keft as a function of Af/f,.
its associated material coupling factor, for virtually all Use of this graph with the curves of Fig. 1 allows rapid
possibleuncoupledresonantmodes,arerelatedvery calculation of the material coupling factors k31, k,, k33,
nearly as in (8). With values of k greater than about k15, and k t . The appropriate piezoelectric constants may
0.25, however,thedependence of theratio kmat/keff then be calculated. An alternate method, convenient for
upon the exact nature of the stress distribution in the thicknessshear ( k ~ )andthicknessextensional (kt)
dynamic mode, the value of k, and the electric boundary modes, requires measurement of the fundamental mode
condition becomes significant. Figure 1 shows the ratio f. and a t least one overtone of fa. The anharmonicity of
as a function of keff for the PE mode of a disk (k,) and the overtones is readily related to the appropriate ma-
the LE, and LE, modes of a bar (kt1 and k33). The ratio terial coupling factor [17], [18].
 TABLE IV
PROPERTIES OF COMMONLY IJSEDrIEZOEI.ECTKIC CERAMICS-I,OW SIGNAL I'ARAMETERS AT 2.5' UNLESS OTHERWISE SPECIFIED
__ .-_.____ - . ~ _ _ _ ___ ~ __~ ___ _ __ _ ___ _ _____
lO-W/N lOloN/mam'/C lO-lzm'/N
kp ka kaa klo kt w T / w emN/eo auT/eo at"/a -~ -
dm dz1 dts cu em a b s$ m R x d P sea 'a
s stlo suo cuE caE cuD cnD
___ __ _____
PZT-4" -0.58
0.51
0.71
0.70
-0.33 73014756351300 289496 -123 15.1 -5.2 12.7 15.5 12.3
3Y.O 32.7 13.9
7.90
11.519.310.9 15.9 14.5
PZTSA" -0.60 -0.34 0.705
0.685
0.49 584
-171
374
916
1730
830
1700 15.8 -S.4 12.3 18.814.4
9.46
44.3
47.5
16.4 25.2 12.1
11.1 14.7 12.6
PZT-SH" -0.65 -0.39 0.675
0.75 0.505
741
-274
593
1700
3130
1470
3400 17.0
-6.5
23.3 20.714.1
8.99
42.6
43.5
16.5 23.7 15.7
12.6
11.7 13.0
~
PZT-6Aa -0.42 -0.25 0.54 0.39 1050 730 -- ~ 189 - 80 - 12.5 - - 13.0 10.7 - 27.8 9.2 10.1 - 13.1 - 15.5 -
PZT-6BB -0.25 -0.145 0.375 0.377 0.30
407475386460 71 - 27 130 7.1 -0.9 4.6 9.35 9.0 28.2 24.0 8.05 8.8 24.2 16.9
17.7
16.8
16.3
PZT-7Aa -0.51 -0.30 0.67
0.66 0.50 425 235 840 1.50460 - 60 362 9.5 -2.1 9.2 13.9 27.8
39.5
10.7 7.85 13.1
21.8
9.7 14.8 17.5 15.7
PZT-8* -0.50 -0.295 0.62 - 0.44 1000 600 - - 218 - 93 - - ~ 11.1
13.9 _ - 29.6 8.5 10.1 - - _ - -
PZT-2" -0.47 --0.28 0.63 0.70 0.51 260450 990 152504 - 60 440 9.0 -1.9 9.8 14.8 11.6 45.0 29.9 9.0 10.7 22.') 11.3 13.5 13.6
14.8
BaTiOI -0.36 -0.21 0.50 0.48 0 . 3 81115
1450
1260
1700 190 260
- 78 9.19.5
11.4
-4.3
17.5 214.6
217.5
. 88.77.1
23.6 15.0 15.0
17.1
95w%BaTiOl CaTiOa
Sw% -0.33 -0.19 0.38
0.48
0.48 1200 910 149
1000
1300 - 58 242 -3.1
13.5 10.9 8.6
9.1 22.2 22.4 8.3
7.0 17.1 15.0 15.8 17.7
YSw%BaTidr CaTIOl
Swgr -0.31 0.46-0.18 0.46 0.36 1420 1110 - - 150 - 59 - - - - 8.1 - - - - - _ - - - 15.Y
{0.75w% C o C d r N k E - 4 1281
l'bNbr4b -0.07 -0.045 0.38 - 0.37 225 - - - 85 -4 - - 25.4 - - - 21.8 - - - _
Pbo.aBao.dN&
1151 -0.38 -0.22 0.55 - - 1500 - - - 220 - YO - - _- _- - 11.5 - 10.9 - _ - -- -- -e
Na~.1K~.1NbO~(Hotpressed)[29]
-0.46 -0.27 0.605
0.645
0.46 545938306496 127 306
- 51 - -
- -7.6 6.4
11.3 10.1 8.2 27.1 15.5- - - - -
~ _ ~ ~ _ . . ~ _ _ _ _ _ _ ~ . w
m
a Trademark Clevite Corp. m
I,General Elktric Company. zz
__-
2
-___~ ____. __ _____.___~ ____~
U
e
j!
Cycle m/s m/s constant Time dielectric, s kV/cm rms ac field a m
QM QE N~ N , ~ w lw~, ~ JyE for Tan 6 ~ 0 . 0 4 El3 ;
200°C100°C 25°C @ 100°C 25°C 2.2 m
- 0 m
-9
0 bo
d N h%
~-
PZT-4 2630 4600
500 250
2000 1650 328 7.5 420 2.1 11,000 3500 +1.5% -2.3% -5.8% 4.8% > 100 - 5 . 0 -. 0.07 >10 3.9(17%)* 3.3 30
PZT-SA 75 50 1400 1890
3652260
4350 7.75 420 1.5 11,000 4000 +0.2% -0.2% -1.0% 2.6% >2000 -1800 250.0 - 7 0.4.5(11%) 0.45 38
PZT-SH 193 2375 4560 SO
65 2000 1420 7.5 420 1.5 11,000 4000 +0.25% -0.35% -1.59 9.0% >ZOO0 >ZOO0 -1000.0 4 0.3(5%) 0.2 33
--
PZT-6A 450 50 1770
2140
4570 - 335 7.45 420 11,000
2.1 3500 <O.l% -0.2% -0.6d < 0.20/ > 10 4 .41. 50 0 2 -8 3 .2 30 2.8
PZT-6B 2340
4820
2225
1920
110
1300 -350 7.55 420 2.1 11,000 3500 <O.lY, -0.2% -0.6% < 0.2d > 100 -1.5 4.03 > 10 11.0 5.0 1s
PZT-7A 2490
4800
2100
1750 60 600 -350 7.6 420 11,000
2.1 3500 -0.08% 0.0% +2.Oy0 2.9% > 10 -0.5 4.03 10
>1.3 2.6 42
PZT-8 1000 250 1700 - - - 300 7.6 420 2 . 1 11,000 3500 +l.O% -2.0% -5.0% - 2.0% > 100 -2.0 4.01 >15
tan6=0.015
tan6=0.03 25
at at
6kV/cm (8%) 6kV/cm
PZT-2 680 200 1680 2090
3702400
4410 7.6 420 2 . 1 11 000+0.6oJ
3500 -1.8% -2.87 1.5% > 100 -2.0 -0.03 > 10 1.8 1.6 40
BaTiOl 3160
5470 300
2520
2200100 115 5.7 500 3.5 3000
7:500 +l.ld -2.5% -4.1% 19.0% > 150 4 . 5 -0.002 -4 1.0 0.8(75'C) 8
400 170 2290115
3240
5640
2740 5.55 500 3.5 7,500 3000 +O.Su/, 71.8y0 -0.8% -lS.OUl, > 100 -0.3 -0.002 -4 1.7 1.0(7SoC) 8
105 2760 2310 5.7 500 3.5 7,500 3oM) +0.4% -1.9% -1.3% -15.0% - - - 9
- -4.0 - 8
11 100 - - - - 570 6.0 - - - - _ - - - >lo00 -500 -10 >6.0 >10 - -
Pbo.sBao.rN& 250 100 1915 - - - 260 5.9 - - - 2.5% >lo00 50 1 - 1.4(1770) - -
Nao.oKo.,NbO~(Hotpressed) 240 70 2570 - - - 420 4.46 - -- _- - - _ - - - 3.3% 50
- -- -- - - - -30

* The number in parenthesis gives increase in mTat theindicated electric field.

1965 JAFFE ATD BEKLISCOVKT: I’Il~~%OI<LI:Cl
IlIC 1 KASSDUCER MATERIALS 1377

CERAMICS
PIEZOELECTRIC

Piezoelectricceramicsaregenerallymadebysolid-
state reaction of several oxides or carbonates, followed
by high temperature firing involving crystal
grain
growth,andtheelectric polingprocess. l l o s t piezo-
electric ceramics are solid solutions; variation of chemi-
cal composition allows the optimizing of properties, as
one optimizes them in single crystals by selection of a
suitable “cut.” Table IV listscomprehensive data for
ceramics that are in use today. Those designated PZT
are commercial versions of lead titanate-zirconate solid
solutions with approximately equal molar concentration
of titanium and zirconium [19]. The advantage of such
compositions is due to the proximity of a phase bound-
ary between atitanium-richtetragonalphaseanda
zirconium-rich rhombohedral phase (Fig. 3). The phase
boundary composition is analogous to a ferromagnetic
alloy of zero crystal anisotropy. Dielectric constant and
piezoelectriccouplingshow a sharp peak at the phase
boundary, but coupling remains fairly high over a wide
range on the zirconiumside[20].PZT-2 is sucha
rhombohedralcomposition.Calcium,strontium[21],
or barium [22] may be substituted for a fraction of the
lead,andtin forzirconium[23],resulting in lowered
Curie point and increased permittivity. PZT-4 is such a
composition. The substituent atom in this case has the
samevalenceasthe replaced
one. Nore profound
changes in physical properties occur \\-hen a substituent
n
of higher valence is introduced in the amount of 1 atom
percent or less,such as 5-valent niobium replacing 4-
valenttitanium,or3-valentlanthanumreplacing 2-
valent lead [24].ThePZT-5compositionsare such
electron-donordoped lead titanate-zirconates,charac-
terized by enhanced permittivity and compliance with
increased loss tangent, increased dcresistivity,and
reduced aging rates [25].
Theinherentnonlinearnature of piezoelectric ce-
ramics or ferroelectric crystals leads to considerable diffi-
culty in characterization.Withvery low electricor
.d-- mechanical
the
drive piezoelectric
ceramics may be
considered strictly linear in their behavior, even though
reversibledomain wall motionenhancesthe piezo-
electric and dielectric constants and increases compli-
ance. With increasing electric or mechanical drive there
is a disproportionate increase in piezoelectric response.
Highelectricdrive also results in amorethanlinear
increase in dielectricdisplacementandan increase in
dielectric loss [26].Highmechanicaldrivesimilarly
produces disproportionate
a increase in mechanical
displacement and an increase in mechanical loss [27].
These effects are frequency-dependent, being
most
severe under very low frequency and static conditions.
The limits of linear behavior vary widely .for different
piezoelectric ceramics, being roughly related to thecoer-
civeforce.
The propertieslisted in Table I\- are subject to statis-
tical and systematic fluctuations due to a variety of cir-
cumstances related to the method of manufacture. It is
stated in the 1961 I R E Standards on Piezoelectric Crys-
1378 PROCEEDIXGS OF THE IEEE OCTOBER

tals [8] that coefficients of ceramics of definite composi- resonancefrequencyovertheambienttemperature

tion with a t least 95 percent of crystal density shall have range and device lifetime is of the order one part in 103,
values which vary no more than 5 percent for elastic, withonepartin lo4 highlydesirable.Thenecessary
10 percent for piezoelectric, and 20 percent for dielectric temperature stability is of the order 10-5/”C. Typical
constants. The data listed in Table IV are representa- temperature coefficients of high melting oxides are nega-
tive and as far as possible self consistent for each com- tive and several times this value. The presence of vari-
position. ous closely related crystallographic phases in the lead
Study of the table reveals that different compositions titanate-zirconate system causes temperature anomalies
are outstanding with regard to different characteristics. whichallow reduction of averagetemperature coeffi-
Thisaccounts for theproliferation of piezoelectric cientstoanacceptable level-typically10-5/0C from
ceramic compositions during the past several years. I t -40 to 85OC.
is the experience of these authors that the compositions The drift of resonance frequency with time is a nat-
based on lead titanate-zirconate offer the widest range ural result of thestrainsintroduced in poling. I t is
of desirable properties and that they are, for the great approximately linear with the logarithm of time over a
majority of applications, a more desirable choice than technically significantrange-onehour to
several
compositionsbasedonbariumtitanate,leadmetani- years.4WiththePZT-6materialsthemajorrequire-
obate, or sodium niobate. The leading position of the ments of voice channel intermediate-frequency filtering
leadtitanate-zirconatecompositions is duetotheir in the range from about 200 kc/s to a few Mc/s can be
intrinsically strong piezoelectric effect and high Curie met.Filtersforspecialapplications below 200 kc/s
point, whichallow a wide variation in chemicalcom- based on bending structures have also been made. The
position to obtain awide range of operating parameters bandwidth of filters utilizing piezoelectric ceramics can
without serious reduction of the piezoelectric effect. be controlled by adjustment of poling level. With PZT-
The following list highlights the data of Table IV, 6A and PZT-6B the planar coupling factors are adjust-
showing materials that are outstanding with respect to able in the ranges 0.20 to 0.44 and 0.0 to 0.25, respec-
special characteristics: tively.
Figures 4-15 show changes in parameters with tem-
Piezoelectric coupling: PZT-5H. peratureforseveralleadtitanate-zirconatecomposi-
High permittivity: PZT-5H. tions. The remarkable differences are the result of varia-
tion in the relative proportion of titanium and zirco-
Low permittivity:PbNbz06,PZT-7A, nium, isomorphous substitution, and control of donor-
Na0.5K0.ENb03. acceptor balance. The effectsof some additives, notably
High acoustic velocity: Na0.5K~.5Nb03. the transition metals, are still little understood.
Lead metaniobate remains a unique material of very
Highmechanical Q: PZT-6BandPZT-8. high Curiepoint, low permittivity,and a reasonable
Low mechanical Q: PbNbt?Os. level of k t and k33. Its very low mechanical Q, which for
many applications is deleterious, actually has encour-
Time stability: PZT-6A and PZT-6B. aged its use in ultrasonic flaw detection, where the low
Temperature stabilityof N 1 :PZT-6A and PZT-6B. Q helps the suppressionof ringing. Substantial substitu-
tion of barium or strontium for lead causes fundamental
Low dielectric loss a t high electric drive: PZT-8. changes in the properties of lead metaniobate. Just as
in the leadtitanate-zirconatesystem,optimal piezo-
The highpiezoelectriccouplingandpermittivity of electric properties are obtained near a phase boundary.
PZT-5H have led to its use in acoustic devices such as Niobates with fairly high mechanical Q and relatively
phonographpickups,whereits highelectric anddi- low temperature drift of resonance frequency have been
electric losses arenotharmful.Forhydrophonesor found [15], [30].Data available to the authors do not,
instrumentapplicationsPZT-SA is abetterchoice, however,show thatthestability of thePZT-6type
since its higher Curie point leads to better temperature materialshas been duplicatedorthatanyother ex-
stability.Its high resistivity a t elevatedtemperature tremesobtainedwiththeseveral PZT variantshave
allows use to very low frequencies. been attained with modified lead niobates.
The low elastic and dielectriclosses of the new PZT-8 Sodium-potassium niobate was developed specifically
composition a t high drive level point to its use in high for use in high-frequencytransducers (10-40 Mc/s)
power sonic or ultrasonic transducers, a field presently
served by PZT-4 or equivalent lead titanate-zirconate 4 Until recently it was generally observed that piezoelectric cou-
and NRE-4 type barium titanate. pling, permittivity, and compliance decreased with time afterpoling.
Thedevelopment of the PZT-6compositionswas Table I V shows that anomalous behavior is encountered with
PZT-7A. This is not yet understood, but it has been possible to syn-
aimed a t filterapplications.Therequiredstability of thesize compositions with virtually no aging.
1965 JAFFE AKD BERLIXCOL'RT: PIEZOELECTRIC TRANSDUCER MATERIALS 1379

-kP

- 1 I I I
0 IO0 200 2 IO

I I I I I I I Fig. 7.
TEMPERATURE.OC

Dielectric constant vs. temperature for temperature

stabilized PZT-6.\, PZT-6B, and PZT-7.\.
TEMPERATURE, O C

Fig. 4. Planar coupling factor vs. temperature for temperature

stabilized PZT-4, PZT-S-A, and PZT-SH.

0 TEMPERATURE, O C
TEMPERATURE, O C

Fig. 5. Planar coupling factor vs. temperature for temperature Fig. 8. N I vs. temperature for temperature stabilized
stabilized PZTdA, PZT-6l3, and PZT-7A. PZT-4, PZT-5 1, and PZT-5H.

TEMPERATURE, *C
TEMPERATURE, OC

Fig. 6. Dielectric constant vs. temperature for temperature Fig. 9. N I vs. temperature for temperature stabilized
stabilized PZT-4, PZT-SA, and PZT-5H. PZT-6.4, PZT-6B, and PZT-7A.
1380 PROCEEDINGS OF THE IEEE OCTOBER

I I I
0!2k -A0 -Id0 0 100 200 300
TEMPERATURE.'C TEMPERATURE, C

Fig. 10. d r l vs. temperature for temperature stabilized Fig. 13. gll vs. temperature for temperature stabilized
PZT-4, PZT-SA, and PZT-SH. PZT6A, PZTdB, and PZT-7A.

O!&
ole:
-& -IL d 100
TEMPERATURE, OC
200 x0I 1 0 0
TEMPERATURE, 'C
200 300

Fig. 11. vs. temperature for temperature stabilized Fig. 14. QM vs. temperature for temperature stabilized
PZTdA, PZTdB, and PZT-7A. PZT-4, PZT-SA, and PZTJH (planar mode).

TEMPERATURE - O C TEMPERATURE, 'C

Fig. 12. gal vs. temperature for temperature stabilized Fig. 15. Q M vs. temperature for temperature stabilized
PZT-4, PZT-SA, and PZT-SH. PZTdA, PZTdB, and PZT-7A (planar mode).
1965 JAFFE APIEZOELECTRIC
S D BERLISCOCRT: TRASSDCCER MATERIALS 1381

[29]. I t is made by the hot-pressing process, an expen- of the sectors may be increased either by usingseeds
sive but effective means for densification with limited wider in the X direction or byslower growth.
grain growth. The expense is justified for manufacture of The Q factors, both dielectric and elastic, are strongly
very thin high-frequency transducers. Its high acoustic structure-sensitive, and can therefore be affected in a
velocity gives T\;a.5K.5Nb03 someadvantage over PZT- majorwayevenbyminorimpurities. It has recently
7A in high-frequency thickness extensional and thick- been demonstrated that
hydrogen inclusion is the
ness shear transducers, since this allows greater thick- dominant cause for variation of the mechanical Q factor
ness and therefore lower capacitance. of natural and cultured quartz near room temperature
[36a].Intherelativelyfast-grown \Vestern Electric
QCARTZ quartz this impurity limitsQ of a 5 Mc/s AT cut to the
Themost significantdevelopment in piezoelectric range of 100 000 to 500 000, while nearly 3 000 000 is
quartzoverthelastdecadewastheintroduction of obtainedwiththehighestgrade of the moreslowly
synthetic or “cultured” quartz crystalson a commercial grown Sawyer Research Products quartz.
scale. The basic laboratoryworkwasdonebetween The maximum Q of quartz attained in resonators or
about 1945 and 1955, with major contributions by the transmission lines from 1 Nc/s upward is inversely pro-
BrushDevelopment Co. (laterCleviteCorp.)under portional to frequency :.fQ=constant= 15 000 000 Mc/s
U. S. Army Signal Corps sponsorship, by the Bell Tele- [37]. Such a relation can be accounted for by nonlinear-
phoneLabs.,andbytheGeneralElectricCompany ity of the elastic properties, specifically by relaxation of
Ltd.(GreatBritain).Thesedevelopmentshave been the thermal phonon spectrum to theperiodic stress con-
well summarized [31]. The principal manufacturers of dition of the elastic wave (Xkhiezer effect) [38]. Since
cultured quartz at present are Sawyer Research Prod- Q in the gigacyclepersecond rangehas beenfound
ucts,Eastlake,Ohio,andtheWesternElectricCo., little dependenton the quality of quartz, it appears that
IIerrimack Valley Plant. The principle of the quartz- the limit set by the intrinsic nonlinearity of quartz has
crystal growth process is in each case the same:dissolu- been reached in that range, and probably nearly so a t
tion of quartz supply in an alkaline aqueous medium 5 Rlc/s. It has been realized that quartz is inferior to
nearthecriticaltemperatureandabovethecritical someothercrystals,notablythegarnets, in intrinsic
pressure of water, and deposition from supersaturated mechanical Q. The position of quartz in frequency con-
solution on oriented quartz seeds maintained a t a lower trol remains, nevertheless, unique by the extraordinary
temperaturethanthesupply.TheWesternElectric coincidence of first- and second-order temperature coef-
growth process uses sodiumhydroxideandpressures ficients of resonancefrequency thatare zero for the
over 20 000 psi, while Sawyer Research Products uses A T c u t a t room temperature. As an ultrasonictrans-
sodiumcarbonatesolution at about 10 000 psi,with duceranddelaymedium for the 10 lIc/s to 1 Gc,/s
aboutone-thirdthegrowthrate.Theseeds used are range, quartz will see increasing competition from ma-
now generaliy rods or strips elongatedparallel to or at a terials of higherpiezoelectriccoupling andapplicable
small angle to the Y axis [32] (Fig. 16). The resulting in thin layers on the one hand, and of higher Q media
‘(Y-bar” crystals are well shaped for cutting the most on theother,butavailability of largehigh-quality
widely used orientations of quartz resonators, especially quartz crystals of Iow costandtheconvenience of a
the rotated Y cuts including the AT cut. piezoelectric effect adequate for many purposes assure
Oscillator grade natural quartz and cultured quartz them continued use.
are materials of high chemical and structural perfection, Properties of the quartz cuts that are most important
with impurity levels well below one part in a thousand. for high-frequencytransducersarelisted in Table V.
In properties which are not structure-sensitive, includ- The Y cut has the highest piezoelectric shear coupling,
ingpiezoelectric,dielectric, and elastic constants, one buttheelastic crosscoupling in trigonalcrystals,al-
would not expect significantdifferences between natural ready mentioned, causes the direction of sound propa-
and cultured quartz, and none have been reported. The gation to diverge from the wave normal. When quartz
use of quartzcrystals for frequencycontroldepends, is boththetransducerandpropagationmedium for
however, on theexactcancellation of first-ordertem- shear waves, the AC or BC cuts must be chosen; for
perature coefficients of sound velocity in certain direc- these cross coupling is zero. Table V also lists data for
tions.Variations in theangle of the AT cut for zero commonly used cuts of three of the older water-soluble
temperature coefficient up to about 20 minuteshave crystals: ADP, Rochelle salt,andlithium sulfate
been reported[33], [X]. Thesechangesappeartobe ( L i S 0 4 .HZO). ADPand Rochelle saltarepredom-
connected with a relaxation peak near 50”K, probably inantly used in longitudinalmodes,lithiumsulfate in
causedby
sodiumimpurity[35].
Fortunatelythe thethicknessextensionalmode.Thesecrystalshave
inclusion of sodium and other impurities is minimal in acoustic impedance better matched to water or organic
the two sectorsof the Y bar which are formed by deposi- liquids than either quartz or the piezoelectric ceramics.
tion on the basal faces (normal to the 2 axis). The size Rochelle salt is ferroelectric along the X axis between
 PKOCEEDISGS OF THE I E E E OCTOBER

Fig. 16.Y-Bar cultured quartz crystal sliced into XT cuts.

T-ABLE 1:
PROPERTIES
OF COMMOX
CUTSOF OLDERPIEZOELECTRIC
CRYSTALS

IRE Common 1O-lZC/N C/m? m/second 10--6/0C 1Oa kg/m3

notation [39] notation Mode*
k d e K z' T.C. Density

Ouartz
X X TE -0.09
0.17 2.3 4.5 5700 - 20 2.65
"Y Y-bar 4 . 5 - 0L. 1E7, - 2 . 3 -0.10 5400 - 2 to -5 2.65
V 4.5 - 0 .Y1 7 -T4S. 6 -0.14 3800 +90 2.65
( y s ~ ) + 3T 5S~ 1 5 ' A T -0.08 -3.4 -0.085 4.5 3320 0 2.65
(ysw)+3l0 Ac TS -0.10-0.11 -3.7 4.5 3300 +20 2.65
( Y E W ) - 59O BC TS -0.04 -0.9 -0.064 4.6 So00 - 25 2.65
~VHJIZPOI( A D P )
(34450 2-45 LEt 0.28 24 1 5 . 30( .K3 ~0 ~ ) 3250 -300 1 .80
Li2SOI. H?O
Y Y T E 16.3** 0.30
0.66 9(K n s ) 5470 -300 2.06
Rochelle Salt, 3OoC
(xyt)450 X-45 LE1 0.65 275 3 .O 350i KIIT) 100 3 $3x 104 1 .77
Y-45(yZt)45' LE1 0.32 30 0.16 9 .4(K 2 ) 2340 -300 1.77

* Mode Abbreviations are explained In Table 111.

** Erroneously given as 18.3 in 1121.

its -18and +23"C Curiepoints.Ferroelectricityen- much higher curvature of the resonance frequency vs.
hances the piezoelectriceffect well beyond this range, temperature relation. Below about 1 Mc/s the limita-
andtemperaturedependence is severe. The Y-45 cut tionofquartzwithrespect tobandwidthandthe
is used instead of X-45when better stability is required.somewhat less criticalrequirement on stabilityhave
A D P has largely lost its role as a major transducer ma-allowed considerable penetration
by
the
stabilized
terial to the piezoelectricceramics. Lithiumsulfate is piezoelectricceramics.
technologically important because of its relatively Several crystals havebeen grown and evaluatedwhich
strong piezoelectric coupling in the thickness extensional
meet the need for low dielectric constant materials with
mode and its strong response to hydrostatic pressure. piezoelectric coupling better than quartz and with good
mechanical properties. These may serve for delay line
NEWER PIEZOELECTRIC CRYSTALS and other transducersin the frequency range above that
The propertiesof mineral and synthetic crystals have adequately covered by
the piezoelectric
ceramics.
been investigated for many years. Inevitably the search Mechanicalworkabilityandstrengthare of vitalim-
has been to a considerable extent directed to finding a portance,sincethethickness of afundamentalmode
substitute for quartz for frequency control. In this re- transducer is only a fraction of amillimeter. Water
spect these efforts have not been successful. Ethylene soluble crystals such as lithium sulfate do not have the
diamine tartrate (EDT) [40] and dipotassium tartrate required mechanical stability for operation in the fre-
(DKT) [41] for example, have cuts with zero frequency quency range above about 5 Mc/s. A number of com-
temperature coefficients, but they
are
not rugged pound 11-VI semiconductorscrystallize in the cubic
mechanically,havequiteinferior Q-factors, andhave sphalerite and hexagonal wurtzite structures. Semicon-
1965 JAFFE 4SD BERLISCOURT: PIEZOELECTRIC TRASSDUCER MATERIALS 1383

ducting I I I-\T compounds(exceptaluminumnitride VI). LiGaOz has been included as its structure approxi-
with u-urtzite structure) crystallize in the cubic sphal- mates that of ZnO as discussed previously. The natural
eritestructure,buttheseandthesphalerite 11-VI crystal cinnabar (HgS) cannot be compared directly, as
crystals have considerably weaker piezoelectriceffects it is of different symmetry (32, the class of quartz).
thanthewurtzitestructure 11-VI compounds.Addi- Recentmeasurementsonverysmallcrystalplates
tionalinterestespeciallyinhexagonalCdSandCdSe (Table VIII) indicate that the piezoelectric effect is a
crystals has beenaroused by demonstration of deple- little stronger than that of CdS. This fits the general
tion[42]and diffusion
[43] layertransducersand trend of Table VII, as mercury is just below cadmium
acoustic amplification [44] in thesematerials,covered in the periodic system.
by May, this issue, page 1465. Table VI11 also lists partial data for hexagonal wurt-
Considerableefforthasbeendevoted togrowth of zite-structure aluminum nitride(AIX). The piezoelectric
crystals of zinc oxide [44a], which is the most strongly effect is stronger than with the cubic sphalerite-struc-
piezoelectric crystal known which is not a ferroelectric turegroup 111-V compounds,asexpected.Lithium
[ 1 1. ZnO is also a candidate for use as an acoustic ampli- niobate was originally identified as a ferroelectric over
fier, and diffusion layer transducers may be formed. I t fifteen yearsago[54],butquantitative piezoelectric
is not likely, however, that high resistivity evaporated measurements [sa] and observation of domain reversal
layers of ZnO will be easily developed. [54a] have been made only recently. The magnitudeof
Very recently Remeika and Ballman [4] announced the piezoelectriceffect appearsto be afurtherargu-
the discovery of a new piezoelectric crystal,lithium ment for ferroelectricity. The ratherlow symmetry leads
gallate (LiGaOz), with electromechanical coupling over to complicated coupled modesas discussed previously.
twice that of quartzandwithmechanicalproperties The ferroelectricsemiconductorSbSI [ 5 5 ] has a
comparabletoquartz.Warnerthenreported piezo- verystrong piezoelectriceffect [53] below its 22°C
electricmeasurements on LiGa02[5],and his results Curie point. The Curie point can be raised well above
together with data obtained in the authors' laboratory room temperature by partial substitution of oxygen for
are listed in Table VI. Agreement is quite satisfactory sulfur [56], but piezoelectric data are not yetavailable.
a t this stage. The structure of LiGaOz [48] consists of The crystal symmetry of SbSI is 2mm, but since the
alternating3-valentgalliumandmonovalentlithium peculiar needle- or blade-like crystal habit leads, in most
ions tetrahedrally surrounded by oxygen; it is in this cases, to polycrystallineaggregateswith c axes of in-
senseclosely related to the wurtzite structure. There- dividual crystals aligned and with a and b axes random,
fore, even though the symmetry is orthorhombic 2mm, the macroscopic symmetry is equivalent to that of the
it is listed in the table along with the hexagonal (6mm) piezoelectricceramics. Data in Table VIII, therefore,
crystals ZnO, CdS, and CdSe.It maybe noted that only reflect this symmetry rather than thatof the individual
negative frequency-temperature coefficients have been crystals. The elastic constants and coupling factors are
encountered. LiGaOz is subjectto apeculiarelectric relativelytemperature-insensitive below about 10°C,
twinningnotfound in the wurtzite structure crystals but as is characteristic with ferroelectrics, d3, and K33T
[49]. There appears to be a reversal of c-axis direction changedrastically.SbSIhas,byfar,thestrongest
across the twinboundary. response to hydrostatic stress of any known piezoelec-
It has been demonstrated that there is a regular pro- tric. X11 values in Table VI11 hold for a single crystal
gression of piezoelectric effects in the group 11-VI com- as well astheorientedpolycrystallinebundle,except
pounds of zinc and cadmium with oxygen, sulfur,selen- those for dal and k,.
ium,andtellurium [SI. The strength of the effect in- Until recently a piezoelectric crystal with significant
creases with increasing weight of the group I1 element conductivity was unattractive for study and useless for
and decreasing weight of the group VI element. It was technical application. This is nolonger true with the
shown thatanelementaryatomic model,postulating acoustic amplifier and increasing emphasis on high-fre-
constant bond length during elastic deformation, leads quency transducers. Piezoelectric data on GaAs, cubic
to a simple relationship between the piezoelectric strain sphalerite structure, have recently been obtained [.Si]
constants and effective atomic charge in binary com- (k14= 0.065). CuCl, also cubic sphalerite structure, was
pounds of cubic sphalerite and hexagonal wurtzite type found in 1946 [58] to have k-0.12. Coupling over 30
structures. Valuesfor charge obtained range from a frac- percentwasrecentlyreported for tellurium[59],al-
tion of an electronic charge up to a little more than one though conductivityis excessive even a t 77°K. Selenium
electron, in linewith the partly ionic nature of these also has a strong piezoelectric effect [60], and conduc-
compounds. The charge increases with increasing weight tivity isconsiderablylower.Reference [6O] lists dl1
of the cation and decreasing weightof the anion, in con- =65 X lo-'? C/N for selenium and other data shown
formity with chemical experience. lead to kt-0.25, but elastic and dielectric constants are
TableVI1lists effective charges,includingvalues not listed. Selenium and tellurium are of the symmetry
basedon the improved measurements on ZnO (Table class of quartz, 32.
~~

ZnO 1451, I461 6 m m 0.408 -0.18'J -0.316 0.282 11.0 8.84 9.26 8.33 10.6 -5.2 -13.9 1.14 -0.61 -0.59 6.94 7.86 21.1 21.0 4.25 4.43 22.9 21.5 4.72 6400 2945 5.68 - -
CdS [3I 6 m m 0.262 -0.119* -0,188 0.154 10.3 Y.53 9 . 3 5 0.02 10.3 -5.2 -14.0 0.44 -0.24 -0.21 17.0 20.7 Y.38 0.07 1.50 1.63 9.62 9.13 1.56 4500 1800 4.82 -I08 -48
CdSe 131 6 m m 0.194 -0.084 -0.130 0.124 10.6 10.2 Y.70 9.53 7.8 -.{.(J -10.5 0.35 -0.16 -0.14 17.5 23.4 8.36 7.40 1.32 1.44 8.48 7.42 1.34 3860 1540 5.68 - -
LiCaOI 1471 2mm 8.8
0.25'
-0.17
-0.12 - 7.2-2.87.7t
7.0 - 5 . 9 0.00 ~ -0.30 16.47.1 ~ 4.98 ~- 17.5 5.13
- 6450 3500 4.19 - 70 -43
-0.OYt
-2.4 -0.17 6.0 6.2 - 5.2 -0.20 44.0 5.68 5.85 3740 -32
LiGaot (SI 0.11 9.50.24
0.17 ~ 6.8 7.0 - 2 . 8 0.88 6.4 - 0.28 ~ 14.7 7.3 ~- 4.45 - 15.6 - 3306
6100
4.58 - 60 -46
0.14 05.42
.15 v.2 6.0 5 . 8 0.25 4.0 4.7 5.55 3642 -31

Si ns of pieiroelectricconstants are not given in 151.

for LdS is0.119~0.001from -1% to I00'C: kt for LiGaO:, decreases -2.5 percent from -60°C to +8S"C.
t Crystal used for this measurement very badly twinned ( s e text).
t d u = d h - d a - d n ; with d,,=+O.Y. dn=-Z.R. dn=--J.O, then dr.r=7.7.
I'or LiGaOl ka,, km, cu, L ! , dm. 01, CIS, cu, .UI,u U all listed first and kn. km, em. drr, Ju, eJx, d m , cad, sn,and ut' all listed in 1451,1461, and 1471.

TABLE VI1
SYSTEMATICS 01;EFFECTIVE ATOMICCHARGE ON METALATOM
CALCULATED 1:ROM BOND LENGTH ANI) PIEZOELECTRIC
CONSTANTS OF WURTZITE ANI) SIBHALEHITIC
STKUCTURI? T Y P E 11-VI CRYSTALS

Cd'l'c
0.081

i
CdSe Decreasing
atomic weight
0.68,O.SS of nonmetal

ZnS CdS
0.27 0.90,0.77
~
-- + Increasing atomic weight of metal
For hexagonal (wurtzite) crystals (except BeO) the number listed
He0 %I10 first is derived from e33-e31, the number listed second from el5. For
Be0 [SO] the ligure is estimated from e33-e3l. I,iGaOa structure closely
0.077 .32, 1.33 resembles wurtzite, and theaverage bond length was used. Values for
e31 and ex:! of LiGa0.l are not known; for the calculation i t was as-
sumed that 2e33/(e31 +e,,) is the same as e33/e31 for CdSe.
1965 JAFFE ASD BERLISCOVRT: PIEZOELECTRIC TRASSDUCER MATERIALS 1385

COSCLUSIOS
The science and technology of piezoelectric materials
has seen several phases of rapid growth followed by con-
solidation.Thefirstphasewasthediscovery of the
piezoelectric effect by the brothers Curie and its study
as a phenomenon of crystal physics. The second phase
had its beginning in World \Tar I and culminated in the
rapid growth in usage of quartz crystals for frequency
control and filters, and as high-frequency transducers,
and of Rochelle salt for audio devices. The third phase
occurred in the 1940’s and is characterized by the intro-
duction of water-soluble crystals such as ADP, particu-
larly for sonar purposes. In this paperu e have discussed
primarily the two most recent phases. One is the de-
velopment of piezoelectric ceramics, beginning in 1945
andcontinuingtothisday.Thesematerialshave
reachedadominantpositionforsonicandthe lower
range of ultrasonic piezoelectric transducers. The most
recent phase is still in a state of rapid growth and is
bringingforwarda new family of piezoelectricsingle
crystals and film devices of great promise for the ultra-
v) v) high-frequency range.
9 h!
m v)

- REFEREKCES
[l] A. R. Hutson, “Piezoelectricity and conductivity in ZnO and
CdS,” Phys. Rev. Letters, vol. 4, pp. 505-507, May 1960.
(21 f;’.Jaffe, D. A. Berlincourt, H. H. A. Krueger, and L. Shiozawa,
Plezoelectric properties of cadmium sulfide crystals, ” presented
*n
3

a t the 1960 14th. Ann. Symp. on Frequency Control, sponsored by

4 Frequency Control Div. of U. S. Army Signal R and D Labora-
FI tory, Fort Monmouth, N. J., May 31-June 2.
[3] D. A. Berlincourt, H. Jaffe, and L. R. Shiozawa, ‘Electroelastic
properties of the sulfides, selenides, and tellurides of zinc and
cadmium,” Phys. Rev., vol. 129, pp. $)09-1017, February 1963.
[4] J. P. Remeika and A. A. Ballman, Flux growth, Czochralski
growth, and hydrothermal synthesis of lithium metagallate
single crystals,” Appl. Phys.Letters, vol. 5, pp. 180-181, Novem-
ber 1964.
[SI A. A. Ballman, “Growth of piezoelenctric and ferroelectric ma-
terials by the Czochralski technique, J . Amer. Ceram. SOC.,vol.
‘9 48, pp. 112-113, February 1965.
* [Sa] A. W. Warner, ‘New piezoelectric materials,” presented a t the
II 19th Ann. Frequency Control Symp., sponsored by U. S.
E Army Electronics Command, Fort Monmouth, N. J., April 20-
22, 1965 (to be published).
[6] R. Nitsche, “Crystal growth and electro-optic effect of bismuth-
germanate, Bia(GeO&,” J . Appl. Phys, vol. 36, pp. 2358-
2361, August 1965.
- [7] ‘IRE standards on piezoelectric crystals: Determination of the
elastic, piezoelectric, and dielectric constants-The electro-
E mechanical coupling factor, 1958,” Proc. IRE, vol. 46, pp. 764-
E 778, April 1958.
rr)
[SI “IREStandards on piezoelectric crystals: Measurements of
piezoelectric ceramics, 1961,” Proc. I R E , vol. 49, pp. 1161-1169,
July 1961.
[9] IV. G. Cady, Piezoelectricity, vols. 1 and 2. Sew York: Dover,
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