
Handbook of dielectric, piezoelectric and ferroelectric materials110
Because of the small array element sizes, a very high relative dielectric
constant and high coupling factor are necessary in modern ultrasonic array
applications. The most important parameters in ultrasonic array are k
33
, d
33
and g
33
. The piezoelectric coefficient d
33
measures the strain developed per
applied field and is a measure of the effectiveness of the material as a driver
or transmitter. The constant g
33
is the electric field generated per applied
stress and is a measure of the effectiveness when used as a receiver. The
materials with higher coupling coefficients k
33
can give better bandwidths
and pulse response in medical applications.
27
To overcome the disadvantages of conventional PZT ceramics, the
multilayer/polymer composite technology is introduced into transducers.
28
The current performance status of a multilayer/polymer composite transducer
is almost the same as a normal single crystal transducer using a single layer,
but it is very difficult for a multilayer/polymer composite PZT transducer to
get high manufacturing yields.
The piezoelectric properties of PZT ceramics have shown little improvement
over the past two decades. On the other hand, the PZN–PT and PMN–PT
single crystals exhibit an ultra-high piezoelectric constant, d
33
, and a very
large electromechanical coupling factor, k
33
, in comparison with those of
PZT ceramics, making them attractive for both actuator and ultrasonic
transducer applications.
Many research results concerning medical transducers using single crystals
have been reported since the mid-1990s.
28–31
Saitoh et al. reported the first
images of B-mode and color Doppler images obtained by 3.5MHz 96 channels
phased array made from a PZN–PT single crystal.
32
The two-way sensitivity
of PZN–PT transducer is 6dB higher than that of conventional PZT transducer
and –6dB fractional bandwidth is 30% broader. Because the dielectric constant
Table 4.2
Elastic, dielectric, and piezoelectric data set of rhombohedral PMN–PT
crystals
Properties Values Properties Values
1
εε
3
T
0
()
6110 10
k
31
0.51
2
εε
1
T
0
()
1717 11
k
15
0.31
3
d
33
(10
–12
C/N) 1658 12
k
t
0.58
4
d
31
(10
–12
C/N) –894 13
s
11
E
(10
–12
m
2
/N) 56.2
5
d
15
(10
–12
C/N) 150.6 14
s
12
E
(10
–12
m
2
/N) –22.1
6
g
33
(10
–3
V m/N) 30.6 15
s
13
E
(10
–12
m
2
/N) –29.7
7
g
31
(10
–3
V m/N) –16.5 16
s
33
E
(10
–12
m
2
/N) 60.6
8
d
15
(10
–3
V m/N) 9.9 17
s
44
E
(10
–12
m
2
/N) 15.2
9
k
33
0.92 18
s
66
E
(10
–12
m
2
/N) 16.3