Decay of d Direct Measurement Berlincourt Method
123
Figure 5-13: Photographs of a a clamped sample printed across a score line on a substrate and b an unclamped sample held with a pair of tweezers.
Figure 5-14 shows the
d
33
measurement results for the clamped sample at a continuous alternating mechanical force of 0.25 N at 110 Hz for 15 minutes at two conditions; one
of which is taken just after polarisation and the other one is taken after six months from the first measurement. At the beginning of the measurement, a
d
33
value of 42 pCN was measured which gradually dropped to 31 pCN after 15 minutes. At the second
measurement, 6 months after polarisation, the initial value decreased to 32 pCN and after 15 minutes of continuous application of alternating force, the value decreased
further to 22 pCN, which shows a decaying rate of 29 over a period of 6 months.
Figure 5-14:
d
33
as a function of time elapsed over 15 minutes for measurements taken just after polarisation and six months after polarisation for a clamped sample.
Tweezer
Exposed Electrode Multilayer Films
Detached
b Substrate
Score Line Multilayer Films
a
124 The measured value of
d
33
for a free-standing sample, similar to those of sample D series, is shown in Figure 5-15. The
d
33
of the sample decays from 78 pCN to 55 pCN as a continuous dynamic force is applied for 15 minutes. After a period of 6 months, the
measured
d
33
decays from 48 pCN to 35 pCN for the same dynamic force, which corresponds to a decay rate of 36 .
In another experiment, a comparison was made between unclamped free-standing samples co-fired at 850 °C and 950 °C. The initial value of
d
33
for the sample co-fired at 950 °C is 116 pCN, which is more than a factor 1.5 greater than the value measured for
the sample co-fired at 850 °C. After 8 hours of continuous application of dynamic force, the values of
d
33
for both of the samples decrease to 88 pCN and 51 pCN respectively, which correspond to decay rates of 24 and 32 . This verified that piezoelectric
materials co-fired at a peak temperature of 950 °C perform better than those co-fired at 850 °C.
In the same way as samples C and D series, the piezoelectric properties of a sample fabricated at a co-firing profile of 950 °C was measured and incorporated into Table
5-4. The measurement results are compared with sample co-fired at 850 °C and commercial bulk PZT material.
Figure 5-15:
d
33
as a function of time elapsed for an unclamped sample just after polarisation and six months after polarisation.
125
Figure 5-16: The d
33
value as a function of time elapsed for free-standing samples co-fired at 850 °C and 950 °C.
Table 5-4: Summary of measurement results for fabricated samples at standard 850 °C and 950 °C in comparison with bulk PZT from Morgan Electroceramics Ltd.
Piezoelectric Constant Co-firing profile
Bulk PZT- 5H [31]
850 °C 950 °C
Constant electric field elastic compliance
s
11 E
10
-12
m
2
N 8.4
7.11 17.7
Constant displacement elastic compliance
s
11 D
10
-12
m
2
N 8.31
6.96 15.5
Coupling factor
k
31
dimensionless 0.126
0.145 0.35
Relative dielectric constant
K
33 T
dimensionless 336
617 3250
Piezoelectric charge coefficient
d
31
10
-12
CN -19
-28.6 -250
d
33
10
-12
CN 53
82 620
Piezoelectric voltage coefficient
g
31
10
-3
VmN -6.73
-5.24 -6.7
g
33
10
-3
VmN 17.8
21.2 21.9
Mechanical quality factor
Q
m
dimensionless 130
98.1 65
126