112 voids is largely due to the nature of the screen-printing process and the size of the
granules used in the thick-film paste formulation. They are responsible for the reduction of fracture strength [105] and capacity of polarisation, which explains why some
piezoelectric material samples experienced internal short circuits when polarised above an electrical field strength of 3 MVm, as discussed in the previous chapter.
Figure 5-3: SEM micrographs of samples co-fired at 850 °C and 950 °C under magnification of ×300, ×800 and ×4000.
a d
b e
c f
850 Profile × 300
950 Profile × 300
850 Profile × 800
950 Profile × 800
850 Profile × 4000
950 Profile × 4000
PZT PZT
PZT AgPd
AgPd AgPd
AgPd
PZT AgPd
AgPd
PZT AgPd
113 As sintering temperature increases from 850 °C to 950 °C, the adhesion of granules was
improved as shown in Figure 5-3 f, therefore increasing the density of the material. A denser piezoceramic typically has higher piezoelectric activity. At higher temperature,
however, the AgPd expands and contracts faster when cooled to room temperature. This effect results in deformation of the electrode layer and may weaken the overall
structure.
5.4 Resonant Measurement
The resonant measurement method is commonly used to measure piezoelectric properties of the bulk material. However, it is not suitable for the measurement of
piezoelectric properties of thick-film PZT when it is printed on a substrate due to mechanical clamping effects of the substrate [82]. Hence, a non-clamped thick-film in
free-standing form is an alternative solution as a tool to characterise the thick-film piezoelectric properties. The properties that were measured were constant electric field
elastic compliance,
s
11 E
, constant displacement elastic compliance,
s
11 D
, coupling factor,
k
31
, piezoelectric charge coefficient,
d
31
, piezoelectric voltage coefficient,
g
31
and mechanical quality factor,
Q
m
of the piezoelectric materials.
Before calculating relevant piezoelectric parameters, the capacitance at constant stress or stress free of the devices was measured. This was carried out with an LCR meter at 1
kHz Wayne Kerr. Sample D series which were polarised at a higher dc voltage of 220 V produce higher capacitance compared to sample C series which were polarised at 200
V. A plot of capacitance against the dimensions of the material for both samples, as illustrated in Figure 5-4, shows a linear relationship between the capacitance and the
ratio of area to the thickness of the materials, which is in a good agreement with equation 2-5. From the extrapolation of the graph in Figure 5-4, the average value of
permittivity,
33 T
of sample C series can be calculated as 4 nFm and sample D series as 4.3 nFm.
114
Figure 5-4: Comparison of sample D and C series for the value of capacitance over the ratio of areathickness with ± 5 error.
The resonant and antiresonant frequencies that correspond to the minimum and maximum impedances of the materials are important variables to determine the
piezoelectric constants of the materials. The frequency response of the samples was measured by using NetworkSpectrum Analyser HP 4195A between 100 kHz to 500
MHz. The resonant and antiresonant frequencies for sample D series can be identified by the magnitude of the impedance as shown in Figure 5-5.
There are a few possible modes of vibration in the range of 120 kHz to 280 kHz: lateral, longitudinal and thickness modes. For all the samples of series C and D, the thickness
vibration mode is not significant compared to the lateral and longitudinal modes. This is due to the fact that the length and the width of the samples are more than 50 times
bigger than their thickness.
The lateral vibration mode was observed for samples D1 and D2 which is about 180 kHz, however, the lateral mode diminishes as the length of the sample increases which
can be see in sample D3 – D5 as shown in Figure 5-5. The resonant frequency of the
longitudinal mode for sample D1 is about 240 kHz and reduced to about 185 kHz for sample D5. From equation 2-4, the average value of
d
31
for sample D series is about 33.9 pCN.
