CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
RECENT PROGRESS IN UNDERSTANDING THE SHOCK RESPONSE
OF FERROELECTRIC CERAMICS
R. E. Setchell
Sandia National Laboratories, Albuquerque, NM, 87185
Abstract. Ferroelectric ceramics exhibit a permanent remanent polarization, and shock depoling of
these materials to achieve pulsed sources of electrical power was proposed in the late 1950s. During
the following twenty years, extensive studies were conducted to examine the shock response of
ferroelectric ceramics primarily based on lead zirconate titanate (PZT). Under limited conditions,
relatively simple analytical models were found to adequately describe the observed electrical behavior.
A more complex behavior was indicated over broader conditions, however, resulting in the
incorporation of shock-induced conductivity and dielectric relaxation into analytical models.
Unfortunately, few experimental studies were undertaken over the next twenty years, and the
development of more comprehensive models was inhibited. In recent years, a strong interest in
advancing numerical simulation capabilities has motivated new experimental studies and
corresponding model development. More than seventy gas gun experiments have examined several
ferroelectric ceramics, with most experiments on lead zirconate titanate having a Zr:Ti ratio of 95:5
and modified with 2% niobium (PZT 95/5). This material is nominally ferroelectric but is near an
antiferroelectric phase boundary, and depoling results from a shock-driven phase transition.
Experiments have examined unpoled, normally poled, and axially poled PZT 95/5 over broad ranges of
shock pressure and peak electric field. The extensive base of new data provides quantitative insights
into both the stress and field dependencies of depoling kinetics, and the significance of pore collapse at
higher stresses. The results are being actively utilized to develop and refine material response models
used in numerical simulations of pulsed power devices.
INTRODUCTION
zirconate titanate ceramics. Axial mode studies
continued, primarily with PZT 65/35 (5), but the
A ferroelectric ceramic exhibits a remanent
majority of experiments were done with normal
polarization when poled by an electric field. The
mode configurations in which shock propagation
bound charge associated with this polarization was
occurs in a direction perpendicular to the poling
recognized as a means of achieving pulsed electrical
axis. These studies focused on ceramics having a
power more than forty years ago (1). Early studies
Zr:Ti ratio of 95:5 and modified with 2% niobium,
examined how shock waves could release the bound
subsequently referred to as PZT 95/5 (6-8). The
charge in barium titanate and in other materials
nominal state of this material is ferroelectric (FE),
based on solid solutions of lead zirconate and lead
but it is near an antiferroelectric (AFE) phase
titanate (2-4). These studies used axial mode
boundary. Bound charge is released through shock
configurations, where shock propagation occurs
compression into the AFE phase. A simple model
along the poling axis. Issues that were considered
for the depoling current was used by Lysne (6) to
included shock-induced conduction and whether
analyze external circuit voltages generated across
charge release resulted from domain reorientation
different resistance loads during shock propagation,
or through phase transitions. Extensive studies
This model assumed instantaneous and complete
followed during the 1970s, primarily on lead
depoling at a discontinuous shock front, and the
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this series of experiments. The complex curve has
multiple reversals in curvature resulting from a FE
phase with anomalous behavior, an extended
mixed-phase region, and the onset of pore collapse.
released charge was partitioned between passing
through the external circuit and being retained on
the sample electrodes to account for capacitance.
Dielectric constants were assumed to differ between
shocked and unshocked material. This model was
fairly successful in predicting measured voltages at
shock pressures sufficient to completely depole the
PZT 95/5 samples. To improve comparisons,
particularly with experiments having inductive
loads, Lysne added finite resistivity (9) and
dielectric relaxation (10) to his analysis.
A period of nearly twenty years followed in
which few studies were conducted on the shock
response of ferroelectric ceramics. About five years
ago, however, a strong interest developed in
establishing a capability for numerically simulating
the operation of pulsed power devices that utilize
PZT 95/5. This interest has motivated significant
new experimental and analytical efforts to
understand the complex behavior of this material.
Some of the resulting experimental work has been
previously reported (11-13). The purpose of the
present paper is to provide a selected summary of
experiments performed to date which have been
most useful for gaining insights into the mechanical
and electrical response of PZT 95/5 under shock
loading.
UNPOLED PZT 95/5
\
\
CARBON FOAM
FUSED SiLICA BUFFER/WiNDOW
FIGURE 1. Configuration for reverse-impact experiments.
r^ —————————
0.25-
/
IMPACT VELOCfTY 0.41 7 km/s,
AXIAL STRESS 3.23 GPa
\
\
0.20-
0.15;
^f
0.230 kmfe. 1.93 GPa
^X
v_
0.10-
0.1 12 km/s, 0.92 GPa
0.05-
HUGONIOT STATES
-0.05 0.00 0.05 0.10 0.15
^^^^^--^_
0.20 0.25 0.30 0.35 0.40 0.45
TIME - MICROSECONDS
0.50
0.55 0.60
FIGURE 2. Typical waveforms at the impact interface recorded in
reverse-impact experiments.
Although a Hugoniot curve based on available
transmitted-wave data was reported previously (11),
a more accurate determination was desired over the
stress range of interest.
The reverse-impact
configuration used for these measurements is shown
in Fig. 1. Samples of unpoled PZT 95/5 having a
nominal density of 7.30 g/cm3 were impacted into a
fused silica window, and the particle velocity at the
impact interface was determined using velocity
interferometry (VISAR). PZT 95/5 at this density
has a pore volume fraction of approximately 9%.
Typical profiles recorded at different impact
velocities are shown in Fig. 2. The top profile in
this figure shows a transient overshoot,
characteristic of impacts resulting in stress states
above the threshold for the onset of pore collapse.
Figure 3 shows the Hugoniot curve resulting from
1997 HUGONIOT
£4
O
- ONSET OF PORE COLLAPSE
-AFEPHASE
- MIXED-PHASE REGION
0.10
0.15
0.20
PARTICLE VELOCITY- km/s
FIGURE 3. Hugoniot curve for 7.30 g/cm3 PZT 95/5 obtained
from reverse-impact experiments. The curve reported previously
(11) is shown for comparison.
192
NORMALLY POLED EXPERIMENTS
A more complex experimental configuration is
required for investigating the response of normally
poled PZT 95/5 samples, as shown in Fig. 4.
Z-CUT SAPPHIRE OR ALUMINA-FILLED EPOXY (ALOX)
GROUND RETURN
CURRENT
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
TIME-MICROSECONDS
0.70
0.80
0.90
1.00
FIGURE 5. Examples of input waves introduced into PZT 95/5
0.13
PREDICTED FNAL AXIAL STRESS: 4.52 GPa
0.12-
0.11
2.24 GPa NPZT 95/5
388Gpa
«. °-10
1 0.09
£ °'°8
00.07-
FIGURE 4. Configuration used for planar shock experiments on
normally poled PZT 95/5 samples.
id 0.06 •
liJ0.05-
o
Although this configuration has been described
previously (12), one change used in more recent
experiments should be noted. For introduction of a
sharp shock jump into the PZT 95/5 sample, a
sapphire disc on the projectile face is impacted into
a similar disc in the target. The resulting shock
discontinuity propagates through the target disc and
into the PZT 95/5 sample. If the sapphire elements
are replaced by 828/Z ALOX, an alumina-filled
epoxy (14), the inelastic response of this material
results in an extended wave front having a rise time
of several hundred nanoseconds. The resulting
input wave into a PZT 95/5 sample is shown in Fig.
5, and will be referred to as a "ramp" input.
Figure 6 shows waveforms recorded after input
shocks had propagated through 4.0 mm of normally
poled material, under short-circuit conditions. The
wave having a final stress of 0.93 GPa shows an
extended structure consistent with the lower part of
the Hugoniot curve (Fig. 3), which has negative
curvature. The 1.8 GPa case has a two-wave
structure corresponding to the phase transition. At
shock stresses of 2.5 GPa or higher, a distinct
plateau is evident at a state corresponding to 2.2
GPa in PZT 95/5. This plateau identifies the onset
of pore collapse in the ceramic. At higher stresses
the velocity slowly rises from the plateau value to
P 0.04-
& 0.03
0.02
0.01
0.00
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
TIME FROM IMP ACT- MICROSECONDS
FIGURE 6. Observed waveforms after shock inputs propagate
through 4.0 mm samples of PZT 95/5 with short-circuit loads.
the final state that would be predicted from the
Hugoniot curve. Useful VISAR data typically
terminates before the final state is reached, due to
the transmitted shock wave in the sapphire window
reaching the window's free surface (approximately
1.1 |j,s after the start of the waveform).
Figure 7 shows waveforms recorded with 2.5 GPa
input shocks, with the different curves
corresponding to increasing load resistance in the
external circuit. A field of 37 kV/cm is reached in
the sample for the highest load resistance. The
transmitted waveforms show essentially no change
in their final state, indicating that electromechanical effects on Hugoniot states are not
apparent under these conditions.
Figure 8 shows short-circuit currents generated
during the transit of shocks having different
strengths. At a shock stress of 2.4 GPa, a very flat
current profile is recorded. The level of this current
193
in a reflected shock propagating back into the
sample, hence the continuing depoling later in time.
Similar short-circuit currents are shown in Fig. 9,
except that shock input cases are compared with
ramp inputs. At a peak stress of 2.5 GPa the
differences are small, with the ramp case showing a
slightly slower rise and a smaller average value
during wave transit. At a shock stress of 0.9 GPa
the differences are quite large, with depoling rates
much lower for the ramp input.
0.00
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
TIME FROM IMPACT- MCROSECONDS
FIGURE 7. Observed waveforms after 2.5 GPa shock inputs
propagate through 4.0 mm samples with increasing loads.
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
TME- MCROSECONDS
FIGURE 9. Comparison of short-circuit currents generated during
transit of shock and ramp inputs.
0.8
1.2
1.6
Figure 10 shows currents generated during the
transit of 2.5 GPa shocks, with the different curves
corresponding to increasing resistance loads in the
external circuit. The current through a finite load
TIME - MICROSECONDS
FIGURE 8. Short-circuit currents generated from shock inputs.
is accurately predicted by the simple model (6):
(1)
where the short-circuit current Isc simply equals the
product of the shock velocity Us, the remanent
polarizarion Pr, and the electrode dimension L that
is perpendicular to the shock direction. This model
represents complete, instantaneous depolarization
by a steady shock discontinuity. The overshoots
appearing at higher stresses as the shock enters the
PZT 95/5 are possibly a transient effect associated
with the onset of pore collapse. The fact that higher
stresses do not result in higher average currents will
be discussed in a subsequent section. As input
shock stresses are decreased, complete depoling is
inhibited and current levels during shock transit
drop rapidly. The high-impedance sapphire window
at the back of the PZT 95/5 sample (Fig. 4) results
TIME- MCROSECONDS
FIGURE 10. Currents generated by 2.5 GPa shock inputs with
increasing loads.
results in a voltage drop across the electrodes of the
PZT 95/5 sample, and the capacitance of the sample
dictates that some of the initially bound charge be
retained. This results in the "RC" time constant
shown by the current rise, and these profiles can be
194
adequately predicted by a simple depoling model
(6). At lower shock pressures, however, such a
model cannot account for the inhibited depoling of
the material. Figure 11 shows a comparison of
currents generated with waves having a peak stress
of 0.9 GPa. The current resulting from a shock
input is significantly reduced throughout the wave
transit when a large load is added. The bottom
profile shows a further reduction in current when a
large load and a ramp input are combined.
0.4
0.6
0.8
1.0
TME- MCROSECONDS
FIGURE 12. Using the simplest model for depoling, an effective
shock velocity can be found by integrating short-circuit currents.
impact (in an elastic material) are the same as if the
impactor strikes the sample directly at the same
impact velocity. Figure 13 shows a comparison
between the effective stress-velocity states found in
this manner and the Hugoniot states found in the
reverse-impact experiments. A curve fitted to the
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
TIME - MCROSECONDS
m- EFFECTIVE (STRESS, VELOCrTY) STATES
NFERRED FROM SHORT-CIRCUIT
CURRENTS N NORMALLY POLED
EXPERIMENTS
FIGURE 11. Currents generated by 0.9 GPa shock and ramp
waves with different loads.
g 3-°:
EFFECTIVE SHOCK STATES OBTAINED
FROM SHORT-CIRCUIT CURRENTS
W
'
2
3 -°'
The history of charge release in short-circuit
experiments is found by simply integrating the
current over time. For experiments conducted at
shock pressures of 2.5 GPa or higher, the charge
divided by the electrode area rises linearly to a final
value corresponding to the initial remanent
polarization, as shown in Fig. 12. This provides an
accurate measure of the initial polarization. Using
the simple model for depoling given by Eq. (1), the
slope of this curve (the average current during
shock transit) can be used to find an "effective"
shock velocity. The product of the initial density
and this velocity defines a linear curve in a stress,
particle velocity space. Using normal impedancematching procedures, the intersection can be found
between this line and a left-facing Hugoniot curve
for sapphire originating at the impact velocity.
Note that conditions produced in a sample by the
transmission of a wave generated by symmetric
-HUGONIOT STATES FROM
REVERSE-IMPACT EXPERIMENTS
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28
PARTICLE VELOCITY - knVs
FIGURE 13. The effective stress-velocity states shown with the
Hugoniot curve found from reverse-impact experiments.
effective states progressively separates from the
Hugoniot curve at stresses above the threshold for
pore collapse. This curve slowly deviates from a
linear curve starting at the origin, indicating that
the effective shock velocities are increasing very
slowly with increasing stress.
The effective stress-velocity states correspond to
the plateau condition shown by transmitted wave
profiles at the higher stress conditions (Fig. 6).
This part of the wave structure is responsible for
depoling the PZT 95/5, effectively decoupling the
depoling process from the final states achieved
following pore collapse.
195
REFERENCES
SUMMARY
The experimental results presented in this paper
represent an ongoing effort to understand the
fundamental behavior of PZT 95/5 under carefully
controlled, planar impact conditions. Two aspects
of this behavior have been emphasized. The first is
1.
2.
3.
4.
5.
Neilson, F. W., Bull. Am. Phys. Soc. 2, 302 (1957).
Halpin, W. J., J. Appl Phys. 37, 153-163 (1966).
Halpin, W. J., J. Appl. Phys. 39, 3821-3826 (1968).
Doran, D. G., J. Appl. Phys. 39, 40-47 (1968).
Lysne, P. C., and Bartel, L. C., J. Appl. Phys. 46,
222-229 (1975).
6. Lysne, P. C., and Percival, C. M., J. Appl. Phys. 46,
1519-1525(1975).
7. Lysne, P. C., J. Appl Phys. 48, 1020-1023 (1977).
8. Dick, J. J., and Vorthman, J. E., J. Appl. Phys. 49,
2494-2498(1978).
9. Lysne, P. C., J. Appl Phys. 48, 4565-4568 (1977).
10. Lysne, P. C., "Electrical Response of Shock-WaveCompressed Ferroelectrics," in High Pressure Science
and Technology, Vol. 7, edited by K. D. Timmerhaus
and M. S. Barber, Plenum Press, New York, 1978,
pp. 202-209.
11. Setchell, R. E., Chhabildas, L. C., Furnish, M. D.,
Montgomery, S. T., and Holman, G. T., "Dynamic
Electromechanical
Characterization
of
the
Ferroelectric Ceramic PZT 95/5," in Shock
Compression of Condensed Matter - 1997, edited by
S. C. Schmidt et al., AIP Conference Proceedings
429, New York, 1998, pp. 781-784.
12. Setchell, R. E., Montgomery, S. T., Chhabildas, L.
C., Furnish, M. D., 'The Effects of Shock Stress and
Field Strength on Shock-Induced Depoling of
Normally Poled PZT 95/5," in Shock Compression of
Condensed Matter - 1999, edited by M. D. Furnish et
al., AIP Conference Proceedings 505, New York,
2000, pp. 979-982.
13. Furnish, M. D., Chhabildas, L. C., Setchell, R.,
Montgomery, S. T., "Dynamic Electromechanical
Characterization of Axially Poled PZT 95/5," in
Shock Compression of Condensed Matter — 1999,
edited by M. D. Furnish et al., AIP Conference
Proceedings 505, New York, 2000, pp. 975-978.
14. Montgomery, S. T., Brannon, R. M, Robbins, J,
Setchell, R. E., and Zeuch, D. H., "Simulation of the
Effects of Shock Stress and Electrical Field Strength
on Shock-Induced Depoling of Normally Poled PZT
95/5," this volume.
15. Setchell, R. E., Turtle,, B. A, Voigt, J. A, and
Venturini, E. L., "Effects of Initial Porosity on the
Shock Response of Normally Poled PZT 95/5," this
volume.
the reduction in depoling rates by decreasing shock
pressures and increasing electric fields. The results
using ramp input waves show that the rate of
compression, in addition to the final stress, can
strongly influence the depoling rate. In order to
develop a predictive capability for the shock
response of PZT 95/5, a description for depoling
kinetics must account for these dependencies. This
is under active investigation (14).
The second
aspect is the apparent decoupling at higher stresses
between shock-driven depoling and the pore
collapse process that occurs in the material at these
stresses. The threshold stress for pore collapse in
our samples is 2.2 GPa, and a wave structure with
this amplitude persists regardless of the final state.
Under short-circuit conditions, the depoling kinetics
at this stress must be fast compared to the time scale
of the pore collapse process. The presence of a
strong electric field could reduce this difference. In
addition, recent studies have shown that the
threshold stress for the onset of pore collapse is very
sensitive to the initial material density (15). For
shock stresses above the threshold in materials
having a lower density, the depoling will be driven
by a weaker wave and the decoupling may not be
complete.
ACKNOWLEDGMENTS
The author would like to thank David E. Cox for
skillfully preparing and conducting the many
experiments. Many individuals have been involved
in these studies, but the author would like thank S.
T. Montgomery and M. U. Anderson in particular.
Sandia is a multiprogram laboratory operated by
Sandia Corporation, a Lockheed Martin Company,
for the United States Department of Energy under
Contract DE-AC04-94AL85000.
196