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Review
Antiferroelectric Shape Memory Ceramics
Kenji Uchino
International Center for Actuators and Transducers, The Pennsylvania State University, University Park,
PA 16801, USA; [email protected]; Tel.: +1-814-863-8035
Academic Editor: Delbert Tesar
Received: 21 March 2016; Accepted: 11 May 2016; Published: 18 May 2016
Abstract: Antiferroelectrics (AFE) can exhibit a “shape memory function controllable by electric
field”, with huge isotropic volumetric expansion (0.26%) associated with the AFE to Ferroelectric
(FE) phase transformation. Small inverse electric field application can realize the original AFE
phase. The response speed is quick (2.5 ms). In the Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )1-y Tiy ]0.98 O3 (PNZST)
system, the shape memory function is observed in the intermediate range between high temperature
AFE and low temperature FE, or low Ti-concentration AFE and high Ti-concentration FE in the
composition. In the AFE multilayer actuators (MLAs), the crack is initiated in the center of a pair of
internal electrodes under cyclic electric field, rather than the edge area of the internal electrodes in
normal piezoelectric MLAs. The two-sublattice polarization coupling model is proposed to explain:
(1) isotropic volume expansion during the AFE-FE transformation; and (2) piezoelectric anisotropy.
We introduce latching relays and mechanical clampers as possible unique applications of shape
memory ceramics.
Keywords: antiferroelectrics; PNZST; shape memory ceramics; phase transformation; two-sublattice
polarization coupling model; electrostriction
1. Development Trend of Solid State Actuators
Development of solid state actuators aimed at replacing conventional electromagnetic motors
has been remarkable in the following three areas: precision positioning, vibration suppression and
miniature motors. Particular attention has been given to piezoelectric/electrostrictive ceramic actuators,
shape memory devices of alloys such as Ni-Ti and Cu-Zn-Al, and magnetostrictive actuators using
Terfenol D (Tb-Fe-Dy) alloys. Rigid strains induced in a piezoelectric ceramic by an external electric
field have been used as ultraprecision cutting machines, in the Hubble telescope on the space shuttle
and in dot-matrix printer heads [1–5]. There has also been proposed a parabolic antenna made of
shape memory alloy, which is in a compactly folded shape when first launched on an artificial satellite,
and subsequently recovers its original shape in space when exposed to the heat of the sun. Smart skins
on submarines or military tanks were targets for solid state actuators [6].
In general, thermally-driven actuators such as shape memory alloys can show very large strains,
but require large drive energy and exhibit slow response. Magnetic field-driven magnetostrictive
devices have serious problems with size because of the necessity for the magnetic coil and shield.
The subsequent Joule heat causes thermal dilatation in the system, and leakage magnetic field
sometimes interferes with the operating hybrid electronic circuitry. On the contrary, electric field-driven
piezoelectric and electrostrictive actuators have been most developed because of their high efficiency,
quick response, compact size, no generation of heat or magnetic field, in spite of relatively small
induced strains.
This article reviews shape memory properties of ceramics, focusing on antiferroelectric lead
zirconate titanate (Pb(Zr,Ti)O3 , PZT) based ceramics. The shape memory effect can be observed,
not only in special alloys and polymers, but also in ceramics such as partially stabilized zirconia
Actuators 2016, 5, 11; doi:10.3390/act5020011
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and ferroelectric lead zirconate titanate. A new concept of “shape memory” is proposed in this
article: the elastic strain change associated with the electric field-induced phase transition is utilized
instead of stress-induced or thermally-induced phase transitions, which enables many smarter actuator
applications than the normal piezoelectrics or electrostrictors.
The principle of the ceramic shape memory effect is described firstly in comparison with the case
of alloys. Phase diagrams, domain reversal mechanisms and fundamental actuator characteristics are
then discussed, followed by the practical distinctions between these new ceramics and shape memory
alloys. Phenomenological explanations are described on the field-induced strain jump associated
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with
the phase transformation, and on the piezoelectric anisotropy in a two-sublattice polarization
coupling model. Finally, possible unique applications are proposed including a latching relay and a
When the free energy of the antipolar state is close to the energy of the polar state, the dipole
mechanical clamp.
configuration is rearranged by the external electric field or stress. Figure 4 shows the applied electric
This review paper is to provide author’s comprehensive idea on the AFE-FE phase transition by
field versus induced polarization curves in PE, FE and AFE materials. A linear relation and a
coupling experimental results [7] and theoretical approach [8].
hysteresis due to the spontaneous polarization reversal between positive and negative directions are
observed
in a PE and
in a FE, respectively. On the contrary, an AFE exhibits an electric field-induced
2.
Shape Memory
Ceramics
phase transition to a FE state above a critical field Et, accompanied by a hysteresis above Et. Reducing
Shape
memory
effect
observed not
only in special
or polymers,
also in ceramics.
the field
down
to zero,
theis remanent
polarization
is not alloys
observed,
providingbut
a so-called
“double
The
shape
memory
effect
in
alloys
(such
as
NiTiNOL)
originates
from
a
thermally-induced
or
hysteresis” curve in total. A large strain jump is theoretically associated with this phase transition,
stress-induced
“martensitic”
phase
transformation.
After
the
alloy
is
deformed
largely
in
the
which also appears as a double hysteresis. In a certain case, once the FE state is induced, this FE state
martensitic
apparently
permanent
strainto
is zero;
recovered
to its originaltoshape
when heated
to
is sustainedstate,
eventhis
if the
electric field
is decreased
this corresponds
the “shape
memory”
cause
the reverse
Then,memory
upon cooling,
thethe
shape
to its
state
phenomenon.
Themartensitic
mechanismtransition.
for the shape
effect in
AFEreturns
ceramics
is original
schematically
(Figure
1a).
illustrated in Figure 1b.
Figure 1. Comparison of the mechanisms for the shape memory effect in alloys (a) and in
Figure 1. Comparison of the mechanisms for the shape memory effect in alloys (a) and in
antiferroelectric ceramics (b).
antiferroelectric ceramics (b).
A similar effect is anticipated in ceramics with a certain phase transition, i.e., a “ferroelastic” phase
transition. Reyes-Morel et al. demonstrated the shape memory effect, as well as superelasticity in a
CeO2 -stabilized tetragonal zirconia (ZrO2 ) polycrystal [9]. Under uniaxial compression, the specimen
Ti 4+
deforms plastically owing to a stress-induced tetragonal
to monoclinic transition in Ce-doped zirconia.
Ba 2+
O 2-
T>T C
T<T C
T C : Curie temperature
field versus induced polarization curves in PE, FE and AFE materials. A linear relation and a
hysteresis due to the spontaneous polarization reversal between positive and negative directions are
observed in a PE and in a FE, respectively. On the contrary, an AFE exhibits an electric field-induced
phase transition to a FE state above a critical field Et, accompanied by a hysteresis above Et. Reducing
the field down to zero, the remanent polarization is not observed, providing a so-called “double
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hysteresis” curve in total. A large strain jump is theoretically associated with this phase transition,
which also appears as a double hysteresis. In a certain case, once the FE state is induced, this FE state
is sustained deformation
even if the electric
field is decreased
to load
zero;drops,
this corresponds
the “shape
memory”
Continuous
is interrupted
by repeated
providing atonearly
constant
upper
phenomenon.
TheGPa.
mechanism
forunloading,
the shape large
memory
effectplastic
in theaxial
AFEstrain
ceramics
is schematically
yield
stress of 0.7
Even after
residual
(«0.7%)
is observed.
illustrated inheating
Figure 1b.
Subsequent
produces a gradual recovery of the residual strain due to the reverse phase
transition starting at 60 ˝ C and a burst of strain recovery at 186 ˝ C. The burst is very sharp, above
which approximately 95% of the prior axial strain is recovered. Though recent conventional shape
memory studies based on Martensitic phase transformation in structural ceramics can be found [10],
we do not discuss them because they are out of our objective; that is, electric-field controllable
shape memory.
Ceramics “shape memory” has also been reported for certain ferroelectricity-related transitions,
namely paraelectric–ferroelectric [11] and antiferroelectric (AFE)–ferroelectric (FE) transitions [12,13].
The former thermally-induced transition revealed a shape-recovery phenomenon similar to zirconia
ceramics. On the contrary, the latter is related to an electric field-induced transition, and exhibits large
displacement (0.4%) with a “digital” characteristic or a shape memory function, which is in contrast to
the essentially “analogue” nature of conventional piezoelectric and electrostrictive strains with 0.1% in
magnitude (Figure 1b). Note that the “memory” terminology is different in the AFE shape memory;
that is, field-induced FE expanded shape is “memorized” even after removing the field, and to recover
the original AFE small shape, we apply a small reverse electric field.
Let us review ferroelectricity and antiferroelectricity here for further understanding [14]. Figure 2
shows the crystal structure changes in a typical ferroelectric, barium titanate (BaTiO3 , BT). At an
elevated temperature above the transition point of 130 ˝ C (Curie temperature, denoted as TC ), BT shows
a cubic “perovskite” structure (paraelectric (PE) phase), as illustrated in Figure 2a. With decreasing
temperature below TC , the cations (Ba2+ and Ti4+ ) shift against the anions (O2´ ) as illustrated in
Figure 2b, exhibiting spontaneous polarization as well as spontaneous strain (ferroelectric (FE) phase).
Notice that the electric dipole moments in each crystal unit cell are arranged in parallel in a ferroelectric.
On the other hand, there exists an antiferroelectric where the dipoles are arranged antiparallel to each
1. Comparison
of polarization.
the mechanisms
for the
shapethe
memory
effect
in alloys
(a) and models
in
otherFigure
so as not
to produce net
Figure
3 shows
antipolar
dipole
arrangement
antiferroelectric
ceramics
(b).
in contrast to nonpolar and polar models.
Ti 4+
Ba 2+
O 2-
T>T C
T<T C
T C : Curie temperature
(a)
(b)
Figure 2.
2. Crystal
paraelectric state
and in
in the
the ferroelectric
ferroelectric
Figure
Crystal structures
structures of
of barium
barium titanate
titanate in
in the
the paraelectric
state (a)
(a) and
4 of 22
state
(b).
state (b).
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Figure 3. Two antipolar dipole arrangement models (c) in contrast to nonpolar (a) and polar (b) models.
Figure 3. Two antipolar dipole arrangement models (c) in contrast to nonpolar (a) and polar
(b) models.
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When the free energy of the antipolar state is close to the energy of the polar state, the dipole
configuration is rearranged by the external electric field or stress. Figure 4 shows the applied electric
field versus induced polarization curves in PE, FE and AFE materials. A linear relation and a hysteresis
due to the spontaneous polarization reversal between positive and negative directions are observed in a
PE and in a FE, respectively. On the contrary, an AFE exhibits an electric field-induced phase transition
to a FE state above a critical field Et , accompanied by a hysteresis above Et . Reducing the field down
to zero, the remanent polarization is not observed, providing a so-called “double hysteresis” curve
in total. A large strain jump is theoretically associated with this phase transition, which also appears
as a double hysteresis. In a certain case, once the FE state is induced, this FE state is sustained even
if the electric
field
is decreased
to zero;
this corresponds
phenomenon.
Figure 3.
Two
antipolar dipole
arrangement
models to
(c)the
in “shape
contrast memory”
to nonpolar
(a) and polarThe
(b) models.
mechanism
for the shape memory effect in the AFE ceramics is schematically illustrated in Figure 1b.
Figure4. 4.Electric
Electricfield
fieldvs.vs.induced
inducedpolarization
polarizationcurves
curvesin:in:paraelectric
paraelectric(a);
(a);ferroelectric
ferroelectric(b);
(b);and
and
Figure
antiferroelectric
materials.
antiferroelectric
(c)(c)
materials.
SamplePreparation
Preparationand
andExperiments
Experiments
3.3.Sample
Thissection
sectionintroduces
introducessample
samplepreparation
preparationand
andexperimental
experimentalprocedures
proceduresofofshape
shapememory
memory
This
3
rich
compositions)
have
ceramics.
Antiferroelectric
perovskite
ceramics
from
the
PZT
system
(PbZrO
ceramics. Antiferroelectric perovskite ceramics from the PZT system (PbZrO3 rich compositions) have
been
investigated,
in which
successive
phase
transitions
a PE, through
to a appear
FE state
been
investigated,
in which
successive
phase
transitions
from from
a PE, through
an AFE,antoAFE,
a FE state
appear
with decreasing
temperature
[15]. PZTPb
ceramics
Pb
0.99NbSn
0.02[(Zr
0.6Ti
Sn
0.4)1-yO
Ti
y(0.05
]
0.98O3<(0.05
<y<
with
decreasing
temperature
[15]. PZT ceramics
Nb
[(Zr
)
]
y
< 0.09)
0.99
0.02
0.6
0.4 1-y y 0.98 3
0.09)
(abbreviated
hereafter
as
PNZST)
were
prepared
from
reagent
grade
oxide
raw
materials,
(abbreviated hereafter as PNZST) were prepared from reagent grade oxide raw materials, PbO, Nb2PbO,
O5 ,
Nb22,OSnO
5, ZrO
2, SnO
2 and
TiO
2. We introduced
“Sn”
to
stabilize
the
antiferroelectric
phase,
and
“Nb”
to
ZrO
and
TiO
.
We
introduced
“Sn”
to
stabilize
the
antiferroelectric
phase,
and
“Nb”
to
increase
2
2
˝
increase
the
sinterability
basically.
Bulk
samples
were
prepared
by
hot-press
sintering
at
1200
°C.
the sinterability basically. Bulk samples were prepared by hot-press sintering at 1200 C. Unimorphs
Unimorphs
were
with two thin
rectangular
mmmm
× thick)
7 mmbonded
× 0.2 mm
thick)
were
fabricated
withfabricated
two thin rectangular
plates
(22 mm ˆplates
7 mm(22
ˆ 0.2
together.
bonded together.
mmmm
× 4.3
mmwith
× 4.3
mmlayer
thick)
with
layer 140 were
μm in
Multilayer
samplesMultilayer
(12 mm ˆsamples
4.3 mm(12
ˆ 4.3
thick)
each
140
µmeach
in thickness
thickness
were
also
fabricated
using
the
tape
casting
technique:
Those
with
platinum
electrodes
were
also fabricated using the tape casting technique: Those with platinum electrodes were sintered at
a
˝
sintered at aoftemperature
temperature
about 1250 of
C.about 1250 °C.
Thefield-induced
field-inducedlattice
latticechange
changewas
wasdetermined
determinedbybyX-ray
X-raydiffraction.
diffraction.The
Thesurfaces
surfacesofofthe
thethin
thin
The
ceramic
plate
(t
=
0.2
mm)
were
coated
with
carbon
evaporated
electrode.
X-ray
diffraction
patterns
ceramic plate (t = 0.2 mm) were coated with carbon evaporated electrode. X-ray diffraction patterns
wererecorded
recordedatatthe
theelectrode
electrodesurface
surfacefor
forseveral
severaldifferent
differentbias
biasvoltages.
voltages.The
Thedisplacement
displacementororstrain
strain
were
induced
by
an
alternating
electric
field
(0.05
Hz)
was
detected
with
a
strain
gauge
(Kyowa
Dengyo,
induced by an alternating electric field (0.05 Hz) was detected with a strain gauge (Kyowa Dengyo,
Tokyo,
Japan,
KFR-02-C1-11),
a magneto-resistive
potentiometer
(Midori
Precisions,
Tokyo,
Japan,
KFR-02-C1-11),
a magneto-resistive
potentiometer
(Midori
Precisions,
Tokyo,Tokyo,
Japan, Japan,
LP-1
or a differential
transformer-type
Tokyo,
Japan,For
No.
Fordisplacement
the dynamic
U)LP-1
or a U)
differential
transformer-type
(Millitron, (Millitron,
Tokyo, Japan,
No. 1202).
the1202).
dynamic
unimorphs, aeddy
noncontact-type
eddy current
displacement
sensor
(Kaman,
indisplacement
unimorphs, a in
noncontact-type
current displacement
sensor (Kaman,
Colorado
Springs,
CO,
Colorado Springs, CO, USA, KD-2300) was used. The electric polarization and the permittivity were
measured with a Sawyer–Tower circuit and an impedance analyzer (Hewlett-Packard, now Agilent,
Santa Clara, CA, USA, 4192A), respectively. To observe the domain structures, a CCD microscope
Actuators 2016, 5, 11
5 of 23
USA, KD-2300) was used. The electric polarization and the permittivity were measured with a
Sawyer–Tower
Actuators 2016, 5, 11circuit and an impedance analyzer (Hewlett-Packard, now Agilent, Santa Clara,5 CA,
of 22
USA, 4192A), respectively. To observe the domain structures, a CCD microscope with a magnification of
ˆ1300
applied to aofthinly-sliced
sample of
grain (>50sample
µm) PNZST
ceramics
withμm)
interdigital
with awas
magnification
×1300 was applied
tolarge
a thinly-sliced
of large
grain (>50
PNZST
electrodes
on the
surface. electrodes on the surface.
ceramics with
interdigital
Figure
Figure5a
5ashows
showsaaPZT
PZTphase
phasediagram
diagramwith
withaaparticular
particularinterest
interestin
inPbZrO
PbZrO33 (PZ)
(PZ) rich
rich region,
region, and
and
2+ ionic shift in a PZ unit cell to visualize the antipolar structure
Figure5b
5billustrates
illustratesthe
thePb
Pb2+
structure [16].
[16].
Figure
(a)
(b)
Figure5.5. (a)
(a)PZT
PZTsystem
systemphase
phasediagram
diagramwith
withaaparticular
particularinterest
interestin
inthe
thePZ
PZrich
richregion;
region;and
and(b)
(b)Pb
Pb2+2+
Figure
ionicshift
shiftin
inaaPZ
PZunit
unitcell
cellto
tovisualize
visualizethe
theantipolar
antipolarstructure
structure[16].
[16].
ionic
4. Fundamental Properties of the Electric Field-Induced Phase Transition
4. Fundamental Properties of the Electric Field-Induced Phase Transition
The antiparallel arrangement of electric dipoles in the sublattices of AFE is rearranged in parallel
The antiparallel arrangement of electric dipoles in the sublattices of AFE is rearranged in parallel
by an applied electric field, and the dielectric and electromechanical properties are changed
by an applied electric field, and the dielectric and electromechanical properties are changed remarkably
remarkably at this phase change.
at this phase change.
4.1. Electric
Electric Field
Field Dependence
Dependence of
of Lattice
Lattice Parameters
Parameters
4.1.
The field-induced
field-induced change
change in
in lattice
lattice parameters
parameters for
for aa sample
Nb0.02[(Zr0.6Sn0.4)1-yTiy]0.98O3 with
The
sample Pb
Pb0.99
0.99 Nb0.02 [(Zr0.6 Sn0.4 )1-y Tiy ]0.98 O3
y = 0.06
plotted
in Figure
6a [7].6aThe
transition
from from
the AFE
theto
FEthe
phase
gives gives
rise torise
the
with
y = is
0.06
is plotted
in Figure
[7].forced
The forced
transition
theto
AFE
FE phase
simultaneous
increase
of
a
and
c
in
the
perovskite
unit
cell,
thereby
keeping
the
tetragonality,
c/a,
to the simultaneous increase of a and c in the perovskite unit cell, thereby keeping the tetragonality,
nearly
constant.
Since
the the
angle
γ makes
onlyonly
a negligible
contribution
to the
volume
change,
the
c/a,
nearly
constant.
Since
angle
γ makes
a negligible
contribution
to the
volume
change,
−4
strain
change
at the
transition
is nearly
isotropic
with with
a magnitude
of ΔL/L
8.5 ×=108.5. Though
the
strain
change
at phase
the phase
transition
is nearly
isotropic
a magnitude
of =∆L/L
ˆ 10´4 .
we
observe
minor
changes
in
the
parameters
c,
c/a
and
γ
between
AFE-FE
On-set
and
FE-AFE
OffThough we observe minor changes in the parameters c, c/a and γ between AFE-FE On-set and FE-AFE
set electric
fields,
wewe
cannot
discuss
further
on aa
Off-set
electric
fields,
cannot
discuss
furtherononthis,
this,because
becausethe
the measurement
measurement was
was made
made on
polycrystalline
sample
and
the
effective
electric
field
on
a
certain
crystal
orientation
in
each
grain
was
polycrystalline sample and the effective electric field on a certain crystal orientation in each grain
distributing.
was distributing.
The intensity change of the X-ray reflections with the application of an electric field suggests that
the spontaneous polarization in the FE state lies in the c-plane, parallel with the perovskite [1 1 0]
axis, and that the sublattice polarization configuration in the AFE state is very similar to that of PbZr03
(see Figure 5b) [16]. Figure 6b illustrates the simplest two-sublattice model.
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(a)
(b)
Figure 6. (a) Variation of lattice parameters with bias electric field at room temperature (y = 0.06); and
Figure 6. (a) Variation of lattice parameters with bias electric field at room temperature (y = 0.06); and
(b) two-sublattice model of the polarization configuration for the AFE and FE states. (After Uchino
(b) two-sublattice model of the polarization configuration for the AFE and FE states. (After Uchino and
and Nomura
Nomura
[7]). [7]).
4.2. Temperature Dependence of the Permittivity
The intensity change of the X-ray reflections with the application of an electric field suggests that
Figure 7 shows
change in
of the
permittivity
with
temperature
under with
various
electric[1field
in a
the spontaneous
polarization
FE state lies
in the
c-plane, parallel
the bias
perovskite
1 0] axis,
composition
y
=
0.06,
Pb
0.99
Nb
0.02
[(Zr
0.6
Sn
0.4
)
0.94
Ti
0.06
]
0.98
O
3
[7].
With
an
increase
in
temperature
the
ferroand that the sublattice polarization configuration in the AFE state is very similar to that of PbZr03
to antiferroelectric
is clearly
observed
in a poled specimen
(see
Figure 5b) [16].phase
Figuretransition
6b illustrates
the simplest
two-sublattice
model. as a permittivity hump.
Note that the reverse antiferro- to ferroelectric transition occurs with a considerably large hysteresis
4.2.
Dependence
of theThough
Permittivity
withTemperature
temperature
decreasing.
we observe another narrow pseudo-cubic antiferroelectric
phase
(which
may correspond
Aβ Phase inwith
Figure
5a) just below
the various
Neel temperature
under
Figure
7 shows
change oftopermittivity
temperature
under
bias electric
fieldsmall
in a
bias
electric
field,
we
will
not
discuss
its
details
in
this
paper.
composition y = 0.06, Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.94 Ti0.06 ]0.98 O3 [7]. With an increase in temperature the
8a shows the relation
between is
theclearly
electric
field andinpolarization.
The typical
double and
ferro-Figure
to antiferroelectric
phase transition
observed
a poled specimen
as a permittivity
ferroelectric
hysteresis
areantiferroobserved to
at room
temperature
and −76
°C, with
respectively,
while a
hump.
Note
that the loops
reverse
ferroelectric
transition
occurs
a considerably
transitive
shape
with
humps
is
observed
at
intermediate
temperatures.
large hysteresis with temperature decreasing. Though we observe another narrow pseudo-cubic
The transitive
process
can may
be observed
moretoclearly
in theinstrain
curve.
Figure
8b shows
the
antiferroelectric
phase
(which
correspond
Aβ Phase
Figure
5a) just
below
the Neel
transversely under
induced
strains.
The forced
transition
from AFE
to FEin at
temperature
small
bias electric
field, we
will not discuss
its details
thisroom
paper.temperature is
characterized
by
a
huge
strain
discontinuity.
On
the
other
hand,
a
typical
ferroelectric
butterfly-type
Figure 8a shows the relation between the electric field and polarization. The typical double and
hysteresis is observed at −76 °C, corresponding to polarization reversal. It is important to note that
ferroelectric hysteresis loops are observed at room temperature and ´76 ˝ C, respectively, while a
the strain discontinuities associated with the phase transition have the same positive expansion in
transitive shape with humps is observed at intermediate temperatures.
both longitudinal and transverse directions with respect to the electric field (i.e., the apparent
The transitive process can be observed more clearly in the strain curve. Figure 8b shows
Poisson’s ratio is negative!), while the piezo-striction is negative and positive in the transverse and
the transversely induced strains. The forced transition from AFE to FE at room temperature is
longitudinal directions, respectively, which will further be discussed in Section 4.4.
characterized by a huge strain discontinuity. On the other hand, a typical ferroelectric butterfly-type
The shape memory effect is observed on this loop at −4 °C. When a large electric field is applied
hysteresis is observed at ´76 ˝ C, corresponding to polarization reversal. It is important to note that the
to the annealed AFE sample, a massive strain ΔL/L of about 7 × 10−4 is produced and maintained
strain discontinuities associated with the phase transition have the same positive expansion in both
metastably even after the field is removed. After applying a small reverse field or thermal annealing,
longitudinal and transverse directions with respect to the electric field (i.e., the apparent Poisson’s
the original AFE shape is observed.
ratio is negative!), while the piezo-striction is negative and positive in the transverse and longitudinal
The reverse critical field related to the FE-AFE transition is plotted with solid lines in the phase
directions, respectively, which will further be discussed in Section 4.4.
diagram for the sample with y = 0.06 in Figure 9, in which the
temperature-field points are based on
The shape memory effect is observed on this loop at ´4 ˝ C. When a large electric field is applied
the measurements in permittivity, polarization and strain. In the temperature range from −30 °C to
to the annealed AFE sample, a massive strain ∆L/L of about 7 ˆ 10´4 is produced and maintained
10 °C, a hump-type hysteresis in the field versus polarization curve and an inverse hysteresis in the
metastably even after the field is removed. After applying a small reverse field or thermal annealing,
field-induced strain are observed: this has previously often been misinterpreted as another AFE
the original AFE shape is observed.
phase different from the phase above 10 °C. The annealed state below −30 °C down to −200 °C is AFE.
However, once the FE state is induced, the AFE phase is never observed during a cycle of rising and
falling electric field. The critical field line for the FE to AFE transition (the solid line) in the
Actuators 2016, 5, 11
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temperature range −30 °C to 10 °C intersects the coercive field line for the + FE to − FE reversal (the
7 of 23
temperature
range −30
dashed line) below
−30 °C
°C.to 10 °C intersects the coercive field line for the + FE to − FE reversal (the
dashed line) below −30 °C.
Actuators 2016, 5, 11
Figure
Change of
of permittivity
permittivity with
with temperature
temperature under
under various
various bias
bias electric
Figure 7.
7. Change
electric field
field in
in PNZST
PNZST
(y
=
0.06)
[7].
Figure
7.
Change
of
permittivity
with
temperature
under
various
bias
electric
field
in
PNZST
(y = 0.06) [7].
(y = 0.06) [7].
(a)
(a)
(b)
(b)
Figure 8. Polarization (a) and transverse elastic strain (b) induced by electric field for several
Figure
8. Polarization
transverse
electric field
field for
for several
several
temperatures
in PNZST(a)
(y
0.06).
Figure
8.
Polarization
(a)=and
and
transverse elastic
elastic strain
strain (b)
(b) induced
induced by
by electric
temperatures in
in PNZST
PNZST (y
(y == 0.06).
0.06).
temperatures
The reverse critical field related to the FE-AFE transition is plotted with solid lines in the phase
diagram for the sample with y = 0.06 in Figure 9, in which the temperature-field points are based
on the measurements in permittivity, polarization and strain. In the temperature range from ´30 ˝ C
to 10 ˝ C, a hump-type hysteresis in the field versus polarization curve and an inverse hysteresis in
Actuators 2016, 5, 11
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the field-induced strain are observed: this has previously often been misinterpreted as another AFE
phase different from the phase above 10 ˝ C. The annealed state below ´30 ˝ C down to ´200 ˝ C is AFE.
However, once the FE state is induced, the AFE phase is never observed during a cycle of rising and
falling electric field. The critical field line for the FE to AFE transition (the solid line) in the temperature
range ´30 ˝ C to 10 ˝ C intersects the coercive field line for the + FE to ´ FE reversal (the dashed line)
Actuators 2016, 5, 11
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below ´30 ˝ C.
(a)
Figure
9.
(a)
Phase
diagram
(b)
on
the
temperature-bias
electric
field
plane
for
Figure 9. (a) Phase
on the temperature-bias electric field plane for Pb0.99 Nb0.02
[(Zr0.6 Sn0.4 )0.94
Pb0.99Nbdiagram
0.02[(Zr0.6Sn0.4)0.94Ti0.06]0.98O3). (b) Schematic 3D view for improved understanding
of the
Antiferroelectric
–
Ferroelectric
(AFE-FE)
transformation
hysteresis.
Ti0.06 ]0.98 O3 ). (b) Schematic 3D view for improved understanding of the Antiferroelectric – Ferroelectric
(AFE-FE) transformation hysteresis.
4.3. Composition Dependence of the Induced Strain
Figure 10 shows the strain curves induced transversely by the external field at room temperature
4.3. Composition
Dependence
of the
Induced
Strain [8]. The molar fraction of Ti, y, is increased from 0.06
for samples
of several
different
compositions
(Figure 10a) to 0.065 (Figure 10c). The initial state was obtained by annealing at 150 °C, which is above
Figure 10theshows
the strain curves induced transversely by the external field at room temperature
Curie (or Neel) temperature for all the samples. A typical double hysteresis curve (Type I) is
for samples of
several
different
compositions
[8].jumps
The in
molar
fraction
of Ti,
y, is
increased
from 0.06
observed
in the
sample containing
y = 0.06. Large
the strain
are observed
at the
forced
phase
In comparison,
the strain change
with˝ C, which is
the AFE
to the
FE initial
phase (ΔL/L
= 8was
× 10−4).
(Figure 10a) transitions
to 0.065 from
(Figure
10c).
The
state
obtained
by annealing
at 150
electric field in either the AFE or FE state is rather small: this suggests a possible application for the
above the Curie
(or Neel)
temperature
fortransducer,
all the samples.
A typical
double
hysteresis
curve (Type I) is
material
as a “digital”
displacement
having OFF/ON
displacement
states.
The difference
observed in the
sample
containing
y = 0.06.in Large
jumps
in the
areinobserved
at theatforced phase
in the
strain between
that occurring
the initial
state and
thatstrain
appearing
a cyclic process
4 ). In comparison,
E = 0 kV/cm
is also
and will(∆L/L
be explained
the´following
section.
transitions from
the AFE
tonoteworthy
the FE phase
= 8 ˆin10
the strain change with
In the sample with y = 0.063, a Ti concentration slightly higher than that just described, the fieldelectric field induced
in either
AFE
or FE
state
is AFE
rather
this
suggests
possible
application
for the
FE the
phase
will not
return
to the
statesmall:
even after
decreasing
the afield
to zero (Type
II,
10b): this
is called “memorizing”
the FEhaving
strain state.
In order todisplacement
obtain the initial AFE
state,The
a
material as a Figure
“digital”
displacement
transducer,
OFF/ON
states.
difference
reverse that
bias field
is required.inFigure
showsstate
the strain
the sample with
0.065, process at
in the strain small
between
occurring
the 10c
initial
andcurve
thatforappearing
in ya= cyclic
which exhibits irreversible characteristics during an electric field cycle (Type III). The initial strain
E = 0 kV/cm state
is also
noteworthy
will be
explained
in°C.
the following section.
can only
be recoveredand
by thermal
annealing
up to 50
Datawith
derived
these strain
may be utilizedslightly
to construct
a phase than
diagram
of thejust
system
In the sample
yfrom
= 0.063,
a Ticurves
concentration
higher
that
described, the
Pb0.99Nb0.02[(Zr0.6Sn0.4)1-yTiy]0.98O3 at room temperature with respect to the composition y and the
field-induced FE phase will not return to the AFE state even after decreasing the field to zero (Type II,
applied electric field E (Figure 11). If the Ti concentration of the horizontal axis is redefined in terms
Figure 10b): of
this
is calledand
“memorizing”
the FEdirection,
strain this
state.
Indiagram
orderisto
obtain the
temperature
evaluated in the opposite
phase
topologically
the initial
same AFE state,
as the
phase
diagram
of Figure 9.
The key10c
feature
of thisthe
phase
diagram
is thefor
existence
of the three
a small reverse
bias
field
is required.
Figure
shows
strain
curve
the sample
with y = 0.065,
phases, namely the AFE, the positively poled FE (+ FE), and the negatively poled FE (− FE) phases,
which exhibits irreversible characteristics during an electric field cycle (Type III). The initial strain state
the boundaries of which are characterized by the two transition lines corresponding to rising and
can only be recovered
byfields.
thermal annealing up to 50 ˝ C.
falling electric
The
composition
regions curves
I and IV exhibit
the utilized
typical double
hysteresis and
ferroelectric
domainof the system
Data derived
from
these strain
may be
to construct
a phase
diagram
reversal, respectively. The shape memory effect is observed in regions II and III. It is important to
Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )1-y Tiy ]0.98 O3 at room temperature with respect to the composition y and the
consider the magnitude of the electric field associated with the + FE → AFE transition (notice the
applied electric
fieldofEthe
(Figure
If consider
the Ti concentration
of the
horizontal
axis
is after
redefined
in terms
direction
arrow!).11).
Let us
the transition process
under
an inverse bias
field
the
+
FE
is
induced
by
the
positive
electric
field.
If
the
magnitude
of
the
field
for
the
+
FE
→
AFE
transition
of temperature and evaluated in the opposite direction, this phase diagram is topologically the same
smaller than the coercive field for + FE → − FE (Region II, 0.0625 < y < 0.065), the AFE phase appears
as the phase is
diagram
of Figure 9. The key feature of this phase diagram is the existence of the three
once under a small inverse field, then the − FE phase is induced at the AFE → − FE transition field. In
phases, namely the AFE, the positively poled FE (+ FE), and the negatively poled FE (´ FE) phases, the
boundaries of which are characterized by the two transition lines corresponding to rising and falling
electric fields.
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this case, the shape memory is reversible to the initial state only with the application of a reverse
this
case,
the(Type
shapeII):
memory
is reversible
theother
initial
stateif the
only+ FE
with
of is
a reverse
electric
field
this is very
useful! Ontothe
hand,
→ the
− FEapplication
coercive field
smaller
electric
II):field
this (Region
is very useful!
On the
hand,
the + FEreversal
→ − FE to
coercive
field iswithout
smaller
than thefield
+ FE(Type
→ AFE
III, 0.0625
< Y other
< 0.085),
theifdomain
− FE appears
Actuators 2016, 5, 11
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than
the +through
FE → AFE
< 0.085),
domain reversal
to − FE annealing
appears without
passing
thefield
AFE(Region
phase. III,
The0.0625
initial< Ystate
can the
be obtained
by thermally
up to
passing
the AFE phase. The initial state can be obtained by thermally annealing up to
50–70 °Cthrough
(Type III).
50–70 °C (Type III).
Figure 10.
10. Transverse
Nb0.02[(Zr0.6Sn0.4)1-yTiy]0.98O3 at room temperature: (a) for
Figure
Transverse induced
induced strains
strainsin
inPb
Pb0.99
0.99 Nb0.02 [(Zr0.6 Sn0.4 )1-y Tiy ]0.98 O3 at room temperature:
y =for
0.06;
for (b)
y =for
0.063;
(c)
for y
= for
0.065.
Figure
Transverse
induced
strains
Pby0.99=Nb
0.02[(Zr0.6Sn0.4)1-yTiy]0.98O3 at room temperature: (a) for
(a)
y10.
=(b)
0.06;
y
= and
0.063;
and
(c)in
0.065.
y = 0.06; (b) for y = 0.063; and (c) for y = 0.065.
Figure 11. Phase diagram of Pb0.99Nb0.02[(Zr0.6Sn0.4)1-yTiy]0.98O3 at room temperature with respect to the
Figure
11.
diagram
of
Nb0.02
[(Zr0.6E.
Oroom
temperature
respect
to
y ]O
composition
y and
the applied
electric
field
0.02
0.6
1-yy]Ti
0.98
3 at room
Figure
11. Phase
Phase
diagram
of Pb
Pb0.99
0.99
Nb
[(Zr
SnSn
0.40.4
)1-y)Ti
0.98
3 at
temperature
withwith
respect
to the
the
composition
y and
applied
electric
field
composition
y and
the the
applied
electric
field
E. E.
4.4. Domain Reorientation Mechanism in Antiferroelectrics
4.4. Domain
Reorientation
Mechanism IV
in Antiferroelectrics
The
composition
regions
exhibit
the typical double
hysteresis
andthey
ferroelectric
domain
Antiferroelectrics
cannotI and
be poled
macroscopically.
However,
since
have sublattice
reversal,
respectively.
The
shape
memory
effect
is
observed
in
regions
II
and
III.
It
is
important
to
Antiferroelectrics
cannotwith
be the
poled
macroscopically.
However,
since they
have sublattice
polarizations
closely coupled
lattice
distortion, it is possible
to consider
ferroelastic
domain
consider
the in
magnitude
of thewith
electric
field
associated
with
the
+ FEtoÑconsider
AFE transition
(notice
polarizations
closely
coupled
the is
lattice
distortion,
it is possible
ferroelastic
domain
orientations
antiferroelectrics.
This
a possible
approach
to understanding
the
difference
in the
the
direction
of
the
arrow!).
Let
us
consider
the
transition
process
under
an
inverse
bias
field
after
the
FE
orientations in antiferroelectrics. This is a possible approach to understanding the difference in+ the
is induced by the positive electric field. If the magnitude of the field for the + FE Ñ AFE transition is
smaller than the coercive field for + FE Ñ ´ FE (Region II, 0.0625 < y < 0.065), the AFE phase appears
once under a small inverse field, then the ´ FE phase is induced at the AFE Ñ ´ FE transition field.
In this case, the shape memory is reversible to the initial state only with the application of a reverse
Actuators 2016, 5, 11
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electric field (Type II): this is very useful! On the other hand, if the + FE Ñ ´ FE coercive field is
smaller than the + FE Ñ AFE field (Region III, 0.0625 < Y < 0.085), the domain reversal to ´ FE appears
Actuators 2016, 5, 11
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without passing through the AFE phase. The initial state can be obtained by thermally annealing up to
˝ C (Type III).
50–70
strain between
that occurring in the initial state and that arising in a cyclic process, as shown in
Figure 12b (retraced from Figure 10a).
4.4. Domain Reorientation Mechanism in Antiferroelectrics
Figure 12a shows the longitudinal and transverse strains induced in the sample y = 0.075 in
Antiferroelectrics
cannot
be poled
macroscopically.
have
sublattice
Region
III [8]. The strain
induction
process
can be consideredHowever,
to consistsince
of twothey
stages:
first,
there is
−4
polarizations
closely
coupled
with
the
lattice
distortion,
it
is
possible
to
consider
ferroelastic
domain
an isotropic volume expansion (0 → A, A’: ΔL/L = 8 × 10 ) due to the AFE to FE phase transition
orientations
in antiferroelectrics.
This is a possible
approach
to understanding
difference
the
(remember Figure
6a, where the perovskite
cell expands
almost
isotropically bythe
ΔL/L
= 8 × 10−4in
); and
strain
between
the initial
state and
in a cyclic
process,
in
second,
there isthat
an occurring
anisotropicinstrain
associated
withthat
the arising
FE domain
rotation
(A → as
B, shown
A’ → B’:
−4
−4
Figure
12b
(retraced
from
Figure
10a).
x3 = 9×10 , x1 = −3 × 10 ).
(a)
(b)
Figure
12. (a)
Longitudinal
and
transverse induced strains
in the
sample
Figure 12. (a) Longitudinal and transverse induced strains in the sample Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.925
Pb0.99Nb0.02[(Zr0.6Sn0.4)0.925Ti0.075]0.98O3; and (b) transverse strains in Pb0.99Nb0.02[(Zr0.6Sn0.4)0.94Ti0.06]0.98O3.
Ti0.075 ]0.98 O3 ; and (b) transverse strains in Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.94 Ti0.06 ]0.98 O3 .
This process is shown schematically as the antiferroelectric domain reorientation in Figure 13,
Figure
12a shows
the
and transverse
strains
the is
sample
y = 0.075 in
where
a probable
model
forlongitudinal
the double-hysteresis
sample
(Typeinduced
I, Figurein12b)
also illustrated.
In
Region
III
[8].
The
strain
induction
process
can
be
considered
to
consist
of
two
stages:
first,
the Type I PNZST, in comparison with the original annealed AFE state, once the ferroelectricthere
state is
is
´4 ) due to the AFE to FE phase transition
an
isotropic
volume
expansion
(0
Ñ
A,
A’:
∆L/L
=
8
ˆ
10
electrically induced, the same AFE state exhibits lower strain status along the transversal direction
4 );
(remember
Figurestatus
6a, where
thethe
perovskite
cell expands
isotropically
10´
(or higher strain
along
electric field).
Taking almost
into account
Figureby
6a,∆L/L
a/c =
> 81,ˆwe
can
and
second, the
there
is anreduction
anisotropic
strain associated
withphase
the FEatdomain
rotation
(Athe
Ñ B,
A’ Ñthat
B’:
understand
strain
in Figure
12b in the AFE
E = 0 kV/cm
from
model
´
4
´
4
xthe
9ˆ10 , xorientation
).
3 =antipolar
1 = ´3 ˆ 10is re-arranged
along the electric field direction. As previously pointed out,
This
process
is
shown
schematically
as the through
antiferroelectric
domain
in Figure 13,
even for AFEs, domain reorientation is possible
the forced
phase reorientation
transition to FEs.
where
a probable
model forinthe
double-hysteresis
sample
I, Figure
12b) is also
illustrated.
Domain
configuration
PNZST
y = 0.063 (Type
II) was(Type
observed
as a function
of electric
field
In
the
Type
I
PNZST,
in
comparison
with
the
original
annealed
AFE
state,
once
the
ferroelectric
at room temperature [17]. No clear domains were observed in the initial state obtained by annealing
state
is electrically
induced,
the same
AFE
state exhibits
lower strain
alongabove
the transversal
the sample
at 70 °C.
As the electric
field
increased,
clear domain
wallsstatus
appeared
20 kV/cm,
direction
(or
higher
strain
status
along
the
electric
field).
Taking
into
account
Figure
6a,
a/c
>
1, we can
arranged almost perpendicularly to the electric field direction. This value of electric field is coincident
understand
the
strain
reduction
in
Figure
12b
in
the
AFE
phase
at
E
=
0
kV/cm
from
the
model
that
with the critical field that can cause the transition from AFE to FE. Therefore, these domain walls
the
antipolar
orientation
is
re-arranged
along
the
electric
field
direction.
As
previously
pointed
were caused by the induced ferroelectricity. The domain walls did not diminish whilst removingout,
the
even
forfield,
AFEs,because
domainthe
reorientation
possible
through the
forced
to FEs.
electric
sample hasisthe
shape memory
effect.
Thephase
walls transition
disappeared
when slightly
Domain
inexpected
PNZST yin= the
0.063
(Type
II) was observed as a function of electric field
negative
bias configuration
was applied, as
Type
II specimen.
at room
[17].
No response
clear domains
were observed
the initial
state obtained
by annealing
Let temperature
us discuss the
strain
time relating
with theindomain
reorientation.
As we
discussed
˝ C. As the electric field increased, clear domain walls appeared above 20 kV/cm,
the
sample
at
70
above, there are two stages for the strain generation in the shape memory ceramics: (1) phase
arranged
almost from
perpendicularly
the and
electric
direction.
Thisinduced
value of ferroelectric
electric field is
coincident
transformation
the AFE totoFE;
(2) field
alignment
of the
domains.
In
with
the
critical
field
that
can
cause
the
transition
from
AFE
to
FE.
Therefore,
these
domain
walls
were
particular, since the phase transformation requires a “latent” heat, a longer response time is expected.
caused
the induced
ferroelectricity.
Thestrain
domain
walls did
diminish
whilstfrequency
removing measure
the electric
Figure by
14 shows
the transverse
induced
response
as anot
function
of drive
in
field,
because
the
sample
has
the
shape
memory
effect.
The
walls
disappeared
when
slightly
negative
the Type I sample, Pb0.99Nb0.02[(Zr0.6Sn0.4)0.94Ti0.06]0.98O3. The phase transformation seems to follow up
bias
wasHz.
applied,
as expected
inHz,
the the
Type
II specimen.
to 5–10
However,
above 50
induced
FE phase may not return to the AFE phase anymore
during the short interval, exhibiting a piezoelectric butterfly-like transverse strain curve. This time
delay due to the latent heat will be discussed again in Section 7.
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Figure13.
13.Schematic
Schematicillustration
illustration
of the
antiferroelectric
domain
reorientation
associated
with
the
Figure
of the
antiferroelectric
domain
reorientation
associated
with the
forced
forcedtransition.
phase transition.
phase
Let us discuss the strain response time relating with the domain reorientation. As we
discussed above, there are two stages for the strain generation in the shape memory ceramics:
(1) phase transformation from the AFE to FE; and (2) alignment of the induced ferroelectric domains.
In particular, since the phase transformation requires a “latent” heat, a longer response time is expected.
Figure 14 shows the transverse induced strain response as a function of drive frequency measure in the
Type I sample, Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.94 Ti0.06 ]0.98 O3 . The phase transformation seems to follow up
to 5–10 Hz. However, above 50 Hz, the induced FE phase may not return to the AFE phase anymore
Figure 13. Schematic illustration of the antiferroelectric domain reorientation associated with the
during the short interval, exhibiting a piezoelectric butterfly-like transverse strain curve. This time
forced phase transition.
delay due to the latent heat will be discussed again in Section 7.
Figure 14. Transverse induced strain response as a function of drive frequency measure in
Pb0.99Nb0.02[(Zr0.6Sn0.4)0.94Ti0.06]0.98O3.
4.5. Pressure Dependence of the Field-Induced Strain
One of the most important criteria for an actuator is reliable and stable driving under a large
applied stress, as required for its application as a positioner in precision cutting machinery.
Figure 15 shows the longitudinally induced strains in a shape memory sample of PNZST y = 0.0707
in both the AFE and FE states at room temperature plotted as a function of uniaxial compressive
stress for several electric fields [13]. For comparison, a similar plot for a lead magnesium niobate
Figure
14.ceramic
Transverse
induced
response
as a function
of drive frequency
measure
in
(PMN)
based
(Pb(Mg
1/3Nb2/3strain
)0.65Ti0.35
O3, a well-known
electrostrictive
material)
is also shown.
Figure
14. Transverse
induced
strain
response
as a function
of drive frequency
measure
in
Pb
Nb
[(Zr
Sn
)
Ti
]
O
.
Roughly
speaking,
the
strain
versus
stress
curve
for
the
AFE
PNZST
ceramic
is
shifted
along
the
0.02
0.6 0.4 0.94 0.06 0.98 3
0.99Nb0.02[(Zr0.6Sn0.4)0.94Ti0.06]0.98O3.
Pb0.99
strain axis with respect to that for PMN due to the difference between the spontaneous strains in the
AFEPressure
and theDependence
FE states. Consequently,
the Strain
maximum generative force obtained when the ceramic is
4.5.
of the Field-Induced
mechanically clamped so as not to generate a displacement is raised to 80 MPa, in comparison with
One of the most important criteria for an actuator is reliable and stable driving under a large
the normal value for the ferroelectric, 35 MPa in the PMN.
applied stress, as required for its application as a positioner in precision cutting machinery.
Figure 15 shows the longitudinally induced strains in a shape memory sample of PNZST y = 0.0707
in both the AFE and FE states at room temperature plotted as a function of uniaxial compressive
Actuators 2016, 5, 11
12 of 22
Crack
Actuators
2016, 5, 11generation
and
propagation
process
is
very
unique
in
12 of 23a
Pb0.99Nb0.02[(Zr0.6Sn0.4)0.955Ti0.045]0.98O3 multilayer (ML) sample, as pictured in Figure 16 [18]. As is wellknown, the crack is usually initiated around the edge of the internal electrode, then propagates to the
4.5.
Dependence
of the
Field-Induced
MLPressure
side-wall
in a regular
piezoelectric
MLStrain
sample. However, in the PNZSM ML, the crack is initiated
between
two
layers slightly
electrode
edge area,
propagates
in under
parallela to
the
One of
theelectrode
most important
criteriainside
for anthe
actuator
is reliable
and stable
driving
large
electrode
layer,
then
branches
into
a
Y-shape
around
the
electrode
edge
area.
This
unique
crack
applied stress, as required for its application as a positioner in precision cutting machinery. Figure 15
propagation
mechanism induced
may be originated
the
negative
Poisson’s
ratio or
volumetric
shows
the longitudinally
strains in afrom
shape
memory
sample
of PNZST
y isotropic
= 0.0707 in
both the
expansion
associated
with
the
AFE
to
FE
phase
transformation.
Supposing
that
theseveral
phase
AFE and FE states at room temperature plotted as a function of uniaxial compressive stress for
transformation
starts
from
the
electrode
and
the
phase
boundary
moves
to
the
center
between
a pair
electric fields [13]. For comparison, a similar plot for a lead magnesium niobate (PMN) based ceramic
of the electrodes,
is induced
around thematerial)
center area,
leading
to the crack initiation.
(Pb(Mg
Nb ) large
Ti tensile
O , a stress
well-known
electrostrictive
is also
shown.
1/3
2/3 0.65
0.35
3
Figure
Longitudinalinduced
induced
strains
a shape
memory
sample
Pb0.02
Nb0.6
Sn0.07
)0.93
0.99[(Zr
0.02
0.6Ti
0.4]0.98
Figure 15.
15. Longitudinal
strains
in ainshape
memory
sample
Pb0.99Nb
Sn[(Zr
0.4)0.93
O3
Tiat0.07
]
O
at
room
temperature
plotted
as
a
function
of
uniaxial
compressive
stress
[13].
0.98
3
room temperature plotted as a function of uniaxial compressive stress [13].
Roughly speaking, the strain versus stress curve for the AFE PNZST ceramic is shifted along the
strain axis with respect to that for PMN due to the difference between the spontaneous strains in the
AFE and the FE states. Consequently, the maximum generative force obtained when the ceramic is
mechanically clamped so as not to generate a displacement is raised to 80 MPa, in comparison with
the normal value for the ferroelectric, 35 MPa in the PMN.
Crack generation and propagation process is very unique in a Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.955
Ti0.045 ]0.98 O3 multilayer (ML) sample, as pictured in Figure 16 [18]. As is well-known, the crack
is usually initiated around the edge of the internal electrode, then propagates to the ML side-wall
in a regular piezoelectric ML sample. However, in the PNZSM ML, the crack is initiated between
two electrode layers slightly inside the electrode edge area, propagates in parallel to the electrode
layer, then branches into a Y-shape around the electrode edge area. This unique crack propagation
mechanism may be originated from the negative Poisson’s ratio or isotropic volumetric expansion
associated with the AFE to FE phase transformation. Supposing that the phase transformation starts
from the electrode and the phase boundary moves to the center between a pair of the electrodes, large
tensile stress is induced around the center area, leading to the crack initiation.
Figure 16. Crack generation and propagation process in a Pb0.99Nb0.02[(Zr0.6Sn0.4)0.955Ti0.045]0.98O3
multilayer sample under cyclic electric field application [18]. (Top)during first field cycle, (middle)
during the 30th cycle, (bottom) during the 70th cycle.
Figure
induced strains in a shape memory sample Pb0.99Nb0.02[(Zr0.6Sn0.4)0.93Ti0.07]0.98O13
3 of 23
Actuators
2016,15.
5, Longitudinal
11
at room temperature plotted as a function of uniaxial compressive stress [13].
Figure 16.
16.Crack
Crackgeneration
generation
and
propagation
process
in a Nb
Pb0.99Nb
0.02[(Zr0.6Sn0.4)0.955Ti0.045]0.98O3
Figure
and
propagation
process
in a Pb
0.99
0.02 [(Zr0.6 Sn0.4 )0.955 Ti0.045 ]0.98 O3
multilayer
sample
under
cyclic
electric
field
application
[18].
(Top)during
fieldfirst
cycle,
(middle)
multilayer sample under cyclic electric field application [18]. (Top) first
during
field
cycle,
th cycle, (bottom) during the 70th cycle.
during
the
30
(middle) during the 30th cycle, (bottom) during the 70th cycle.
5. Phenomenological Approach
5.1. Electrostrictive Coupling in Antiferroelectrics
We will discuss here the introduction of electrostrictive coupling in Kittel’s free energy expression
for antiferroelectrics [19,20]. The simplest model for antiferroelectrics is the “one-dimensional
two-sublattice model”. It treats the coordinates as one-dimensional, and a superlattice (twice the
unit lattice) is formed from two neighboring sublattices each having a sublattice polarization Pa and
Pb . The state Pa = Pb represents the ferroelectric phase, while Pa = ´Pb , the antiferroelectric phase.
For the electrostrictive effect, ignoring the coupling between the two sublattices, the strains from the
two sublattices are QPa 2 and QPb 2 , respectively (assuming equal electrostrictive constants Q for both
sublattices). The total strain of the crystal becomes
x “ Q¨pPa 2 ` Pb 2 q{2
(1)
However, since antiferroelectricity originates from the coupling between the sublattices, it is
appropriate to consider the sublattice coupling also for the electrostrictive effect. The coupling term
for the electrostriction Ω was introduced by Uchino et al. first in the following form [8,21]:
G1 “ p1{4q¨α¨pPa 2 ` Pb 2 q ` p1{8q¨β¨pPa 4 ` Pb 4 q ` p1{12q¨γ¨pPa 6 ` Pb 6 q
` p1{2q¨η¨Pa Pb ´ p1{2q¨χT ¨p2 ` p1{2q¨Qh ¨pPa 2 ` Pb 2 ` 2Ω¨Pa Pb q p
(2)
in which hydrostatic pressure p was employed, and χT is the isothermal compressibility,
Qh (= Q11 + 2Q12 ) and Ω are the electrostrictive constants. Introducing the L. E. Cross’ transformations
PF = (Pa + Pb )/2 and PA = (Pa ´ Pb )/2 leads to the following expression:
G1 “ p1{2q¨α¨pPF 2 ` PA 2 q ` p1{4q¨β¨pPF 4 ` PA 4 ` 6¨PF 2 PA 2 q ` p1{6q¨γ¨pPF 6 ` PA 6 ` 15¨PF 4 PA 2
` 15¨PF 2 PA 4 q ` p1{2q¨η¨pPF 2 ´ PA 2 q ´ p1{2q¨χT ¨p2 ` Qh ¨rPF 2 ` PA 2 ` Ω¨ pPF 2 ´ PA 2 qs¨p
(3)
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The dielectric and elastic equations of state follow as
BG1 {BPF “ E “ PF rα ` η ` 2Qh p1 ` Ωqp ` β¨PF 2 ` 3β¨PA 2 ` γ¨PF 4 ` 10γ¨PF 2 PA 2 ` 5γ¨PA 4 s
(4)
BG1 {BPA “ 0 “ PA rα ´ η ` 2Qh ¨p1 ´ Ωqp ` β¨PA 2 ` 3β¨PF 2 ` γ¨PA 4 ` 10γ¨PF 2 PA 2 ` 5γ¨PF 4 s
(5)
BG1 {Bp “ ∆V{V “ ´ χT ¨p ` Qh ¨p1 ` Ωq¨PF 2 ` Qh ¨p1 ´ Ωq¨PA 2
(6)
Hence, the induced volume change in the paraelectric phase can be related to the induced ferroelectric
polarization by the following formula:
p∆V{Vqind “ Qh ¨p1 ` ΩqPF,ind 2
(7)
Below the phase transition temperature (this temperature for antiferroelectrics is called Neel
temperature) the spontaneous volume strain and the spontaneous antiferroelectric polarization are
related as
p∆ V{VqS “ Qh ¨p1 ´ ΩqPA,S 2
(8)
Even if the perovskite crystal shows Qh > 0, the spontaneous volume strain can be positive or
negative depending on the value of Ω (Ω < 1 or Ω > 1), that is, if the inter-sublattice coupling is
stronger than the intra-sublattice coupling (i.e., Ω > 1), a volume contraction is observed at the Neel
point. This is quite different from ferroelectrics, which always show a volume expansion at the Curie
point, such as in BaTiO3 and PbTiO3 . The large change in the strain associated with the field-induced
transition from the antiferroelectric to ferroelectric phase can be estimated to be
p∆V{Vq “ Qh ¨p1 ` ΩqPF,S 2 ` Qh ¨p1 ´ ΩqPA,S 2 “ 2¨Qh ¨Ω¨PF,S 2
(9)
Here, we assume that the magnitudes of Pa and Pb do not change drastically through the phase
transition; that is, PF,S « PA,S .
Figure 17 illustrates the spontaneous strains in a crystal schematically for Ω > 0 (you may interpret
Ω = q33 /Q33 in the figure). When Pa and Pb are in the parallel configuration (ferroelectric phase),
the Ω-term acts to increase the strain xS , when they are in the anti-parallel configuration (antiferroelctric
Actuatorsthe
2016,Ω-term
5, 11
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phase),
acts to decrease the strain.
Figure 17.
17. Spontaneous
Spontaneous strain
strain changes
changes associated
associated with
with sublattice
sublattice interactions
interactions in
in the
the electrostrictive
electrostrictive
Figure
effect.
>0.0.
effect. Illustration
Illustration is
is drawn
drawn in
inthe
thecase
caseof
ofqq33
33 and q33
33 >
Using the above physical parameters in Section 5.2 and ε3 = 600 in Figure 7, we can evaluate
d31 = 2(Q31 + q31)∙ε0∙ε3∙PF3,S = −8 × 10−12 m/V. This value is close to the experimentally obtained
d31 = −7 × 10−12 m/V, as shown in Figure 18, though we use a rough cubic-symmetry approximation
such as s33E = s11E, s31E = s12E, etc. The “piezoelectric Poisson’s” ratio d31/d33 is given by
Actuators 2016, 5, 11
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We expand the phenomenology to a three-dimensional formulation [22]. Considering the simplest
case of a tetragonal spontaneous distortion of the primitive perovskite cell, let us start by reducing the
3D polarization (P1 P2 P3 ) to a simple form (0 0 P3 ). The Gibbs elastic free energy is represented by
using two-sublattice polarization Pa and Pb , and stress X under a cubical supposition that s33 E = s11 E ,
s31 E = s12 E , etc.:
G “ p1{4q α¨pPa3 2 ` Pb3 2 q ` p1{8q β¨pPa3 4 ` Pb3 4 q ` p1{12q γ¨pPa3 6 ` Pb3 6 q ` p1{2q η¨Pa3 ¨Pb3
´ p1{2q s33 E ¨pX1 2 ` X2 2 ` X3 2 q ´ s31 E ¨pX1 X2 ` X2 X3 ` X3 X1 q ´ p1{2q s44 E ¨pX4 2 ` X5 2 ` X6 2 q
´ p1{2q Q33 ¨pPa3 2 ` Pb3 2 qX3 ´ p1{2q Q31 ¨pPa3 2 ` Pb3 2 qpX1 ` X2 q ´ q33 Pa3 Pb3 X3 ´ q31 Pa3 Pb3 ¨pX1 ` X2 q
(10)
Here, Q33 and Q31 denote the conventional longitudinal and transverse electrostrictive coefficients
(intrasublattice coupling), and q33 and q31 are the corresponding intersublattice coupling parameters
(the ratio q/Q was denoted as Ω in the above). Introducing the transformations
PF3 “ pPa3 ` Pb3 q{2, PA3 “ pPa3 ´ Pb3 q{2
(11)
leads to four types of stable states under zero applied electric field: nonpolar (PF3 = PA3 = 0), polar
(PF3 ‰ 0, PA3 = 0), antipolar (PF3 = 0, PA3 ‰ 0), and semipolar (PF3 ‰ 0, PA3 ‰ 0) states. The spontaneous
polarization and strains derived from the free-energy function are summarized as follows for the
ferroelectric and antiferroelectric and antiferroelectric states:
Ferroelectric:
PF3
2
PA3 “ 0
“ r´β ` tp1{4q β2 ´ 4γpT ´ TC pXqq{ε0 Cu1/2 s{2γ
(12)
TC pXq “ TC ` 2ε0 CtpQ33 ` q33 qX3 ` pQ31 ` q31 qpX1 ` X2 qu
(13)
x3 “ s33 E X3 ` s31 E pX1 ` X2 q ` pQ33 ` q33 q¨PF3 2
(14)
x1 “ s33 E X1 ` s31 E pX2 ` X3 q ` pQ31 ` q31 q¨PF3 2
(15)
p∆ V{Vq “ ps33 E ` 2s31 E qpX1 ` X2 ` X3 q ` pQ33 ` 2Q31 ` q33 ` 2q31 q¨PF3 2
(16)
Antiferroelectric:
PA3
2
PF3 “ 0
“ r´β ` tp1{4q β2 ´ 4γpT ´ TN pXqq{ε0 Cu1/2 s{2γ
(17)
TN pXq “ TN ` 2ε0 CtpQ33 ´ q33 qX3 ` pQ31 ´ q31 qpX1 ` X2 qu
(18)
x3 “ s33 E X3 ` s31 E pX1 ` X2 q ` pQ33 ´ q33 q¨PA3 2
(19)
x1 “ s33 E X1 ` s31 E pX2 ` X3 q ` pQ31 ´ q31 q¨PA3 2
(20)
p∆V{Vq “ ps33 E ` 2s31 E qpX1 ` X2 ` X3 q ` pQ33 ` 2Q31 ´ q33 ´ 2q31 q¨PA3 2
(21)
Here, TC and TN are the Curie and Neel temperatures, respectively, and C is the Curie–Weiss
constant. Note again that we presume the cubical symmetry physical parameter components.
5.2. Estimation of q33 and q31
The values of q33 and q31 can be obtained from the strain changes associated with the
electric-field-induced and thermally induced phase transitions. The spontaneous strains generated at
the phase transition from paraelectric to antiferroelectric are described as
x3 “ pQ33 ´ q33 q¨PA3 2
(22)
x1 “ pQ31 ´ q31 q¨PA3 2
(23)
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The strain changes associated with the field-induced transition from antiferroelectric to
ferroelectric are given by
∆x3 “ pQ33 ` q33 q¨PF3 2 ´ pQ33 ´ q33 q¨PA3 2 “ 2q33 ¨PF3 2
(24)
∆x1 “ pQ31 ` q31 q¨PF3 2 ´ pQ31 ´ q31 q¨PA3 2 “ 2q31 ¨PF3 2
(25)
Here we have assumed that PF3 = PA3 because only the flipping of polarizations Pa and Pb
would occur at the transition. Let us estimate the q33 and q31 values using experimental strains and
polarization data for Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.94 Ti0.06 ]0.98 O3 (Figures 6 and 8a) [7] and δTN /δp of the
PbZrO3 -based sample [21]:
PF3 “ PA3 “ 0.4 pC¨ m-2 q
∆x3 “ ∆x1 “ 8 ˆ 10-4
Qh “ Q33 ` 2Q31 “ 0.5 ˆ 10-2 pm4 ¨ C-2 q
qh “ q33 ` 2q31 “ 0.9 ˆ 10-2 pm4 ¨ C-2 q
Then we derive the followings:
Q33 “ 1.5 ˆ 10-2 pm4 ¨ C-2 q, Q31 “ ´ 0.5 ˆ 10-2 pm4 ¨ C-2 q, q33 “ 0.3 ˆ 10-2 pm4 ¨ C-2 q,
q31 “ 0.3 ˆ 10-2 pm4 ¨ C-2 q
It is noteworthy that q33 and q31 have the same positive sign (accidentally almost the same value),
while Q33 and Q31 have the opposite sign with a “piezoelectric Poisson’s” ratio of 1/3.
5.3. Piezoelectric Anisotropy in Antiferroelectrics
Let us derive the piezoelectric coefficients for the ferroelectric state with the sublattice polarization
coupling. Under a small external field E applied, the polarization is given by
PF3 “ PF3,S ` ε0 ε3 E3
(26)
where ε3 is the relative permittivity. Using Equations (14) and (15), longitudinal and transversal strains
are represented as
x3 “ pQ33 ` q33 q¨PF3,S 2 ` 2pQ33 ` q33 q¨ε0 ¨ε3 ¨PF3,S ¨E3 ` pQ33 ` q33 q¨ε0 2 ¨ε3 2 ¨E3 2
(27)
x1 “ pQ31 ` q31 q PF3,S 2 ` 2pQ31 ` q31 q ε0 ε3 PF3,S ¨E3 ` pQ31 ` q31 q ε0 2 ε3 2 E3 2
(28)
The first term describes the spontaneous strains, and Figure 17 illustrates the spontaneous strain
changes due to the sublattice interactions in the case of q33 , q31 > 0. When the spontaneous polarization
PF3,S exists, the third term (pure electrostriction) is negligibly small in comparison with the second
term (piezostriction), and the piezoelectric d coefficients are denoted as
d33 “ 2pQ33 ` q33 q¨ε0 ¨ε3 ¨PF3,S
(29)
d31 “ 2pQ31 ` q31 q¨ε0 ¨ε3 ¨PF3,S
(30)
Using the above physical parameters in Section 5.2 and ε3 = 600 in Figure 7, we can evaluate
d31 = 2(Q31 + q31 )¨ε0 ¨ε3 ¨PF3,S = ´8 ˆ 10´12 m/V. This value is close to the experimentally obtained
d31 = ´7 ˆ 10´12 m/V, as shown in Figure 18, though we use a rough cubic-symmetry approximation
such as s33 E = s11 E , s31 E = s12 E , etc. The “piezoelectric Poisson’s” ratio d31 /d33 is given by
(Q31 + q31 )/(Q33 + q33 ) and it can differ from the usual value Q31 /Q33 (« ´1/3) of the normal
Figure 17. Spontaneous strain changes associated with sublattice interactions in the electrostrictive
effect. Illustration is drawn in the case of q33 and q33 > 0.
Using the above physical parameters in Section 5.2 and ε3 = 600 in Figure 7, we can evaluate
d31 = 2(Q31 + q31)∙ε0∙ε3∙PF3,S = −8 × 10−12 m/V. This value is close to the experimentally obtained
Actuators 2016, 5, 11
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d31 = −7 × 10−12 m/V, as shown in Figure 18, though we use a rough cubic-symmetry approximation
such as s33E = s11E, s31E = s12E, etc. The “piezoelectric Poisson’s” ratio d31/d33 is given by
ferroelectrics,
to the
values
q33 the
andusual
q31 . value
UsingQthe
values
again,
weferroelectrics,
can estimate
(Q31 + q31)/(Q33 owing
+ q33) and
it can
differof
from
31/Qabove
33 (≈ −1/3)
of the
normal
d
/d
=
´(1/9).
owing
to
the
values
of
q
33
and
q
31
.
Using
the
above
values
again,
we
can
estimate
d
31
/d
33
= −(1/9).
31
33
Figure 18.18.Piezoelectric
Piezoelectric
d31 measurement
in the
induced phase
ferroelectric
phase
in
Figure
d31 measurement
in the induced
ferroelectric
in Pb0.99 Nb
0.02 [(Zr0.6
Pb
0.99
Nb
0.02
[(Zr
0.6
Sn
0.4
)
0.94
Ti
0.06
]
0.98
O
3
.
Sn0.4 )0.94 Ti0.06 ]0.98 O3 .
The electromechanical coupling factors kt and kp are represented as
The electromechanical coupling factors kt and kp are represented as
Supposing again that
≈
E « sE ,
Supposing again that s33
11
,
c
d
kt =
ε x33
d33
kt “ b
D
c33
E εX
s33
33
kp =
c ‒
d31
2
kp “ b
1´σ
E εX
s11
≈ 0.75,
and
33 σ ≈ 1/3, we obtain
ε x33
D
c33
(31)
(31)
(32)
(32)
« 0.75, and σ « 1/3, we obtain
kt {kp « 0.5 d33 {d31
(33)
For the antiferroelectric-based piezoelectrics, taking into account the above discussion, kt /kp will
be equal to 4.5, much larger than the normal PZT value around 2.0.
Table 1 lists several anisotropic piezoelectric data for field-biased PNZST’s, PbZrO3 - and
PbTiO3 -based ceramics [23]. The electromechanical coupling factors kt (thickness mode) and kp
(planar mode) range from 0.5 to 0.6 and 0.05 to 0.15, respectively, and the anisotropy kt /kp reaches
more than 4.0. In contrast, the ratio kt /kp for the intermediate composition of the solid solution
Pb(Zr,Ti)O3 will not exceed 2.5, which is also listed in Table 1 [23].
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Table 1.
Anisotropic
PbTiO3 -based ceramics.
piezoelectric
constants
in
field-biased
PNZST,
PbZrO3 -
and
Electromechanical Coupling Factor
Composition
Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.937 Ti0.063 ]0.98 O3
Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.936 Ti0.064 ]0.98 O3
Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.934 Ti0.066 ]0.98 O3
Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.920 Ti0.080 ]0.98 O3
Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.910 Ti0.090 ]0.98 O3
Pb(Zr0.9 Ti0.1 )O3 [24]
(Pb0.8 Ca0.2 )TiO3 [25]
Pb(Zr0.5 Ti0.5 )O3 [26]
under 22.5 kV/cm
under 22.5 kV/cm
under 22.5 kV/cm
under 22.5 kV/cm
under 22.5 kV/cm
kt
kp
kt /kp
0.456
0.501
0.622
0.575
0.564
0.325
0.530
0.752
0.114
0.123
0.137
0.145
0.136
0.072
0.050
0.388
4.00
4.15
4.56
4.02
4.15
4.52
10.60
1.938
It is important to note that most of the samples exhibiting piezoelectric anisotropy are closely
related to antiferroelectricity or sublattice structure. Some of them based on PbZrO3 are originally
antiferroelectric at a low temperature or even at room temperature, and the ferroelectricity is induced
after a very high electric field is applied (i.e., poling process). In Ca-modified PbTiO3 ceramics [25],
a crystallographic superlattice structure has been observed in the annealed state, which suggests an
antiferroelectric sublattice structure. In conclusion, we would remark that even if the sample is not
originally antiferroelectric, it seems to possess rather large sublattice dipole coupling.
6. Comparison with Shape Memory Alloys
The phenomenon associated with shape memory alloys is attributed to the stress-induced (as well
as thermally-induced) phase transition referred to as “martensitic”. The new strain phenomena in
AFE ceramics described here are very easily understandable, if we use the terminology conventionally
used for these alloys, replacing electric field E for stress X. The “digital displacement” and the
ferroelectric-state memorization discussed here correspond to the “superelasticity” and the shape
memory effect in the alloys, respectively.
Outstanding merits of the ceramics over the alloys are:
1.
2.
3.
4.
quick response in ms;
good controllability by electric field to memorize and recover the shape without generating heat;
low energy consumption as low as 1/100 of the alloy; and
wide space is not required to obtain the initial shape deformation.
Numerical comparison among the shape memory alloys and antiferroelectric ceramics is
summarized in Table 2.
Table 2. Comparison of the shape memory characteristics between alloys and antiferroelectric ceramics.
Properties
Antiferroelectrics
Shape Memory Alloy
Driving power
Strain (∆L/L)
Generative force
Response speed
Durability
Voltage (mW~W)
10´3 ~ 10´2
100 MPa
1 ~ 10 ms
>106 cycles
Heat (W~kW)
10´2 ~ 10´1
1000 MPa
s ~ min
104 cycles
7. Applications of Shape Memory Ceramics
The conventional piezoelectric/electrostrictive actuators have been developed with the aim
of realizing “analogue displacement transducers”, in which a certain magnitude of electric field
corresponds to only one strain state without any hysteresis during rising and falling electric field.
Durability
>106 cycles
104 cycles
7. Applications of Shape Memory Ceramics
The conventional piezoelectric/electrostrictive actuators have been developed with the aim
of
19 of 23
realizing “analogue displacement transducers”, in which a certain magnitude of electric field
corresponds to only one strain state without any hysteresis during rising and falling electric field.
This is exemplified by the electrostrictive PMN based ceramics. On the
the contrary,
contrary, the antiferroelectrics
introduced in this article may be utilized in a device based on a new concept, “a digital displacement
transducer”, in
in which
whichbistable
bistableON
ONand
andOFF
OFF
strain
states
exist
a certain
electric
field.
idea
strain
states
exist
forfor
a certain
electric
field.
This This
idea may
may
be interpreted
as a stepping
motor
the conventional
terminology
of electromagnetic
motors.
be interpreted
as a stepping
motor
in theinconventional
terminology
of electromagnetic
motors.
The
The
discrete
movement
through
a
constant
distance
achieved
by
the
new
actuator
is
well
suited
discrete movement through a constant distance achieved by the new actuator is well suited for
applications such as an optical-grid manufacturing apparatus or aa swing-type
swing-type charge
charge coupled
coupled device.
device.
The shape memory ceramics were applied to devices such as latching relays and mechanical
mechanical
clampers, where the ceramic is capable of maintaining the excited ON state even when electricity is
not applied continuously to it.
Actuators 2016, 5, 11
7.1.
Latching Relay
Relay
7.1. Latching
Figure
relay, which
Figure 19
19 shows
shows the
the structure
structure of
of aa fabricated
fabricated latching
latching relay,
which is
is composed
composed essentially
essentially of
of aa
mechanical
snap-action
switch
and
a
shape
memory
unimorph
driving
part
[27].
The
snap-action
mechanical snap-action switch and a shape memory unimorph driving part [28]. The snap-action
switch
bistable
states.
The
unimorph
is
switch is
is easily
easily driven
drivenby
byaa50-µm
50-μmdisplacement,
displacement,having
havingmechanically
mechanically
bistable
states.
The
unimorph
fabricated
with
two
y=
is fabricated
with
two
y =0.063
0.063ceramic
ceramicplates
platesofof2222mm
mmˆ×77mm
mmarea
areaand
and 0.2
0.2 mm
mm thickness,
thickness, bonded
bonded
together
with
adhesive.
together with adhesive.
Figure 19. Structure of the latching relay using shape memory ceramic.
Figure 19. Structure of the latching relay using shape memory ceramic.
Figure 20 shows the
It is noteworthy that the phase
the dynamical
dynamical response
response of
of the
the unimorph.
unimorph. It
transition arises quickly enough to generate
generate the
the following
following mechanical
mechanical resonant
resonant vibration
vibration (Figure
(Figure 20a).
20a).
When the rise time of the electric field is adjusted to 4.7 ms (Figure 20b), which is the sum of the
mechanical resonance period (2.2 ms) and the lag time to cause the phase transition (2.5 ms), the
ringing can be suppressed completely. As shown in Figure 20c, too slow pulse exhibits again the
vibration ringing, which may
may induce
induce the
the “chattering”
“chattering” problem
problem in
in the
the relay.
relay.
Figure 21 shows the unimorph tip displacement degradation under an external load, which
guarantees the 50 µm, minimum displacement to ensure the snap-action, under a couple of tens of
gram force, which needs to operate the snap-action switch.
The new relay is very compact in size (20 ˆ 10 ˆ 10 mm3 ), 1/10 of a conventional electromagnetic
type (20 ˆ 26 ˆ 34 mm3 ), and is operated by a pulse voltage, which provides a significant energy
saving. The relay is turned ON at 350 V with 4 ms rise time, and turned OFF at ´50 V, as depicted
in Figure 22. Figure 23 demonstrates dynamical response of the latching relays of shape memory
ceramic type (Figure 23a), and a conventional electromagnetic coil type (Figure 23b). The required
duration of the drive voltage 600 V is only 3.4 ms (maximum 10 mA) for the ceramic, while it is 16 ms
for the electromagnetic type (i.e., 1/5 energy saving, compared with the electromagnetic type!). Note
also the response time (to realize ON) difference of only 1.8 ms in the ceramic from 8.0 ms in the
electromagnetic coil type, which is originated from the actuator response speed (i.e., electromagnetic
actuators are slow!). The existing chattering problem in the antiferroelectric ceramic for 11 ms will be
solved technically in the snap-action switch design improvement.
Actuators 2016, 5, 11
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20 of 23
19 of 22
Figure 20.
20. Dynamical
Dynamical response
response of
of the
the tip
tip displacement
displacement of
the shape
shape memory
memory unimorph
0.063
Figure
of the
unimorph with
with yy =
= 0.063
under
various
drive
pulse
conditions
for
the
rise
time
of
(a)
3
ms,
(b)
4.7
ms,
(c)
6
ms.
under various drive pulse conditions for the rise time of (a) 3 ms, (b) 4.7 ms, (c) 6 ms.
Figure 21 shows the unimorph tip displacement degradation under an external load, which
guarantees the 50 μm, minimum displacement to ensure the snap-action, under a couple of tens of
gram force, which needs to operate the snap-action switch.
The new relay is very compact in size (20 × 10 × 10 mm3), 1/10 of a conventional electromagnetic
type (20 × 26 × 34 mm3), and is operated by a pulse voltage, which provides a significant energy
saving. The relay is turned ON at 350 V with 4 ms rise time, and turned OFF at −50 V, as depicted in
Figure 22. Figure 23 demonstrates dynamical response of the latching relays of shape memory
ceramic type (Figure 23a), and a conventional electromagnetic coil type (Figure 23b). The required
duration of the drive voltage 600 V is only 3.4 ms (maximum 10 mA) for the ceramic, while it is
16 ms for the electromagnetic type (i.e., 1/5 energy saving, compared with the electromagnetic type!).
Note also the response time (to realize ON) difference of only 1.8 ms in the ceramic from 8.0 ms in
the electromagnetic coil type, which is originated from the actuator response speed (i.e.,
electromagnetic
actuators
are slow!).
Theshape
existing
chattering
problem
the antiferroelectric
Figure 21. Tip
displacement
of the
memory
unimorph
(y = in
0.063)
as a function of ceramic
the
for
11
ms
will
be
solved
technically
in
the
snap-action
switch
design
improvement.
external
load.
Actuators 2016, 5, 11
20 of 22
Figure 21. Tip displacement of the shape memory unimorph (y = 0.063) as a function of the external
load. Figure 22. Basic ON/OFF function of the latching relay using the shape memory ceramic.
Figure 22. Basic ON/OFF function of the latching relay using the shape memory ceramic.
Actuators 2016, 5, 11
Figure 22. Basic ON/OFF function of the latching relay using the shape memory ceramic.
(a)
21 of 23
(b)
Figure
23. Dynamical
type; and
Figure 23.
Dynamical response
response of
of the
the latching
latching relay:
relay: (a)
(a) shape
shape memory
memory ceramic
ceramic type;
and
(b)
electromagnetic
coil
type.
(b) electromagnetic coil type.
7.2. Mechanical Clamper
7.2. Mechanical Clamper
A mechanical damper suitable for microscope sample holders has been constructed by
A mechanical damper suitable for microscope sample holders has been constructed by combining
combining a 20-layer shape memory stacked device (y = 0.0635) and a hinge-lever mechanism as
a 20-layer shape memory stacked device (y = 0.0635) and a hinge-lever mechanism as shown in
shown in Figure 24 [29]. Application of a 1 ms pulse voltage of 200 V can generate the longitudinal
Figure 24 [28]. Application of a 1 ms pulse voltage of 200 V can generate the longitudinal displacement
displacement of 4 μm in the 4 mm-thick multilayer device, leading to 30 μm tip movement of the
of 4 µm in the 4 mm-thick multilayer device, leading to 30 µm tip movement of the hinge lever after
hinge lever after the displacement amplification. Stable grip was verified for more than several hours.
the displacement amplification. Stable grip was verified for more than several hours. This gripper is
This gripper is useful for optical and/or electron microscope sample stages, because no continuous
useful for optical and/or electron microscope sample stages, because no continuous electric voltage
electric voltage application is required during the experiment. To release the sample, small reverse
application is required during the experiment. To release the sample, small reverse pulse voltage is
pulse voltage is applied on the multilayer actuator.
applied on the multilayer actuator.
Figure 24.
24. Construction
Construction of
of the
the mechanical
mechanical damper
damper using
using aa shape
shape memory
memory multilayer
multilayer device.
device.
Figure
8. Summary
Antiferroelectrics (AFE) can exhibit a shape memory function controllable by electric field,
with huge isotropic volumetric expansion (0.26%) associated with the AFE to Ferroelectric (FE) phase
transformation. Small inverse electric field application can realize the original AFE phase. The response
speed is quick (2.5 ms). In the Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )1-y Tiy ]0.98 O3 (PNZST) system, the shape memory
function is observed in the intermediate range between high temperature AFE and low temperature
FE, or low Ti-concentration AFE and high Ti-concentration FE. In the AFE multilayer actuators
(MLAs), the crack is initiated in the center of a pair of internal electrodes under cyclic electric field,
rather than the edge area of the internal electrodes in normal piezoelectric MLAs. The two-sublattice
polarization coupling model was proposed to explain: (1) isotropic volume expansion during the
AFE-FE transformation; and (2) piezoelectric anisotropy. We introduced latching relays and mechanical
clampers as possible unique applications of shape memory ceramics.
Actuators 2016, 5, 11
22 of 23
The study of shape memory antiferroelectric materials was initiated by our group in the
1980s–1990s. Further investigations on the improvement of the induced strain magnitude, the stability
of the strain characteristics with respect to temperature change, mechanical strength and durability
after repeated driving are required to produce practical and reliable devices. This category of ceramic
actuators, as well as piezoelectric/electrostrictive materials, will be a vital new element in the next
generation of “micro-mechatronic” or electromechanical actuator devices.
Conflicts of Interest: The author declares no conflict of interest. All the data used in the paper belong to
Kenji Uchino, and include reference information for the previously reported figures.
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