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STRUCTURAL PECULIARITIES IN NORMAL AND RELAXOR
FERROELECTRIC CRYSTALS
M. Rotha, E. Mojaeva, E. Dul'kina and M. Tseitlinb
Faculty of Science, The Hebrew University of Jerusalem, Jerusalem
91904, Israel
b
The Research Institute, University Center of Judea and Samaria, Ariel
44837, Israel
a
Structural transformations in two groups of ferroelectrics, normal
and relaxor-type, have been studied mainly by measuring the associated
phase transformation temperatures. Normal ferroelectrics have been
represented by the KTP-family single crystals grown by the top-seeded
solution method from self-fluxes, with an emphasis in the RbTiOPO4
compound. The Curie temperatures of the latter show a spread from 770
to 800°C, pointing at the correlation between the crystal stoichiometry
and the flux chemical composition. Moreover, each growth sector in a
nominally pure crystal exhibits its specific Curie temperature. This
effect has been discussed in terms of the diverse incorporation
mechanisms of the stoichiometric components or native defects into
specific crystallographic faces during growth. The acoustic emission
(AE) method, in parallel with the dielectric measurements, has been
used to study a variety of phase transitions in prototypical relaxors, e.g.
Pb(Zn1/3Nb2/3)O3 and Pb(Mg1/3Nb2/3)O3 and their solid solutions with
PbTiO3, including the AE anomaly associated with the "waterfall effect"
and ergodic-to-nonergodic phase transformation. We show that
determination of the high-temperature Néel points of multiferroic
Pb(Fe2/3W1/3)O3-xPbTiO3 solid solutions by AE is straightforward. By
combination with strain, dielectric and electric polarization
measurements, monitoring of AE allows to assign the complex sequence
of phase transitions also in lead-free Na0.5Ba0.5TiO3-xBaTiO3 relaxor
compounds.
1. Introduction
Ferroelectricity is a physical property of materials whereby it
exhibits a spontaneous electric polarization, the direction of which can
be switched between equivalent states by the application of an external
122
electric field [1]. The prefix ferro-, meaning iron, is used to describe the
property despite the fact that most ferroelectric materials do not have
iron in their lattice. Regular, or normal, ferroelectrics are key materials
in microelectronics [2,3]. Their excellent dielectric properties make
them suitable for electronic components such as tunable capacitors and
memory cells. The permittivity of normal ferroelectrics, such as MTiO 3
(M = Pb, Ba), is not only tunable but commonly also very high in
absolute value, especially when close to the phase transition temperature
which is the displacive type (cations shift against anions).
A quite different behavior is exhibited by relaxor ferroelectrics
which have broad and temperature dependent relaxation distribution
functions resulting in a diffuse frequency dependent dielectric constants
[4,5]. Relaxor ferroelectrics exist in a number of crystal structures,
including tungsten bronzes, such as M1-xBaxNb2O6 (M = Sr, Pb) and
prototype disordered perovskites, (A'A")BO3 (A'A'' = Pb1-3x/2Lax or
K1-xLix and B = ZryTi1-y or Ta) or A(B'B")O3 (A = Pb and B'B" =
Zn1/3Nb2/3, Mg1/3Nb2/3, In1/2Nb1/2 or ZrxTi1-x). The last type of perovskites
is most extensively studied due to their technological advantages. There,
symmetry breaking caused by intermediate scale ordering of different
valence and size ions on the octahedral B'B" sites occurs already in the
high-temperature paraelectric phase. The long range order is thus
broken, and nanodomain polar structure, or polar nanoregions (PNR), is
established at temperatures far above the maximum permittivity peak.
The onset of a local polarization can be determined by measuring the
index of refraction [6], electrostictive strain [7], inverse dielectric
permittivity [4] and lately also acoustic emission (AE) [8]. In addition,
X-ray diffraction and neutron scattering techniques allow to monitor the
majority of zero field and electric-field-induced phase transitions and
thus structural changes in relaxor ferroelectrics [9], but the phenomenon
of dielectric relaxation in these materials is still meagerly understood.
All ferroelectrics are required by point symmetry considerations
(lack of inversion) to be also piezoelectric and pyroelectric. The
combined properties of memory, piezoelectricity, and pyroelectricity
make ferroelectric capacitors very useful, e.g. for sensor and mechanical
actuator applications [7]. Also, electro-optic modulators that form the
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backbone of modern optical communications and laser Q-switching [10]
are made of ferroelectric crystals. Many of such crystals exhibit also
large optical nonlinearity, which makes them an important class of
materials for application in laser systems utilizing frequency conversion,
such as second harmonic generation (SHG) and optical parametric
oscillations (OPO), including periodically poled structures [11,12]. In
terms of materials of this type, in biggest demand are high quality KTP
(KTiOPO4) crystals and their isomorphs belonging to the KTP-family of
high-temperature ferroelectric compounds with the general composition
of MTiOXO4, where M = {K, Rb} and X = {P, As}.
All KTP-family crystals exhibit large optical nonlinearity, high
laser damage threshold and excellent thermal stability. However,
apparent variations in the properties of these crystals have been observed
and related to the variation of their chemical composition and defect
distribution during growth from self-fluxes [13-15]. It has been
demonstrated that both in KTP and RTP (RbTiOPO4) crystals the
ferroelectric transition, or Curie, temperature (Tc) may vary in a broad
range depending on the type of the self-flux and the solute concentration
in the flux. Moreover, the Tc varies from the seed area to the periphery
of the crystal indicating that there is a continuous change in the
composition of the solidified mass. The considerable variation in the
Curie temperatures in all KTP-family compounds is explained in terms
of the broad existence range of their solid solutions, which has been
explicitly demonstrated for KTP [16].
In the present work we examine the structure/properties
relationship in both normal ferroelectrics, such as the KTP-family
compounds, and a broad family of lead-based and lead-free relaxor
ferroelectrics. In particular, with regard to the former, the variation of
maximal dielectric permittivity value at Tc in RTP crystals grown from
high-temperature self-fluxes will be discussed in terms of changes in the
flux chemical composition during growth. A peculiar dependence of the
Tc values on the RTP crystal morphology will be elucidated as well. The
phenomenology of the temperature dependent maxima in the dielectric
permittivity of relaxor ferroelectrics has been studied by means of
acoustic emission in addition to dielectric spectroscopy. We show that
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the AE measurement is a powerful nondestructive and inexpensive
method for studying the evolution of phase transformations in relaxor
ferroelectrics, starting from the high-temperature nucleation of PNRs
responsible for the relaxor properties.
2. KTP-family crystals – normal ferroelectrics
2.1 Crystal structure
The four more extensively studied KTP-family crystals are
KTiOPO4 (KTP), RbTiOPO4 (RTP), KTiOAsO4 (KTA) and RbTiOAsO4
(RTA). They have identical crystal structures at room temperature. The
orthorhombic structure (a  b  c,  =  =  = 90°) of KTP belongs to
the space group Pna21 [17]. There are 64 atoms in a unit cell in the
KTP-type lattice. This 64-atom group separates into four subgroups of
16 atoms each, and within each such subgroup there are two
inequivalent K (Rb) sites, two inequivalent titanium sites, two
inequivalent P(As) sites and ten inequivalent oxygen sites. Two of the
latter oxygen sites represent bridging ions located between titanium ions,
while the other eight are contained in PO4 (AsO4) groups where they link
one Ti and one P (As) ion. One 16-atom subgroup can be transformed
into one of the other three subgroups by simple transformations within
the unit cell. The [010] projection of the structure with respect to RTP is
shown in Fig. 1.
Fig. 1. A view of the RTP crystal structure along the b-axis direction.
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The physical structure of the KTP-type crystal contains helical
chains of distorted TiO6 octahedra running parallel to the <011>
crystallographic directions and forming a 2-dimensional network in the
b-c plane. The TiO6 octahedra are linked at two corners by alternately
changing long and short Ti(1)-O bonds which are commonly assumed as
primarily responsible for the optical nonlinearity. The other four oxygen
ions around Ti4+ are parts of the PO4 (or AsO4) tetrahedra. These
tetrahedra bond the --Ti--O--Ti--O-- networks into a 3-dimensional
covalent (TiOPO4) framework. The crystal structure is completed by K +
(or Rb+) ions occupying cavities, or cages, within this framework. These
monovalent ions are either 8- or 9-coordinated with respect to oxygen,
and they are denoted as Rb(1) and Rb(2) respectively. Each Rb atom is
asymmetrically coordinated by O atoms in the two inequivalent sites,
and at a short distance along the b-direction from each Rb atom there is
a void similar in size and coordination to the Rb site. The voids are
termed "hole sites", h(1) and h(2) [18], and they are pseudosymmetrically related to the Rb(2) and Rb(1) sites respectively, as it is
apparent from Fig. 1. At high temperatures, above the transition to the
ferroelectric (Pna21) to paraelectric (centrosymmetric) Pnan phase, the
Rb(1) and h(1) as well as Rb(2) and h(2) sites merge along the bdirection into positions halfway between the room-temperature Rb sites
and their associated holes sites. In the case of KTP, the K(1) cage has a
volume 25% smaller than the K(2) cage. This may explain why the
larger Rb atoms substituting for K atoms in mixed KxRb1-xTiOPO4
crystals occupy preferentially the larger K(2) sites, independently of the
Rb incorporation mechanism, by crystal growth or ion-exchange [19].
2.2 Ionic Conductivity
According to Fig. 1, there are additional consequences to the quite
different environments for the Rb(1) and Rb(2) atoms. The Rb(2)O9
cage forms a channel, parallel to the c-axis, which runs through the
entire crystal structure and along which the Rb(2) atoms are expected to
move relatively freely. On the other hand, the Rb(1) atom is constrained
from a similar motion by the confinement of the P(1)O4-Ti(2)O6 chain
which restricts its movement along the c-axis. Although the Rb(1)O8
cage forms a channel along the a-axis, the Rb(1) atom does not show
any significant movement along this axis even at high pressures.
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Therefore, when The KTP-family crystals are described as a quasi-onedimensional superionic conductors, with the conductivity 33 being
much larger than 11 and 22 [11], mainly K(2) or Rb(2) ions can diffuse
through cavities combined into channels along the c-axis direction via a
vacancy mechanism. The concentration of potassium/ rubidium
vacancies, or the degree of deviation from stoichiometry, depends on the
crystal growth method and on specific growth parameters that will be
discussed below.
2.3 Growth kinetics and Curie temperatures
KTP and its isomorphs decompose on heating before melting and,
therefore, can be grown only from solutions. Use of self-fluxes
introducing no foreign impurities has become the optimal choice [20].
The solvents then are potassium or rubidium phosphates or arsenates of
the types: K6 (K6P4O13), Rb4 (Rb4P2O7), K5 (K5As3O10), etc. containing
all ingredients except for titanium. Consequently, dilute solutions are
relatively richer in the M- and X-ions, and the crystals are more
stoichiometric in terms of these components. It is generally believed that
the PO4 tetrahedra are basic building blocks of the KTP structure, which
makes the phosphorus nonstoichiometry unlikely. On the contrary, the
existence of potassium [21] and rubidium [22] vacancies in KTP and
RTP respectively has been demonstrated.
We have grown a series of relatively small (< 1 cm3) KTP, RTP, KTA
and RTA crystals by the top-seeded solution growth (TSSG) method
[12,23] from high-temperature K6, K4, R6 and R4 self-fluxes containing
different starting concentrations of the (KTP, KTA) and (RTP, RTA)
solutes respectively. The Tc values of the crystals have been measured
using a standard dielectric technique described elsewhere [13], and Fig.
2 shows their dependencies on the solute concentration in the flux. The
trend-lines expanded for the two arsenate crystals do not represent
accurate slopes, since only a few growth experiments have been carried
out, at small solute concentrations. There is a difficulty in obtaining such
crystals with reliably changing compositions from highly concentrated
solutions, namely at higher growth temperatures, due to the arsenic
evaporation. New experiments attempting to suppress the arsenic
evaporation are underway. Yet, the common rule for all isomorphs is
quite apparent: the more dilute is the solution the higher is the Curie
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temperature, which reflects the fact that at smaller solute concentrations
the crystal solidifies from solutions richer primarily in potassium or
rubidium ions with respect to titanium.
The results of Fig. 2 imply that when a large KTP-type single
crystal grows out, it becomes progressively richer in M-ions. The
concentration gradient is building up and it freezes in, since the diffusion
coefficient of even the smaller K+-ion is low at growth temperatures
[24]. The diffusion coefficients of Rb+-ions in RTP and RTA are
expected to be even lower due to their larger ionic radii. The degree of
the variation of physical properties depends also on the specific
parametrs of crystal growth, as will be discussed with respect to RTP in
the following section.
Curie temperature (°C)
1000
950
900
RTA
KTA
850
KTP
RTP
800
750
0
0,2
0,4
0,6
0,8
1
1,2
Solute concentration in flux (g / g flux)
Fig 2. Curie temperature dependence on solute concentration in the K6 or Rb6
flux for four KTP isomorphs.
2.4 The case of RTP
The ferroelectric transition temperature, Tc, of a variety of RTP
samples were determined using crystals grown from four selective
rubidium phosphate self-fluxes (with R = [Rb]/[P]) varying from 1.25 to
2) and different initial concentrations of the solute. The details of crystal
growth and Tc measurements (capacitance versus temperature)
128
techniques were described elsewhere [14, 15]. By definition, the first
and last to crystallize portions of the crystal had solidified from fluxes
with lower and higher Rb concentrations in the liquid respectively. The
latter should be richer in the stoichiometric Rb component and have a
higher Tc value. A direct proof of this assumption is given in Fig. 3(a),
where the Curie temperatures of the top and bottom parts of a 400 g RTP
crystal pulled on a [100]-oriented seed from an R6 flux are given. The
specific separation between the Tc values (782 and 787°C hereby)
depends not on the crystals weight, but rather on the relative solute
content in the solution. This is the case of a sample cut from a single
growth sector.
Fig 3. Capacitance versus temperature curves: (a) of the top and bottom
parts of an RTP crystal grown by the TSSG method with pulling on an Xoriented seed and cut from the (100) growth sector; (b) of samples cut from
crystal areas around the (201)/(100) growth sector boundary
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A peculiar effect is revealed when the sample is cut at a boundary
between two growth sectors. Fig. 3(b) shows the resulting C = C(T)
curve which is composed of two peaks featuring two Curie temperatures.
In this case, Pt electrodes cover areas containing both sectors. In general,
RTP crystals like other KTP-family crystals contain fourteen growth
sectors displayed through four types of well developed facets: 2{100},
4{110}, 4{011} and 4{201}, in its typical morphological habit as
shown in Fig. 4(a). Fig. 4(b) shows schematically the structure of main
growth sectors in a RTP crystal grown by the TSSG method with pulling
on an X-oriented seed. Samples for Tc measurements are machined from
Z-cut slices shown in the figure. Apparently, the Pt electrode covers two
sectors, and thus a double-peaked C = C(T) characteristic is obtained.
Fig. 4. (a) Typical habit of a solution-grown RTP-type crystal; (b) schematic
representation of growth sectors developed in RTP crystals grown on Xoriented seeds; Z-cut slices may contain two growth sectors, which can be
buried below the Pt electrode.
The results described above imply that the variation of the Curie
temperature, or of the chemical composition of RTP crystals, as a
130
function of the flux chemical composition must be studied for each
growth sector separately. In Fig. 5, the results for three growth sectors,
of the {100}, {011} and {201} types, are presented separately. The
nearly linear dependencies obtained are in full similarity with the KTP
case [13]: a) the lower is the RTP concentration, the higher is the T c of
the crystal. Thus, a higher Curie temperature corresponds to a higher
overall concentration of the Rb-ions in the solution and, therefore, to
higher rubidium content in the crystal. Naturally, in course of RTP
crystal growth, the solution becomes gradually enriched in rubidium.
The important practical consequence of this behavior is that a rubidium
concentration gradient builds up in the as-grown crystal. This gradient is
not averaged out during the cool-down stage, since the diffusion
coefficient of Rb-ions is presumably very small.
Fig. 5. Curie temperatures as a function of RTP concentration in the R4 flux
measured for three growth sectors: {100}, {011} and {201}.
The observed span of Tc values, from 775 to 795°C, at least for the
R4 self-flux, is much narrower than that of KTP (880-980°C). In
addition, the slopes of the linear dependencies are shallower in the case
of RTP. We presume, therefore, that the overall extent of change of Rbstoichiometry in RTP crystals is essentially smaller than the
corresponding variation of K-stoichiometry in KTP crystals. The main
distinctive feature of RTP crystals is that they exhibit abrupt “jumps” in
the Curie temperature over boundaries between any pair of
simultaneously solidifying growth sectors of different types, as can be
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deduced from Fig. 5. In KTP, only deliberately doped crystals may show
double peaks in the C(T) characteristic with an electrode spreading over
two adjacent growth sectors [15]. In the case of RTP, residual metal
impurities, mainly potassium, may originate from the 3N Rb2CO3 used
in the synthesis of the starting materials. In order to check the effect, we
have grown an RTP crystal with a deliberate potassium doping.
Chemical analysis has shown that the sample prepared for Curie
temperature measurements contains 2,300 ppm of K-ions. Its C = C(T)
characteristic is shown in Fig. 6 together with a similar sample
fabricated of an undoped RTP crystal (electrodes covering the
(100)/(011) growth sector boundary have been applied to both samples
in a similar fashion). Obviously, the potassium doping introduces some
disorder into the RTP crystal lattice causing a shift (increase) in the
Curie temperature. A very slight increase in the peak separation can be
explained by the existence of two distinct Rb sites in the
noncentrosymmetric room-temperature RTP phase, Rb(1) and Rb(2),
that have an oxygen coordination of VIII and IX respectively, and the
selective occupation of these sites by the K- and Rb-ions as explained
above (Fig. 1).
25
(011)
784C
(100)
Capacitance, nF
20
782,9C
15
Pure RTP
785,6C
783,8C
10
5
0
780
K-doped RTP
782
784
786
788
790
Temperature, °C
Fig. 6. Curie temperature shift in K-doped RTP crystal.
The existence of double peaks in the C(T) curves of nominally
pure RTP crystals, with a separation of over 10°C between the Curie
temperatures on a single sample, cannot be explained by the presence of
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trace impurities. We recall also that the growth temperatures are 100200°C higher than the Tc s in our experiments, and the crystals solidify
in the pseudosymmetric mmm phase, where the R(1) and R(2) sites are
symmetrically identical [25]. However, the likely diverse formation
mechanisms of native defects within the various growth facets at high
temperatures may cause a variation in the statistical distribution of the
Rb-ions between the Rb(1) and Rb(2) sites during cooling through the
ferroelectric phase transition. The defects may be associated not only
with the rubidium and associated oxygen vacancies, but also with other
stoichiometric components, namely titanium and phosphorus ions. Initial
attempts to identify any deviation from the stoichiometric composition
of these components using the electron-microprobe technique did not
contribute positive results. More deliberate experiments involving hightemperature X-ray diffraction, electron paramagnetic resonance and
electron-nuclear double resonance are being planned.
3. Relaxor ferroelectrics
In the following we will address the properties of relaxor
ferroelectrics exhibiting a complex perovskite structure described by the
general formula A(B',B")O3, where both types of B-site cations have
octahedral coordination, and the A-site cations are at the centers of
cavities formed by eight BO6 octahedra, as shown in Fig. 1. In the high
temperature no-polar paraelectric (PE) phase, similar to that of normal
ferroelectrics, the B-site disordered regions have a single- perovskite
structure of Pm3m symmetry with a unit cell constant of ~ 4 Å. Upon
cooling below Td, the Burns temperature [5], the crystal transforms into
the ergodic relaxor (ER) state in which polar regions of nanometer scale
(PNR's) with randomly distributed directions of dipole moments appear.
133
Fig. 7. Fragment of cubic perovskite-type structure. Polarization directions for
the rhombohedral, orthorhombic and tetragonal distortions are indicated.
On further cooling, the dynamics of PNRs slows down enormously
and at a low enough temperature, Tf (typically hundreds degrees below
Td), the PNRs in the canonical relaxors become frozen into a nonergodic
state, while the average symmetry of the crystal still remains cubic. The
nonergodic relaxor (NR) state existing below Tf can be irreversibly
transformed into a FE state by a strong enough external electric field.
This is an important characteristic of relaxors which distinguishes them
from typical dipole glasses. Upon heating the FE phase transforms to the
ER one at the temperature Tc which is very close to Tf. In many relaxors
the spontaneous (i.e. without application of electric field) phase
transition from the ER into a low-temperature FE phase still occurs at Tc
and thus the NR state does not exist.
3.1 Acoustic Emission in PZN-PT
PZN-xPT, or Pb(Zn1/3Nb2/3)O3 (PZN) and its solid solutions with
PbTiO3 (PT), with x up to 15%, are prototypical A(B',B")O3-class
relaxor ferroelectrics. Like in other relaxors, the PNR's develop a static
polarization and undergo a local ferroelectric phase transition, while the
other parts of the crystal remain in the paraelectric phase. The incoherent
phase boundaries between the growing in size ferroelectric domains and
the paraelectric matrix are apt to generate appreciable mechanical
stresses at the PNR boundaries. In order to minimize the accumulated
134
elastic energy, the small domains may break down into twinned domains
for stress accommodation. This twinning produces changes in the
internal strain field accompanied by generation and movements of
dislocations at the PNR-matrix boundary, giving rise to elastic waves
propagating within the crystal, or to AE around Twf as shown for various
PZN-xPT compositions in Fig. 8. The AE experimental technique is
based on detecting the acoustic wave signal using a piezoelectric sensor
attached to the sample, and it is described in detail elsewhere [26]. When
formed through high-temperature microscopic ferroelectric phase
transition, as suggested above, the static polar nanodomains are expected
to continue to exist below the macroscopic first-order phase transition at
Tc (most likely, by heterogeneous nucleation on PNR's and growth [5]).
AE count rate, s
-1
20
PZN- 4.5PT
PZN- 6.0PT
PZN- 7.0PT
15 PZN- 9.0PT
PZN-12.0PT
Twf
10
Tc
5
0
400
420
440
460
480
500
520
540
Temperature, K
Fig. 8. AE activity as a function of temperature during cooling of PZN-xPT
crystals (x-values are indicated in the figure).
Two groups of AE peaks can be distinguished in Fig. 8. The lower
temperatures group comprises peaks varying from 435 to 465 K with an
increasing PT-content. They correspond to the paraelectric (cubic) to
ferroelectric (rhombohedral/orthorhombic or monoclinic/ tetragonal)
phase transition temperatures, Tc, dependent on the PT-content in
135
agreement with recent phase diagram [27]. Generally, the bursts of AE
at Tc are explained by formation of a ferroelectric domain-twin structure
due to relaxation of mechanical stresses on the boundary between the
paraelectric and ferroelectric phases [26]. In addition, Fig. 8 features a
higher temperature group of peaks which are densely spaced around 500
K (from 498 to 507 K) and are on the average more intense than the
regular Tc peaks. Apparently, the anomalous AE activity appearing at
500 K in the macroscopically cubic paraelectric phase is very weakly
dependent of the titanium addition. This is presumably not accidental. It
is characteristic also of the so-called “waterfall" phenomenon that has
been discovered in PZN-type relaxor ferroelectrics [28]. The "waterfall"
is manifested in a precipitous drop of the transverse optical (TO) phonon
branch (soft mode characteristic of normal ferroelectrics) into the lower
transverse acoustic (TA) branch, which occurs at reduced wave vector
values less than qwf ~ 0.2 Å-1. It has been initially proposed that the large
damping of TO modes is due to the presence of PNR’s which prevent
the propagation of phonons with wavelength larger than the size of the
PNR’s, and thus the wave vector qwf is the measure of the average size
of the PNR’s [29].
A detailed study of the PZN-xPT system has been carried out by LaOrauttapong et al. [30,31] using diffuse elastic neutron scattering. The
width of the diffuse scattering peak, which is related to , the correlation
length, is shown to provide a measure of the average PNR size. They
find that a relatively rapid increase in  begins at a similar characteristic
temperature T*, which marks the onset of condensation and eventual
orientational (polarization) freezing of the PNRs on further temperature
decrease. A parallel rise in the diffuse scattering intensity, which is
proportional to the spontaneous electric polarization, indicates an
increase in the net local polarization within the PNR. They also find that
T* is composition-dependent (PZN: ~ 450 K, PZN-4.5%PT: ~ 500 K,
PZN-9%PT: ~ 550 K). However, a closer examination of the
temperature dependences of the correlation lengths reveals that at 500 K
they are of the order of c = 25-30 Å for all three compositions in
scattering around the (011) and (100) Bragg reflections. If we presume
that this average size of the PNRs is associated with a critical volume for
local ferroelectric phase transitions, due to electrostrictive coupling
136
between strain and polarization, the existence of a nearly constant T wf ~
500 K can be understood. In fact, the cubic-to-tetragonal phase
transformation at 500 K upon zero-field cooling has been detected by
neutron diffraction measurements in PZN-8.0PT [32].
To summarize out results, we reiterate that strong AE bursts have
been observed in PZN-xPT (x = 0-12%) crystals at a practically constant
temperature Twf  500 K for all values of x studied. Twf corresponds to
the characteristic 500 K anomaly at which the PNR-related "waterfall"
effect has been discovered at a wave vector qwf ~ 0.2 Å-1 from the zone
center in the cubic phase of PZN-xPT crystals. We suggest that the AE
activity generated at the Twf temperature originates from local
microscopic ferroelectric phase transitions within the growing in size
PNRs when the latter reach a critical volume corresponding to the
correlation length c ~ 25-30 Å, and thus qwf = 2/c ≈ 0.2 Å-1. Strong
AE registered at 500 K implies martensite-like cubic-tetragonal
ferroelectric transitions, typically followed by twinning. A sample
calculation of the electrostrictive strain balance at the PNR boundary has
been carried out for PZN-8.0PT to verify the feasibility of head-to-tail
90°-twinning observed experimentally in PMN-xPT on a nanoscale [33].
Similar studies on PMN-xPT and other systems are underway, and the
AE method may prove itself as a useful nondestructive diagnostic tool
for studying the PNR-related phase transitions in relaxor ferroelectrics.
3.2 Nonergodic phase of PMN relaxor
Pure PbMg1/3Nb2/3O3 (PMN) is intermediate between dipolar
glasses and normal ferroelectrics and exhibits both substitutional and
charge disorder. As with other relaxors, the key to the understanding of
their nature is their local structure. At any temperature between 1000
and 4 K the average symmetry of PMN is cubic. This is true even on the
micrometric scale. Yet, experiments on the nanometric scale have shown
that the local structure is different from the average structure, and
randomly oriented polar nanoclusters appear below the Burns
temperature, Td ≈ 600 K [5]. (The size of the nanoclusters is smaller
than 500 Å, since they are not seen on the profile of the X-ray diffraction
lines.) Further cooling results in an increase of the number and/or size of
these regions down to ~ 350 K, temperature at which these regions begin
to interact and grow in size. Finally, freezing of the dipole dynamics
137
occurs at Tf ~ 215 K, temperature below which the system is in a socalled dipole glass state. This evolution is well reproduced by the
unifying “spherical random bond-random field” model [34] in which a
cluster-glassiness results from dipolar disorder and frustrated
interactions, combined with quenched random fields arising from space
charges associated with chemical inhomogeneities.
The low-temperature metastable mesostructure can be destroyed by
an electric field. Indeed, as evidenced in the past by X-ray diffraction
and NMR measurements [35], application of a dc electric field to PMN
induces a first-order ferroelectric phase transition. It was also
demonstrated that cooling of PMN in an external field above a threshold
value (Eth ≈ 1.7 kV/cm) along <111> directions gave rise to a
rhombohedral ferroelectric phase [36]. Therefore, initiation of an AE
study of such structural transformation seemed appropriate.
We have measured the AE activity of a (111)-cut 330.3 mm3
PMN sample with electric fields E > Eth, 3 or 4 V/cm, applied to it
during both cooling and heating within the 100-300 K temperature
range. The results are shown in Fig. 9(a). With an electric field of 3
kV/cm, AE signals were detected near 203 K on cooling and near 210 K
on heating (temperature hysteresis T = 7K). At a higher field, 4 kV/cm,
AE signals of similar activity were detected near 202 K on cooling and
near 215 K on heating (a larger temperature hysteresis, T = 13K). Our
results for the field of 3 kV/cm are depicted also within the E-T phase
diagram [36] shown in Fig. 9(b). Clearly, with E > Eth an electric-fieldinduced phase transition takes place around the critical temperature, Tc.
The AE results under the field cooling (FC) regime indicate that
small polar domains appear in the paraelectric phase on temperature
decrease, with a continuous growth in size through displacement of the
domain boundaries. The AE signal is to be associated with the relaxation
of stresses between these domains of different polarization orientations
as they grow into macrodomains at Tc similarly to the martensitic phase
transition.
In proof, 207Pb NMR measurements [35] also show that in the FC
regime a first-order induced phase transition is observed, and it is
associated with an orientational percolation of ferroelectric polar clusters
with polarizations parallel to the <111> directions. Moreover, according
to the NMR data, about 50% of the crystal remains in the glassy matrix
138
state along with the occurrence of a macroscopic ferroelectric phase. The
latter is, in fact, imbedded in a matrix of pre-existing polar nanoregions.
Fig. 9. (a) AE of a PMN crystal during thermal cycling under 3 and 4 kV/cm
bias electric fields. (b) Field-temperature phase diagram from Ref. [20]. FE, PE
and GL correspond to ferroelectric, paraelectric and glassy phases respectively;
field cooling (FC) and zero-field-cooling (FaZFC) paths are shown with arrows;
the characteristic 203 and 210 K temperatures associated with AE signals are
marked by stars in the field-induced FE region.
It is noteworthy that if the sample is cooled down in the zero-field
regime (ZFC), no AE activity or NMR signal are detected. During the
ZFC, the new phase appearing into the nonergodic state consists of ~ 70
nm size nanometric polar domains [37] which do not transform into
macrodomains. In this case the scattered elastic waves clearly drop to
values within the experimental noise, and no AE is detected. When
electric field is switched on after the ZFC, the number of these domains
increases with time, whereas their size remains constant. In this process
again, no AE is expected. When the number of such domains (embryos)
is sufficient, the phase transition occurs at t =  by percolation, where 
is the incubation time. The reason why no AE is detected even at t »  is
still unclear. One possible explanation is that the relaxation between the
domain boundaries is absent due to the percolation nature of the break of
ergodicity and phase transition to the nonergodic state. Alternative
possibilities have been also considered [38]. In addition, comparison of
139
AE behavior in course of the FC and ZFC processes shows that the
relaxation of stress is path dependent.
3.3 Multiferroic relaxors
Lead iron-tungstate, Pb(Fe2/3W1/3)O3 (PFW), was discovered as a
multiferroic compound almost five decades ago [39], but it was less
studied than other Pb(B'B")O3-type relaxors. The distinctive feature of
pure PFW is that it undergoes a very low distortion with an angle of less
than 0.01°, and transforms from a cubic to pseudocubic or rhombohedral
phase, for ceramics and single crystals respectively, below the dielectric
maximum temperature Tm and remains in this phase down to 10 K. PFW
contains paramagnetic Fe3+ (3d5) ions at the B'-sites with an occupancy
of 66.7%, which leads to the existence of a weak
ferromagnetic↔antiferromagnetic Néel phase transition at TN1 = 20K
and antiferromagnetic↔paramagnetic phase transition at TN2 = 350K in
single crystals [40]. Its multiferroic behavior is explained by coexistence of anomalies in the dielectric constant and the dissipation
factor at TN1. Addition of titanium (PFW-xPT solid solutions) shifts Tm
to higher temperatures; the frequency dispersion vanishes, and the phase
transition gradually transforms from relaxor-type to normal ferroelectric,
i.e. Tm steadily changes to Tc. The room temperature MPB compositions
are 0.2  x  0.37 in ceramics and 0.25  x  0.35 in crystals. The
coexistence of pseudocubic and tetragonal (due to PT) phases within the
MPB in ceramics was experimentally verified by a transmission electron
microscopy, which inferred a core-shell structure of ceramics grains,
where the core of the grains was Ti-rich and the shell was W-rich with
respect to the bulk composition [41]. Titanium addition to B perovskite
sites dilutes the concentration of Fe3+ ions; therefore, the
antiferromagnetic temperature TN2 decreases with rising Ti
concentration. However, different dependences of TN2 on PT content are
observed in single crystals and ceramics. For the former, a small
decrease in the TN2 is observed with the increase of x (TN2 = 274 K at x
= 0.27), yet TN2 decreases more rapidly, from 350 K (x = 0) to 170 K (x
140
= 0.2), and above x = 0.25 no antiferromagnetic phase transition is
distinguished from magnetic hysteresis loops measurements [42].
The high-temperature properties of PFW-xPT solid solutions have
been poorly investigated, since they typically exhibit extrinsic
conductivity (probably associated with oxygen vacancies and variable
iron valence), which deteriorates dielectric data near and above room
temperature. Even the Burns temperature, Td, has not been determined
as well as other phase transformation events. Thus, the AE method
becomes indispensable for studying the structural transformations in
these materials. Fig. 10 shows the traces of AE activity in 8 mm
diameter and 2 mm thick ceramic PFW-xPT samples (x = 0, 0.25 and
0.37) taken during heating and cooling above room temperature. Three
sets of peaks have been observed. The first set around 640-660 K
corresponds to the Td, where PNRs nucleate and begin to grow upon
cooling. Td slightly increases, whereas the AE count rate decreases, with
PT concentration. The latter implies a lower concentration of PNRs the
PFW-xPT material gradually transform into an ordinary ferroelectric
with rising x. The Td values near 650 K are similar to the Td of 620 K in
the PMN relaxor thus confirming the similarity in nature of the PNRs in
the PFW and PMN materials.
Fig. 10. AE activity in PFW-xPT ceramics versus temperature; solid and open
symbols mark AE during heating and cooling respectively.
141
The location of the maxima of the second set peaks at around
520 K is independent on the composition. This peak corresponds to both
the temperature of anomalies observed in the Raman spectra of pure
PFW [43] and the "waterfall effect", or the 500 K AE anomaly in PZNxPT and PMN described above in paragraph 3.1. The AE signal due to
elastic strain between static polar clusters and nonpolar matrix
presumably appears at a specific temperature where the PNRs attain the
critical size necessary for the local martensitic ferroelectric phase
transition by twinning.
The AE response observed in the third, 330–350 K, temperature
interval is the most interesting one because it reveals the magnetic phase
transitions to the antiferromagnetic phase in pure PFW (TN2 ≈ 350 K).
The AE signal can be explained by the creation of strain as a
consequence of magnetostriction in magnetic domains during the
antiferromagnetic phase transition undergoing without any structural
changes. The 20 K hysteresis emphasizes the first order character of the
antiferromagnetic phase transition. What is surprising at the first sight,
the AE peaks near 350 K also for x > 0. The most probable explanation
lies in the core-shell structure of the PFW-xPT ceramic grains described
above. Since the Ti dopant is incorporated primarily in the grain core,
one can expect two separate magnetic phase transitions in the cores and
the shells, whereas the Néel temperature in the shells is independent of
the PT concentration. Moreover, the PT content in the cores will be
higher than its nominal concentration in ceramic sample. Therefore, a
stronger dependence of the TN2 on x is expected in ceramics than in
crystals, which has been observed experimentally [42]. The second
possible explanation is that the PFW-xPT ceramics always contains a
certain amount of pure PFW grains, and the coexistence of pseudo-cubic
and tetragonal phases has been indeed observed in X-ray diffraction
measurements [43]. In both cases, the compositional dependence (x) of
the high-temperature Néel anomaly at TN2 corresponding to the
antiferromagnetic phase transition in the cores of ceramic grains of
PFW-xPT is expected. This effect has been clearly observed by AE in
PFW-0.25PT and PFW-0.37PT samples, which is discussed in detail
elsewhere [44].
142
3.4 Lead-free relaxors
All relaxor materials discussed above as well as the most famous
Pb(Zr1-xTix)O3 compound, which is broadly used for high performance
actuators and transducers, contain lead. However, the toxicity of PbO
and its high vapor pressure during processing have stimulated an
increasing demand for environment-friendly materials. Sodium bismuth
titanate, Na0.5Bi0.5TiO3 (NBT) and its solutions with other perovskites,
e.g. K0.5Na0.5NbO3 (KNN) or BaTiO3 (BT), are considered to be good
candidates to replace lead-based piezoelectrics. NBT is rich in phase
transitions: cubic paraelectric (PE) ↔ tetragonal ferroelastic (FEa) ↔
trigonal I antiferroelectric (AFE) ↔ trigonal II ferroelectric (FE) [45].
Other phase diagram studies show that the room temperature
ferroelectric phase is rhombohedral [46]. Yet most of the existing
controversy is associated with the trigonal I phase and its
antiferroelectric state assignment [47]. Both the (T) dependences and
electric polarization curves are frequently smeared. Therefore, the use of
complementary AE measurements is very useful.
We have applied the AE method to studying phase transitions in
0.94NBT-0.06BT (NBT-6BT) single crystals, namely crystals with the
most interesting (for applications) composition corresponding to the
morphotropic phase boundary between trigonal (rhomohedral) NBT and
tetragonal BT. The crystals were grown by slow cooling of hightemperature fluxes. The details of crystal growth as well as of the
dielectric and AE measurements are given elsewhere [48]. Room
temperature electric field cycling of the NBT-6BT polarization, strain
and AE show that the crystal is a ferroelectric with a coercive field of
about 3 kV/mm.
Figure 1 shows the results of concurrent measurements of the
temperature dependencies of the crystal's dielectric constant and AE
activity upon heating and cooling. The most notable feature of the e(T)
dependence is the high value, but a very broad maximum around 380°C.
A much sharper and also pronounced AE response indicates that there is
a first order phase transition with a thermal hysteresis of about 25°C.
Based on the published NBT-xBT phase diagram [46], it can be
attributed to the transition from the cubic paraphrase to the tetragonal
ferroelectric phase in pure NBT. Much smaller AE signals and minor
cusps in the  = (T) dependences just below 300°C may correspond to
143
the NBT-6BT composition. This implies that the grown crystals are
highly inhomogeneous in terms of composition, with NBT being the
dominant crystal phase.
Fig. 11. Temperature dependences of the dielectric constant and AE activity of
an NBT-6BT single crystal (up and down triangles – heating and cooling
respectively).
In order to verify that the trigonal I phase is antiferroelectric, we
have measured the AE response of our sample at 140°C (temperature
where this phase exists) with an electric field turned on and off. The
results are shown in Fig. 12. Clearly, on loading at increasing |E|,
pronounced AE responses are detected at E = ±0.85 kV/mm, which are
due to the field-induced AFE→FE transition. A similar response
corresponding to the reverse FE→AFE transition is observed upon the
field unloading at ±0.7 kV/mm, leading to an apparent transition field
hysteresis.
144
Fig. 12. AE activity during the electric field induced AFE ↔ FE phase
transition at 140°C.
Obviously, the detection of the AFE ↔ FE transition by AE is
much more precise than by conventional electrical measurements, which
often yield only a distorted hysteresis loop, leaving plenty of leeway in
the determining the phase at a given T or E.
3. Conclusions
Investigation of phase transition temperatures in both normal and
relaxor ferroelectrics provides important information on their properties
related structural transformations. With regard to the KTP-family
superionic ferroelectric crystals, it has been shown that the actual Curie
temperature values measured are defined primarily by the alkali ion
stoichiometry in the crystal. In the case of RTP, the rubidium
stoichiometry turns out to depend on the growth sector, and this effect is
not associated with trace impurities present in the melt, but rather with
the existence of two different types of rubidium sites in the crystal.
The AE method is shown to be a powerful tool for studying the
relaxor-based systems, including the being on demand lead-free
materials. Monitoring of AE allows to detect the structural changes
accompanied by strain relief due to all macroscopic phase transitions
(thermally activated or induced by the application of an electric field)
145
and, especially, due to the formation and interaction of PNRs that are
responsible for the exceptional piezolelectric and electrostrictive
properties of relaxor ferroelectrics.
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