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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 123 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 124 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. 125 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. 126 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 127 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 129 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 131 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 132 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 330.3 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. 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