Neutron and x-ray scattering studies on relaxor ferroelectric systems Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$ (PZN), Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$ (PMN), and their solid solutions with PbTiO$_3$ (PT) have shown that inhomogeneities and disorder play important roles in the materials properties. Although a long-range polar order can be established at low temperature - sometimes with the help of an external electric field; short-range local structures called the ``polar nano-regions'' (PNR) still persist. Both the bulk structure and the PNR have been studied in details. The coexistence and competition of long- and short-range polar orders and how they affect the structural and dynamical properties of relaxor materials are discussed.
The phase diagram of the Pb(Mg1/3Nb2/3)O3 and PbTiO3 solid solution (PMN-xPT) indicates a rhombohedral ground state for x < 0.32. X-ray powder measurements by Dkhil et al. show a rhombohedrally split (222) Bragg peak for PMN-10%PT at 80 K. Remarkably, neutron data taken on a single crystal of the same compound with comparable q-resolution reveal a single resolution-limited (111) peak down to 50 K, and thus no rhombohedral distortion. Our results suggest that the structure of the outer layer of these relaxors differs from that of the bulk, which is nearly cubic, as observed in PZN by Xu et al.
X-ray and neutron scattering studies of the lead-based family of perovskite relaxors PZN-$x$PT and PMN-$x$PT have documented a highly unusual situation in which the near-surface region of a single crystal can exhibit a structure that is different from that of the bulk when cooled to low temperatures. The near-surface region, or "skin" can also display critical behavior that is absent in the crystal interior, as well as a significantly different lattice spacing. By varying the incident photon energy, and thus the effective penetration depth, x-ray measurements indicate a skin thickness of order…
In this review we address some of the experimental challenges found in the x-ray diffraction characterization of the low-symmetry phases recently discovered in the PZT, PZN-PT and PMN-PT piezoelectric systems around their morphotropic phase boundaries. In particular, we discuss the need for special care in the preparation of powder samples made from single crystals in order to avoid degradation and peak-broadening effects.
High-energy x-ray diffraction experiments peformed on rhombohedral (1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3(PZN-xPT) crystals with x= 4.5 and 8% show that an electric field applied along the [001] direction induces the tetragonal phase, as proposed by Park and Shrout. Our experiments reveal that in 4.5PT such phase change occurs via a third phase with monoclinic symmetry, MA, which is observed at intermediate field values. This is in agreement with first-principles calculations by Fu and Cohen predicting the rotation of the polarization between the rhombohedral and tetragonal phases in this material. A d…
Diffuse neutron scattering is a valuable tool to obtain information about the size and orientation of the polar nanoregions that are a characteristic feature of relaxor ferroelectrics. In this paper, we present new diffuse scattering results obtained on Pb(Zn1/3Nb2/3)O3 (PZN for short) and (1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3(PZN-xPT)single crystals (with x=4.5 and 9%), around various Bragg reflections and along three symmetry directions in the [100]-[011] zone. Diffuse scattering is observed around reflections with mixed indices, (100), (011) and (300), and along transverse and diagonal directions o…
We performed x-ray diffraction studies on a series of (1-$x$)Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$-$x$PbTiO$_3$ (PZN-$x$PT) single crystals with different incident photon energies, and therefore different penetration depths. Our results show that outer-layers of $\sim 10$ to 50 $μ$m thick are present in all samples. The structure of those outer-layers is different from that of the inside of the crystals, by having much greater (rhombohedral) distortions. With increasing $x$, rhombohedral-type lattice distortions develop, both in the outer-layer and the inside.
We report high $q$-resolution neutron scattering data on PMN-$x$PT single crystals with $x=20%$ and 27%. No rhombohedral distortion occurs in the 20PT sample for temperatures as low as 50 K. On the other hand, the 27PT sample transforms into a rhombohedral phase below T$_C \sim 375$ K. Our data provide conclusive evidence that a new phase with an average cubic lattice is present in the bulk of this relaxor system at low PT concentration, in which the ferroelectric polarization and lattice distortion are decoupled. The rhombohedral distortion is limited to the outermost tens of microns of the c…
We report measurements of the neutron diffuse scattering in a single crystal of the relaxor ferroelectric material 95.5%Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$-4.5%PbTiO$_3$ (PZN-4.5%PT). Our results suggest that the nanometer scale structure in this compound exhibits both $<100>$ and $<110>$ polarizations, which contribute to different portions of the total diffuse scattering intensity. These contributions can be distinguished by the differing responses to an electric field applied along [001]. While diffuse scattering intensities associated with $<110>$ (T2-type) polarizations show little to no change…
PbZr_{1-x}Ti_xO_3 (PZT) and Pb(Mg_{1/3}Nb_{2/3})_{1-x}Ti_xO_3 (PMN-$x$PT) are complex lead-oxide perovskites that display exceptional piezoelectric properties for pseudorhombohedral compositions near a tetragonal phase boundary. In PZT these compositions are ferroelectrics, but in PMN-xPT they are relaxors because the dielectric permittivity is frequency dependent and exhibits non-Arrhenius behavior. We show that the nanoscale structure unique to PMN-xPT and other lead-oxide perovskite relaxors is absent in PZT and correlates with a greater than 100% enhancement of the longitudinal piezoelectr…
A review is given of the phonon anomalies, which have been termed ``waterfalls,'' that were recently discovered through a series of neutron inelastic scattering measurements on the lead-oxide relaxor systems PZN-xPT, PMN, and PZN. We discuss a simple coupled-mode model that has been used successfully to describe the basic features of the waterfall, and which relates this unusual feature to the presence of polar micro-regions.
High energy (67 keV) x-ray diffuse scattering measurements were performed on single crystals of Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$-$x$PbTiO$_3$ (PZN-$x$PT). A novel technique was developed to map out the diffuse scattering distribution in all three dimensions around a large number of Bragg peaks simultaneously, taking advantage of the almost flat Ewald sphere of the high energy x-ray beam. For $x=0, 4.5%$, and 8%, the results are very similar, indicating same type of correlations of polarizations in these compounds. Our results show that the diffuse scattering intensity consists of six $<110>$ rod-…
Neutron elastic diffuse scattering experiments performed on Pb(Zn1/3Nb2/3)O3 (PZN) and on its solid solution with PbTiO3(PT), known as PZN-xPT, with x=4.5% and 9% around many reflections show that diffuse scattering is observed around reflections with mixed indices in the transverse and diagonal directions only. From the width of the diffuse scattering peak a correlation length is extracted. In PZN, we have reported that the diffuse scattering is more extended in the transverse than in the diagonal directions. In the present work, the results show that the addition of PT leads to a broadening …
We review some of the current research on two of the ultra-high piezoelectric relaxors Pb(Mg1/3Nb2/3)O3 (PMN) and Pb(Zn1/3Nb2/3)O3 (PZN). The discovery of a monoclinic phase in Pb(Zr1-xTix)O3 (PZT) in 1999 by Noheda et al. forced a reassessment of the structural symmetries found near the morphotropic phase boundary in PZT, as well as in the PbTiO3 (PT) doped systems PZN-PT, and PMN-PT. All three systems are now known to have nearly identical phase diagrams that exhibit a rhombohedral-monoclinic-tetragonal structural sequence with increasing PbTiO3 concentration. The dynamical properties of the…
A key to optimizing the growth of the new single-crystal relaxor ferroelectrics is resolving basic questions concerning their structural properties and energetics. We report on initial first-principles total energy and force calculations, examining the energetics of local order in PZN type relaxors.
We report measurements of the neutron diffuse scattering in a single crystal of the relaxor ferroelectric material 95.5%Pb(Zn1/3Nb2/3)O3-4.5%PbTiO3 (PZN-4.5%PT). We show that the diffuse scattering at high temperatures has a quasielastic component with energy width $\agt$ 0.1 meV. On cooling the total diffuse scattering intensity increases, but the intensity and the energy width of the quasielastic component gradually diminish. At 50 K the diffuse scattering is completely static (i.e.the energy width lies within the limits of our instrumental resolution). This suggests that the dynamics of the…
We report measurements of the neutron diffuse scattering from a single crystal of the relaxor ferroelectric Pb(Zn_1/3Nb_2/3)O_3 doped with 8% PbTiO_3 (PZN-8%PT) for temperatures 100 K < T < 530 K and electric fields 0 kV/cm < E < 10 kV/cm. The diffuse scattering is strongly suppressed transverse to the (003) Bragg peak at 400 K for E = 2 kV/cm applied along the [001] direction. However, no change in the diffuse scattering is observed transverse to (300), even for field strengths up to 10 kV/cm. Thus the application of an external electric field in the tetragonal phase does not produce a macros…
It is now well established that the unique properties of relaxor ferroelectrics are due to the presence of polar nanoregions (PNR's). We present recent results from Neutron and Raman scattering of single crystals of PZN, PZN-xPT, and PMN. Both sets of measurements provide information on the condensation of the PNR's and on their slow dynamics, directly through the central peak and, indirectly, through their coupling to transverse phonons. A comparative analysis of these results allows identification of three stages in the evolution of the PNR's with decreasing temperature: a purely dynamic sta…
The microstructure and phase transition in relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 (PMN) and its solid solution with PbTiO3 (PT), PMN-xPT, remain to be one of the most puzzling issues of solid state science. In the present work we have investigated the evolution of the phase symmetry in PMN-xPT ceramics as a function of temperature (20 K < T < 500 K) and composition (0 <= x <= 0.15) by means of high-resolution synchrotron x-ray diffraction. Structural analysis based on the experimental data reveals that the substitution of Ti^4+ for the complex B-site (Mg1/3Nb2/3)^4+ ions results in the develop…
We have examined the local structure of PMN-PT and PZN-PT solid solutions using density functional theory. We find that the directions and magnitudes of cation displacement can be explained by an interplay of cation-oxygen bonding, electrostatic dipole-dipole interactions and short-range direct and through oxygen Pb-B-cation repulsive interactions. We find that the Zn ions off-center in the PZN-PT system, which also enables larger Pb and Nb/Ti displacements. The off-centering behavior of Zn lessens Pb-B-cation repulsion, leading to a relaxor to ferroelectric and a rhombohedral to tetragonal ph…
We have applied a shell model potential developed by fitting first principle results to describe the behavior of the relaxor-ferroelectric PMN-xPT as function of concentration. The solid solution exhibits three regions with different characteristics according to Ti content in agreement with the experiments. At low Ti the polar and structural disorder dominates, and the symmetry is rhombohedral. The intermediate region is ferroelectric with easy rotation of the polarization direction, and the symmetry appears orthorhombic. Finally, in the high Ti content region, the solid solution adopts a ferr…
The relaxors Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PZN) and Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) have very similar properties based on the dielectric response around the critical temperature $T_{c}$ (defined by the structural transition under the application of an electric field). It has been widely believed that these materials are quite different below $T_{c}$ with the unit cell of PMN remaining cubic while in PZN the low temperature unit cell is rhombohedral in shape. However, this has been clarified by recent high-energy x-ray studies which have shown that PZN is rhombohedral only in the skin …
Inelastic neutron scattering study of the perovskite relaxor ferroelectric PZN:8%PT elucidates the origin of the previously reported unusual kink on the low frequency transverse phonon dispersion curve (known as "waterfall" effect). We show that its position depends on the choice of the Brillouin zone and that the relation of its position to the size of the polar nanoregions is highly improbable. The observation is explained in the framework of a simple model of coupled damped harmonic oscillators representing the acoustic and optic phonon branches.
Recently, a new orthorhombic phase has been discovered in the ferroelectric system Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-xPT) for x= 9%, and for x= 8% after the application of an electric field. In the present work, synchrotron x-ray measurements have been extended to higher concentrations, 10% <= x <=15%. The orthorhombic phase was observed for x= 10%, but, surprisingly, for x>= 11% only a tetragonal phase was found down to 20 K. The orthorhombic phase thus exists only in a narrow concentration range with near vertical phase boundaries on both sides. This orthorhombic symmetry (MC-type) is in contras…
Synchrotron x-ray powder diffraction measurements have been performed on unpoled ceramic samples of (1-x)PbMg(1/3)Nb(2/3)O3-xPbTiO3 (PMN-xPT) with 30%<= x<= 39% as a function of temperature around the morphotropic phase boundary (MPB), which is the line separating the rhombohedral and tetragonal phases in the phase diagram. The experiments have revealed very interesting features previously unknown in this or related systems. The sharp and well-defined diffraction profiles observed at high and intermediate temperatures in the cubic and tetragonal phases, respectively, are in contrast to the bro…
Local inhomogeneities known as polar nanoregions (PNR) play a key role in governing the dielectric properties of relaxor ferroelectrics - a special class of material that exhibits an enormous electromechanical response and is easily polarized with an external field. Using neutron inelastic scattering methods, we show that the PNR can also significantly affect the structural properties of the relaxor ferroelectric Pb(Zn1/3Nb2/3)O3-4.5%PbTiO3 (PZN-4.5%PT). A strong interaction is found between the PNR and the propagation of sound waves, i.e. acoustic phonons, the visibility of which can be enhan…
We have performed molecular dynamics simulations using a shell model potential developed by fitting first principles results to describe the behavior of the relaxor-ferroelectric (1-x)PbMg1/3Nb2/3O3-xPbTiO3 (PMN-xPT) as function of concentration and temperature, using site occupancies within the random site model. In our simulations, PMN is cubic at all temperatures and behaves as a polar glass. As a small amount of Ti is added, a weak polar state develops, but structural disorder dominates, and the symmetry is rhombohedral. As more Ti is added the ground state is clearly polar and the system …
Temperature dependent studies of the 1/2(hk0) superlattice reflections αspots by synchrotron x-ray scattering measurements were performed in (PMN) and (PMN-xPT) with Ti doping x<0.32 single crystals. Separation of the αspots from the underlying diffuse scattering background allowed studying them as separate entities for the first time. Structure factor calculations have shown that alpha spots constitute the presence of a new kind of anti-ferrodistortive nanoregions (AFR) in the form of fluctuations produced by anti-parallel short-range correlated <110> Pb^2+ displacements. AFR appear to be dif…
We present the evidence of lattice rotation vortices having an average radius of ~7 nm at the monoclinic ferroelectric domain boundary of (1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-xPT, x=0.08). Maps of crystal orientations, domain configurations, symmetry breaking are obtained using scanning convergent beam electron diffraction (SCBED). Such measurements suggest the merging of 2D and 1D topological defects, with implications for domain-switching mechanisms in relaxor ferroelectric crystals, and the possibility of a new form of nanoscale ferroelectric devices.
We review results obtained from recent neutron scattering studies of the lead-oxide class of perovskite relaxors PMN and PZN. A ferroelectric soft mode has been identified in PMN at 1100 K that becomes overdamped near 620 K. This is the same temperature at which polar nanoregions (PNR) begin to form, denoted by Td, and suggests that a direct connection exists between the soft mode and the PNR. The appearance of diffuse scattering intensity at Td reported by Naberezhnov et al. lends further support to this picture. At lower temperature the soft mode in PMN reappears close to Tc = 213 K (defined…
Relaxor ferroelectrics are difficult to study and understand. The experiment shows that at low energy scattering there is an acoustic mode, an optic mode, dynamic quasi-elastic scattering and strictly elastic scattering as well as Bragg peaks at the zone centre. We have studied the scattering using the TASP spectrometer at PSI and have analysed the data using a model with interactions between the different components particularly to determine the properties of the elastic scattering. The quasi-elastic scattering begins to become significant at the Burns temperature of 620 K. It steadily increa…
We have performed a series of neutron diffuse scattering measurements on a single crystal of the solid solution Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$ (PZN) doped with 8% PbTiO$_3$ (PT), a relaxor compound with a Curie temperature T$_C \sim 450$ K, in an effort to study the change in local polar orders from the polar nanoregions (PNR) when the material enters the ferroelectric phase. The diffuse scattering intensity increases monotonically upon cooling in zero field, while the rate of increase varies dramatically around different Bragg peaks. These results can be explained by assuming that correspondin…
The structure and the dielectric properties of Pb(Zn1/3Nb2/3)O3 (PZN) crystal have been investigated by means of high-resolution synchrotron x-ray diffraction (with an x-ray energy of 32 keV) and dielectric spectroscopy (in the frequency range of 100 Hz - 1 MHz). At high temperatures, the PZN crystal exhibits a cubic symmetry and polar nanoregions inherent to relaxor ferroelectrics are present, as evidenced by the single (222) Bragg peak and by the noticeable tails at the basis of the peak. At low temperatures, in addition to the well-known rhombohedral phase, another low-symmetry, probably fe…
The consideration of oxygen vacancies influence on the relaxors with perovskite structure was considered in the framework of Landau-Ginzburg-Devonshire phenomenological theory. The theory applicability for relaxors is based on the existence of some hidden soft phonon polar mode in them, and its frequency could be zero at some negative temperature TC*. Main attention was paid to PZN-PLZT relaxor described by formula 0.3Pb(Zn1/3Nb2/3)O3-0.7(Pb0.96La0.04(ZrxTi1-x)0.99O3) with x = 0.52, where earlier experimental investigation of oxygen vacancies influence on the polar properties was performed and…
A review is given of recent neutron and x-ray scattering studies of the lead-oxide perovskite relaxor systems Pb(Zn1/3Nb2/3)O3-xPbTiO3 and Pb(Mg1/3Nb2/3)O3-xPbTiO3. X-ray measurements by Noheda et al. have established that these two systems exhibit nearly identical phase diagrams in which a rhombohedral-monoclinic-tetragonal structural sequence takes place with increasing PbTiO3 concentration. Recent high-energy x-ray and neutron measurements on single crystals of PZN and PMN-10PT, however, show that the rhombohedral distortions occur only in the outermost 20 - 40 microns, while the bulk of ea…
Relaxor ferroelectric perovskites are highly polarizable and can exhibit giant coupling between elastic strain and an applied electric field. Here, we report an in situ extended X-ray absorption fine structure (EXAFS) study of a PbZn1/3Nb2/3O3 (PZN) single crystal as a function of the electric field. We show that the strong dipoles in the NbO6 octahedra bonds are aligned along the four \textless{} 011 \textgreater{} directions close to the orientation of the electric field, while a small reversible polar shift occurs for Zn in the direction of the electric field, i.e., positive or negative. Th…
X-ray diffraction studies on a Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$ (PZN) single crystal sample show the presence of two different structures. An outer-layer exists in the outer most $\sim$ 10 to 50~$μ$m of the crystal, and undergoes a structural phase transition at the Curie temperature $T_C\approx410$ K. The inside phase is however, very different. The lattice inside the crystal maintains a cubic unit cell, while ferroelectric polarization develops below $T_C$. The lattice parameter of the cubic unit cell remains virtually a constant, i.e., much less variations compared to that of a typical relaxor…
High-temperature (T) and high-electric-field (E) effects on Pb[(Zn_{1/3} Nb_{2/3})_{0.92} Ti_{0.08}]O_3 (PZN-8%PT) were studied comprehensively by neutron diffraction in the ranges 300 <= T <= 550 K and 0 <= E <= 15 kV/cm. We have focused on how phase transitions depend on preceding thermal and electrical sequences. In the field cooling process (FC, E parallel [001] >= 0.5 kV/cm), a successive cubic (C) --> tetragonal (T) --> monoclinic (M_C) transition was observed. In the zero field cooling process (ZFC), however, we have found that the system does not transform to the rhombohedral (R) phase…
Using neutron elastic and inelastic scattering and high-energy x-ray diffraction, we present a comparison of 40% Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$-60% PbTiO$_{3}$ (PMN-60PT) with pure Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) and PbTiO$_{3}$ (PT). We measure the structural properties of PMN-60PT to be identical to pure PT, however, the lattice dynamics are exactly that previously found in relaxors PMN and PZN. PMN-60PT displays a well-defined macroscopic structural transition from a cubic to tetragonal unit cell at 550 K. The diffuse scattering is shown to be weak indicating that the structural dist…
Brillouin spectroscopic measurements have been carried out on relaxor ferroelectric Pb(Zn1/3Nb2/3)0.85Ti0.15O3 (PZN-PT) single crystal over the temperature range 300-585 K. The longitudinal acoustic phonon begins to soften below 650 K, which is attributed to the Burns temperature (TB). On the other hand, the line width of the longitudinal acoustic (LA) phonon mode exhibits a sharp Landau-Khalatnikov-like maximum and an accompanying anomaly in the LA mode frequency around 463 K, the tetragonal-cubic phase transition temperature (Ttc). In addition, a broad central peak, found below the character…
Strain-mediated magnetoelectric (ME) coupling in ferroelectric (FE) / ferromagnetic (FM) heterostructures offers a unique opportunity for both fundamental scientific research and low power multifunctional devices. Relaxor-ferroelectrics, like (1-x)Pb(Mg1/3Nb2/3)O3-(x)PbTiO3 (PMN-xPT), are ideal FE layer candidates due to their giant piezoelectricity. But thin films of PMN-PT suffer from substrate clamping which substantially reduces piezoelectric in-plane strains. Here we present the first demonstration of low voltage ME coupling in an all-thin-film heterostructure which utilizes the anisotrop…
We report neutron inelastic scattering on single crystal 0.68Pb(Mg1/3Nb2/3O3)-0.32PbTiO3 (PMN-0.32PT), a relaxor ferroelectric material that lies within the compositional range of the morphotropic phase boundary (MPB). Data were obtained between 100 K and 600 K under zero and non-zero electric field applied along the cubic [001] direction. The lowest energy, zone-center, transverse optic phonon is strongly damped and softens slowly at high temperature; however the square of the soft mode energy begins to increase linearly with temperature as in a conventional ferroelectric, which we term the s…
