Session B32: Focus Session: Dielectric, Ferroelectric, and Piezoelectric Oxides - Relaxors, Nanostructures, and Morphotropic Phase Boundary

Symmetry determination of piezoelectric (1-x)Pb(Mg$_{1/3}$Nb$_{2/3})$O$_{3}$-xPbTiO$_{3}$ single crystal near morphotropic phase boundary

The symmetry of (1-x)Pb(Mg$_{1/3}$Nb$_{2/3})$O$_{3}$-xPbTiO$_{3}$ single crystal (PMN-xPT) is investigated at the morphotropic phase boundary with x=31{\%}. The XRD result indicates that the average symmetry of annealed PMN-31{\%}PT single crystal is in close agreement with the monoclinic M$_{C}$ (Pm) phase, but with strain. The local symmetry of PMN-31PT are then investigated at three different directions of [001]$_{C}$, [010]$_{C}$, [011]$_{C}$ and [111]$_{C}$ by using convergent electron diffraction (CBED) technique with a probe size of 2 nm. The dynamical theory is used to simulate the CBED patterns for the reported phases of PMN-xPT. The CBED results show that significant deviations of the experimental CBED patterns from the simulations. The deviations in the CBED results are considered as a result from a local distortion induced by the different B cations of Mg$^{2+}$, Nb$^{5+}$ and Ti4$^{+}$ The local symmetry of PMN-31{\%}PT is not defined by any reported phases and the symmetry of PMN-31{\%}PT seen in X-ray diffraction is the average of local structures   

Phase diagram and skin effect of the relaxor ferroelectric $(1-x)$Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$+$x$PbTiO$_3$

We revisit the phase diagram of the relaxor ferroelectric PMN-$x$PT using neutron powder diffraction to test suggestions that defects in the oxygen stoichiometry and/or strain affect the ground state crystal structure. Two identical sets of PMN-$x$PT powders were prepared with $x=0.10$, 0.20, 0.30, and 0.40. One set was annealed in air at 873K for 2h. For a given composition and temperature the same structural phase is observed in each set, thus indicating that the effects of strain and oxygen vacancies are minimal. But the distortions measured in the annealed samples are consistently smaller than those in the as-grown samples. In addition, the average grain size of the annealed samples is approximately twice that of the as-grown samples ($1.2\pm0.6$ microns vs $0.6\pm0.3$ microns). This result is consistent with a skin effect in which Ti-poor bulk crystals show significantly smaller distortions than do powders of the same composition. The diffraction patterns for both the as-grown and annealed samples with compositions $x=0.10$ and $x=0.20$ are best refined using the monoclinic $Cm$ space group, which agrees with recent speculation by Singh et al., Phys. Rev. B {\bf74}, 024101 (2006).   

Model for Relaxor Ferroelectrics

We consider a model of a lattice made of polarizable unit cells with local and dipole interactions and disorder. Without disorder, it is well known that dipole interactions alone do not lead to ferroelectricity. We show by a cluster expansion in disorder and by a high temperature series expansion that in the presence of sufficient disorder, the model with both local and dipole interactions has locally correlated regions at low temperatures but has no long-range order. We compare our results with measurements of the static and dynamic structure factor by neutron scattering~[1]. References: 1. S.N.~Gvasaliya, B.~Roessli, R.A.~Cowley, P.~Huber, S.~Lushnikov, J. Phys.: Condens. Matter 17 4343 (2005).   

Molecular Dynamics Studies of Structure, Dynamics and Dielectric Response in a Relaxor Ferroelectric

Since the first synthesis of the classic PbMg$_{1/3}$Nb$_{2/3}$O$_3$ (PMN) material in 1961, relaxor ferroelectrics have been the subject of ongoing experimental and theoretical investigation due to their fundamental scientific interest and their importance in technological applications. We use atomistic molecular dynamics simulations to study relaxor behavior in the 0.75PMN-0.25PT material. Even for a fairly small simulation size of 1000 atoms, the system exhibits frequency dispersion and deviation from the Curie-Weiss law typical of relaxor materials. Analysis of the time autocorrelation functions for individual atoms allows us to identify the Nb atoms with a high concentration of neighboring Ti atoms as the nucleation sites for the relaxor behavior. This is due to the higher coupling between the cation displacements induced by the presence of overbonded oxygen atoms. We also analyze local structure and dynamics in PMN-PT using instantaneous, time-averaged and frequency resolved pair distribution functions (PDF). We find that dynamic Pb and Ti off-centering is present even in the paraelectric phase, below $T_b$ the rate of growth of local Pb off-centering increases, followed by the freezing in of the local displacement direction at an intermediate temperature $T_c$ and a transition to a ferroelectric-like phase at $T_f$. Thus there is a sequence of four phases, PE, dynamic relaxor, mixed dynamic and frozen phase, and the non-ergodic frozen relaxor phase. We identify the average instantaneous local cation off-centering as the order parameter for the dynamic relaxor phase, and the time-averaged local cation off-centering as the order parameter for the two lower-temperatures relaxor phases. Examination of the dynamic PDF data reveals the shape and the range of correlation between the cation displacements. We also show that the relaxor phase is characterized by the appearance of strong nearest-neighbor correlation between the off-center displacements along the Cartesian directions.   

First-principles calculations of finite temperature Sc and O NMR parameters in Pb(Sc$_{2/3}$W$_{1/3}$)O$_3$

Understanding the dynamics of complex relaxor ferroelectrics is important to characterizing their large electromechanical coupling. Preliminary NMR measurements of Sc electric-field-gradients (EFG) in Pb(Sc$_{2/3}$W$_{1/3}$)O$_3$ (PSW) show a strong temperature dependence in the range $T = 250 - 330$ K. To understand this behavior, we use the first-principles GIPAW\footnote{C.~\ J.~\ Pickard and F.~\ Mauri, Phys. Rev. B {\bf 63}, 245101 (2001);} method within the Quantum Espresso (QE) package\footnote{P. Giannozzi et al., Journal of Physics: Condensed Matter {\bf 21}, 395502 (2009)} to calculate $^{45}$Sc and $^{17}$O chemical-shifts and EFG tensors. To study finite temperature effects, we incorporate the thermal expansion of the lattice and sample thermal disorder, using the phonon degrees of freedom. As in our previous studies of perovksites,\footnote{D.~\ L.~\ Pechkis, E.~\ J.~\ Walter, and H.~\ Krakauer. J.~\ Chem. Phys. {\bf 135}, 114507 (2011); {\em ibid.} {\bf 131}, 184511 (2009)} we show that the $^{17}$O chemical shifts in PSW also exhibit a linear correlation with the nearest-neighbor B-O bond length.   

Critical Slowing Down in the Relaxor Ferroelectric K$_{1-x}$Li$_{x}$TaO$_{3}$(KLT)

In this report, we illustrate an essential characteristic of mixed crystals such as KLT: the strong dependence of their macroscopic properties on the spatial distribution of the mixed ions in the crystal. As a prototypical relaxor ferroelectric, KLT exhibits a large dielectric constant, low frequency dispersion and a broad relaxation peak. Lithium randomly substitutes for potassium and, because of its smaller size, moves off-center in one of six possible $<$100$>$ directions thus forming a local dipole. Correlations between these dipoles lead to the appearance of Polar Nanodomains (PNDs), the size and polarization of which depend on local density fluctuations or type of distribution of the Li ions (random homogeneous or locally clustered). The dielectric constant of two KLT crystals with almost identical average Li concentrations displays two radically different behaviors, which can be traced to two very different distributions of the lithium ions in the two crystals. This is particularly striking of the critical behaviors in the two separate crystals. A first order structural transition is observed in one crystal but critical slowing down is observed in the other. The type of spatial distribution present in each crystal can be inferred from the dielectric results.   

EIT-like effect due to hetero-phase oscillations near the phase transition of relaxor ferroelectrics

We report the observation of a remarkable ``transparency window'' in the dielectric resonant absorption spectrum of the relaxor ferroelectric K$_{1-x}$Li$_{x}$TaO$_{3 }$(KLT) in the vicinity of its weakly first order transition. This phenomenon is shown to be conceptually similar to the electro-magnetically induced transparency (EIT) phenomenon observed in certain atomic vapors. In KLT however, it reveals the presence of hetero-phase (cubic-tetragonal) fluctuations and provides unique information on the nature and mechanism of the phase transition in relaxors.   

Temperature evolution of the linear birefringence in striated single crystals of KTa$_{1-x}$Nb$_{x}$O$_{3 }$(KTN)

We report the temperature evolution of a special linear birefringence in 3 crystals of KTa$_{1-x}$Nb$_{x}$O$_{3 }$(KTN), with x=0.155, 0.27 and 0.36 respectively, upon approaching the cubic-tetragonal phase transition. This birefringence, which is in violation of crystalline symmetry conditions, is caused by growth striations in the crystal that give rise to local strain and result in an average uniaxial behavior due to the photoelastic effect. Simultaneously, the set of parallel striations acts as a volume phase grating which can produce diffracted beams. Upon approaching the phase transition, the measured birefringence displays a rapid temperature dependence which is due to the formation of polar nano-domains (PND). These are incipient tetragonal uniaxial domains preferentially oriented with their c-axis perpendicular to the plane of the striations. As the birefringence increases, the diffraction efficiency unexpectedly decreases, indicating that the phase grating amplitude is occluded by the PND formation. The striation pattern is well defined in the 15.5{\%} crystal, more diffuse in the 36{\%} crystal, and there are no obvious striations in the 27{\%} crystal. Experimental results are presented and a simple phenomenological model for the birefringence behavior is proposed and discussed.   

Strain effects on Coherent Epitaxial Ferroelectric Pb(Zr0.2Ti0.8)O3

A comprehensive study of strain coupling to ferroelectricity in coherent epitaxial Pb(Zr0.2Ti0.8)TiO3 thin films is presented. The epitaxial strain variants are obtained by growing coherent PZT thin films on three different substrates, SrTiO3, DyScO3 and GdScO3 by pulsed laser deposition technique. The strain sensitivity of remnant polarization is found to be less in the epitaxial strain variants with larger tetragonality. Despite the fact that the tetragonality of PZT is more sensitive to the epitaxial strain than that of BaTiO3, the polarization-strain coupling is weaker in PZT than in BTO. These results underpins that the strong sensitivity of ferroelectricity to epitaxial strain is not a universal characteristic of complex oxide ferroelectrics and may depend on the intricate details of individual material systems.   

Structural and Ferroelectric Properties of Epitaxial ultrathin PbZr$_{0.52}$Ti$_{0.48}$O$_{3 }$Films Prepared on La$_{0.67}$Sr$_{0.33}$MnO$_{3}$/(LaAlO$_{3})_{0.3}$(Sr$_{2}$AlTaO$_{6})_{0.7}$ Substrates

The existence of ferroelectricity in ultrathin films open the possibility to further miniaturize devices based on FE materials, i.e. ferroelectric tunnel junctions take advantage of tunnel electroresistance effect. We have fabricated epitaxial PbZr$_{0.52}$Ti$_{0.48}$O$_{3 }$thin and ultrathin films using pulsed laser deposition on (001) on La$_{2/3}$Sr$_{1/3}$MnO$_{3}$/(LaAlO$_{3})_{0.3}$(Sr$_{2}$AlTaO$_{6})_{0.7}$ (LSMO/LSAT) substrates. The film thickness ranged between 3 to 100 nm. X-ray diffraction analysis revealed PZT and LSMO films are (00l) oriented perovskite structure. Atomic force microscopy of the PZT/LSMO(40nm)/LSAT structures show the surface is smoothness, densely packed, and free of cracks. The surface roughness on a 3 x 3 $\mu $m$^{2}$ area of the 100 nm and 3 nm thick films is $\sim $2 nm and $\sim $0.3 nm respectively. Well defined ferroelectric loop was observed in Pt/PZT(100nm)/LSMO(40nm)/LSAT structure with a remanent polarization $\sim $38 $\mu $C/cm$^{2}$ and a coercive field $\sim $80 kV/cm. The ferroelectric nature of the PZT ultrathin films (7--3 nm) was characterized using piezo force microscopy, a clear contrast between up and down ferroelectric domains was observed after writing positive and negative polarized in 2x2 $\mu $m$^{2}$ and 1x1 $\mu $m$^{2}$ areas respectively.   

Ab Initio Investigation of Free Energy Landscape near Morphotropic Phase Boundary

For pressure induced morphotropic phase boundary (MPB) in PbTiO3, although ground states have been investigated intensely, the overall free energy landscapes and so the transition paths are never systemically considered by ab initio method. Also there is little information about the oxygen octahedral tilts in monoclinic (M), orthorhombic (O) and triclinic (Tri) structures. In this work, in order to obtain the free energy landscapes, necessary oxygen octahedral tilts are considered not only in tetragonal (T) and rhombohedral (R) but also in M, O and Tri. According to the landscapes in the vicinity of MPB, firstly, the T-R transition path is not unique, since T-R and T-O-R paths have similar barriers; secondly, T-R barrier is ultra-low. Those explain the easy polarization rotation and so the ultra-high piezoelectric constant. Also, ground states are obtained by considering the oxygen octahedral tilts in T, R, M and O, and our results consist with the conclusion by J. Frantti, et.al in 2007. The fully relaxed M is actually T or R, which is indicated by the free energy landscapes. The ground state goes directly from T to R through MPB.   

Measuring the curves of dispersion for dielectrics using a low-energy laser and a thermal source of radiation

We propose a simple and accurate method for finding curves of dispersion for solid and liquid dielectrics using polarized light reflected by their surface near the Brewster angle. A precision of 0.0001 for indices of refraction can be achieved from running a parabolic fit through the experimental data for the parallel component of the reflectance normalized to the total reflectance in a region only 15 degrees wide around the Brewster angle [1]. This precision allows accurate measurements of small changes in the indices of refraction that cannot be measured with other existing methods. For example, such changes can be produced by the temperature variation on the dielectric surface. In this paper we show that using a low-energy laser beam (such as the inexpensive red diode laser of 650 nm) and a thermal (blackbody) source of radiation one can easily generate precise curves of dispersion in the visible and ultraviolet spectrum for any dielectric transparent to this radiation. Our interpretation is based on the Lorentz model for the interaction between dipoles on the dielectric surface and the incident optical field. The average thermal energy of the blackbody source can be associated to an effective frequency. This thermal energy contributes to a higher frequency of oscillation of these dipoles and can be measured as a slight increase in the value of the refractive index. The project was partially supported by the McNair Scholars Program and STAIRSTEP-NSF-DUE grant{\#} 0757057. [1] Bahrim C and Hsu W-T, 2009 \textit{Am. J. Phys.} \textbf{77} (4) 337-343.