Breaking of macroscopic centric symmetry in paraelectric phases of ferroelectric materials and implications for flexoelectricity

A centrosymmetric stress cannot induce a polar response in centric materials; piezoelectricity is, for example, possible only in non-centrosymmetric structures. An exception is meta-materials with shape asymmetry, which may be polarized by stress even when the material is centric. In this case the mechanism is flexoelectricity, which relates polarization to a strain gradient. The flexoelectric response scales inversely with size, thus a large effect is expected in nanoscale materials. Recent experiments in polycrystalline, centrosymmetric perovskites [e.g., (Ba,Sr)TiO3] have indicated values of flexoelectric coefficients that are orders of magnitude higher than theoretically predicted, promising practical applications based on bulk materials. We show that materials with unexpectedly large flexoelectric response exhibit breaking of the macroscopic centric symmetry through inhomogeneity induced by the high temperature processing. The emerging electro-mechanical coupling is significant and may help to resolve the controversy surrounding the large apparent flexoelectric coefficients in this class of materials.

Origins of the macroscopic symmetry breaking in centrosymmetric phases of perovskite oxides

Sina Hashemi Zadeh

Many perovskite materials experience a temperature-driven phase transition at the Curie temperature from a non-centrosymmetric polar ferroelectric phase to a paraelectric phase, where polarization is lost. The paraelectric phase is usually centrosymmetric and therefore non-piezoelectric. However, ferroelectrics still show some forms of electro-mechanical coupling in their paraelectric phase like flexoelectricity, which is not symmetry limited and is practically strong in ferroelectrics. It has been shown that the flexoelectric coefficient of perovskite (Ba0.67,Sr0.33)TiO3 in its centrosymmetric paraelectric state at room temperature is up to three to four orders of magnitude larger than its theoretically predicted values. Such enormous discrepancy demonstrates that either the theory is unable to fully explain the flexoelectric response, or that another electro-mechanical mechanism is playing a role in the apparently large flexoelectric response of the material. It was found that Ba0.60Sr0.40TiO3 (BST6040) samples with apparently large flexoelectric coefficient exhibit symmetry breaking and consequently exhibit forbidden piezoelectric- and pyroelectric-like behavior in its paraelectric phase. In this thesis work, our interest lies in describing and interpreting the conditions where breaking of the symmetry is not associated with the external field nor with the flexoelectricity, but is proper to the material. Origins and mechanism of symmetry breaking were investigated in two different cases: local breaking of centrosymmetry; and macroscopic symmetry breaking. The local breaking of the centrosymmetry may refer to the existence of microscopic polar entities and/or disordered displacement of ions in the unit cell. The global symmetry breaking could be associated with a non-uniform distribution of charged defects and/or the coupling of polar nanoâregions with the strain gradient in the sample. We compared dielectric, elastic, and pyroelectric properties of the Ba1-xSrxTiO3 (BST) family, pure BaTiO3 in perovskite (p-BTO) and hexagonal (h-BTO) forms, and SrTiO3 to study the governing mechanisms of symmetry breaking. In addition, the atomic structure of BST6040 was studied by high resolution scanning transmission electron microscopy for direct evidence of polar regions and to understand their exact nature and origin. According to experimental data, the paraelectric phase of p-BTO shows local and global breaking of nominal centrosymmetricity and possesses microscopic and macroscopic polarizations, which are associated with precursors of the ferroelectric phase ordered by the strain gradient in the sample. On the other hand, h-BTO does not exhibit macroscopic pyroelectric response because the precursors are paraelectric-ferroelastic at room temperature, and therefore non-polar. Studying the material response to dynamic electric field showed that the Rayleigh-like relation, which describes dynamics of domain walls in a random pinning environment, cannot describe the dynamics of polar entities in these materials. Results of our high-resolution atomic studies showed distinct static polar clusters with the average size of few nanometers where A-site, B-site and O ions are displaced from their ideal cubic positions. We believe that all presented experimental data can be consistently explained by the presence of microscopic precursors of the ferroelectric phase and their interaction with the strain gradient in the material.

EPFL2017

Softening and hardening transitions in ferroelectric Pb(Zr,Ti)O3 ceramics

Hysteretic and nonlinear dielectric behaviour in ferroelectric ceramics has been of interest since 1950s, when these materials found application in various electronic devices. Presently, these phenomena concern with important areas of science, technology and engineering. In particular, nonlinearity and hysteresis are the key factors in performance, precision and accuracy of modern devices. Many theoretical and experimental studies have been aimed at understanding the origins of hysteresis and nonlinearity in ferroelectrics. Nowadays, there are several models that describe major contributions to nonlinearity and hysteresis on phenomenological, microscopical or statistical levels. These models have a limited area of applicability due to the complexity of physical processes occurring in real materials. Empirically, hysteresis and nonlinearity in ferroelectrics can be controlled by softening and hardening of the material. This is the case of most widely used ferroelectric, lead zirconate titanate (PZT). The soft compositions possess large electro-mechanical coefficients but also large hysteresis and nonlinearity while the opposite is true for the hard compositions. After fifty years since introduction of these materials, the mechanisms of softening and hardening remain poorly understood. The present study is aimed at a better understanding of the processes leading to hardening and softening of Pb(Zr,Ti)O3 ceramics in order to verify the key principles required for a more universal physical model of hysteresis and nonlinearity. Based on the present state of knowledge, such model should consider domain wall contribution to nonlinear and hysteretic polarization response and at the same time account for hardening and softening of the ferroelectric. For this purpose the well known lead zirconate titanate (PZT) ceramics doped with various concentrations of niobium (soft materials) or iron (hard materials) are chosen as a prototype of the ferroelectric system. The starting hypothesis of the thesis' approach is that the softening and hardening are a result of electrostatic arrangement of charged defects in the ceramic bulk: the hard materials are characterized by the ordered and the soft by disordered defects. The thesis then develops in detail the idea that hardening-softening transitions in a ferroelectric system may occur under the influence of (i) dopants, depending on their type and concentration, (ii) a cyclically applied electric field, (iii) a thermal treatment, and (iv) time. The transition from microscopic order to microscopic disorder is confirmed experimentally using carefully analyzed phenomenological parameters of the macroscopic hysteresis and nonlinearity. Among the nonlinear and hysteretic parameters characterizing the polarization response of a ferroelectric material, some (e.g., third harmonic of polarization) are shown to be particularly sensitive to the softness and hardness of ferroelectric system and thus may serve as the characteristics of ferroelectric hardening-softening transitions. Contribution of domain walls to hysteresis and nonlinearity is analyzed in terms of domain wall energy potential and degree of ordering of pinning centres. It is shown that two existing models characterizing hard (V-potential) and soft (random potential) materials are ideal, limiting cases and that some real materials are described by an intermediary case, which can evolve with time and under influence of external factors. The dielectric characterization performed at wide range of frequencies has revealed an increase of the apparent frequency dispersion of the dielectric permittivity with the transition from the hard to soft state in PZT ceramics. The investigation of dielectric response over a wide temperature range has revealed the profound presence of hopping conductivity in iron doped PZT ceramics below the Curie temperatures and its absence in niobium doped PZT ceramics. The role of hopping charged species in ferroelectric hardening – softening transitions is analyzed and discussed. The thesis is organized in the following way. A brief introduction (Chapter 1) and a literature review of the theoretical description of domain wall contribution to dielectric nonlinearity and hysteresis in ferroelectrics (Chapter 2) is followed by the thesis outline and discussion of a unified model of hysteresis and nonlinearity in ferroelectrics with ordered and disordered states of domain wall pinning centres (Chapter 3). Processing of ceramics is described in Chapter 4 and mathematical and experimental background for the dielectric spectroscopy study in Chapter 5. The results and discussion of detailed experimental studies of polarization response in ferroelectric PZT ceramics under subswitching and switching conditions are given in Chapters 6 and 7. The summary of the main results and conclusions are given in the last thesis section.

EPFL2005

Experimental and first-principles study of point defects, domain walls, and point-defect/domain-wall interactions in ferroelectric oxides

Anand Chandrasekaran

Ferroelectric oxides, such as lead zirconate titanate, have proved invaluable due to their excellent dielectric and piezoelectric properties. These classes of materials possess a large electric polarization below the Curie temperature. Regions of the crystal lattice having different directions of polarization are separated by nano-scale interfaces known as domain walls. These interfaces, which can be moved by electric and mechanical fields, are not only important for electromechanical properties but they also exhibit unique structural and electronic properties that may be exploited through novel application in nanoelectronics and photovoltaics. The mobility of domain walls is strongly dependent on the defect chemistry of the material due to defect-domain wall interactions. Indeed, aliovalent doping of these materials has been used to tune the properties of ferroelectric oxides for specific applications. In this work, we investigate the origin of the so-called âhardâ and âsoftâ behavior in lead zirconate titanate. Experimental evidence suggests that small concentrations of donor dopants (such as niobium) results in enhanced domain wall motion while doping with acceptor dopants (such as iron) leads to an inhibited domain wall response. The microscopic origin of this phenomena is best investigated using first-principles simulations of the atomistic properties of defects and domain wall in these materials to bring to light novel structural and electronic properties. First, we show that polar defect complexes are likely to exist in both acceptor-doped and undoped PbTiO3 . These defects and defect associates are attracted to 180o domain walls and cause pinning of such interfaces. Donor- doped materials, on the other hand, do not show the presence of polar defect complexes. A closer investigation of the 180o domain wall in PbTiO3 reveals the presence of a âBlochâ component of polarization at the domain wall. In other words, due to polarization rotation, there exists a ferroelectric phase within the domain wall itself. We characterize the strain dependence of this phenomena and calculate the piezoelectric properties of such domain walls. A complete study of domain walls in PbTiO3 also entails looking closer at the properties of the ferroelastic âhead-to-tailâ 90o domain boundary. We show the presence of an asymmetry in the variation of the lattice parameter across the domain wall. This asymmetry is verified using high resolution aberration corrected electron microscopy. We look at the energy landscape of oxygen vacancies in the vicinity of these walls to explain the pinning effect in terms of random-bond and random-field defects. Next we look at the electronic properties of the recently discovered charged domain walls. We characterize the band bending phenomena in 90o head-to-head and tail-to-tail domain wall in PbTiO3 . We then look at the long range effects of clusters of oxygen vacancies in BaTiO3; especially in terms of the formation of 180o tail-to-tail domain wall. In parallel to the first priciples work, we also prepared high quality samples of PZT 50/50 with different concentrations of donor dopant. We characterized the microstructure and hysteresis loops as a function of donor dopant concentration. Based on experimental observations and ab initio calculations we propose ideas on the origins of hardening and softening in PZT.

EPFL2016