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

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.

Ferroelectric Nanowires

Jin Wang

Ferroelectric perovskites exhibit superior dielectric, piezoelectric and ferroelectric properties. Architecting ferroelectrics in the small scale holds interest in both application and fundamental research. Compared to their 2D counterparts – thin films, ferroelectric nanowires –1D structuresndash; are far less studied. A number of important features of ferroelectric nanowires, such as their piezoelectric activity, domain structure, switching behavior and phase transitions, have not been yet fairly studied, nor understood. In this thesis, we treat central issues in the synthesis, structure, and functionality of monocrystalline nanowires of two of the most important ferroelectric perovskites – Pb(Zr, Ti)O3 (PZT) and KNbO3 (KN). This is complemented by theoretical modeling aiming to understand finite size effects in ferroelectric nanowires. Monocrystalline PZT nanowires have been synthesized by a polymer-assisted hydrothermal approach. The ferroelectricity of the PZT nanowires was attested by local switching under DC field applied from the conductive tip of the piezoresponse force microscope (PFM). The ferroelectric-paraelectric phase transition in an individual PZT nanowire and the formation and disappearance of 90° domains upon thermal cycling through its phase transition temperature Tc (Curie temperature) have been observed. PZT nanowires prepared by this direct hydrothermal method showed Ti-rich composition despite of the equal molarity of Zr and Ti in the well-mixed starting materials. This compositional problem was found to be related to the growth mechanism during the hydrothermal treatment, in which an acicular PX-PZT phase was the first to grow, consequently transforming into perovksite PZT nanowires. The existence of an upper limit of solubility of Zr in this precursor PX phase, determined the Ti-rich composition of the converted monocrystalline perovskite PZT nanowires. The atomic structure of the acicular PX phase has been resolved by combining synchrotron X-ray diffraction, electron diffraction and first-principles calculation, showing a unique open-channel structure with 1D cavities about 5.5 Å diameter throughout the acicular wires. The 1D growth habit of the PX phase along its [0 0 1] axis could be related to the large portion of vacant space leading to a high energy of the (001) plane. The doping of Zr in the PX-phase lattice was confirmed to be limited to 17 atom% at most. Taking the advantage of the uniform acicular morphology of the PX phase, we have developed a two-step route to prepare perovskite PZxT1-x (0≤ x ≤0.17) nanowires in which the pure perovskite nano-wires phase has been obtained by annealing PX-PZT in air. An O2 absorption at about 455 °C has been identified as a necessary step occurring during transformation from the PX to perovskite phase in air. The perovskite PZT nanowires had usually a monocrystalline porous structure with 90° domains. The tetragonality of the single PbTiO3 (PT) nanowires with diameters ranging from 20 nm to hundreds of nm has been measured, the c/a ratio of all the measured nanowires has not shown any suppression compared to the bulk value. A maximum c/a up to 1.14, which is larger than the bulk value of 1.065 was observed in nanowires with thickness around 100 nm. DSC measurement confirmed the first-order ferroelectric phase transition and showed a remarkable decrease of the transition latent heat compared to bulk PT/PZT. Annealing PX-PT/PZT on conductive substrate resulted in perovskite PT/PZT nanowires which are attached to the substrates, providing an almost ideal sample for PFM measurements. Prominent piezoelectric response of individual PbZ0.1T0.9 nanowires relative to a reference film with a d33 about 50 pm/V and squared hysteresis loop with sharp swiTching indicated pronounced piezoelectric and ferroelectric properties. Monocrystalline KN nanowires have been processed by a hydrothermal approach. The morphology of the products has been confirmed to be sensitive to the concentration of Nb sources, and could vary from nanowires/nanorods to cubes. Both monodomain and multidomain structures have been observed by PFM. The integration of KN nanowires on the Si substrate as a device prototype has been demonstrated using electron beam lithography. PFM measurements proved that piezoelectric deformation can be excited up to 25 pm by an electric field induced by the lithographically fabricated electrodes. In the theoretical modeling part, we first studied the shift of Tc due to the surface-effect-controlled size effects in ferroelectric nanowires with an axial equilibrium polarization. An effective-surface-energy framework based on the Landau-Ginzburg-Devonshire (LGD) theory has been proposed in the study. The result indicated that for a second order phase transition in the axially-polarized ferroelectric nanowires, Tc shifts down inversely proportional to square of the wire radius (R2) in the case of a strong suppression (close to 0) of polarization at the surface, while it decreases inversely proportional to the radius (R) in the case of a weak suppression of polarization at the surface. The surface tension plays an enhancing role in nanowires of most perovskites, giving an upshift on Tc inversely proportional to R. The competition between the suppressing effect of the short-range surface relaxation and the enhancing role of the surface tension could result in an enhancement of the ferroelectricity in nanowires with certain size. The size-induced shift of Tc due to the surface effect and the surface tension in the axially-polarized nanowires which undergo a first-order paraelectric-ferroelectric phase transition is simply proportional to 1/R in most cases. With the LGD theory, we have also investigated the situation when the axis of the nanowire is not parallel to the crystallographic direction of the polarization of the bulk material. In this case the depolarization field acts "against" the spontaneous polarization, leading, in general, to a polarization rotation. Modeling of the phase transition in cylindrical PT nanowires with their axis parallel to [111]C direction, with the depolarizing field due to the incomplete screening considered as the dominant source of the finite size effects, shows that the competition between the geometrical symmetry of the ferroelectric nanowires and the crystalline symmetry of the material results in an additional phase transition and the usual first order cubic to ferroelectric phase transition of PT becomes a second order phase transition in the small diameter regime.

EPFL2010

Phase transitions, anisotropy and domain engineering

Matthew Davis

Relaxor-ferroelectric single crystals PZN-xPT [(1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3] and PMN-xPT [(1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3] continue to attract much interest due to their anomalously large piezoelectric properties (d33 > 2000 pm/V; k33 > 90%) when poled ("domain-engineered") along a non-polar [001]C direction. In this thesis, the bulk dielectric, pyroelectric, ferroelectric and piezoelectric properties of single crystal PMN-xPT and PZN-xPT with morphotropic phase boundary (MPB) compositions are investigated. The concept of "pseudo-rhombohedral" ("R") and "pseudoorthorhombic" ("O") phases is introduced to encompass the rhombohedral, orthorhombic, and monoclinic (MA, MB and MC) ferroelectric phases occurring in poled crystals; all bulk measurements are rationalized in this way. Poling in different orientations affects the thermal stabilities of the "R", "O" and tetragonal (T) phases, likely due to the presence of residual bias fields. Phase diagrams are constructed for [001]C-poled crystals based on bulk electrical measurements, which agree well with those derived elsewhere from diffraction experiments. Large pyroelectric coefficients (< 1000 µCm-2K-1) are evidenced in [111]C-poled PMN-28PT; these might be exploitable in heat sensing and thermal imaging applications. A "R" phase is induced metastably in otherwise pseudo-orthorhombic PZN-8PT by poling along the [111]C direction at sub-zero temperatures. The related electric field induced ("O" - "R") phase transition is evidenced in strain-field measurements and, in situ, by polarized light microscopy. Hysteresis, and discontinuities in polarization and strain, are due to nucleation and growth of the induced phase; this first-order phase transition corresponds to a discontinuous "jump" of the polar vector within the MB plane. Further electric-field induced phase transitions are evidenced in unipolar strain-field loops for [001]C-poled PZN-xPT and PMN-xPT, with various MPB compositions, at temperatures between 25°C and 100°C. In PZN-6.5PT, PMN-30PT and PMN-30.5PT, the polarization rotation path "R" - "O" - T is evidenced by two first-order "jumps" in strains, one between the MA and MC monoclinic planes, and one within the MC plane to the tetragonal phase. Electric field-temperature (E-T) phase diagrams are constructed from the experimental data; trends for the electrical stabilities of the "R", "O" and T phases are shown. The (direct) piezoelectric response of [001]C-poled PZN-4.5PT, PZN-6.5PT, PZN-8PT and PMN-31PT is investigated under compressive stresses both along and perpendicular to the poling direction (longitudinal d33 and transverse d31 modes, respectively). Dynamic measurements are made in a Berlincourt-type press, over a range of stresses (< 20 MPa) and temperatures (25 to 200°C). In the longitudinal mode, Rayleigh-law hysteresis and nonlinearity indicates a significant extrinsic contribution from the irreversible (pinned) motion of interfaces, and likely ferroelastic domain walls; however, domain switching is not generally expected in domain engineered, pseudo-rhombohedral crystals. It is postulated that domain wall motion is driven by a local stress-induced phase transition, clearly evidenced in quasi-static, charge-stress loops and in situ X-ray diffraction at larger stresses (< 100 MPa). The reversible contribution to the response is always found to be larger than the irreversible (extrinsic) contribution in the "R" and "O" phases, the latter accounting for around 20% of d33 in PZN-8PT, at room temperature, and 5% in PZN-4.5PT. Both contributions are shown to increase upon heating towards the tetragonal phase; the increase in extrinsic contribution is likely due to increased domain wall mobility as the ferroelectric-ferroelectric phase transition temperature is approached. In contrast, the transverse response of PMN-31PT and PZN-4.5PT is anhysteretic ("non-lossy") and linear at low stresses (< 10 MPa). This might be exploitable in sensing applications. The difference between the behaviors is likely related to differing directions of polarization rotation. In the transverse mode, rotation is towards the [001]C poling direction and the domain engineered structure is retained during the stress-induced phase transition. Lastly, published monodomain properties are used to calculate the piezoelectric (d33* and d31* ) coefficients of domain-engineered 3m PMN-33PT and mm2 PZN-9PT; both positive and negative transverse coefficients can be application tailored by domain-engineering. According to such calculations, intrinsic crystal anisotropy accounts for at least 50% of the "giant" piezoelectric response of polydomain, [001]C-poled, PMN-33PT and PZN-9PT. Both compositions show inherently strong piezoelectric anisotropy (d15/d33 ≫ 1) in accordance with an "easy" polarization rotation. This is related to a high dielectric anisotropy (ε11/ε33) and the degeneracy of the "R", "O" and T phases near the MPB. Similar effects are observed in all ferroelectric perovskites, although the effect is uncommonly large in PMN-xPT and PZN-xPT: it is noted that all monodomain compliances, piezoelectric coefficients and permittivities are around an order of magnitude larger in PMN-xPT and PZN-xPT compared to their simpler perovskite relatives. This is likely a result of their background "relaxor" nature. Finally, it is suggested that the presence of zero-field monoclinic phases in PMN-xPT and PZN-xPT is related to their inherently large piezoelectric response in the presence of residual stresses and bias fields, not the other way round as is commonly accepted.

EPFL2006

Atomic scale symmetry and polar nanoclusters in the paraelectric phase of ferroelectric materials

Dragan Damjanovic, Sina Hashemi Zadeh, Takuya Hoshina, Emadeddin Oveisi

The nature of the "forbidden" local- and long-range polar order in nominally nonpolar paraelectric phases of ferroelectric materials has been an open question since the discovery of ferroelectricity in oxide perovskites (ABO3). A currently considered model suggests locally correlated displacements of B-site atoms along a subset of cubic directions. Such offsite displacements have been confirmed experimentally, however, being essentially dynamic in nature they cannot account for the static nature of the symmetry-forbidden polarization implied by the macroscopic experiments. Here, in an atomically resolved study by aberration corrected scanning transmission electron microscopy (STEM) complemented by Raman spectroscopy, we reveal, directly visualize and quantitatively describe static, 2-4 nm large polar nanoclusters in the nominally nonpolar cubic phases of (Ba,Sr)TiO3 and BaTiO3. These results have implications on understanding of the atomic-scale structure of disordered materials, the origin of precursor states in ferroelectrics, and may help answering ambiguities on the dynamic-versus-static nature of nano-sized clusters