There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A large body of work has been reported in the last 5 years on the development of lead-free piezoceramics in the quest to replace lead–zirconate–titanate (PZT) as the main material for electromechanical devices such as actuators, sensors, and transducers. In specific but narrow application ranges the new materials appear adequate, but are not yet suited to replace PZT on a broader basis. In this paper, general guidelines for the development of lead-free piezoelectric ceramics are presented. Suitable chemical elements are selected first on the basis of cost and toxicity as well as ionic polarizability. Different crystal structures with these elements are then considered based on simple concepts, and a variety of phase diagrams are described with attractive morphotropic phase boundaries, yielding good piezoelectric properties. Finally, lessons from density functional theory are reviewed and used to adjust our understanding based on the simpler concepts. Equipped with these guidelines ranging from atom to phase diagram, the current development stage in lead-free piezoceramics is then critically assessed.

Perspective on the Development of Lead-free Piezoceramics

Piezoelectric materials, which convert mechanical to electrical energy (and vice versa), are crucial in medical imaging, telecommunication and ultrasonic devices. A new generation of single-crystal materials, such as Pb(Zn1/3Nb2/3)O3-PbTiO3 (PZN-PT) and Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), exhibit a piezoelectric effect that is ten times larger than conventional ceramics, and may revolutionize these applications. However, the mechanism underlying the ultrahigh performance of these new materials-and consequently the possibilities for further improvements-are not at present clear. Here we report a first-principles study of the ferroelectric perovskite, BaTiO3, which is similar to single-crystal PZN-PT but is a simpler system to analyse. We show that a large piezoelectric response can be driven by polarization rotation induced by an external electric field. Our computations suggest how to design materials with better performance, and may stimulate further interest in the fundamental theory of dielectric systems in finite electric fields.

Polarization rotation mechanism for ultrahigh electromechanical response in single-crystal piezoelectrics

Relaxor ferroelectrics were discovered almost 50 years ago among the complex oxides with perovskite structure. In recent years this field of research has experienced a revival of interest. In this paper we review the progress achieved. We consider the crystal structure including quenched compositional disorder and polar nanoregions (PNR), the phase transitions including compositional order-disorder transition, transition to nonergodic (probably spherical cluster glass) state and to ferroelectric phase. We discuss the lattice dynamics and the peculiar (especially dielectric) relaxation in relaxors. Modern theoretical models for the mechanisms of PNR formation and freezing into nonergodic glassy state are also presented.

Recent progress in relaxor ferroelectrics with perovskite structure

Investigations in the development of lead-free piezoelectric ceramics have recently claimed comparable properties to the lead-based ferroelectric perovskites, represented by Pb(Zr,Ti)O3, or PZT In this work, the scientific and technical impact of these materials is contrasted with the various families of “soft” and “hard” PZTs On the scientific front, the intrinsic nature of the dielectric and piezoelectric properties are presented in relation to their respective Curie temperatures (T
 C) and the existence of a morphotropic phase boundary (MPB) Analogous to PZT, enhanced properties are noted for MPB compositions in the (Na,Bi)TiO3-BaTiO3 and ternary system with (K,Bi)TiO3, but offer properties significantly lower The consequences of a ferroelectric to antiferroelectric transition well below T
 C further limits their usefulness Though comparable with respect to T
 C, the high levels of piezoelectricity reported in the (K,Na)NbO3 family are the result of enhanced polarizability associated with the orthorhombic-tetragonal polymorphic phase transition being compositionally shifted downward As expected, the properties are strongly temperature dependent, while degradation occurs through the thermal cycling between the two distinct ferroelectric domain states Extrinsic contributions arising from domains and domain wall mobility were determined using high field strain and polarization measurements The concept of “soft” and “hard” lead-free piezoelectrics were discussed in relation to donor and acceptor modified PZTs, respectively Technologically, the lead-free materials are discussed in relation to general applications, including sensors, actuators and ultrasound transducers

Lead-free piezoelectric ceramics: Alternatives for PZT?

New morphotropic phase boundary (MPB) piezoelectrics, with ferroelectric phase transition (Tc) exceeding that of PbZrO3–PbTiO3 (PZT), were investigated. Based on a perovskite tolerance factor-Tc relationship, new high Tc MPB systems were projected in the Bi(Me)O3–PbTiO3 system, where Me is a relatively large B+3-site cation. For the (1-x)BiScO3–(x)PbTiO3 solid solution, a MPB was found at x-0.64 separating the rhombohedral and tetragonal phases, with correspondingly enhanced dielectric and piezoelectric properties. A transition temperature Tc of ~ 450°C was determined with evidence of Tc's on the order of ≥ 600°C in the BiInO3 and BiYbO3 analogues, though issues of perovskite stability remain for the smaller tolerance end-member systems.

https://iopscience.iop.org/article/10.1143/JJAP.40.5999/pdf

New High Temperature Morphotropic Phase Boundary Piezoelectrics Based on Bi(Me)O3?PbTiO3 Ceramics

Crystallographic texturing of polycrystalline ferroelectric ceramics offers a means of achieving significant enhancements in the piezoelectric response. Templated grain growth (TGG) enables the fabrication of textured ceramics with single crystal-like properties, as well as single crystals. In TGG, nucleation and growth of the desired crystal on aligned single crystal template particles results in an increased fraction of oriented material with heating. To facilitate alignment during forming, template particles must be anisometric in shape. To serve as the preferred sites for epitaxy and subsequent oriented growth of the matrix, the template particles need to be single crystal and chemically stable up to the growth temperature. Besides templating the growth process, the template particles may also serve as seed sites for phase formation of a reactive matrix. This process, referred to as Reactive TGG (RTGG), has been used to obtain highly oriented Pb(Mg1/3Nb2/3)O3-PbTiO3, Sr0.53Ba0.47Nb2O6, and (N...

Templated Grain Growth of Textured Piezoelectric Ceramics

Single crystals of Ba(ZrxTi1−x)O3 were grown by templated grain growth (TGG). Millimeter size single crystals of Ba(ZrxTi1−x)O3 were produced by heating a BaTiO3 crystal in contact with a sintered polycrystalline matrix of 4.5, 5.0, or 8.5 mol % Zr-doped barium titanate for 30 h at 1350 °C. To facilitate boundary migration, the ceramic compact was made 3 mol % TiO2 excess. The 4.5 and 5.0 mol % Zr-doped crystals were orthorhombic at room temperature, and for a pseudocubic (001) orientation, they showed remanent polarizations of 13 μC/cm2 and a high field d33 of 340–355 pC/N. The 8.5 mol % Zr-doped crystal [again oriented along the pseudocubic (001)] was rhombohedral at room temperature with a remanent polarization of 10 μC/cm2. A k33 value of 0.74 from resonance measurements was observed for the 4.5 mol % Zr-doped crystal.

Piezoelectric properties of zirconium-doped barium titanate single crystals grown by templated grain growth

High-energy x-ray-diffraction experiments performed on rhombohedral $\mathrm{Pb}({\mathrm{Zn}}_{1/3}{\mathrm{Nb}}_{2/3}{)}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x}{\mathrm{O}}_{3}$ $(\mathrm{PZN}\ensuremath{-}x%\mathrm{PT})$ 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 PZN-4.5%PT such a phase change occurs via a third phase with monoclinic symmetry ${M}_{A},$ 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 different polarization path between the rhombohedral and tetragonal phases, through a second monoclinic phase ${M}_{C},$ has been previously reported in PZN-8%PT. The microscopic characterization of these crystals allows us to explain the ultrahigh macroscopic strain observed in $\mathrm{PZN}\ensuremath{-}x%\mathrm{PT}$ under an electric field. Furthermore, some unusual scattering profiles displayed by exceptionally good crystals provide experimental evidence of the high anharmonicities and near degeneracy of the different phases in these extremely deformable materials.

/pdf/electric-field-induced-phase-transitions-in-rhombohedral-pb-53bpzlh8q0.pdf

Electric-field induced phase transitions in rhombohedral pb(zn1/3nb2/3)1-xtixo3

High-temperature (high-$T)$ and high-electric-field (high-$E)$ effects on $\mathrm{Pb}[({\mathrm{Zn}}_{1/3}{\mathrm{Nb}}_{2/3}{)}_{0.92}{\mathrm{Ti}}_{0.08}]{\mathrm{O}}_{3}$ were studied comprehensively by neutron diffraction in the ranges $300l~Tl~550\mathrm{K}$ and $0l~El~15\mathrm{k}\mathrm{V}/\mathrm{c}\mathrm{m}.$ We have focused on how phase transitions depend on preceding thermal and electrical sequences. In the field-cooling process $(E\ensuremath{\Vert}[001]g~0.5\mathrm{k}\mathrm{V}/\mathrm{c}\mathrm{m}),$ a successive cubic $(C)\ensuremath{\rightarrow}\mathrm{tetragonal}(T)\ensuremath{\rightarrow}$ monoclinic ${(M}_{\mathrm{C}})$ transition was observed. In the zero-field-cooling process, however, we have found that the system does not transform to the rhombohedral (R) phase as widely believed, but to an unidentified phase, which we call X. X gives a Bragg-peak profile similar to that expected for R, but the c axis is always slightly shorter than the a axis. As for field effects on the X phase, it transforms into the ${M}_{\mathrm{C}}$ phase via another monoclinic phase ${(M}_{\mathrm{A}})$ as expected from a previous paper [Noheda et al., Phys. Rev. B 65, 224101 (2002)]. At a higher electric field, we confirmed the field-induced ${M}_{\mathrm{C}}\ensuremath{\rightarrow}T$ transition, which shows a gradual c-axis jump contrary to a sharp c-axis jump observed by strain and x-ray diffraction measurements.

http://arxiv.org/pdf/cond-mat/0207726.pdf

Paul W. Rehrig

Papers

New High Temperature Morphotropic Phase Boundary Piezoelectrics Based on Bi(Me)O3?PbTiO3 Ceramics

Templated Grain Growth of Textured Piezoelectric Ceramics

Piezoelectric properties of zirconium-doped barium titanate single crystals grown by templated grain growth

Electric-field induced phase transitions in rhombohedral pb(zn1/3nb2/3)1-xtixo3

Neutron diffraction study of field-cooling effects on the relaxor ferroelectric Pb [ ( Zn 1 / 3 Nb 2 / 3 ) 0.92 Ti 0.08 ] O 3