Phase transitions, anisotropy and domain engineering

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.

Piezoelectric anisotropy and free energy instability in classic perovskites

Marko Budimir

Several members of the perovskite family are investigated: the temperature dependence of dielectric, elastic, piezoelectric and coupling coefficients of KNbO3 in its orthorhombic ferroelectric phase is determined experimentally; the values of dielectric stiffness coefficients at constant stress, α, are estimated for the 6th order Landau-Ginzburg-Devonshire phenomenological description of KNbO3; the origins of the enhanced piezoelectric responses along non polar directions in perovskites are investigated by studying phenomenologically the temperature evolution of the piezoelectric anisotropy in a material with a sequence of ferroelectric-ferroelectric phase transitions (BaTiO3) and in a material with only one ferroelectric phase (PbTiO3); the influence of external bias fields on piezoelectric response and its anisotropy in ferroelectric perovskites is discussed phenomenologically by studying tetragonal BaTiO3, PbTiO3 and Pb(Zr,Ti)O3 under electric bias field applied anti-parallel to the spontaneous polarization and uniaxial compressive bias stress along the polarization direction; a discussion about a common underlying thermodynamic process able to generally describe the enhancement of the piezoelectric response and its anisotropy is given by investigating the Gibbs free energy flattening in tetragonal BaTiO3, PbTiO3 and Pb(Zr,Ti)O3 upon changes of temperature, bias fields and composition. The main conclusions resulting from this work are: a comparison of the results of electromechanical properties measurements on KNbO3 obtained in this work, the ones found in the literature, and estimates using LGD phenomenology from this work gives discrepancies that suggest that published measurements should be redone; in the absence of bias fields, the intrinsic origin of the enhanced piezoelectric responses in perovskites is the anticipation of a phase transition, no matter what is the cause of that transition (temperature, composition); in the presence of sufficiently high bias fields, an enhanced piezoelectric response along non-polar direction can be predicted in some materials (PbTiO3 under high uniaxial compressive stress along the polar direction); the influence of the external bias fields on electromechanical properties of perovskites may generally be of significant importance: if the electric fields applied anti-parallel to the spontaneous polarization or the uniaxial compressive bias stresses applied along the polarization axis are high enough, the perovskite system can be strongly dielectrically softened (metastable state), increasing the values of dielectric permittivities and piezoelectric coefficients; in the vicinity of a coercive field or a phase transition these electromechanical coefficients can increase by several orders of magnitude; the flattening of the Gibbs free energy profile of each of examined perovskite systems, regardless of whether this flattening is caused by temperature or composition variation, or by applying compressive pressure or antiparellel electric field bias, leads to enhancements of dielectric susceptibilities and of the piezoelectric response; the anisotropy of the free energy flattening is the origin of the anisotropic enhancement of the piezoelectric response, which can occur either by polarization rotation or by polarization contraction.

EPFL2006

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

Conductivity, dielectric and piezoelectric properties of SrBi4Ti4O15

Strontium Bismuth Titanate is a very promising material for high temperature piezoelectric applications, its elevated ferroelectric phase transition (530°C), linear piezoelectric properties under low field and relatively low room temperature conductivity (compared to others Bismuth Titanates) make it very attractive for precision sensors. However, under severe conditions (low frequency, high field, high temperature or low oxygen partial pressure) some of those advantages disappear. Piezoelectric response is dominated by charge drift in general becomes unstable. Above all, at high temperature and low oxygen partial pressure, a large conductivity increase reduces the piezoelectric efficiency of the material, in this work, electrical conductivity, piezoelectric properties and dielectric permittivity of SrBIT ceramic have been investigated in conditions of high temperature, low oxygen partial pressure, low to moderate driving field and frequency. As a result of this research, a better understanding of SrBIT properties was achieved. Thanks to a careful study of SrBIT processing as a bulk ceramic, a reproducible route was established. Many basic mechanisms leading to both SrBIT crystallization and sintering have been identified. It was demonstrated that a detailed knowledge of the exact processing conditions is required in order to achieve high quality material. DC conductivity measurements were carried out as a function of temperature, oxygen partial pressure and dopant concentration. It was found that the apparent activation energy for conduction for undoped SrBIT was 1 eV between 140 and 220°C and 1.5 eV between 450 and 700°C. Decrease of the activation energy in the lower temperature range has been discussed considering grain boundary conductivity, as a transition from electronic to ionic conduction or as consequence of small polarons conduction. It was shown that lower activation energy resulted from Manganese doping (0.5 eV), this was interpreted as either growing influence of grain boundary conductivity as dopant concentration increases or as shallow hole trap formation. DC conductivity measurements and acceptor/donor doping experiments demonstrated p-type conductivity in the low temperature range (up to 220°C) as donor doping decreases conductivity, while oxygen partial pressure controlled measurements indicated n-type conductivity at higher temperature (above 700°C). An electrical impedance analysis was performed with several equivalent circuits. The aim of these models was to simulate the impedance of SrBIT. The best approximation was found with a distributed element of Havriliak-Negami type. However, as the physical justification for this circuit was not clear, the investigation of the grain, grain boundary and electrode impedances was performed with multiple discrete parallel RC elements. With temperature, grain size and oxygen activity variations, the identification of three separate contributions as grain, grain boundary and electrode was realized. The anisotropy of conductivity and permittivity was demonstrated with textured material and both DC and AC analysis. With the master curves built for the electrical modulus, it was found that the impedance probably related to Bismuth oxide layers produces an additional high frequency are. From this finding and by comparing characteristic relaxation frequencies of undoped, 2 mol.% Mn and 4 mol.% Nb SrBIT, it was determined that conductivity is higher in the ab plane direction than in the c direction within both perovskite units and Bismuth oxide layers. With conductivity measurements under controlled oxygen partial pressure, it was found that an acceptor-based (intrinsic or extrinsic) model could be used to describe the electrical conductivity under controlled oxygen partial pressure of both undoped and 2 mol.% Mn doped SrBIT. However, as neither a pO2-1/6 region (intrinsic oxygen vacancies compensated by electrons) for undoped SrBIT nor a pO2-1/4 region (oxygen vacancies compensated by singly ionized acceptors) for Mn doped SrBIT were seen, it was concluded that the acceptorcontrolled model is not sufficient for a complete description of SrBIT. For this reason and in order to include the low oxygen partial pressure behavior of undoped SrBIT, a donor-based (intrinsic) model was also considered. The source of intrinsic donors would be in that case Bi3+ cations sitting on Sr2+ sites in the perovskite sublattice. Considering Bismuth vacancies as the negative compensating species, both pO2-1/4 and pO2-independent regions could be predicted with the model. However, even if the donor-controlled model seems to better match conductivity measurements in the full PO2) range, rejecting the acceptor-based model would be an error. It is actually not demonstrated that in SrBIT the concentration of exchanged Bismuth cations is always (all temperature, pressure) larger than the natural acceptor impurity concentration. It is very likely that the cation exchange is dependent of the oxygen partial pressure. It is also not proved as suggested in the literature that direct compensation between exchanged Strontium and Bismuth exists, reducing the net donor-excess. With the acceptor-controlled model, the mass-action constants for reduction and for ionization of intrinsic carriers across the band gap were determined. The band gap of SrBIT was estimated to be 3.5 eV. The ionic conductivity of SrBIT was determined at high temperature with measurements under controlled oxygen partial pressure. It was found that the electrical conductivity of SrBIT is probably mixed (electronic and ionic) as the estimation of the transference number provided quite large values (t=0.8 at 800°C). From electronic and ionic conductivity data, mixed conduction can actually be predicted in a large temperature range (above room temperature). The piezoelectric measurements using direct effect demonstrated that it is actually possible to unlock piezoelectrically active ferroelectric domain walls and create non-linear piezoelectric properties in undoped SrBIT. This occurs above a threshold elastic field, which is thermally activated. With a piezoelectric composite, it was demonstrated that the electromechanical coupling between two different phases creates a piezoelectric relaxation. This one could be positive or negative depending on the respective properties of each composite's component. It was shown experimentally that a small temperature change is sufficient to transform a positive relaxation into a negative one. While these experiments did not provide a detailed microstructural explanation for the piezoelectric relaxation observed in 2 mol.% Mn doped SrBIT, they gave a first insight into an original phenomenological approach. Microstructure and piezoelectric properties were related with the calculation of a piezoelectric relaxation composite made of two textured samples. This demonstrated that a piezoelectric relaxation may occur just because of anisotropy. Microstructural reproduction of this coupling is actually an important feature of Aurivillius phases.

EPFL2000