Morphotropic Phase Boundary Systems Research Articles

Topology of ferroelectric phase diagrams with morphotropic phase boundary and their piezoelectric properties

ABSTRACT Ferroelectric materials at morphotropic phase boundary (MPB) exhibit large piezoelectric coefficients and thus are widely used as piezoelectric actuators and sensors. Three different phase diagram topologies have been reported in various ferroelectric MPB systems: one with a cubic(C)-tetragonal(T)-orthorhombic(O)-rhombohedral(R) quadruple point; another with a C-T-R triple point and the other with a C-T-R along with a T-O-R triple point. However, it is unclear which phase diagram topology would give the best piezoelectric property. Here in this work, we obtain the above three different MPB phase diagram topologies by Landau free energy. It was found that among the three phase diagram topologies, the one with a T-O-R triple point exhibits superior piezoelectric property at the T-O-R triple point because of the small polarization anisotropy required by the simultaneous thermodynamic equilibrium of three ferroelectric phases. This work could guide the design of piezoelectric materials.

Understanding the correlation between intermediate monoclinic phase (Cc) and piezoelectric properties in NaNbO3-BaTiO3-CaZrO3 ternary system with octahedral tilt

Compared with traditional tetragonal (T) P4mm - rhombohedral (R) R3m morphotropic phase boundary (MPB) system, the structure-property relationship of MPB systems with octahedral tilt is still unclear. In this work, the phase structure evolution under composition and electric field modulations in lead-free (0.9-x)NaNbO3-0.1BaTiO3-xCaZrO3 (NN-BT-xCZ) close to the untilt P4mm-tilt R3c MPB was investigated in details by means of the ex- and in-situ x-ray diffraction and various electrical property measurements. Both P4 mm and R3c phases can irreversibly transform into a Cc phase under electric field loading, which should be considered as a result of the cooperative coupling between ferroelectric and antiferrodistortive instabilities. Quantitative analysis indicates that little composition dependent lattice strain and domain switching of P4 mm phase can be observed, and the variation of piezoelectric coefficient is closely related to Cc phase, which exhibits an enhancement of both lattice strain and domain switching within MPB. This suggests that lattice strain and domain switching of Cc phase are coupled. On the contrary, both of them are competed in P4 mm phase because the P4 mm phase is dominated by irreversible domain switching. The experimental results would benefit for deeply understanding the origin of piezoelectric response for many octahedral-tilt MPB piezoelectric systems.

Designed morphotropic relaxor boundary ceramic exhibiting large electrostrain and negligible hysteresis

Electromechanical materials with large electrostrain and low hysteresis are strongly desired for high-precision actuator applications. Despite extensive studies for more than half a century, it is still a challenge to obtain large electrostrain and low hysteresis simultaneously due to the so-called strain-hysteresis trade-off. Here, we report a mechanism to overcome this trade-off: a ceramic composition locating at a morphotropic relaxor boundary (MRB), exhibits enhanced electrostrain and reduced hysteresis as compared with off-MRB compositions. The MRB, a composition-induced boundary separating two relaxors with different local polar symmetries, is attained by transforming an morphotropic phase boundary (MPB) in Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT) through doping lanthanum. The performances of large electrostrain of 0.227% and negligible hysteresis of 3% of MRB composition are the best, as evidenced by occupying a virgin region in the strain-hysteresis chart of relaxor electromechanical ceramics. Moreover, this MRB ceramic maintains the large electrostrain and low hysteresis over a temperature range from 35 to -35 °C. The understanding of abnormal effects of MRB is established through combining microstructure observations and Landau theory analysis: the MRB composition with morphotropic nanodomain structure and higher degree of local structural heterogeneity shows a flatter energy profile with much lower energy barrier, thereby leading to a large electrostrain and negligible hysteresis. Our work demonstrates that the MRB is an effective mechanism to design relaxor materials with large electrostrain and low hysteresis simultaneously. We predict that more high-performance MRB electromechanical materials will be found in properly doped MPB systems.

Ferroelectric flexible composite films based on morphotropic phase boundary for self-powered multisensors

The synthesized 0.3(Ba0.7Ca0.3TiO3)-0.7(BaSn0.12Ti0.88O3) nanoparticles (BCST NPs) and their morphotropic phase boundary (MPB) evolution characterized based on the structural, vibrational, dielectric, and ferroelectric properties of the individual Ba0.7Ca0.3TiO3 (BCT), BaSn0.12Ti0.88O3 (BST) NPs. The MPB system had a dielectric constant/loss of 710/0.088 at 1 kHz frequency, with remnant polarization (Pr) of 8.5 μC/cm2, under a coercive field of 15 kV/cm at 1 Hz and its fatigue property evaluated up to 108 cycles. The BCST has a piezoelectric coefficient of 65 pC/N. Flexible polyvinylidene fluoride/BCST NP composite films (PBCST-CFs) were fabricated and characterized. The optimal loading of 15 wt% provided a more electroactive phase (70.93%), a dielectric constant of 33 and loss of 0.0066, and a Pr of 0.8 µC/cm2. The PBCST-CF (15%)-based nanogenerator (PBCST-CFNG) generated electrical output of 92 V, 440nA upon applied 8 N force under acceleration of 2 m/s2, with power density of 44 mW/m2 at 160 MΩ. Electrical poling, durability, and switching polarity testing, charging of commercial capacitors, and the driving of low-power electronics were also performed. A PBCST-CFNG (15%)-based piezoelectric ball was designed and used to monitor the ball height/distance, rotations, and impact positions/counts.

Reconstruction and uncertainty quantification of lattice Hamiltonian model parameters from observations of microscopic degrees of freedom

The emergence of scanning probe and electron beam imaging techniques has allowed quantitative studies of atomic structure and minute details of electronic and vibrational structure on the level of individual atomic units. These microscopic descriptors, in turn, can be associated with local symmetry breaking phenomena, representing the stochastic manifestation of the underpinning generative physical model. Here, we explore the reconstruction of exchange integrals in the Hamiltonian for a lattice model with two competing interactions from observations of microscopic degrees of freedom and establish the uncertainties and reliability of such analysis in a broad parameter-temperature space. In contrast to other approaches, we specifically specify a loss function inherent to thermodynamic systems and utilize it to estimate uncertainty in simulated realizations of different models. As an ancillary task, we develop a machine learning approach based on histogram clustering to predict phase diagrams efficiently using a reduced descriptor space. We further demonstrate that reconstruction is possible well above the phase transition and in the regions of parameter space when the macroscopic ground state of the system is poorly defined due to frustrated interactions. This suggests that this approach can be applied to the traditionally complex problems of condensed matter physics such as ferroelectric relaxors and morphotropic phase boundary systems, spin and cluster glasses, and quantum systems once the local descriptors linked to the relevant physical behaviors are known.

Effect of Sm and Mn Co-doping on the Crystal Structure and Magnetic Properties of \(\text{BiFeO}_{3}\) Polycrystalline Ceramics

The crystal structure, phonon vibration, microstructure, and magnetic properties have been investigated in multiferroics Bi0.9Sm0.1Fe1-xMnxO3 for \(x = 0.02 – 0.1\). The structural analysis by XRD and Rietveld refinement suggest that Mn doping compounds crystallize in the polar R3c rhombohedral symmetry (isostructural with BiFeO3). Raman analysis confirms no structural transformation but the change of line widths and peak intensities reveal the lattice distortion in Mn-substitution samples. The study of microstructure shows no obvious change of grain size and shape. The magnetic properties of the as-prepared samples show the linear magnetic field dependence of magnetization, suggesting the antiferromagnetic feature of polycrystalline ceramics. The field dependence of magnetization measured after two-years synthesis and after applying an electric field reveal a decrease of maximum magnetization but the hysteresis loops retain the antiferromagnetic behavior. The implication of these results is that the magnetic properties of single structural phase compound, including coercivity and remanent magnetization, do not show the aging behavior as observed in the morphotropic phase boundary systems.

Evidence for pressure-induced polarization rotation, octahedral tilting, and reentrant ferroelectric phase in tetragonal (Pb0.5Bi0.5)(Ti0.5Fe0.5)O3

Despite the technological significance of the tetragonal PbTiO3 for the piezoelectric transducer industry, its high pressure behaviour is quite controversial as two entirely different scenarios, involving pressure induced (1) morphotropic phase boundary (MPB) like structural transition with concomitant rotation of the ferroelectric polarization vector and (2) antiferrodistortive (AFD) phase transition followed by emergence of a reentrant ferroelectric phase, have been proposed in recent theoretical and experimental studies. We have attempted to address these controversies through a high resolution synchrotron x-ray diffraction study of pressure induced phase transitions in the tetragonal phase of a modified PbTiO3 composition containing 50% BiFeO3, where BiFeO3 was added to enhance the AFD instability of PbTiO3. We present here the first experimental evidence for the presence of the characteristic superlattice reflections due to an AFD transition at a moderate pressure pc1 ~2.15 GPa in broad agreement with scenario (2), but the high pressure ferroelectric phase belongs to the monoclinic space group Cc, and not the tetragonal space group I4cm predicted under scenario (2), which permits the rotation of the ferroelectric polarization vector as per scenario (1). We show that the monoclinic distortion angle and ferroelectric polarization of the Cc phase initially decrease with increasing pressure for p < 7 GPa, but start increasing above pc2 ~ 7 GPa due to an isostructural Cc-I to Cc-II transition reminiscent of MA(apc > bpc ~ cpc) to MB(apc< bpc ~ cpc) transition predicted for MPB systems. We also show that octahedral tilting provides an efficient mechanism for accommodating pressure induced volume reduction for the stabilisation of the reentrant ferroelectric phase Cc-II.

Large electromechanical response in ferroelectrics: Beyond the morphotropic phase boundary paradigm

Ferroelectric based piezoceramics exhibiting large electromechanical response are used as sensors, actuators, and transducers in wide-ranging applications spanning sectors like space, defense, medical diagnostics, etc. In general, the large piezoelectric response in ferroelectric solid solutions is associated with a composition driven interferroelectric instability, commonly known as a morphotropic phase boundary (MPB). Here, we show that MPB is not necessarily required to achieve electromechanical response equivalent to, or even more than what can be achieved in MPB based ferroelectric solid solutions. We show this on two ferroelectric solid solution systems, namely, $(1--x)\mathrm{PbTi}{\mathrm{O}}_{3}\ensuremath{-}(x)\mathrm{Bi}(\mathrm{N}{\mathrm{i}}_{1/2}\mathrm{H}{\mathrm{f}}_{1/2}){\mathrm{O}}_{3}$ (PT-BNH) and $(\mathrm{Bi},\mathrm{La})\mathrm{Fe}{\mathrm{O}}_{3}\ensuremath{-}\mathrm{PbTi}{\mathrm{O}}_{3}$ (BF-PT:La) which show large piezoelectric response (${d}_{33}\ensuremath{\sim}450\phantom{\rule{0.16em}{0ex}}\mathrm{pC}/\mathrm{N}$) and extraordinarily high electrostrain of \ensuremath{\sim}1.3%, respectively. Although analogous to the conventional MPB systems, the critical compositions of these two alloys mimic a two-phase structural state (cubic + tetragonal), detailed analysis that suggests that it is not so. The cubic phase is rather a manifestation of short correlation length of the tetragonal regions and appears when the system is compositionally driven from a normal ferroelectric state to a relaxor ferroelectric state. This proves that, in contrast to conventional MPB systems, the large electromechanical response of the critical compositions of PT-BNH and BF-PT:La is not due to interferroelectric instability enabled polarization rotation. In the absence of the MPB, the sole contributor to large electromechanical response is a process associated with domain wall motion, large local polarization, and (non-MPB) lattice softening. The generalized ideas derived from our investigation offer scope for expanding the basket of high-performance piezoelectric materials by exploring solid solutions outside of the MPB framework.

Long-period structural modulation on the global length scale as the characteristic feature of the morphotropic phase boundaries in the Na0.5Bi0.5TiO3 based lead-free piezoelectrics

The inherent structural disorder has a profound effect on the dielectric, ferroelectric and the electromechanical response of the Na0.5Bi0.5TiO3 (NBT) based lead-free piezoelectrics. While analogous to the lead-based classical morphotropic phase boundary (MPB) systems the existence of MPB has been recognized in some derivatives of NBT displaying enhanced electromechanical response, there is a lack of clarity on the structural state of the MPB compositions on NBT-based systems on the global length scale. We have examined this issue on the well known MPB system (1-x)Na0.5Bi0.5TiO3-(x)K0.5Bi0.5TiO3(NBT-KBT) by carrying out structural investigations on local and global length scales using Eu+3 photoluminiscence and high-resolution neutron powder diffraction techniques, respectively. Our study reveals that the MPB of this system is characterized by the onset of a long-period modulated structure with a periodicity of ∼40 Å on the global scale. Temperature depedent neutron diffraction study revealed that the intermediate temperature P4bm phase which appears in NBT is suppressed for the MPB composition. The MPB composition rather develops a long-period modulated phase on cooling from the cubic phase. The ergodic-nonergodic relaxor ferroelectric transition occurs within this long-period modulated phase. In the non-ergodic regime, however, strong electric field irreversibly transforms the long-period modulated phase to the rhombohedral ferroelectric (R3c). We demonstrate that thermal depolarization of this system is a distinct structural event characterized by the system losing its field-induced long range rhombohedral (R3c) coherence and transforming back to the long-period modulated phase. Our study suggests that the long-period modulated phase is the primary structural feature of the MPB compositions in NBT-based piezoelectrics.

High electromechanical response in the non morphotropic phase boundary piezoelectric system PbTiO3−Bi(Zr1/2Ni1/2)O3

There is a general perception that large piezoelectric response in ferroelectric alloys requires tuning the system towards a morphotropic phase boundary (MPB), i.e., a composition driven inter-ferroelectric instability. Here we show that high piezoelectric response can be realized even in non-MPB alloy systems. This is demonstrated on (1-x)PbTiO3-(x)Bi(Zr0.5Ni0.5)O3 (PT-BNZ) by a comprehensive study involving electric-field and temperature dependent XRD, Raman spectroscopy, dielectric, piezoelectric and high field electrostrain measurements. We found that poling-field irreversibly suppresses the cubic-like phase at room temperature. Based on our results, we argue that that which appears as MPB, comprising of tetragonal and cubic-like phases on the global scale, is not so actually. The large piezoresponse is due to coexistence of tetragonal regions of long and short-range coherence. The PT-BNZ system is therefore qualitatively different from the conventional MPB systems such as PZT, PMN-PT, and PbTiO3-BiScO3, etc., which exhibits coexisting tetragonal and rhombohedral/monoclinic phases in thermodynamic equilibrium. In the absence of inter-ferroelectric instability as a phenomenon, field induced polarization-rotation and inter-ferroelectric transformation are no longer plausible mechanisms to explain the large piezoelectric response in PT-BNZ. The large piezoelectricity is primarily due to enhanced mobility of the tetragonal domain walls enabled by domain miniaturization. Our study proves that attainment of large piezoelectricity does not require inter-ferroelectric instability as a necessary criterion.

Atomic Structure of Domain and Interphase Boundaries in Ferroelectric HfO2

AbstractThough ferroelectric HfO2 thin films are now well characterized, little is currently known about their grain substructure. In particular, the formation of domain and phase boundaries requires investigation to better understand phase stabilization, switching, and phase interconversion. Here, scanning transmission electron microscopy is applied to investigate the atomic structure of boundaries in these materials. It is found that orthorhombic/orthorhombic domain walls and coherent orthorhombic/monoclinic interphase boundaries form throughout individual grains. The results inform how interphase boundaries can impose strain conditions that may be key to phase stabilization. Moreover, the atomic structure near interphase boundary walls suggests potential for their mobility under bias, which has been speculated to occur in perovskite morphotropic phase boundary systems by mechanisms similar to domain boundary motion.

Crucial role of octahedral untilting R3m/P4mm morphotropic phase boundary in highly piezoelectric perovskite oxide

Large piezoelectricity is usually found at morphotropic phase boundary (MPB), a composition-induced phase boundary between two ferroelectric phases. However, only a small fraction of MPBs (e.g., in PZT and PMN-PT) show large piezoelectricity. It remains a long-standing puzzle why not all MPBs yield large piezoelectricity. Here, by a comparative study of two MPB systems of BaZr0.2Ti0.8O3-PbTiO3 (BZT-PT) and Bi0.5Na0.5TiO3-PbTiO3 (BNT-PT), we find that the symmetry relation between the two ferroelectric phases at MPB plays a crucial role in piezoelectric activity. BZT-PT ceramic, having an R3m/P4mm MPB, exhibits strong piezoelectricity of d33 = 500 pC/N, whereas BNT-PT ceramic, having an R3c/P4mm MPB, exhibits much weaker piezoelectricity of d33 = 150 pC/N. The sharp difference between the two types of R/T MPBs is shown to arise from a significant difference in free energy barrier associated with oxygen octahedral tilting at MPB. An oxygen octahedral tilting/untilting transition at R3c/P4mm MPB leads to a high free energy barrier and results in low piezoelectric activity, whereas R3m/P4mm MPB with octahedral untilting produces large piezoelectricity due to low free energy barrier at such MPB. This feature show quite general in most of present MPBs systems and may become a dependable guideline for designing highly piezoelectric Pb-free materials.

Giant Polarization and High Temperature Monoclinic Phase in a Lead-Free Perovskite of Bi(Zn0.5Ti0.5)O3-BiFeO3.

Lead-free piezoelectrics have attracted increasing attention because of the awareness of lead toxicity to the environment. Here, a new bismuth-based lead-free perovskite, (1 - x)Bi(Zn0.5Ti0.5)O3-xBiFeO3, has been synthesized via a high-pressure and high-temperature method. It exhibits interesting properties of giant polarization, morphotropic phase boundary (MPB), and monoclinic phase. In particular, large tetragonality (c/a = 1.228) and giant spontaneous polarization of 110 μC/cm2 has been obtained in 0.6 Bi(Zn0.5Ti0.5)O3-0.4BiFeO3, which is much higher than most available lead-free materials and conventional Pb(Zr,Ti)O3. MPB is clearly identified to be constituted of tetragonal and monoclinic phases at x = 0.5. Notably, a single monoclinic phase has been observed at x = 0.6, which exhibits an intriguing high-temperature property. The present results are helpful to explore new lead-free MPB systems in bismuth-based compounds.

Quantitative phase separation in multiferroic Bi0.88Sm0.12FeO3 ceramics via piezoresponse force microscopy

BiFeO3 (BFO) is a classical multiferroic material with both ferroelectric and magnetic ordering at room temperature. Doping of this material with rare-earth oxides was found to be an efficient way to enhance the otherwise low piezoelectric response of unmodified BFO ceramics. In this work, we studied two types of bulk Sm-modified BFO ceramics with compositions close to the morphotropic phase boundary (MPB) prepared by different solid-state processing methods. In both samples, coexistence of polar R3c and antipolar Pbam phases was detected by conventional X-ray diffraction (XRD); the non-polar Pnma or Pbnm phase also has potential to be present due to the compositional proximity to the polar-to-non-polar phase boundary. Two approaches to separate the phases based on the piezoresponse force microscopy measurements have been proposed. The obtained fractions of the polar and non-polar/anti-polar phases were close to those determined by quantitative XRD analysis. The results thus reveal a useful method for quantitative determination of the phase composition in multi-phase ceramic systems, including the technologically most important MPB systems.

Anomalous polarization in the antiferroelectric-ferroelectric phase coexistence state in PbZrO3-Bi(Mg1/2Ti1/2)O3

The ferroelectric system (1−x)PbZrO3-(x)Bi(Mg1/2Ti1/2)O3 has been investigated as a function of composition, temperature, and electric field by x-ray powder diffraction, dielectric, and ferroelectric measurements. Within the solubility limit (x ∼ 0.25), the system evolves from an orthorhombic-antiferroelectric to rhombohedral-ferroelectric state through a phase coexistence region. The highest polarization was found not for the composition exhibiting a pure ferroelectric state, but for a composition x = 0.15 exhibiting ferroelectric + antiferroelectric phase coexistence close to the rhombohedral phase boundary. Electric poling of the equilibrium two-phase state led to irreversible enhancement in the rhombohedral phase fraction suggesting that the enhanced polarization is related to the enhanced polarizability of the lattice due to first order criticality as in ferroelectric-ferroelectric morphotropic phase boundary systems.

La-Driven Morphotrophic Phase Boundary in the Bi(Zn1/2Ti1/2)O3–La(Zn1/2Ti1/2)O3–PbTiO3 Solid Solution

We explore the Bi(Zn1/2Ti1/2)O3–La(Zn1/2Ti1/2)O3–PbTiO3 pseudoternary phase diagram using density functional theory and a solid solution model. We find a region of stability against phase segregation that contains a morphotropic phase boundary. On the basis of the results, we identify a ferroelectrically active composition-dependent region that is likely to show strong electro-mechanical response. Furthermore, we find that La replacement for Bi not only lowers the polarization as might be expected, but also shifts the balance from tetragonality toward rhombohedral distortions. This may be of general use in modifying phase diagrams of A-site driven perovskite ferroelectric solid solutions to generate new morphotropic phase boundary systems.

Electric-field-driven monoclinic-to-rhombohedral transformation in Na1/2Bi1/2TiO3

The lead free ferroelectric Na${}_{1/2}$Bi${}_{1/2}$TiO${}_{3}$ (NBT) is shown to exhibit electric-field-induced monoclinic ($Cc$) to rhombohedral ($R$3$c$) phase transformation at room temperature. This phenomenon has been analyzed both from the viewpoint of the intrinsic polarization rotation and adaptive phase models. In analogy with the morphotropic phase boundary systems, NBT seems to possess intrinsic competing ferroelectric instabilities near room temperature.

Characterization and Manipulation of Mixed Phase Nanodomains in Highly Strained BiFeO3 Thin Films

The novel strain-driven morphotropic phase boundary (MPB) in highly strained BiFeO(3) thin films is characterized by well-ordered mixed phase nanodomains (MPNs). Through scanning probe microscopy and synchrotron X-ray diffraction, eight structural variants of the MPNs are identified. Detailed polarization configurations within the MPNs are resolved using angular-dependent piezoelectric force microscopy. Guided by the obtained results, deterministic manipulation of the MPNs has been demonstrated by controlling the motion of the local probe. These findings are important for an in-depth understanding of the ultrahigh electromechanical response arising from phase transformation between competing phases, enabling future explorations on the electronic structure, magnetoelectricity, and other functionalities in this new MPB system.

A morphotropic phase boundary system based on polarization rotation and polarization extension

Many ferroelectric solid solutions exhibit enhanced electromechanical properties at the morphotropic boundary separating two phases with different orientations of polarization. The mechanism of properties enhancement is associated with easy paths for polarization rotation in anisotropically flattened free energy profile. Another mechanism of properties enhancement related to free energy flattening is polarization extension. It is best known at temperature-driven ferroelectric-paraelectric phase transitions and may lead to exceedingly large properties. Its disadvantage is temperature instability of the enhancement. In this paper a temperature-composition phase diagram is proposed that exhibits compositionally driven-phase transitions with easy paths for both polarization rotation and polarization extension.

Stability of the various crystallographic phases of the multiferroic (1−x)BiFeO3–xPbTiO3 system as a function of composition and temperature

In this report, we have studied the stability of various crystallographic phases of (1−x)BiFeO3–xPbTiO3 as a function of composition and temperature. The structure of BF-xPT is reconfirmed to be tetragonal and monoclinic in the P4mm and Cc space groups for x&amp;gt;0.31 and 0.10≤x≤0.27, whereas the two phases coexist in the morphotropic phase boundary (MPB) region 0.27&amp;lt;x&amp;lt;0.31. A recent proposition of an orthorhombic phase in the MPB region has been ruled out comprehensively. From the high temperature powder x-ray diffraction (XRD) data it is shown that the MPB in this system is tilted towards the tetragonal side, a unique feature among the family of PbTiO3 based MPB systems. We have established accurately the room temperature phase diagram for this solid solution. By comparing the observed bond lengths between oxygen and other cations, obtained from Rietveld analysis of the room temperature powder XRD data with expected ionic bond lengths, we have shown that the very high c/a ratio in the tetragonal phase of this system is linked with the covalency effects for bonding between both A and B site cations with oxygen.