Monoclinic Ferroelectric Phase Research Articles

Permissible domain walls in monoclinic ferroelectrics. Part II. The case of MC phases.

Monoclinic ferroelectric phases are prevalent in various functional materials, most notably mixed-ion perovskite oxides. These phases can manifest as regularly ordered long-range crystallographic structures or as macroscopic averages of the self-assembled tetragonal/rhombohedral nanodomains. The structural and physical properties of monoclinic ferroelectric phases play a pivotal role when exploring the interplay between ferroelectricity, ferroelasticity, giant piezoelectricity and multiferroicity in crystals, ceramics and epitaxial thin films. However, the complex nature of this subject presents challenges, particularly in deciphering the microstructures of monoclinic domains. In Paper I [Biran & Gorfman (2024). Acta Cryst. A80, 112-128] the geometrical principles governing the connection of domain microstructures formed by pairing MAB type monoclinic domains were elucidated. Specifically, a catalog was established of `permissible domain walls', where `permissible', as originally introduced by Fousek & Janovec [J. Appl. Phys. (1969), 40, 135-142], denotes a mismatch-free connection between two monoclinic domains along the corresponding domain wall. The present article continues the prior work by elaborating on the formalisms of permissible domain walls to describe domain microstructures formed by pairing the MC type monoclinic domains. Similarly to Paper I, 84 permissible domain walls are presented for MC type domains. Each permissible domain wall is characterized by Miller indices, the transformation matrix between the crystallographic basis vectors of the domains and, crucially, the expected separation of Bragg peaks diffracted from the matched pair of domains. All these parameters are provided in an analytical form for easy and intuitive interpretation of the results. Additionally, 2D illustrations are provided for selected instances of permissible domain walls. The findings can prove valuable for various domain-related calculations, investigations involving X-ray diffraction for domain analysis and the description of domain-related physical properties.

Permissible domain walls in monoclinic MAB ferroelectric phases.

The concept of monoclinic ferroelectric phases has been extensively used over recent decades for the understanding of crystallographic structures of ferroelectric materials. Monoclinic phases have been actively invoked to describe the phase boundaries such as the so-called morphotropic phase boundary in functional perovskite oxides. These phases are believed to play a major role in the enhancement of such functional properties as dielectricity and electromechanical coupling through rotation of spontaneous polarization and/or modification of the rich domain microstructures. Unfortunately, such microstructures remain poorly understood due to the complexity of the subject. The goal of this work is to formulate the geometrical laws behind the monoclinic domain microstructures. Specifically, the result of previous work [Gorfman et al. (2022). Acta Cryst. A78, 158-171] is implemented to catalog and outline some properties of permissible domain walls that connect `strain' domains with monoclinic (MA/MB type) symmetry, occurring in ferroelectric perovskite oxides. The term `permissible' [Fousek & Janovec (1969). J. Appl. Phys. 40, 135-142] pertains to the domain walls connecting a pair of `strain' domains without a lattice mismatch. It was found that 12 monoclinic domains may form pairs connected along 84 types of permissible domain walls. These contain 48 domain walls with fixed Miller indices (known as W-walls) and 36 domain walls whose Miller indices may change when free lattice parameters change as well (known as S-walls). Simple and intuitive analytical expressions are provided that describe the orientation of these domain walls, the matrices of transformation between crystallographic basis vectors and, most importantly, the separation between Bragg peaks, diffracted from each of the 84 pairs of domains, connected along a permissible domain wall. It is shown that the orientation of a domain wall may be described by the specific combination of the monoclinic distortion parameters r = [2/(γ - α)][(c/a) - 1], f = (π - 2γ)/(π - 2α) and p = [2/(π - α - γ)] [(c/a) - 1]. The results of this work will enhance understanding and facilitate investigation (e.g. using single-crystal X-ray diffraction) of complex monoclinic domain microstructures in both crystals and thin films.

Фазовые состояния твердого раствора (1-x)PbFe-=SUB=-0.5-=/SUB=-Nb-=SUB=-0.5-=/SUB=-O-=SUB=-3-=/SUB=--xPbTiO-=SUB=-3-=/SUB=-. Описание на основе многоминимумных моделей

Based on the composition of two multiminimum models, a statistical model has been developed on the basis of which the formation of tetragonal and monoclinic ferroelectric phases in a solid solution (1-x)PbFe0.5Nb0.5O3-xPbTiO3 has been investigated and described. By selecting the parameters of the model, it was possible to reproduce the diagram T(x) of this solid solution. The peculiarity of the diagram is that when approaching the concentration of x~0.1, the temperatures of the phase transitions between the tetragonal and monoclinic phases decrease sharply, turning to zero. It is shown that the disappearance of the monoclinic phase is due to the specifics of the statistical properties of the eight-minimum model describing the subsystem of octahedra with eight minima. The features of the thermodynamic properties of a solid solution in the vicinity of the morphotropic boundary between the tetragonal and monoclinic phases are also investigated

The origin of piezoelectric enhancement in compositionally graded ferroelectrics with sinusoidal variation

The direct piezoelectric effect of BaTiO3↔ Ba1−xSrxTiO3 graded ferroelectrics, whose compositions change in a sinusoidal form, is investigated via an extended phase-field method. The obtained results demonstrate that the piezoelectric coefficient can be significantly enhanced by controlling the amplitude of sinusoidal variation. The origin of piezoelectric enhancement is investigated by considering the formation of polarization domain structures and their behaviors under strain. Although a ferroelectric tetragonal phase or a paraelectric cubic phase primarily form in homogeneous Ba1−xSrxTiO3 ferroelectrics with a different content x, interestingly, an unusual ferroelectric monoclinic phase can be formed in compositionally graded ferroelectrics, giving rise to the coexistence of multiple phases. The monoclinic phase emerges as a result of the process that reduces built-in electric potential induced by a large gradient of polarization. In turn, the formation of the monoclinic phase gives rise to transient zones that make the polarization field more susceptible to external strains, thereby enhancing the piezoelectric response. We further demonstrate that the piezoelectric enhancement strongly depends on the volume fraction of the monoclinic phase in compositionally graded ferroelectrics, suggesting a route for the rational design of polarization domains and piezoelectric effects.

Formation of phase states in PbFe-=SUB=-0.5-=/SUB=-Nb-=SUB=-0.5-=/SUB=-O-=SUB=-3-=/SUB=-: Description based on multiminima models

Two ferroelectric phase transitions are observed in the PbFe0.5Nb0.5O3 crystal. The first is between the cubic and tetragonal phase, the second is between the tetragonal and monoclinic phases. To describe phase transitions and emerging phases, a statistical model is proposed, based on the composition of two multi-minimum models --- a six-minima model for the Pb cation and an eight-minima model for the Nb cation. Adjusting the model parameters, makes it possible to reproduce all the characteristic features of the thermodynamic behavior of the crystal. The most interesting is the formation of a ferroelectric, complexly ordered monoclinic phase with Cm symmetry. It is shown that the mentioned monoclinic phase arises due to the fact that the first-order phase transition to the rhombohedral ferroelectric phase occurs in the presence of an "external field" of tetragonal symmetry. The contribution of the subsystems of Pb and Nb cations to the features of the dielectric and structural properties of the crystal is estimated. Keywords: ferroelectric relaxors, phase transitions, multiminima models, ferroelectric monoclinic phase.

Fabrication of bismuth silicate Bi2SiO5 ceramics as a potential high-temperature dielectric material

Bismuth silicate Bi2SiO5 (BSO) is known as an interesting new type of ferroelectric oxide; however, bulk ceramics of BSO have never been obtained because it easily decomposes at high temperature. In this study, we fabricated BSO ceramics for the first time using a sol–gel technique and investigated their potential as a dielectric material for high-temperature capacitor applications. A precursor powder was prepared by a sol–gel synthesis route using tetraethyl orthosilicate and bismuth nitrate pentahydrate as raw materials and then sintered under a small uniaxial pressure of 5 MPa with an addition of CH3COOLi as a sintering aid. A BSO ceramic with the highest relative density of 88.5% was obtained at a very low sintering temperature of 620 °C with preventing significant thermal decomposition. A crystal structure analysis revealed that the obtained BSO ceramic belongs to the ferroelectric monoclinic phase. The dielectric permittivity of the ceramic showed a superior temperature stability (± 5%) at temperatures up to 200 °C, followed by a sharp peak attributed to the ferroelectric–paraelectric phase transition at around 390 °C. The BSO ceramic also showed slim and pinched polarization hysteresis loops due to the random grain orientation and domain wall clamping, leading to a high energy storage efficiency over 75% at temperatures up to 100 °C.

Polymorphic transition and nucleation pathway of barium dititanate (BaTi2O5) during crystallization from undercooled liquid

The nucleation pathway plays an important role in vitrification, preparation of glass-ceramic composites and synthesis of metastable materials. In this paper, we studied the nucleation pathway of a novel ferroelectric BaTi2O5 (BT2) during crystallization from undercooled liquid by aerodynamic levitation (ADL) containerless processing and structural analysis. An interesting polymorphic transition of BT2 regulated by the undercooling was observed during the crystallization process: the ferroelectric monoclinic phase (γ-BT2) was fabricated at low undercoolings and the paraelectric orthorhombic metastable phase (β-BT2) was obtained from hypercooled liquid. This polymorphic transition phenomenon corresponds to a non-classical nucleation pathway: metastable β-BT2 preferentially nucleates from undercooled melt and γ-BT2 is generated from β phase by solid-state phase transition. The two-step nucleation pathway stems from the structural heredity between the undercooled liquid and crystals. A stronger structural homology exists between the undercooled melt and β-BT2 than γ-BT2 based on diffraction data and atomic configurations analysis. This structural homology coupled with nucleation barrier calculation was used to elucidate the non-classical nucleation pathway of BT2 crystallization: the similarity of the structural unit (Ti-O polyhedra) between the undercooled liquid and the metastable β-BT2 reduces the nucleation barrier and contributes to the preferential precipitation of β-like clusters. This work reveals the formation route of BT2 from cooling melt, which not only benefits the synthesis and application of this novel functional material but also provides a guideline of the crystallization process of titanates from melt at atomic level.

Ferroelectric monoclinic phases in strained K0.70Na0.30NbO3 thin films promoting selective surface acoustic wave propagation

We present a detailed analysis of the ferroelectric domain structure of K0.70Na0.30NbO3 thin films on (110) TbScO3 grown by metal–organic chemical vapor deposition. Upon piezoresponse force microscopy and nanofocus x-ray diffraction measurements we derive a domain model revealing monoclinic MC domains. The complex domain pattern is formed out of four co-existing in-plane orientations of the shearing direction of the monoclinic unit cell resulting in four types of superdomains each being composed of well-ordered stripe domains. Finally, we present surface acoustic wave (SAW) experiments that exhibit extraordinary signal intensities given the low thickness of the tested film. Moreover, the SAW propagation is found to occur selectively along the identified shearing directions.

Electric field induced phase transition and accompanying giant poling strain in lead-free NaNbO3-BaZrO3 ceramics

A series of phase transitions in (1-x)NaNbO3-xBaZrO3 ((1-x)NN-xBZ) ceramics was observed from antiferroelectric orthorhombic phase to ferroelectric orthorhombic phase and finally into ferroelectric rhombohedral phase with increasing x. An electric field induced irreversible phase transition was found in different compositions, irrespective of their virgin phase structures. Particularly, an antiferroelectric orthorhombic phase is irreversibly transformed into a ferroelectric monoclinic phase within 0.02 ≤ x ≤ 0.05, leading to a giant poling strain of ∼0.58%. This is much larger than that observed in ferroelectric orthorhombic (0.06 ≤ x ≤ 0.07) and rhombohedral phases (0.08 ≤ x ≤ 0.11) suffering from an irreversible ferroelectric-ferroelectric (monoclinic) phase transition. The synchrotron x-ray diffraction and the measurement of longitudinal and transverse strains suggest that this irreversible phase transition should involve not only a distinct volume expansion, but also an obvious lattice elongation. The present study demonstrates a unique nature of the composition and field dependent phase stability and an underlying mechanism of giant poling strains in NN-BZ ceramics.

Local structure analysis of (Na0.5K0.45Li0.05)NbO3 synthesized by malic acid complex solution method

A monoclinic ferroelectric phase with the space group Pm has been discovered in lead-free (Na0.5K0.45Li0.05)NbO3 solid solution ceramics synthesized by a malic acid complex solution method. At ambient temperature, the lattice parameters of this monoclinic structure were . The average and local structures of this monoclinic phase were analyzed by synchrotron X-ray measurements. The average structure maintained the monoclinic structure down to 20 K, although the local structure changed below room temperature. The distinct short-range order structure was found to be rhombohedral. The results demonstrate the presence of an order–disorder-type phase transition structurally bridging between the rhombohedral local structure and the low-symmetry monoclinic average structure in a (Na0.5K0.45Li0.05)NbO3 solid solution system.

Strain engineering of monoclinic domains in KxNa1−xNbO3 epitaxial layers: a pathway to enhanced piezoelectric properties

A novel concept to obtain a ferroelectric material with enhanced piezoelectric properties is proposed. This approach is based on the combination of two pathways: (i) the evolution of a ferroelectric monoclinic phase and, (ii) the coexistence of different types of ferroelectric domains leading to polarization discontinuities at the domain walls. Each of these pathways enables polarization rotation in the material which is responsible for giant piezoelectricity. Targeted incorporation of anisotropic epitaxial lattice strain is used to implement this approach. The feasibility of our concept is demonstrated for K0.9Na0.1NbO3 epitaxial layers grown on NdScO3 substrates where the coexistence of (100)pc and (001)pc pseudocubic oriented monoclinic domains is experimentally verified. This coexistence results in a complex periodic domain pattern with alternating emergence of ferroelectric in-plane a1a2 and inclined MC monoclinic phases, which differ in the direction of the electrical polarization vector. Our approach opens the possibility to exploit ferroelectric properties in both vertical and lateral directions and to achieve enhanced piezoelectric properties in lead-free material caused by singularities at the domains walls.

Domain configuration evolution, dielectric, ferroelectric and piezoelectric properties of 0.32PIN–0.345PMN–0.335PT single crystals

Domain configuration evolution with temperature of the unpoled [001]C-oriented 0.32Pb(In1/2Nb1/2)O3–0.345Pb(Mg1/3Nb2/3)O3–0.335PbTiO3 (0.32PIN–0.345PMN–0.335PT) single crystals was studied by the polarized light microscopy (PLM). The optical observation of the domain structures reveals the coexistence of polymorphic ferroelectric phases with mainly ferroelectric monoclinic phase at room temperature and the irreversible domain evolution upon thermal cycling, which induce the high piezoelectric response in such relaxor-based ferroelectric single crystals with the morphotropic phase boundary compositions combined with polarization rotation. The temperature dependent domain evolution and dielectric behavior demonstrate the successive temperature-induced second-order ferroelectric M phase to ferroelectric tetragonal (T) phase (FEM–FET) and first-order ferroelectric T phase to paraelectric cubic (C) phase (FET–PC) ferroelectric phase transitions in the unpoled 0.32PIN–0.345PMN–0.335PT single crystals. Two dielectric loss anomalies were detected around the dielectric anomaly below 100 °C in the poled 0.32PIN–0.345PMN–0.335PT single crystals, indicating that the FEM–FET phase transition can be correlated with two different ferroelectric phase transitions, one is MA–MC, and the other is MC–T phase transition. The FEM–FET phase transition was confirmed further by the energy density measurement. The temperature dependent piezoelectric properties proved that the working temperature of the 0.32PIN–0.345PMN–0.335PT single crystals can reach 130 °C, higher around 50 °C than the Pb(Mg1/3Nb2/3)O3–PbTiO3 single crystals, indicating their promising applications in transducers used at elevated temperatures.

Ferroelectric phase transitions of the 0.32PIN-0.345PMN-0.335PT single crystals studied by temperature-dependent Raman spectroscopy, dielectric and ferroelectric performance

ABSTRACTThe ferroelectric phase transition characteristics of the 0.32Pb(In1/2Nb1/2)O3-0.345Pb(Mg1/3Nb2/3)O3-0.335PbTiO3 (0.32PIN-0.345PMN-0.335PT) single crystals were studied by the temperature-dependent Raman spectroscopy and some electrical properties. Ferroelectric monoclinic phase was confirmed at room temperature by the numbers of the Raman modes. Successive ferroelectric phase transitions, i.e. ferroelectric monoclinic phase to ferroelectric tetragonal phase transition (FEM-FET) and ferroelectric tetragonal phase to paraelectric cubic phase transition (FET-PC), are evidenced by the anomalies of Raman modes line width, peaks intensity and their ratios around TM-T and TC/Tm temperatures. The temperature dependent permittivity derivative ξ = dϵ/dT not only provides further evidence of the successive ferroelectric phase transitions, but also demonstrates the second-order transition characteristic of the FEM-FET phase transition and the first-order transition feature of the FET-PC phase transition. The FEM-FET phase transition is also confirmed by the abnormal narrowing of the P-E loops, decrease of the Pr and Ec values, and extremums of the pyroelectric performance.

Study of temperature-dependent Raman spectroscopy and electrical properties in [001]-oriented 0.35Pb(In1/2Nb1/2)O3-0.35Pb(Mg1/3Nb2/3)O3-0.30PbTiO3-Mn single crystals

In this work, the temperature-dependent Raman spectra and electrical properties of the [001]-oriented 0.5 mol. % Mn-doped 0.35Pb(In1/2Nb1/2)O3-0.35Pb(Mg1/3Nb2/3)O3-0.30PbTiO3-Mn (PIMNT-Mn) single crystals were investigated. All the unpoled and poled PIMNT-Mn single crystals experience a ferroelectric tetragonal phase to paraelectric cubic phase transition (FET-PC) around 183 °C (TC), which exhibits a second-order transition behavior. Whereas, the poled PIMNT-Mn single crystals exhibit another two dielectric anomalies around 130 °C (TRM) and 148 °C (TMT), in which the ferroelectric rhombohedral phase to ferroelectric monoclinic phase (FER-FEM) and the ferroelectric monoclinic phase to ferroelectric tetragonal phase (FEM-FET) transitions take place, respectively. Both the two ferroelectric phase transitions exhibit a first-order transition behavior. The discontinuous change of the phase degree (θ) and frequencies (fr and fa) around TRM suggest the occurrence of the FER-FEM phase transition in the poled PIMNT-Mn single crystals. The narrowing of the 510 cm−1 and 582 cm−1 Raman modes around the TRM, TMT, and TC temperatures shown in the temperature-dependent Raman spectra suggests their increased ordering of the local structure. The intensity ratio of I272 cm−1/I801 cm−1 increases obviously around the phase transition temperatures (TRM, TMT, and TC), indicating the reduction of the long-range order. The anomalous broadening of the 272 cm−1 Raman mode around the TRM, TMT, and TC temperatures indicates the occurrence of the successive ferroelectric phase transitions (FER-FEM, FEM-FET, and FET-PC) with increasing temperature in the poled PIMNT-Mn single crystals.

X-ray photoelectron study and first principle calculations of the electronic structure of PbFe1/2Nb1/2O3 single crystal in the ferroelectric and paraelectric phases

The present study is the first in which the theoretical prediction of the changes in the density of states of single crystal of PbFe1/2Nb1/2O3 (PFN) multiferroic depending on a temperature at the ferroelectric – paraelectric transition is experimentally confirmed by the X-ray photoelectron spectroscopy. The valence band XPS spectra of PFN single-crystal at three temperatures T1 = 297 K (monoclinic phase), T2 = 368 K (tetragonal) and T3 = 403 K (cubic) were obtained by X-ray photoelectron study using ESCALAB 250. It is found out that the experimental valence band XPS spectra of PFN single-crystals in ferroelectric and paraelectric phases consist of two main peaks with a difference in relative intensity and energy position of the second peak. The density of states of PFN was calculated for tetragonal ferroelectric (368 K) and cubic paraelectric (403 K) phases. The first main peak corresponds to strongly hybridized Fe3d, Nb3d and O2p states while the second peak is mainly composed of Pb6s states. According to the experimental data, the position of the second main peak of the total density of states of PFN in the ferroelectric monoclinic phase is shifted toward the first peak relatively to its position in the paraelectric phase by 0.28 eV and for the tetragonal phase by 0.15 eV, the latter value coincides well with the calculated value equal to 0.17 eV.

Low-symmetry monoclinic ferroelectric phase stabilized by oxygen octahedra rotations in strained EuxSr1−xTiO3thin films

Using Landau--Ginzburg--Devonshire theory and phase-field modeling, we explore the complex interplay between a structural order parameter (oxygen octahedron rotation) and polarization in Eu${}_{x}$Sr${}_{1\ensuremath{-}x}$TiO${}_{3}$ thin films. Under a biaxially tensile strain, a low-symmetry monoclinic phase with in-plane ferroelectric polarization is found to be stabilized by antiferrodistortive oxygen octahedra tilts. The monoclinic phase is stable over a wide temperature range. It is characterized by a large number of energetically equivalent polar and structural twin domains. This work demonstrates the development of a spontaneous polarization and piezo- and pyroelectricity in a ferroelastic twin boundary arising from flexoelectric coupling and rotostriction.

Room-temperature ferroelectricity in diisopropylammonium bromide

A room-temperature ferroelectric, diisopropylammonium bromide (DPB), with dielectric constant e ≈ 12 000 and a clear hysteresis loop at Tc = 425 K is reported. At 417 K DPB undergoes the irreversible phase transition from nonpolar orthorhombic P212121 to the ferroelectric monoclinic phase (P21) and subsequently, at 425 K, to the paraelectric prototype phase (P21/m). The molecular mechanism of the paraelectric–ferroelectric transition is ascribed to the ‘order–disorder’ behaviour of the diisopropylammonium cations.

A monoclinic-tetragonal ferroelectric phase transition in lead-free (K0.5Na0.5)NbO3-x%LiNbO3 solid solution

A monoclinic ferroelectric phase with space group Pm has been discovered in lead-free (K0.5Na0.5)NbO3-5%LiNbO3 solid solution ceramics by high energy synchrotron x-ray powder diffraction measurements. At ambient temperature, the lattice parameters of this monoclinic structure were (am, bm, cm; β) = (4.015 Å, 3.944 Å, 3.987 Å; 90.34°). This monoclinic phase transformed to a tetragonal (P4mm) one on heating between 340 K and 360 K. The results demonstrate the presence of structurally bridging low symmetry monoclinic phase in (K0.5Na0.5)NbO3-x%LiNbO3 solid solution system: indicating a means to achieve high piezoelectricity in Pb-free systems via domain engineering.

The Role of Proton–Proton Interaction in NH4H2PO4-Type Crystals

The interaction between the protons on the nearby hydrogen bonds in NH 4 H 2 PO 4 (ADP)-type crystals, called the Ishibashi interaction, was analyzed to derive theoretically, i.e., not in an ad hoc way, the effective dipole–dipole interaction between PO 4 radicals, which plays a substantial role in phase transitions. It turns out that at low temperatures the ADP-type antiferroelectric phase is stabilized if the Ishibashi interaction is repulsive, while the monoclinic ferroelectric phase is stabilized otherwise.

Orthorhombic and monoclinic ferroelectric phases investigated by Raman spectroscopy in PZN-4.5%PT and PZN-9%PT crystals

Polarized Raman spectra measurements have been performed on orientated single crystals of Pb[(Zn 1/3Nb 2/3) 0.955Ti 0.045]O 3 (PZN-4.5%PT) and Pb[(Zn 1/3Nb 2/3) 0.91Ti 0.09]O 3 (PZN-9%PT) poled by an electric field along the [ 1 ̄ 01 ] pseudo-cubic direction in order to determine the nature of the induced ferroelectric phases. Under field-cooled (FC) conditions the ferrolectric phase transition sequence, tetragonal–orthorhombic–rhombohedral, was observed in PZN-4.5%PT. Comparison between the phase transitions induced in PZN-9%PT and PZN-4.5%PT crystals in FC shows that the low- temperature ferroelectric phase in PZN-9%PT cannot be orthorhombic and it can be attributed to the monoclinic phase. The characteristic temperatures found by Raman spectroscopy correspond to those obtained by dielectric measurements and by X-ray diffraction reported previously.