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The present paper reviews models of domain structure in ferroelectric crystals, thin films and bulk materials. Common crystal structures in ferroelectric materials are described and the theory of compatible domain patterns is introduced. Applications to multi-rank laminates are presented. Alternative models employing phase-field and related techniq...
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... example, there are two types of domain wall in the tetragonal crystal system: 180° and 90° domain walls. Figure 2a shows a 180° domain wall separating regions of crystal lattice with anti-parallel polarizations and identical strain states. Figure 2b shows a 90° domain wall, across which the polarization rotates through about 90° . ...
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... 2a shows a 180° domain wall separating regions of crystal lattice with anti-parallel polarizations and identical strain states. Figure 2b shows a 90° domain wall, across which the polarization rotates through about 90° . In this crystal system, the compatibility conditions give a unique domain orientation for each 90° domain wall, while 180° domain walls have no such habit plane. ...
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... barium titanate, for example, the tetragonality of the unit cell is close to 1%. Thus the true rotation of the polarization vector across a 90° domain wall is 90.62° [6]; this effect is shown (exaggerated) in Figure 2b. Since the lattice planes turn by 0.62° across each domain wall, a disclination exists at the junction of four 90° domain walls. ...
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... Consequently, knowledge about the thermodynamic order of phase transitions and the characterization of parameters associated with the ferroelectric phase are of high relevance. The archetypal ferroelectric barium titanate (BaTiO 3 , BTO), for example, exhibits multiple ferroelectric phase transitions of different order, which manifest in drastic changes to its microscopic (e.g., the domain structure) and macroscopic properties [11][12][13][14][15] . ...
... This weak SHG intensity is indicative of a much smaller nonlinear susceptibility tensor magnitude. This appears to be consistent with observations from the linear dielectric constants at low frequency, which are also smaller in the orthorhombic phase compared to the tetragonal phase 12,14 . After relaxation back to room temperature an almost identical domain structure with DWs at similar locations does appear. ...
Ferroelectric materials play a crucial role in a broad range of technologies due to their unique properties that are deeply connected to the pattern and behavior of their ferroelectric (FE) domains. Chief among them, barium titanate (BaTiO3; BTO) sees widespread applications such as in electronics but equally is a ferroelectric model system for fundamental research, e.g., to study the interplay of such FE domains, the domain walls (DWs), and their macroscopic properties, owed to BTO's multiple and experimentally accessible phase transitions. Here, we employ Second Harmonic Generation Microscopy (SHGM) to $\it{in-situ}$ investigate the cubic-to-tetragonal (at 126C) and the tetragonal-to-orthorhombic (at 5C) phase transition in single-crystalline BTO via 3-dimensional (3D) DW mapping. We demonstrate that SHGM imaging provides the direct visualization of FE domain switching as well as the domain dynamics in 3D, shedding light on the interplay of the domain structure and the phase transition. These results allow us to extract the different transition temperatures locally, to unveil the hysteresis behavior, and to determine the type of phase transition at play (1st/2nd order) from the recorded SHGM data. The capabilities of SHGM in uncovering these crucial phenomena can easily be applied to other ferroelectrics to provide new possibilities for in-situ engineering of advanced ferroic devices.
... Based on the results of X-ray phase analysis, it was found that the samples of BaTiO 3 and BaTiO 3 /1 % Fe 3 O 4 are in the tetragonal syngony, but BaTiO 3 /10 % Fe 3 O 4 is in the cubic syngony. Therefore, the difference in heat capacity can be explained by the fact that when barium titanate passes from the tetragonal system to the cubic syngony [61,62]. In this case, the absence of a thermal effect in the composite material BaTiO 3 /10 % Fe 3 O 4 is not observed. ...
... A key feature of such a versatile application of BaTiO3 is ability of its crystals to perform spontaneous polarization in a temperature range below 120 °C, which is known as its Curie point. BaTiO3 possesses a typical perovskite structure with a sequence of phase transitions: cubic to tetragonal (120…130 °C), tetragonal to orthorhombic (about 5 °C), orthorhombic to rhombohedral (about -90 °C) [14]. Besides the cubic modification, the mentioned phases demonstrate ferroelectric properties due to their spontaneous polarization, among which the most prominent are reported for the tetragonal BaTiO3. ...
... % acetic acid solution and distilled water to remove the excess of barium ions. 14 Ceramics processing was carried out with the use of 5 wt. % of polyvinyl alcohol aqueous solution as a temporary binder. ...
A facile and environmentally benign method for a single-phase barium titanate synthesis in water vapor medium was studied to reveal the mechanism of phase transformation of the initial simple oxides mixture and estimate the capability of the product to be used as a raw material for low-frequency dielectric ceramics. The composition and structure of the reaction mixture treated in vapor at 130…150 °C as well as 230 °C for various time were investigated by means of XRD, SEM, HRTEM, EDX, and FTIR methods. The kinetics of the occurring phase transformation was described by Johnson-Mehl-Avrami-Erofeev equation. The reaction between the initial oxides was considered as a topochemical process with an apparent activation energy of 74…80 kJ mol-1. A crucial role in this process belonged to the water vapor medium, which facilitated the generation of the reaction zone and its spreading inward the solid particles. The synthesized tetragonal barium titanate powder (mean particle size of 135 ± 24 nm) was sintered by a conventional technique at 1250 °C to obtain ceramics with grains of about 2 μm. Capacitance measurements performed a dielectric constant and loss tangent of ceramics, which reached 3879 and 6.7 10-3, respectively, at 1 kHz and room temperature.
... The observed phase transition peak broadening near the T T-C confirms the improved relaxor nature or the diffused phase transition (DPT). The modified Curie-Weiss law proposed by Uchino and Nomura was utilised to provide a more precise quantification of the DPT behaviour of 1-xBZCT-BTL ceramics, which is given in Eq. (3) [58,59]. ...
This work highlights the electrocaloric (EC) and energy storage (ES) properties of 1-x(0.6Ba(Zr0.2Ti0.8)O3-0.4(Ba0.7Ca0.3)TiO3)-x(BiTa0.5La0.5)O3 (1-xBZCT-xBTL) ceramics with x = 0 to 0.05. The XRD studies revealed that inclusion of BTL content in BZCT does not induce any impurity phase. The peak splitting of BZCT near 2θ = 45∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ$$\end{document} and 66∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ$$\end{document} confirms the presence of morphotropic phase boundary corresponding to tetragonal and rhombohedral phases. Further, the solid solution formation of BZCT-BTL has suppressed its morphotropic phase boundary behaviour. The XRD, Raman and temperature dependent dielectric studies suggest the presence of pseudocubic phase in 1-xBZCT-xBTL at higher values of x = 0.025 and 0.05. Moreover, the inclusion of BTL boosts the diffused phase transition behaviour of BZCT ceramics. Further, BTL strengthened its relaxor nature due to a reduction in grain size as evidenced from SEM analysis. It is observed that the 0.99BZCT-0.01BTL ceramics show 95% efficiency and a maximum recoverable energy density of 479 mJ/cm³ at 100 kV/cm. Moreover, the electrocaloric temperature change and responsivity are found to be 1.06 K and 0.01 Kcm/kV near the transition temperature.
... The spontaneous polarization is induced by a non-centrosymmetric crystal structure such as in BaTiO3 (a perovskite), below the Curie temperature (Tc = 120 °C) above which it is in a paraelectric phase with no net polarization. In the temperature range of 5 °C to 120 °C, BaTiO3 adopts a polar tetragonal phase, which has six stable polarization directions parallel to the edges of the unit cell, resulting in six distinct crystal variants [232]. In rhombohedral phases, 8 variants and, in orthorhombic phases, 12 variants are present [232]. ...
... In the temperature range of 5 °C to 120 °C, BaTiO3 adopts a polar tetragonal phase, which has six stable polarization directions parallel to the edges of the unit cell, resulting in six distinct crystal variants [232]. In rhombohedral phases, 8 variants and, in orthorhombic phases, 12 variants are present [232]. These crystal structures determine the set of available polarization directions. ...
... Within the crystal, a region with uniform polarization constitutes a domain in which only a single crystal variant is found. Wherever domains meet, narrow interfaces known as domain walls form [232][233][234][235][236]. ...
This multi-disciplinary paper aims to provide a roadmap for the development of an integrated, process-intensified technology for the production of H2, NH3 and NH3-based symbiotic/smart fertilizers (referred to as target products) from renewable feedstock with CO2 sequestration and utilization while addressing environmental issues relating to the emerging Food, Energy and Water shortages as a result of global warming. The paper also discloses several novel processes, reactors and catalysts. In addition to the process intensification character of the processes used and reactors designed in this study, they also deliver novel or superior products so as to lower both capital and processing costs. The critical elements of the proposed technology in the sustainable production of the target products are examined under three-sections: (1) Materials: They include natural or synthetic porous water absorbents for NH3 sequestration and symbiotic and smart fertilizers (S-fertilizers), synthesis of plasma interactive supported catalysts including supported piezoelectric catalysts, supported high-entropy catalysts, plasma generating-chemical looping and natural catalysts and catalysts based on quantum effects in plasma. Their performance in NH3 synthesis and CO2 conversion to CO as well as the direct conversion of syngas to NH3 and NH3—fertilizers are evaluated, and their mechanisms investigated. The plasma-generating chemical-looping catalysts (Catalysts, 2020, 10, 152; and 2016, 6, 80) were further modified to obtain a highly active piezoelectric catalyst with high levels of chemical and morphological heterogeneity. In particular, the mechanism of structure formation in the catalysts BaTi1−rMrO3−x−y{#}xNz and M3O4−x−y{#}xNz/Si = X was studied. Here, z = 2y/3, {#} represents an oxygen vacancy and M is a transition metal catalyst. (2) Intensified processes: They include, multi-oxidant (air, oxygen, CO2 and water) fueled catalytic biomass/waste gasification for the generation of hydrogen-enriched syngas (H2, CO, CO2, CH4, N2); plasma enhanced syngas cleaning with ca. 99% tar removal; direct syngas-to-NH3 based fertilizer conversion using catalytic plasma with CO2 sequestration and microwave energized packed bed flow reactors with in situ reactive separation; CO2 conversion to CO with BaTiO3−x{#}x or biochar to achieve in situ O2 sequestration leading to higher CO2 conversion, biochar upgrading for agricultural applications; NH3 sequestration with CO2 and urea synthesis. (3) Reactors: Several patented process-intensified novel reactors were described and utilized. They are all based on the Multi-Reaction Zone Reactor (M-RZR) concept and include, a multi-oxidant gasifier, syngas cleaning reactor, NH3 and fertilizer production reactors with in situ NH3 sequestration with mineral acids or CO2. The approach adopted for the design of the critical reactors is to use the critical materials (including natural catalysts and soil additives) in order to enhance intensified H2 and NH3 production. Ultimately, they become an essential part of the S-fertilizer system, providing efficient fertilizer use and enhanced crop yield, especially under water and nutrient stress. These critical processes and reactors are based on a process intensification philosophy where critical materials are utilized in the acceleration of the reactions including NH3 production and carbon dioxide reduction. When compared with the current NH3 production technology (Haber–Bosch process), the proposed technology achieves higher ammonia conversion at much lower temperatures and atmospheric pressure while eliminating the costly NH3 separation process through in situ reactive separation, which results in the production of S-fertilizers or H2 or urea precursor (ammonium carbamate). As such, the cost of NH3-based S-fertilizers can become competitive with small-scale distributed production platforms compared with the Haber–Bosch fertilizers.
... As we mentioned above, the widening of the dielectric peak and the presence of DPT can be further understood from the modified Curie-Weiss law [29,55,56]. ...
... The domain pattern in a single crystal usually has a laminate structure of periodically alternating domains [57]. Laminate-based micromechanical models [17,[58][59][60][61][62][63][64][65][66][67] attempt to account for the spatial distribution of domains more accurately. Such models are based on the theory of mixtures and are aimed at studying the structure of domains and their evolution under the influence of external electromechanical loads. ...
... These models are based on the total energy minimization principle. A domain pattern is formed by the competition between the energy reduction due to improving alignment of the resulting averaging polarization with the external field and the energy increase due to the domain wall formation [65]. The competition of energies forms a laminate-based microstructure and leads to an equilibrium domain wall spacing. ...
... There are two approaches to modeling the evolution of the spatial domain structure depending on the interpretation of the domain wall: a diffuse interface [43][44][45][46][47][48][49]68] and a sharp interface [62][63][64][65][66]. In diffuse interface models (for example, the phase-field method), domain walls are three-dimensional objects, such as the domains themselves, and they are considered part of a continuum, whose polarization continuously changes within the domain wall. ...
The influence of the domain structure's initial topology and its evolution on the hysteresis curves of tetragonal and rhombohedral polydomain structures of ferroelectroelastic materials is studied. Based on the analysis of electrical and mechanical compatibility conditions, all possible variants of representative volume elements of tetragonal and rhombohedral second-rank-domain laminate structures were obtained and used in simulations. Considerable local inhomogeneity of stress and electric fields within the representative volume, as well as domain interaction, necessitates the use of numerical methods. Hysteresis curves for laminated domain patterns of the second rank were obtained using finite-element homogenization. The vector-potential finite-element formulation as the most effective method was used for solving nonlinear coupled boundary value problems of ferroelectroelasticity. A significant anisotropy of the hysteresis properties of domain structures was established both within individual phases and when comparing the tetragonal and rhombohedral phases. The proposed approach describes the effects of domain hardening and unloading nonlinearity.
... In order to confirm that the domain orientation measured using AES mapping is correct, we also performed an HF etch on the sample. Since HF is known to preferentially etch the -Z domains [24][25][26][27][28][29][30], analysis of the sample after etching confirms the size, shape and location of the poling domains. The HF etch method shows the domain orientation in the sample, but the etch process alters the sample and is not reversible. ...
The +/−Z ferroelectric domains in periodically poled lithium niobate are characterized with Auger electron spectroscopy. The -Z domains have a higher Auger O-KLL transition amplitude than the +Z domains. Based on this, Auger electron spectroscopy mapping can be used on the O-KLL peak to image the +/-Z domain structure. This new characterization technique is confirmed with HF etching, and compared to SEM imaging. Spatial resolution down to 68 nm is demonstrated.
... Of the known methods [23][24][25] that are used to study ferroelectric domains, the method of selective or so-called differential etching was used in this work. The method is based on the different etch rates for the positive and negative ends of ferroelectric dipoles [23,24,26]. ...
The practical significance of ferroelectric domains and various domain boundaries has been growing steadily in recent years. In this work, various domain structures were written with an electron beam through a thin aluminum film on a −Z cut of bulk lithium niobate. The use of relatively low accelerating voltages (5 and 10 kV) and the grounding of the surface metallization made it possible to write periodic structures (1D and 2D) on large areas with domain sizes ≤1 μm. Selective domain etching and AFM in contact mode were used to observe various domain shapes obtained in the experiments. An unusual feature of the submicron-sized domains was needle-like vertices. Importantly, the vertices of the domains were deepened relative to the irradiated surface. It was found that the size and proximity of the irradiated regions to each other in the patterns used can significantly change the upper part of the domains. The experimental data were analyzed and discussed taking into account the computer simulation of the spatial field distribution of injected electron beam charges. The obtained results contribute to the development of controlled writing of submicron-sized domain structures using an electron beam.
... These methods were limited to domain structures with sizes above approximately 0.5 µm. [146] A major achievement in the field was the development of domain imaging techniques pushing the resolution towards the nanoscale. Scanning electron microscopy (SEM) and piezoresponse force microscopy (PFM) have facilitated imaging of the complex coupling between microstructure and domain morphology at length scales well below 100 nm. ...
Ferroelectrics have a spontaneous electrical polarization that is arranged into domains and can be reversed by an externally applied field. This high versatility makes them useful in enabling components such as capacitors, sensors, and actuators. The key to tuning their dielectric, piezoelectric, and electromechanical performance is to control the domain structure and the dynamics of the domain walls. In fixed compositions, this is often realized by chemical doping. In addition, structural and microstructural parameters, such as grain size, degree of crystallographic texture or porosity play a key role. A major breakthrough in the field came with the fundamental understanding of the link between the local electric and mechanical driving forces and domain wall motion. Here, the impact of structure and microstructure on these driving forces is reviewed and an engineering toolbox is introduced. An overview of advances in the understanding of domain wall motion on the micro- and nanoscale is provided and discussed in terms of the macroscopic functional performance of polycrystalline ferroelectrics/ferroelastics. In addition, a link to theoretical and computational models is established. The review concludes with a discussion about beyond state-of-the-art characterization techniques, new approaches, and future directions toward non-conventionally ordered ferroelectrics for next-generation nanoelectronics and energy-storage applications.
