Bipolar charge collecting structure enables overall water splitting on ferroelectric photocatalysts

Ag/Ag2S plasmonic heterostructure promotes piezoelectric photocatalytic activity of BiFeO3 nanofibers for degradation of ciprofloxacin and energy conversion

Piezoelectric effect, plasma effect and semiconductor heterostructure are important strategies for enhanced photocatalytic performance. Herein, we developed a novel heterostructure piezoelectric photocatalyst, Ag/Ag2S/BiFeO3 (AAS/BFO), for photocatalytic degradation of ciprofloxacin from water. Experimental results verified the enhancement of combining heterostructure piezoelectric polarization effect, which promotes efficient migration and separation of photogenerated carriers due to the localized surface plasmon resonance effect of Ag nanoparticles. Additionally, the introduction of Ag2S constructs a new heterostructure, that enhances the electron transport rate and improves the separation efficiency on electron-hole pairs. Under ultrasonic stimulation and visible light irradiation, the degradation efficiencies of 15 %-AAS/BFO towards ciprofloxacin, methyl orange and methylene blue are significantly enhanced compared to pure BFO fibers. The demonstrated AAS/BFO material based on the synergistic piezoelectric effect and plasmon heterostructure shows potential in efficient organic pollutants water treatment and transforming mechanical energy into chemical energy.

Parallel Regulation of Charge Dynamics on Bipolar Ferroelectric Surfaces Breaks the Limits for Water Splitting Efficiency

Ferroelectric materials, known for their non-inversion symmetry, show promise as photocatalysts due to their unique asymmetric charge separation, which separates hydrogen and oxygen evolution sites. However, the strong depolarized field induces a relaxed surface structure, which in turn directly leads to slow hole charge transfer dynamics, hindering their efficiency in water splitting. In this study, a fundamental breakthrough in dramatically enhancing the overall water-splitting activity is presented, through the synergistically regulating of the surface behaviors of photogenerated carriers, resulting in nearly perfect parallel dynamics and balanced amounts. By depositing atomic layers of TiO2 onto the surface of PbTiO3, surface vacancies are effectively passivated, significantly prolonging the hole lifetime from 10-6 to 10-3 s. Spatially resolved transient photovoltage spectroscopy showed that improved hole dynamics led to a 180° phase shift between photogenerated electrons and holes, indicating nearly identical extraction dynamics. Notably, hole and electron concentrations increased to equivalent levels. This leads to a nearly 578-fold increment in the apparent quantum yield, resulting in significantly increased overall water-splitting rates, with a quantum yield of 5.78% at 365 nm. The strategy is also effective with Al2O3 and SiO2, demonstrating its versatility across varied materials, providing a valuable method for creating high-performance ferroelectric photocatalysts.

Plasmonic Au Grid-CdSe Heteropatterned Film by Topochemistry and CdCl2 Surface Passivation for Photoelectrochemical Hydrogen Evolution

Constructing patterned film photoanodes with economizing raw chemicals but enhancing photoelectrochemical (PEC) performance is attractive for practical applications. However, simultaneously optimizing light scattering and interfacial charge transfer through plasmonic enhancement remains challenging. Herein, we developed a novel plasmonic photoanode featuring Au grids and a nanometer-thick CdSe layer (Au grid-CdSe) with well-organized heterointerfaces, fabricated via a facile colloidal topochemical strategy. This design leverages the synergistic coupling between plasmons and excitons in plasmonic heteropatterned films. The underlying patterned Au grids serve dual functions: as an electron collector and light reflector. Their highly ordered Bragg structure effectively scatters incident light into the ultrathin CdSe layer. Furthermore, CdCl2 surface passivation of the Au(grid)-CdSe heteropatterned photoanode, based on this unique light absorption/reflector architecture, yielded a photocurrent density of 4.51 mA cm-2, representing significant enhancement. Compared to similarly prepared Au-CdSe heterofilms, the passivated Au(grid)-CdSe heteropatterned films exhibited 2.0-fold higher PEC hydrogen evolution performance, maintained excellent stability for over 26 h, and reduced Au consumption by 32%. This strategy offers a novel pathway for improving the performance of semiconductor-based optoelectronic devices.

Dynamic regulation of ferroelectric polarization using external stimuli for efficient water splitting and beyond

Establishing and regulating the ferroelectric polarization in ferroelectric nano-scale catalysts has been recognized as an emerging strategy to advance water splitting reactions, with the merits of improved surface charge density, high charge transfer rate, increased electronic conductivity, the creation of real active sites, and optimizing the chemisorption energy. As a result, engineering and tailoring the ferroelectric polarization induced internal electric field provides significant opportunities to improve the surface and electronic characteristics of catalysts, thereby enhancing the water splitting reaction kinetics. In this review, an interdisciplinary and comprehensive summary of recent advancements in the construction, characterization, engineering and regulation of the polarization in ferroelectric-based catalysts for water splitting is provided, by exploiting a variety of external stimuli. This review begins with a detailed overview of the classification, benefits, and identification methodologies of the ferroelectric polarization induced internal electric field; this offers significant insights for an in-depth analysis of ferroelectric-based catalysts. Subsequently, we explore the underlying structure-activity relationships for regulating the ferroelectric polarization using a range of external stimuli which include mechanical, magnetic, and thermal fields to achieve efficient water splitting, along with a combination of two or more fields. The review then highlights emerging strategies for multi-scale design and theoretical prediction of the relevant factors to develop highly promising ferroelectric catalysts for efficient water splitting. Finally, we present the challenges and perspectives on the potential research avenues in this fascinating and new field. This review therefore delivers an in-depth examination of the strategies to engineer the ferroelectric polarization for the next-generation of water electrolysis devices, systems and beyond.

Highly enhanced room-temperature single-atom catalysis of two-dimensional organic-inorganic multiferroics Cr(half-fluoropyrazine)2 for CO oxidation

In modern chemistry, the development of highly efficient room-temperature catalysts is of great significance and remains a long-standing challenge in various typical reactions. Here, we theoretically demonstrate that the two-dimensional (2D) multiferroic, Cr(half-fluoropyrazine)2 [Cr(h-fpyz)2], is a promising single-atom catalyst (SAC) operating at room temperature for CO oxidation. The rate-limiting barrier is merely 0.325 eV, leading to a reaction rate (i.e., 3.47 × 106 s-1) of six orders of magnitude higher than its monoferroic derivative [Cr(pyz)2], due to the synergetic effects of two aspects. First, the more flexible ligand rotations in Cr(h-fpyz)2 facilitate the activation of O2 molecule, simultaneously enhancing the charge transfer and spin-accommodation process. Second, on Cr(h-fpyz)2, O2 adsorption induces a distinctly lower local positive electric field, reducing the electrostatic repulsion of the polar CO molecule. These findings may also pave the way for establishing highly efficient SAC platforms based on 2D multiferroics where multidegree of freedom (e.g., spin, polarity) synergistically matter.

Unveiling charge utilization mechanisms in ferroelectric for water splitting

Charge separation is a critical process for achieving high photocatalytic efficiency, and ferroelectrics hold significant potential for facilitating effective charge separation. However, few studies have demonstrated substantial photocatalytic activity in these materials. In this study, we demonstrate that in ferroelectric PbTiO3, surface Ti vacancy defects near the positively polarized facets impede photocatalytic performance by trapping electrons and inducing their recombination. To tackle this issue, we selectively grew SrTiO3 nanolayers on the polarized facets PbTiO3, effectively mitigating interface Ti defects. This modification establishes a efficient electron transfer pathway at the interface between the positively polarized facets and the cocatalyst, extending the electron lifetime from 50 microseconds to the millisecond scale and significantly increasing electron participation in water-splitting reactions. Consequently, the apparent quantum yield for overall water splitting achieves the highest values reported to date for ferroelectric photocatalytic materials. This work provides an effective strategy for designing advanced ferroelectric photocatalytic systems.

Strong Interfacial Interaction in Polarized Ferroelectric Heterostructured Nanosheets for Highly Efficient and Selective Photocatalytic CO2 Reduction

Heterojunctions are sustainable solutions for the photocatalytic CO2 reduction reaction (CO2RR) by regulating charge separation behavior at the interface. However, their efficiency and product selectivity are severely hindered by the inflexible and weak built-in electric field and the electronic structure of the two phases. Herein, ferroelectric-based heterojunctions between polarized bismuth ferrite (BFO(P)) and CdS are constructed to enhance the interfacial interactions and catalytic activity. The intrinsic polarization field depending on the ferroelectric state causes significant electrostatic potential difference and energy-band bending. This helps overcome the unsatisfactory redox potential that differs from the classical catalytic mechanism, and synergy from the heterostructure facilitates effective separation and transfer of photogenerated charges with an extended lifetime (>20 ns) and significantly enhanced photovoltage (1002 times that of BFO). The optimized charge carrier dynamics allow the heterojunction to achieve a much higher CO yield compared to state-of-the-art ferroelectric-based photocatalysts, and 85.46 and 23.47 times higher than those of pristine CdS and BFO, respectively. Moreover, it maintains an impressive 100% product selectivity together with excellent repeatability and cycling. This work not only sheds light on how a strong inherent polarity promotes the performance of heterojunction photocatalysts but also provides new insights for designing efficient photocatalytic CO2RR.

Polarization-Switchable Electrochemistry of 2D Layered Bi2O2Se Bifunctional Microreactors by Ferroelectric Modulation

Ferroelectric catalysts are known for altering surface catalytic activities by changing the direction of their electric polarizations. This study demonstrates polarization-switchable electrochemistry using layered bismuth oxyselenide (L-Bi2O2Se) bifunctional microreactors through ferroelectric modulation. A selective-area ionic liquid gating is developed with precise control over the spatial distribution of the dipole orientation of L-Bi2O2Se. On-chip microreactors with upward polarization favor the oxygen evolution reaction, whereas those with downward polarization prefer the hydrogen evolution reaction. The microscopic origin behind polarization-switchable electrochemistry primarily stems from enhanced surface adsorption and reduced energy barriers for reactions, as examined by nanoscale scanning electrochemical cell microscopy. Integrating a pair of L-Bi2O2Se microreactors consisting of upward or downward polarizations demonstrates overall water splitting in a full-cell configuration based on a bifunctional catalyst. The ability to modulate surface polarizations on a single catalyst via ferroelectric polarization switching offers a pathway for designing catalysts for water splitting.

Manipulating Ferroelectric Polarization and Spin Polarization of 2D CuInP2S6 Crystals for Photocatalytic CO2 Reduction

Manipulating electronic polarizations such as ferroelectric or spin polarizations has recently emerged as an effective strategy for enhancing the efficiency of photocatalytic reactions. This study demonstrates the control of electronic polarizations modulated by ferroelectric and magnetic approaches within a two-dimensional (2D) layered crystal of copper indium thiophosphate (CuInP2S6) to boost the photocatalytic reduction of CO2. We investigate the substantial influence of ferroelectric polarization on the photocatalytic CO2 reduction efficiency, utilizing the ferroelectric-paraelectric phase transition and polarization alignment through electrical poling. Additionally, we explore enhancing the CO2 reduction efficiency by harnessing spin electrons through the synergistic introduction of sulfur vacancies and applying a magnetic field. Several advanced characterization techniques, including piezoresponse force microscopy, ultrafast pump-probe spectroscopy, in situ X-ray absorption spectroscopy, and in situ diffuse reflectance infrared Fourier transformed spectroscopy, are performed to unveil the underlying mechanism of the enhanced photocatalytic CO2 reduction. These findings pave the way for manipulating electronic polarizations regulated through ferroelectric or magnetic modulations in 2D layered materials to advance the efficiency of photocatalytic CO2 reduction.

Bipolaronic Motifs Induced Spatially Separated Catalytic Sites for Tunable Syngas Photosynthesis From CO2

Photocatalytic reduction of CO2 into syngas is a promising way to tackle the energy and environmental challenges; however, it remains a challenge to achieve reaction decoupling of CO2 reduction and water splitting. Therefore, efficient production of syngas with a suitable CO/H2 ratio for Fischer-Tropsch synthesis can hardly be achieved. Herein, bipolaronic motifs including Co(II)-pyridine N motifs and Co(II)-imine N motifs are rationally designed into a crystalline imine-linked 1,10-phenanthroline-5,6-dione-based covalent organic framework (bp-Co-COF) with a triazine core. These featured structures with spatially separated active sites exhibit efficient photocatalytic performance toward CO2-to-syngas conversion with a suitable CO/H2 ratio (1:1-1:3). The bipolaronic motifs enable a highly separated electron-hole state, whereby the Co(II)-pyridine N motifs tend to be the active sites for CO2 activation and accelerate the hydrogenation to form *COOH intermediates; whilst, the Co(II)-imine N motifs increase surface hydrophilicity for H2 evolution. The photocatalytic reductions of CO2 and H2O thus decouple and proceed via a concerted way on the bipolaronic motifs of bp-Co-COF. The optimal bp-Co-COF photocatalyst achieves a high syngas evolution rate of 15.8 mmol g-1 h-1 with CO/H2 ratio of 1:2, outperforming previously reported COF-based photocatalysts.

Correlating activities and defects in (photo)electrocatalysts using in-situ multi-modal microscopic imaging

Photo(electro)catalysts use sunlight to drive chemical reactions such as water splitting. A major factor limiting photocatalyst development is physicochemical heterogeneity which leads to spatially dependent reactivity. To link structure and function in such systems, simultaneous probing of the electrochemical environment at microscopic length scales and a broad range of timescales (ns to s) is required. Here, we address this challenge by developing and applying in-situ (optical) microscopies to map and correlate local electrochemical activity, with hole lifetimes, oxygen vacancy concentrations and photoelectrode crystal structure. Using this multi-modal approach, we study prototypical hematite (α-Fe2O3) photoelectrodes. We demonstrate that regions of α-Fe2O3, adjacent to microstructural cracks have a better photoelectrochemical response and reduced back electron recombination due to an optimal oxygen vacancy concentration, with the film thickness and extended light exposure also influencing local activity. Our work highlights the importance of microscopic mapping to understand activity, in even seemingly homogeneous photoelectrodes.

Improved Carrier Separation and Recombination by Ferroelectric Polarization in the CuBiP2Se6/C2N Heterostructure: A Nonadiabatic Molecular Dynamics Study

The rapid recombination of photogenerated carriers heavily restricts the photocatalytic efficiency. Here, we propose a new strategy to improve catalytic efficiency based on the ferroelectric van der Waals heterostructure (CuBiP2Se6/C2N). Combining density functional theory and the nonadiabatic molecular dynamics (NAMD) method, we have systematically analyzed the ground-state properties and carrier dynamics images in the CuBiP2Se6/C2N heterostructure. Our calculations showed that the ferroelectric polarization of CuBiP2Se6 provides the internal driving force for the photogenerated carriers separation. NAMD results demonstrate that the excited-state carrier transfer and recombination processes in the CuBiP2Se6/C2N are consistent with a type II mechanism. Meanwhile, constructing the ferroelectric heterostructure can effectively prolong the carrier lifetime, from ∼65.98 to ∼124.54 ps. Moreover, the high quantum efficiency and tunable band edge positions mean that the CuBiP2Se6/C2N heterostructure is an excellent potential candidate material for photocatalytic water splitting.

Customizing precise, tunable, and universal cascade charge transfer chains towards versatile photoredox catalysis

The core factors dictating the photocatalysis efficiency are predominantly centered on controllable modulation of anisotropic spatial charge transfer/separation and regulating vectorial charge transport pathways. Nonetheless, the sluggish charge transport kinetics and incapacity of precisely tuning interfacial charge flow at the nanoscale level are still the primary dilemma. Herein, we conceptually demonstrate the elaborate design of a cascade charge transport chain over transition metal chalcogenide-insulating polymer-cocatalyst (TIC) photosystems via a progressive self-assembly strategy. The intermediate ultrathin non-conjugated insulating polymer layer, i.e., poly(diallyl-dimethylammonium chloride) (PDDA), functions as the interfacial electron relay medium, and simultaneously, outermost co-catalysts serve as the terminal "electron reservoirs", synergistically contributing to the charge transport cascade pathway and substantially boosting the interfacial charge separation. We found that the insulating polymer mediated unidirectional charge transfer cascade is universal for a large variety of metal or non-metal reducing co-catalysts (Au, Ag, Pt, Ni, Co, Cu, NiSe2, CoSe2, and CuSe). More intriguingly, such peculiar charge flow characteristics endow the self-assembled TIC photosystems with versatile visible-light-driven photoredox catalysis towards photocatalytic hydrogen generation, anaerobic selective organic transformation, and CO2-to-fuel conversion. Our work would provide new inspiration for smartly mediating spatial vectorial charge transport towards emerging solar energy conversion.

Gradient tungsten-doped Bi3TiNbO9 ferroelectric photocatalysts with additional built-in electric field for efficient overall water splitting

Bi3TiNbO9, a layered ferroelectric photocatalyst, exhibits great potential for overall water splitting through efficient intralayer separation of photogenerated carriers motivated by a depolarization field along the in-plane a-axis. However, the poor interlayer transport of carriers along the out-of-plane c-axis, caused by the significant potential barrier between layers, leads to a high probability of carrier recombination and consequently results in low photocatalytic activity. Here, we have developed an efficient photocatalyst consisting of Bi3TiNbO9 nanosheets with a gradient tungsten (W) doping along the c-axis. This results in the generation of an additional electric field along the c-axis and simultaneously enhances the magnitude of depolarization field within the layers along the a-axis due to strengthened structural distortion. The combination of the built-in field along the c-axis and polarization along the a-axis can effectively facilitate the anisotropic migration of photogenerated electrons and holes to the basal {001} surface and lateral {110} surface of the nanosheets, respectively, enabling desirable spatial separation of carriers. Hence, the W-doped Bi3TiNbO9 ferroelectric photocatalyst with Rh/Cr2O3 cocatalyst achieves an efficient and durable overall water splitting feature, thereby providing an effective pathway for designing excellent layered ferroelectric photocatalysts.

Polarization Alignment in Polycrystalline BiFeO3 Photoelectrodes for Tunable Band Bending

Polarization in a semiconductor can modulate the band bending via the depolarization electric field (EdP), subsequently tuning the charge separation and transfer (CST) process in photoelectrodes. However, the random orientation of dipole moments in many polycrystalline semiconductor photoelectrodes leads to negligible polarization effect. How to effectively align the dipole moments in polycrystalline photoelectrodes into the same direction to maximize the polarization is still to be developed. Herein, we report that the dipole moments in a ferroelectric BiFeO3 photoelectrode can be controlled under external poling, resulting in a tunable CST efficiency. A negative bias of -40 voltage (V) poling to the photoelectrode leads to an over 110% increase of the CST efficiency, while poling at +40 V, the CST efficiency is reduced to only 41% of the original value. Furthermore, a nearly linear relationship between the external poling voltage and surface potential is discovered. The findings here provide an effective method in tuning the band bending and charge transfer of the emerging ferroelectricity driven solar energy conversion.

Ferroelectric Polarization Modulated Facet-selective Charge Separation in Bi4 NbO8 Cl Single Crystal for Boosting Visible-light Driven Bifunctional Water Splitting

Developing bifunctional water-splitting photocatalysts is meaningful, but challenged by the harsh requirements of specific-facet single crystals with spatially separated reactive sites and anisotropic charge transfer paths contributed by well-built charge driving force. Herein, tunable ferroelectric polarization is introduced in Bi4 NbO8 Cl single crystal nanosheets to strengthen the orthogonal charge transfer channels. By manipulating the in-plane polarization from octahedral off-centering of Nb5+ and out-of-plane polarization from lone pair electron effect of anisotropic Bi3+ , both the fast charge recombination in bulk catalyst and the process of charge trapping into surface states can be effectively modulated. Collaborating with modest polarization electric field and facet junction induced built-in electric field, cooperative charge tractive force is constructed, which reinforces the spatial separation and migration of photogenerated electrons and holes to {110} reductive site facet and {001} oxidation site facet, respectively. While excessive polarization charges impair the facet-selective charge separation characteristics and conversely promote charge recombination on the surface. As a result, polarity-optimized Bi4 NbO8 Cl shows an excellent H2 and O2 evolution rate of 54.21 and 36.08 μmol ⋅ h-1 in the presence of sacrificial reagents under visible light irradiation. This work unveils the function of ferroelectric polarization in tuning the intrinsic facet-selective charge transfer process of photocatalysts.

PdCu nanoalloy decorated photocatalysts for efficient and selective oxidative coupling of methane in flow reactors

Methane activation by photocatalysis is one of the promising sustainable technologies for chemical synthesis. However, the current efficiency and stability of the process are moderate. Herein, a PdCu nanoalloy (~2.3 nm) was decorated on TiO2, which works for the efficient, stable, and selective photocatalytic oxidative coupling of methane at room temperature. A high methane conversion rate of 2480 μmol g-1 h-1 to C2 with an apparent quantum efficiency of ~8.4% has been achieved. More importantly, the photocatalyst exhibits the turnover frequency and turnover number of 116 h-1 and 12,642 with respect to PdCu, representing a record among all the photocatalytic processes (λ > 300 nm) operated at room temperature, together with a long stability of over 112 hours. The nanoalloy works as a hole acceptor, in which Pd softens and weakens C-H bond in methane and Cu decreases the adsorption energy of C2 products, leading to the high efficiency and long-time stability.

Ferroelectric Polarization in BaTiO3 Nanocrystals Controls Photoelectrochemical Water Oxidation and Photocatalytic Hydrogen Evolution

Ferroelectric (FE) semiconductors such as BaTiO3 support a remnant polarization after the application of an electric field that can promote the separation of photogenerated charge carriers. Here, we demonstrate FE-enhanced photocatalytic hydrogen evolution and photoelectrochemical water oxidation with barium titanate nanocrystals for the first time. Nanocrystals of the ferroelectric tetragonal structure type were obtained by a hydrothermal synthesis from TiO2 and barium hydroxide in 63% yield. BaTiO3 nanocrystal films on tantalum substrates exhibit water oxidation photocurrents of 0.141 mA cm-2 at 1.23 V RHE under UV light (60 mW cm-2) illumination. Electric polarization at 52.8 kV cm-1 normal to the film plane increases the photocurrent by a factor of 2 or decreases it by a factor of 3.5, depending on the field polarity. It also shifts the onset potential by -0.15 or +0.09 V and it modifies the surface photovoltage signal. Lastly, exposure to an electric field increases the H2 evolution rate of Pt/BaTiO3 by a factor of ∼1.5, and it raises the selectivity of photodeposition of silver onto the (001) facets of the nanocrystal. All FE enhancements can be removed by heating samples above the Curie temperature of BaTiO3. These findings can be explained by FE dipole-induced changes to the potential drop across the space charge layer of the material. The ability to use the ferroelectric effect to enhance hydrogen evolution and water oxidation is of potential interest for the development of improved solar energy for fuel conversion systems.

Charge Separation in BaTiO3 Nanocrystals: Spontaneous Polarization Versus Point Defect Chemistry

The fate of photogenerated charges within ferroelectric metal oxides is key for photocatalytic applications. The authors study the contributions of i) tetragonal distortion, responsible for spontaneous polarization, and ii) point defects, on charge separation and recombination within BaTiO3 (BTO) nanocrystals of cubic and tetragonal structure. Electron paramagnetic resonance (EPR) in combination with O2 photoadsorption experiments show that BTO nanocrystals annealed at 600 °C have a charge separation yield enhanced by a factor > 10 compared to TiO2 anatase nanocrystals of similar geometries. This demonstrates for the first time the beneficial effect of the BTO perovskite nanocrystal lattice on charge separation. Strikingly, charge separation is considerably hindered within BTO nanoparticles annealed ≥ 600 °C, due to the formation of Ba-O divacancies that act as charge recombination centers. The opposing interplay between tetragonal distortion and annealing-induced defect formation inside the lattice highlights the importance of defect engineering within perovskite nanoparticles.

Bulk Photovoltage Effect in Ferroelectric BaTiO3

Due to the unusual charge separation mechanism and anomalous photovoltaic effects, the bulk photovoltage effect in ferroelectric semiconductors has attracted a great deal of attention in solar energy conversion, especially in attempts to utilize nonthermalized carriers. Among the various mechanisms that have been proposed for interpreting the photovoltaic effect, a shift mechanism was derived from quantum phenomena, which have been modeled and studied for many years. However, the concurrent shift and ballistic mechanism make investigating the ferroelectric bulk photovoltage effect complex and challenging. Here, taking a tetragonal ferroelectric BaTiO₃ single crystal as a prototype, we report an approach for distinguishing the shift and ballistic mechanism-induced surface photovoltage. The results indicate different effects on the charge separation of the ballistic mechanism and shift mechanisms, as evidenced by surface photovoltage measurement. Interestingly, the shift and ballistic mechanisms afford charge separation in two opposite directions but on the same order of magnitude under monochromatic superband illumination. Our results provide facile and efficient methods for clarifying the shift and ballistic mechanisms in ferroelectrics.