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At least 379 records · Page 21

Prediction of structure and cation ordering in an ordered normal-inverse double spinel

Abstract Spinels represent an important class of technologically relevant materials, used in diverse applications ranging from dielectrics, sensors and energy materials. While solid solutions combining two “single spinels” have been explored in a number of past studies, no ordered “double” spinels have been reported. Based on our first principles computations, here we predict the existence of such a double spinel compound MgAlGaO 4 , formed by an equimolar mixing of MgAl 2 O 4 normal and MgGa 2 O 4 inverse spinels. After studying the details of its atomic and electronic structure, we use a cluster expansion based effective Hamiltonian approach with Monte Carlo simulations to study the thermodynamic behavior and cation distribution as a function of temperature. Our simulations provide strong evidence for short-ranged cation order in the double spinel structure, even at significantly elevated temperatures. Finally, an attempt was made to synthesize the predicted double spinel compound. Energy Dispersive X-ray Spectrometry and X-ray diffraction Rietveld refinements were performed to characterize the single-phase chemical composition and local configurational environments, which showed a favorable agreement with the theoretical predictions. These findings suggest that a much larger number of compounds can potentially be realized within this chemical space, opening new avenues for the design of spinel-structured materials with tailored functionality.

36 MATERIALS SCIENCE↗

A chiral switchable photovoltaic ferroelectric 1D perovskite

Spin and valley degrees of freedom in materials without inversion symmetry promise previously unknown device functionalities, such as spin-valleytronics. Control of material symmetry with electric fields (ferroelectricity), while breaking additional symmetries, including mirror symmetry, could yield phenomena where chirality, spin, valley, and crystal potential are strongly coupled. Here we report the synthesis of a halide perovskite semiconductor that is simultaneously photoferroelectricity switchable and chiral. Spectroscopic and structural analysis, and first-principles calculations, determine the material to be a previously unknown low-dimensional hybrid perovskite (R)-(-)-1-cyclohexylethylammonium/(S)-(+)-1 cyclohexylethylammonium) PbI 3 . Optical and electrical measurements characterize its semiconducting, ferroelectric, switchable pyroelectricity and switchable photoferroelectric properties. Temperature dependent structural, dielectric and transport measurements reveal a ferroelectric-paraelectric phase transition. Circular dichroism spectroscopy confirms its chirality. The development of a material with such a combination of these properties will facilitate the exploration of phenomena such as electric field and chiral enantiomer–dependent Rashba-Dresselhaus splitting and circular photogalvanic effects

36 MATERIALS SCIENCE↗

Disentangling Memristive and Memcapacitive Effects in Droplet Interface Bilayers Using Dynamic Impedance Spectroscopy

The underlying principles for generating intelligent behavior in living organisms are fundamentally different from those in traditional solid-state circuits. Biomimetic neuromorphic equivalents based on biological membranes offer novel implementation of tunable plasticity and diverse mechanisms to control functionality. Here, dynamic electrochemical impedance spectroscopy (dEIS) to probe diphytanoylphosphatidylcholine (DPhPC) droplet interface bilayers (DIBs) to better understand the differences in molecular level structure/dynamics that give rise to hysteretic loops and neuromorphic, memelement behaviors in lipid bilayers in response to electrical biasing is used. Importantly, this system does not have ion-conducting channels and is, therefore, not expected to show memristive behavior. Surprisingly, both memristive and memcapacitive behaviors by measuring the time-dependent complex impedance of DPhPC DIBs are detected. Furthermore, it is shown that nonlinear memristance can originate from structural changes in the bilayer, affecting its dielectric properties. This novel dEIS application allows for the simultaneous analysis of the system's changing memristive and memcapacitive properties, which originate from different molecular restructuring processes. Moreover, and importantly, access to this type of information increases the number of neuromorphic processes supported simultaneously in a single two-terminal device.

36 MATERIALS SCIENCE↗

Nanoscale Ferroelectric Control of Novel Electronic States in Layered Two-Dimensional Materials (Final Report)

In this DOE Early Career project “Nanoscale Ferroelectric Control of Novel Electronic States in Layered Two-Dimensional Materials,” the PI’s group has combined ferroelectric field effect with nanoscale domain imaging and writing to design the electronic and optical properties of two-dimensional (2D) van der Waals materials, including graphene and transition metal dichalcogenides MoS2 and ReS2. The van der Waals materials have been prepared into field effect transistor (FET) devices with ferroelectric gates. Through domain patterning in a ferroelectric polymer PVDF-TrEF top-gate via conductive atomic force microscopy, the team has created programmable Schottky junctions in monolayer MoS 2 , where both barrier height and I-V rectifying polarity can be reconfigured. The transport anisotropy of monolayer to few-layer ReS 2 has been mapped out by defining the entire channel into an insulating state and creating nanoscale conducting paths along different directions through domain writing in the ferroelectric top-gate. The result shows that the conductivity along and perpendicular to the Re-chain can differ by >5.5x10 4 . Theoretical modeling points to the band origin of the transport anomaly and reveals the emergence of a flat band in few-layer ReS 2 . The interfacial epitaxial relation between ReS 2 and PVDF-TrFE further promotes the formation of close-packed, highly ordered PVDF-TrFE nanowires with width of 35 nm and 10 nm. Nonvolatile modulation of quantum Hall effect has been achieved in graphene FETs with a ferroelectric oxide Ba 0.4 Sr 0.6 TiO 3 back-gate. Scattering from the remote surface optical phonon in Ba 0.4 Sr 0.6 TiO 3 limits the room temperature mobility of graphene to be about 3x10 4 cm 2 /Vs. Steep-slope switching has been achieved in MoS 2 FETs back-gated by polycrystalline Pb(Zr,Ti)O 3 , which signals a static-state negative capacitance mode without involving an additional dielectric layer. Piezoresponse force microscopy studies show that the sub-threshold swing can be well correlated with the domain wall density in Pb(Zr,Ti)O 3 . The team also observes an unconventional filtering effect of the second harmonic generation response at the MoS 2 /Pb(Zr,Ti)O 3 heterointerface, which can be accounted for by the alignment between one of the polar axes of MoS 2 and the chiral dipole rotation at the surface of domain wall in Pb(Zr,Ti)O 3 . The research supported by this DOE grant has significantly advanced the fundamental understanding and functional design of ferroelectric/2D van der Waals heterostructures for their implementation towards energy applications.

36 MATERIALS SCIENCE↗

A remarkable CHF of 345W/cm 2 is achieved in a wicked-microchannel using HFE-7100

Boiling heat transfer of dielectric fluids is a promising cooling technique for thermal management of microelectronic systems. However, the critical heat flux achievable is generally low, because of the poor thermophysical properties of these fluids. Here, to address this dilemma, we propose a new cooling concept to substantially enhance global liquid supply during phase-change process using enhanced capillary-driven force. Additionally, dedicated vapor pathways are designed among a bank of micro-pillars to facilitate vapor removal. In this work, new wicks comprised of silicon micro-pinfin arrays are explored to significantly enhance the flow boiling heat transfer performance. To examine the functionalities of this wick, experiments on HFE-7100 were carried out with mass velocities varying from 247 to 3,465 kg/m 2 s. To explore the enhancement mechanisms and to analyze the capillary-assisted flow boiling process, visualization studies were conducted. The results indicate that sustainable evaporation induced by wick microstructures and efficient liquid supply are the enhancement mechanisms compared to parallel microchannels with solid walls. It is found that the overall heat transfer coefficient is substantially increased up to 75%. Remarkably, a high critical heat flux (CHF) of approximately 345 W/cm 2 is recorded at G = 3,465 kg/m 2 s at coolant inlet temperature of ~20 °C. Equally importantly, this noticeable enhancement of CHF value is associated with drastically decreased pressure drops compared to microchannels decorated with μ-pinfin fences.

36 MATERIALS SCIENCE↗

A sensing material-free and simple readout MEMS sensor for detecting Helium

Abstract In this work, we report a method that enables a standard electrostatic MEMS device to perform complex sensing functionalities, such as detecting the presence of helium without a sensing material or a conditioning circuit. Helium is a noble, odorless, non-reactive gas that is very challenging to detect. It is used in critical applications such as storing nuclear fuel waste inside a dry cask. In these applications, its leakage from the dry cask may indicate the cask's safe operation's degradation. A departure from the common practice of exciting the MEMS around its mechanical resonance, the method is based on exciting the MEMS around its electrical resonance circuit. This method shows that the tiny difference between the air dielectric constant (1.00059) and helium (1.000067) corresponding to only a few Femtofarad level capacitances produces a 25 mV difference without a conditioning circuit. Simulation results confirmed those findings and explored the sensor response at different operation conditions. This method eliminates the need for a heated microstructure and the need for absorption material. This method is not limited to gas sensing. It can be applied to other sensing mechanisms, such as acceleration and pressure measurements, and eliminate the complex circuit to read small capacitance in these applications.

Mohaidat, Sulaiman↗

Surface Charge Distribution Mapping Using an Electrostatic Probe

Undesired accumulation of charge on dielectric materials causing electrostatic discharges can be an issue in pulsed power systems and electrical systems in general. As such, an understanding of surface charge distribution, charge accumulation, and decay is required. An in-house no-contact electrostatic probe designed with a 2 mm resolution was fabricated to measure and map surface charge distribution. Designed as a contactless instrument, the probe consisting of a metal rod and low leakage amplifier circuit probes the electric potential near the surface. A scan of the surface then provides the raw data, a potential distribution. The actual probe response - i.e., the surface charge to voltage transfer function, is accounted for in post-processing. This is accomplished via an Inverse Wien Filter - a technique often applied in image processing - to deconvolve the probe response from the measured data. A commercially available electrostatic probe, the Trek 341B meter with a 3455ET probe, capable of measuring +/- 20 kV was compared to the in- house probe that is designed to cover a wider range from +/- 35 kV. A resolution better than the simple probe resolution is achieved through the distribution’s scanning voltage method and deconvolution. Applying repeated scans, surface charge decay was tracked on various polymer materials to determine the material and environment dependence; materials included were PA6, PTFE, and others. As an example of material dependence, samples charged to 20 kV at 65% humidity experience full charge decay in approximately 45 seconds for PA5 (152 mm dia.), while it took about 100 times longer for PTFE (51 mm dia.) to observe the same decay/redistribution of charge.

36 MATERIALS SCIENCE↗

Microwave Regeneration and Thermal and Oxidative Stability of Imidazolium Cyanopyrrolide Ionic Liquid for Direct Air Capture of Carbon Dioxide

Abstract Understanding the oxidative and thermal degradation of CO 2 sorbents is essential for assessing long‐term sorbent stability in direct air capture (DAC). The potential degradation pathway of imidazolium cyanopyrrolide, an ionic liquid (IL) functionalized for superior CO 2 capacity and selectivity, is evaluated under accelerated degradation conditions to elucidate the secondary reactions that can occur during repetitive absorption‐desorption thermal‐swing cycles. The combined analysis from various spectroscopic, chromatographic, and thermal gravimetric measurements indicated that radical and S N 2 mechanisms in degradation are encouraged by the nucleophilicity of the anion. Thickening of the liquid and gas evolution are accompanied by 50 % reduction in CO 2 capacity after a 7‐day exposure to O 2 under 80 °C. To prevent long exposure to conventional thermal heating, microwave (MW) regeneration of the CO 2 ‐reactive IL is used, where dielectric heating at 80 and 100 °C rapidly desorbs CO 2 and regenerates the IL without any measurable degradation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Surface chemistry on a polarizable surface: Coupling of CO with KTaO 3 (001)

Polarizable materials attract attention in catalysis because they have a free parameter for tuning chemical reactivity. Their surfaces entangle the dielectric polarization with surface polarity, excess charge, and orbital hybridization. How this affects individual adsorbed molecules is shown for the incipient ferroelectric perovskite KTaO 3 . This intrinsically polar material cleaves along (001) into KO- and TaO 2 -terminated surface domains. At TaO 2 terraces, the polarity-compensating excess electrons form a two-dimensional electron gas and can also localize by coupling to ferroelectric distortions. TaO 2 terraces host two distinct types of CO molecules, adsorbed at equivalent lattice sites but charged differently as seen in atomic force microscopy/scanning tunneling microscopy. Temperature-programmed desorption shows substantially stronger binding of the charged CO; in density functional theory calculations, the excess charge favors a bipolaronic configuration coupled to the CO. These results pinpoint how adsorption states couple to ferroelectric polarization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum Nature of Dielectric Laser Accelerators

Dielectric laser accelerators (DLAs) hold great promise for producing economic and compact on-chip radiation sources. On-chip DLAs benefit from fabrication capabilities of the silicon industry and from breakthroughs in silicon-photonic nanostructures to enhance the interaction between particles and laser fields. Seemingly unrelated recent advances in the quantum interactions of electrons and light have raised interest in the underlying classical-quantum correspondence principle at the foundations of electron acceleration. Here, we present the observation of the underlying quantum nature of DLAs: observing quantized peaks in the electron-energy spectra. Our findings demonstrate quasi-phase-matching between an electron wave function and a light wave, which also demonstrates the role of the quantum wave function in the inverse Smith-Purcell effect. We harness the capabilities of an ultrafast transmission electron microscope (UTEM) to maintain a long electron-light interaction length extending over hundreds of periods of the laser pulse, mediated by a silicon-photonic nanograting DLA. The UTEM is shown as a new platform for characterization of future DLA concepts. The results raise fundamental questions regarding the role of quantum mechanics in DLA design, and more generally about the prospects of manipulating particles’ quantum wave functions in accelerator physics.

43 PARTICLE ACCELERATORS↗

Novel ceramic capacitors with ultrahigh energy density and efficiency (Final Technical Report)

Antiferroelectric ceramics are a special class of material that have shown great potential as the dielectric in electrical capacitors due to their high energy- and power-density. During each charge-discharge cycle, the ceramic undergoes transformation to a ferroelectric phase and resumes its antiferroelectric phase. The hysteresis associated with the transitions leads to a mediocre energy efficiency and service lifetime of antiferroelectric capacitors and, hence, their almost absence in commercial products. Under the support of this research project, we first formulated a universal lattice-compatibility theory that included electrostatic polarization energy along with elastic energy and thermal energy to understand the origin of the hysteresis in antiferroelectric oxides. Guided by this compatibility theory, we conducted high-throughput density functional theory (DFT) calculations to assess chemical modifiers and their effect on crystal structures of 400+ PbZrO 3 -based compositions. Down-selected compositions were experimentally validated for their suppressed hysteresis and higher energy efficiency. The verified low-hysteresis compositions were then expanded to an antiferroelectric ceramic library with nearly 500 new compositions (more than 1,500 samples) using high-throughput experiments involving ceramic synthesis and property screening. The large quantity of data generated (theory and experimental) in these tasks were processed by machine-learning techniques and identified trends were fed to the next iteration. In the end, we successfully discovered four compositions with near-zero hysteresis, yielding a world-record energy efficiency of 98.2% at an energy density of 3.0 J/cm 3 . Furthermore, our antiferroelectric ceramic capacitor reaches 79.5 million charge-discharge cycles lifetime, a factor of 80 enhancement over previous antiferroelectric ceramics with large hysteresis. These research accomplishments have not only met the milestones set in the SOPO, but also led to two patent filings, three journal publications (one of them was in Advanced Materials, impact factor 29.4), and nine oral presentations at various venues. Through the course of the project, three postdocs, four Ph.D. students, and one M.S. student were trained. In short, our project established a new methodology in searching next-generation functional ceramics on the fundamental side and discovered several high-efficiency antiferroelectric compositions for capacitors on the applied side. Once fabricated into the multilayer form for commercial applications, these ceramic capacitors can potentially enable the high temperature high power density DC-link capacitors that are critical for the next generation inverters in electric vehicles. The project also significantly contributed to the nation’s workforce development in the STEM fields.

36 MATERIALS SCIENCE↗

Ion Pairing and Redissociaton in Low-Permittivity Electrolytes for Multivalent Battery Applications

Detailed speciation of electrolytes as a function of chemical system and concentration provides the foundation for understanding bulk transport as well as possible decomposition mechanisms. In particular, multivalent electrolytes have shown a strong coupling between anodic stability and solvation structure. Furthermore, solvents that are found to exhibit reasonable stability against alkaline-earth metals generally exhibit low permittivity, which typically increases the complexity of the electrolyte species. To improve our understanding of ionic population and associated transport in these important classes of electrolytes, the speciation of Mg(TFSI)2 in monoglyme and diglyme systems is studied via a multiscale thermodynamic model using first-principles calculations for ion association and molecular dynamics simulations for dielectric properties. The results are then compared to Raman and dielectric relaxation spectroscopies, which independently confirm the modeling insights. We find that the significant presence of free ions in the low-permittivity glymes in the concentration range from 0.02 to 0.6 M is well-explained by the low-permittivity redissociation hypothesis. Here, salt speciation is largely dictated by long-range electrostatics, which includes permittivity increases due to polar contact ion pairs. The present results suggest that other low-permittivity multivalent electrolytes may also reach high conductivities as a result of redissociation.

25 ENERGY STORAGE↗

Traveling wakefield tube: THz source powered by nonrelativistic electron beam

High peak power, tunable, narrowband terahertz emitters are becoming sought after given their portability, efficiency, and ability to be deployed in the field for industrial, medical, and military applications. The use of accelerator systems producing THz frequencies via Cherenkov radiation, generated by passing an electron beam through a slow-wave wakefield structure, is a promising method to meet future THz requirements. To date, efforts have been dedicated to analysis and design of sources utilizing laser seeded bunched electron beam drivers with relativistic energies beyond 5 MeV. Presented here is a wakefield THz generation scheme based on passing a long quasi-dc nonrelativistic beam (200 keV) through a dielectric loaded travelling wave structure. Reduced energy allows for compactness and portability of the accelerator as the size and weight of the dielectric slow wave structure is vanishingly small compared to the accelerator unit. The presented scheme can serve as a tunable high peak power THz source operated between 0.4-1.6 THz and produces power gain by a factor of five with an average efficiency of 6.8%

43 PARTICLE ACCELERATORS↗

Effect of Diphenyl Content on Viscoelasticity of Poly(dimethyl- co -diphenyl)siloxane Melt and Network

Polydimethylsiloxane (PDMS) is one of the most widely used polymeric materials for sealants, adhesives, lubricants, and thermal as well as electrical insulation. At low temperatures, however, PDMS is subject to crystallization that can cause deterioration in mechanical function. A common way to suppress such crystallization is through the incorporation of phenylsiloxane into the backbone of polysiloxane. Nevertheless, the introduction of phenyl components, even in small quantities, could potentially change the properties of the siloxane in a significant way. In this work, a series of mechanical tests and finite element simulations were performed to study the macroscale viscoelasticity of two poly(dimethyl-co-diphenyl)siloxane formulations in order to understand the effects of a few percent diphenyl contents on the viscoelasticity of the polysiloxane material. Here, we utilized the small-angle X-ray scattering to investigate the microscopic structures of the copolymers and broadband dielectric spectroscopy and rheology to probe the chain dynamics at the microscale. The results of these characterizations were used to inform the finite element simulations. We found that the degree of cross-linking does not significantly alter the microstructure but can profoundly affect the viscoelastic response of the copolymer networks. The corresponding hysteretic behavior is interpreted in terms of reptation-like motion and relaxation of the effective free chains in the cured polymer network. The relaxation of the copolymer chains is slowed significantly by even a small increase in the molar ratio of the diphenyl component.

36 MATERIALS SCIENCE↗

Low-Voltage Haze Tuning with Cellulose-Network Liquid Crystal Gels

Being key components of the building envelope, glazing products with tunable optical properties are in great demand because of their potential for boosting energy efficiency and privacy features while enabling the main function of allowing natural light indoors. However, windows and skylights with electric switching of haze and transparency are rare and often require high voltages or electric currents, as well as not fully meet the stringent technical requirements for glazing applications. Here, by introducing a predesigned gel material we describe an approach dubbed “Haze-Switch” that involves low-voltage tuning of the haze coefficient in a broad range of 2–90% while maintaining high visible-range optical transmittance. The approach is based on a nanocellulose fiber gel network infiltrated by a nematic liquid crystal, which can be switched between polydomain and monodomain spatial patterns of optical axis via a dielectric coupling between the nematic domains and the applied external electric field. By utilizing a nanocellulose network of nanofibers ~10 nm in diameter we achieve <10 V dielectric switching and <2% haze in the clear state, as needed for applications in window products. Finally, we characterize physical properties relevant to window and smart glass technologies, like the color rendering index, haze coefficient, and switching times, demonstrating that our material and envisaged products can meet the stringent requirements of the glass industry, including applications such as privacy windows, skylights, sunroofs, and daylighting.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High throughput, spatially resolved thermal properties measurement using attachable and reusable 3ω sensors

The 3ω method is a well-established thermal technique used to measure the thermal conductivity of materials and the thermal resistance of interfaces. It has significant advantages over other steady state and transient thermal techniques in its ability to provide spatially resolved thermal property measurements over a wide range of thermal conductivity. Despite its advantages, it has been restricted to lab-scale use because of the difficulty involved in sample preparation and sensor fabrication and is limited to non-metallic substrates. High-throughput 3ω measurements with reusable sensors have not been realized yet. In this work, we demonstrate a method of applying reusable 3ω sensors fabricated on flexible polyimide films to measure bulk and spatially resolved thermal properties. Here, we establish the limits of thermal conductivity measurement with the method to be 1 to 200 W/mK, and within the measurement limit, we verify the method by comparing the measured thermal conductivities of standard samples with established values. From the 3ω measurements, we also determine the thermal resistance of an interlayer of thermal grease as a function of pressure and compare it against the resistance calculated from direct thickness measurements to demonstrate the ability of this method to provide spatially resolved subsurface information. The technique presented is general and applicable to both metallic and non-metallic substrates, providing a method for high-throughput 3ω measurements with reusable sensors and without considerable sample preparation.

47 OTHER INSTRUMENTATION↗

Ab Initio Prediction of Ultra‐Wide Band Gap B x Al 1− x N Materials

Abstract Ultra‐wide bandgap (UWBG) materials are poised to play an important role in the future of power electronics. Devices made from UWBG materials are expected to operate at higher voltages, frequencies, and temperatures than current silicon and silicon‐carbide‐based devices and can even lead to significant miniaturization of such devices. In the UWBG field, aluminum nitride and boron nitride have attracted great interest; however, the B x Al 1− x N alloys are much less studied. In this work, using first‐principles simulations combining density‐functional theory and the cluster expansion method, the crystal structure of B x Al 1− x N alloys is predicted. Seventeen ground state structures of B x Al 1− x N with formation energies between 0.11 and 0.25 eV atom ‐1 are found. All of these structures are found to be dynamically stable. The B x Al 1− x N structures are found to have predominantly a tetrahedral bonding environment; however, some structures exhibit sp 2 bonds similar to hexagonal BN. This work expands knowledge of the structures, energies, and bonding in B x Al 1− x N which aids their synthesis, the innovation of lateral or vertical devices, and discovery of compatible dielectric and Ohmic contact materials.

36 MATERIALS SCIENCE↗

DFT-based insight into finite-temperature properties of ferroelectric perovskites with lone-pair: the case of CsGeX 3 (X = Cl, Br, I)

Ferroelectrics remain in the focus of scientific attention for decades owing to their fundamental and practical appeal. Recently, ferroelectricity has been demonstrated in semiconducting halide perovskites (Zhang et al 2022 Sci. Adv. 8 eabj5881), offering both a rare combination of ferroelectricity and semiconductivity in the same material and a possible alternative to the prevailing perovskite oxide ferroelectrics. We propose a route to simulating such materials at finite temperatures capable of reproducing key experimental and first-principle data, such as Curie temperature, phase transition sequence, spontaneous polarization, and soft mode frequencies. The key methodological finding is the superior performance of hybrid exchange correlation functionals in parametrization of effective Hamiltonians for ferroelectrics with lone pair. The parametrization for effective Hamiltonians for CsGeX 3 (X = Cl, Br, I) is reported. The application of methodology to study polarization reversal in CsGeX 3 allows for the development of a ‘minimalistic’ model for polarization reversal in ferroelectrics that provides an insight into the mechanisms of polarization reversal and its key features, such as the relationship between the coercive field, temperature, and AC field frequency. Importantly, the model reveals the origin of the well-known and ever-puzzling overestimation of coercive fields in computations. Furthermore, we report a variety of finite-temperature properties of CsGeX 3 ferroelectrics, such as dielectric susceptibility, pyroelectric coefficients, and energy storage density, which reveal that these halide perovskites possess properties comparable to their oxide counterparts. Here, we believe that our work provides significant methodological advancements, deepens fundamental understanding of ferroelectrics, and reveals the potential of halide perovskite ferroelectrics.

effective Hamiltonian↗