A strain-driven morphotropic phase boundary in BiFeO3

The Ferroelectric Effects of Rhombohedral and Tetragonal BiFeO3 in Photoelectrochemical Water Splitting

The phase of BiFeO3 (BFO) as well as its domain configuration can be tuned by strain engineering. Phase change may greatly influence the properties of the polarization field and hence charge separation. However, the photoelectrochemical properties of different BFO phases have rarely been addressed. Here, the photoelectrochemical study of tetragonal (T-) and rhombohedral (R-) phase BFO films was conducted under visible light illumination. The photocurrent density of R-BFO is 5 times that of T-BFO. A ferroelectric domain study shows that T-BFO features single domain structure in contrast to the polydomain structure of R-BFO. Higher charge separation efficiency is achieved in R-BFO, dominated by the domain walls as conducting pathways for efficient charge separation and transfer. This work provides a fundamental understanding of the photoelectrochemical properties of T- and R-BFO, offering valuable insights for the development of BFO-based materials for solar energy conversion.

Insights into Strain Engineering: From Ferroelectrics to Related Functional Materials and Beyond

Ferroelectrics have become indispensable components in various application fields, including information processing, energy harvesting, and electromechanical conversion, owing to their unique ability to exhibit electrically or mechanically switchable polarization. The distinct polar noncentrosymmetric lattices of ferroelectrics make them highly responsive to specific crystal structures. Even slight changes in the lattice can alter the polarization configuration and response to external fields. In this regard, strain engineering has emerged as a prevalent regulation approach that not only offers a versatile platform for structural and performance optimization within ferroelectrics but also unlocks boundless potential in various functional materials. In this review, we systematically summarize the breakthroughs in ferroelectric-based functional materials achieved through strain engineering and progress in method development. We cover research activities ranging from fundamental attributes to wide-ranging applications and novel functionalities ranging from electromechanical transformation in sensors and actuators to tunable dielectric materials and information technologies, such as transistors and nonvolatile memories. Building upon these achievements, we also explore the endeavors to uncover the unprecedented properties through strain engineering in related chemical functionalities, such as ferromagnetism, multiferroicity, and photoelectricity. Finally, through discussions on the prospects and challenges associated with strain engineering in the materials, this review aims to stimulate the development of new methods for strain regulation and performance boosting in functional materials, transcending the boundaries of ferroelectrics.

Revealing the Optimization Route of Piezoelectric Sonosensitizers: From Mechanism to Engineering Methods

Piezoelectric catalysis is a novel catalytic technology that has developed rapidly in recent years and has attracted extensive interest among researchers in the field of tumor therapy for its acoustic-sensitizing properties. Nevertheless, researchers are still controversial about the key technical difficulties in the modulation of piezoelectric sonosensitizers for tumor therapy applications, which is undoubtedly a major obstacle to the performance modulation of piezoelectric sonosensitizers. Clarification of this challenge will be beneficial to the design and optimization of piezoelectric sonosensitizers in the future. Here, the authors start from the mechanism of piezoelectric catalysis and elaborate the mechanism and methods of defect engineering and phase engineering for the performance modulation of piezoelectric sonosensitizers based on the energy band theory. The combined therapeutic strategy of piezoelectric sonosensitizers with enzyme catalysis and immunotherapy is introduced. Finally, the challenges and prospects of piezoelectric sonosensitizers are highlighted. Hopefully, the explorations can guide researchers toward the optimization of piezoelectric sonosensitizers and can be applied in their own research.

Programming Polarity Heterogeneity of Energy Storage Dielectrics by Bidirectional Intelligent Design

Dielectric capacitors, characterized by ultra-high power densities, are considered as fundamental energy storage components in electronic and electrical systems. However, synergistically improving energy densities and efficiencies remains a daunting challenge. Understanding the role of polarity heterogeneity at the nanoscale in determining polarization response is crucial to the domain engineering of high-performance dielectrics. Here, a bidirectional design with phase-field simulation and machine learning is performed to forward reveal the structure-property relationship and reversely optimize polarity heterogeneity to improve energy storage performance. Taking BiFeO3-based dielectrics as typical systems, this work establishes the mapping diagrams of energy density and efficiency dependence on the volume fraction, size and configuration of polar regions. Assisted by CatBoost and Wolf Pack algorithms, this work analyzes the contributions of geometric factors and intrinsic features and find that nanopillar-like polar regions show great potential in achieving both high polarization intensity and fast dipole switching. Finally, a maximal energy density of 188 J cm-3 with efficiency above 95% at 8 MV cm-1 is obtained in BiFeO3-Al2O3 systems. This work provides a general method to study the influence of local polar heterogeneity on polarization behaviors and proposes effective strategies to enhance energy storage performance by tuning polarity heterogeneity.

Room-temperature stabilizing strongly competing ferrielectric and antiferroelectric phases in PbZrO3 by strain-mediated phase separation

PbZrO3 has been broadly considered as a prototypical antiferroelectric material for high-power energy storage. A recent theoretical study suggests that the ground state of PbZrO3 is threefold-modulated ferrielectric, which challenges the generally accepted antiferroelectric configuration. However, such a novel ferrielectric phase was predicted only to be accessible at low temperatures. Here, we successfully achieve the room-temperature construction of the strongly competing ferrielectric and antiferroelectric state by strain-mediated phase separation in PbZrO3/SrTiO3 thin film. We demonstrate that the phase separation occurs spontaneously in quasi-periodic stripe-like patterns under a compressive misfit strain and can be tailored by varying the film thickness. The ferrielectric phase strikingly exhibitsa threefold modulation period with a nearly up-up-down configuration, which could be stabilized and manipulated by the formation and evolution of interfacial defects under applied strain. The present results construct a fertile ground for further exploring the physical properties and applications based on the novel ferrielectric phase.

Disorder-Broadened Phase Boundary with Enhanced Amorphous Superconductivity in Pressurized In2Te5

As an empirical tool in materials science and engineering, the iconic phase diagram owes its robustness and practicality to the topological characteristics rooted in the celebrated Gibbs phase law free variables (F) = components (C) - phases (P) + 2. When crossing the phase diagram boundary, the structure transition occurs abruptly, bringing about an instantaneous change in physical properties and limited controllability on the boundaries (F = 1). Here, the sharp phase boundary is expanded to an amorphous transition region (F = 2) by partially disrupting the long-range translational symmetry, leading to a sequential crystalline-amorphous-crystalline (CAC) transition in a pressurized In2Te5 single crystal. Through detailed in situ synchrotron diffraction, it is elucidated that the phase transition stems from the rotation of immobile blocks [In2Te2]2+, linked by hinge-like [Te3]2- trimers. Remarkably, within the amorphous region, the amorphous phase demonstrates a notable 25% increase of the superconducting transition temperature (Tc), while the carrier concentration remains relatively constant. Furthermore, a theoretical framework is proposed revealing that the unconventional boost in amorphous superconductivity might be attributed to an intensified electron correlation, triggered by a disorder-augmented multifractal behavior. These findings underscore the potential of disorder and prompt further exploration of unforeseen phenomena on the phase boundaries.

Three-Dimensional Visualization of Oxygen-Vacancy Migration and Redistribution in Ca-Substituted BiFeO3

Ionic movement has received renewed attention in recent years, particularly in the field of ferroelectric oxides, since it is intrinsically linked to chemical reaction kinetics and ferroelectric phase stability. The associated surface electrochemical processes coupled local ionic transport with an applied electric bias, exhibiting very high ionic mobility at room temperature based on a simple electrostatics scenario. However, few studies have focused on the applied-polarity dependence of ionic migration with directly visualized maps. Here, we use incorporated experiments of conductive scanning probe microscopy and time-of-flight secondary ion mass spectrometry to investigate oxygen ionic migration and cation redistribution in ionic oxides. The local concentrations of oxygen vacancies and other cation species are visualized by three-dimensional mappings, indicating that oxygen vacancies tend to be ejected toward the surface. An accumulation of oxygen vacancies and ionic redistribution strongly depend on tip polarity, thus corroborating their role in the electrochemical process. This work illustrates the interplay between ionic kinetics and electric switching.

Liquid Metal Doping Induced Asymmetry in Two-Dimensional Metal Oxides

The emergence of ferroelectricity in two-dimensional (2D) metal oxides is a topic of significant technological interest; however, many 2D metal oxides lack intrinsic ferroelectric properties. Therefore, introducing asymmetry provides access to a broader range of 2D materials within the ferroelectric family. Here, the generation of asymmetry in 2D SnO by doping the material with Hf0.5 Zr0.5 O2 (HZO) is demonstrated. A liquid metal process as a doping strategy for the preparation of 2D HZO-doped SnO with robust ferroelectric characteristics is implemented. This technology takes advantage of the selective interface enrichment of molten Sn with HZO crystallites. Molecular dynamics simulations indicate a strong tendency of Hf and Zr atoms to migrate toward the surface of liquid metal and embed themselves within the growing oxide layer in the form of HZO. Thus, the liquid metal-based harvesting/doping technique is a feasible approach devised for producing novel 2D metal oxides with induced ferroelectric properties, represents a significant development for the prospects of random-access memories.

Surface Effect of Thickness-Dependent Polarization and Domain Evolution in BiFeO3 Epitaxial Ultrathin Films

With the trend of device miniaturization, ultrathin ferroelectric films are gaining more and more attention. However, understanding ferroelectricity in this nanoscale context remains a formidable challenge, primarily due to the heightened relevance of surface effects, which often leads to the loss of net polarization. Here, the influence of surface effects on the polarization as a function of thickness in ultrathin BiFeO3 films is investigated using phase-field simulations. The findings reveal a notable increase in ferroelectric polarization with increasing thickness, with a particularly discernible change occurring below the 10 nm threshold. Upon accounting for surface effects, the polarization is marginally lower than the case without such considerations, with the disparity becoming more pronounced at smaller thicknesses. Moreover, the hysteresis loop and butterfly loop of the ultrathin film were simulated, demonstrating that the ferroelectric properties of films remain robust even down to a thickness of 5 nm. Our investigations provide valuable insights into the significance of ferroelectric thin films in device miniaturization.

Large Electromechanical Response in a Polycrystalline Alkali-Deficient (K,Na)NbO3 Thin Film on Silicon

The demand for large electromechanical performance in lead-free polycrystalline piezoelectric thin films is driven by the need for compact, high-performance microelectromechanical systems (MEMS) based devices operating at low voltages. Here we significantly enhance the electromechanical response in a polycrystalline lead-free oxide thin film by utilizing lattice-defect-induced structural inhomogeneities. Unlike prior observations in mismatched epitaxial films with limited low-frequency enhancements, we achieve large electromechanical strain in a polycrystalline (K,Na)NbO3 film integrated on silicon. This is achieved by inducing self-assembled Nb-rich planar faults with a nonstoichiometric composition. The film exhibits an effective piezoelectric coefficient of 565 pm V-1 at 1 kHz, surpassing those of lead-based counterparts. Notably, lattice defect growth is substrate-independent, and the large electromechanical response is extended to even higher frequencies in a polycrystalline film. Improved properties arise from unique lattice defect morphology and frequency-dependent relaxation behavior, offering a new route to remarkable electromechanical response in polycrystalline thin films.

Large bi-axial tensile strain effect in epitaxial BiFeO3 film grown on single crystal PrScO3

A BiFeO3 film is grown epitaxially on a PrScO3 single crystal substrate which imparts ~ 1.45% of biaxial tensile strain to BiFeO3 resulting from lattice misfit. The biaxial tensile strain effect on BiFeO3 is investigated in terms of crystal structure, Poisson ratio, and ferroelectric domain structure. Lattice resolution scanning transmission electron microscopy, precession electron diffraction, and X-ray diffraction results clearly show that in-plane interplanar distance of BiFeO3 is the same as that of PrScO3 with no sign of misfit dislocations, indicating that the biaxial tensile strain caused by lattice mismatch between BiFeO3 and PrScO3 are stored as elastic energy within BiFeO3 film. Nano-beam electron diffraction patterns compared with structure factor calculation found that the BiFeO3 maintains rhombohedral symmetry, i.e., space group of R3c. The pattern analysis also revealed two crystallographically distinguishable domains. Their relations with ferroelectric domain structures in terms of size and spontaneous polarization orientations within the domains are further understood using four-dimensional scanning transmission electron microscopy technique.

Anion-induced robust ferroelectricity in sulfurized pseudo-rhombohedral epitaxial BiFeO3 thin films via polarization rotation

Polarization rotation caused by various strains, such as substrate and/or chemical strain, is essential to control the electronic structure and properties of ferroelectric materials. This study proposes anion-induced polarization rotation with chemical strain, which effectively improves ferroelectricity. A method for the sulfurization of BiFeO3 thin films by introducing sulfur anions is presented. The sulfurized films exhibited substantial enhancement in room-temperature ferroelectric polarization through polarization rotation and distortion, with a 170% increase in the remnant polarization from 58 to 100.7 μC cm-2. According to first-principles calculations and the results of X-ray absorption spectroscopy and high-angle annular dark-field scanning transmission electron microscopy, this enhancement arose from the introduction of S atoms driving the re-distribution of the lone-pair electrons of Bi, resulting in the rotation of the polarization state from the [001] direction to the [110] or [111] one. The presented method of anion-driven polarization rotation might enable the improvement of the properties of oxide materials.

Morphotropic Phase Boundary in Polarized Organic Piezoelectric Materials

Designing the morphotropic phase boundary (MPB) has been the most sought-after approach to achieve high piezoelectric performance of piezoelectric materials. However, MPB has not yet been found in the polarized organic piezoelectric materials. Here, we discover MPB with biphasic competition of β and 3/1-helical phases in the polarized piezoelectric polymer alloys (PVTC-PVT) and demonstrate a mechanism to induce MPB using the compositionally tailored intermolecular interaction. Consequently, PVTC-PVT exhibits a giant quasistatic piezoelectric coefficient of >32  pC/N while maintaining a low Young's modulus of 182 MPa, with a record-high figure of merit of piezoelectricity modulus of about 176  pC/(N·GPa) among all piezoelectric materials.

Ultrasmall Polar Skyrmions and Merons in SrTiO3 Heterostructures by Polaron Engineering

Topological objects with skyrmionic textures in ferroelectrics, i.e., polar skyrmions, are promising technological paradigms in next-generation electronic devices. While breakthrough discoveries of stable polar skyrmions approximately ten nanometers in size have been very recently witnessed in complex systems, such a nontrivial topological order in ferroelectrics inevitably disappears below the ferroelectric critical size of several nanometers. Herein, we propose a strategy to overcome this limitation and achieve ultrasmall and isolated polar skyrmions by engineering excess-electron polarons in otherwise nonferroelectric SrTiO₃ heterostructures. Our first-principle calculations demonstrate that a polaron localized at a SrTiO₃ surface induces a Neel-type polar skyrmion as small as 1.8 nanometers attributed to the effect of atomic-scale surface roughness. Furthermore, we show that this polar topological structure is tunable by the choice of heterostructures and by the mechanical approach, which undergoes a phase transition to a meron state in the twisted boundary and to an antiskyrmion state in the surface with external shear strain, respectively. Such ultraminiaturization of skyrmions and their transitions unexpectedly unravels the formula of ultrasmall topological orders originating from the interplay between an electron polaron and structural symmetry breaking, which is completely different from the common mechanism of geometric confinement for larger-scale skyrmions. Our results not only provide a mechanism for the exploration of polar skyrmions and their rich topological transitions but also hold potential for ultrahigh-density memories.

Electric and Magnetic Tuning of Gilbert Damping Constant in LSMO/PMN-PT(011) Heterostructure

Electric field control of magnetodynamics in magnetoelectric (ME) heterostructures has
been the subject of recent interest due to its fundamental complexity and promising applications in
room temperature devices. The present work focuses on the tuning of magnetodynamic parameters
of epitaxially grown ferromagnetic (FM) La_0.7Sr_0.3MnO₃(LSMO) on a ferro(piezo)electric (FE)
Pb(Mg_0.33Nb_0.67)O₃-PbTiO₃(PMN-PT) single crystal substrate. The uniaxial magnetic anisotropy
of LSMO on PMN-PT confirms the ME coupling at the FM/FE heterointerface. The magnitude of
the Gilbert damping constant (α) of this uniaxial LSMO film measured along the hard magnetic axis
is significantly small compared to the easy axis. Furthermore, a marked decrease in the α values of
LSMO at positive and negative electrical remanence of PMN-PT is observed, which is interpreted
in the framework of strain induced spin dependent electronic structure. The present results clearly
encourage the prospects of electric field controlled magnetodynamics, thereby realising the room
temperature spin-wave based device applications with ultra-low power consumption.

Tuning Piezoelectricity via Thermal Annealing at a Freestanding Ferroelectric Membrane

Tuning the ferroelectric domain structure by a combination of elastic and electrostatic engineering provides an effective route for enhanced piezoelectricity. However, for epitaxial thin films, the clamping effect imposed by the substrate does not allow aftergrowth tuning and also limits the electromechanical response. In contrast, freestanding membranes, which are free of substrate constraints, enable the tuning of a subtle balance between elastic and electrostatic energies, giving new platforms for enhanced and tunable functionalities. Here, highly tunable piezoelectricity is demonstrated in freestanding PbTiO₃ membranes, by varying the ferroelectric domain structures from c-dominated to c/a and a domains via aftergrowth thermal treatment. Significantly, the piezoelectric coefficient of the c/a domain structure is enhanced by a factor of 2.5 compared with typical c domain PbTiO₃. This work presents a new strategy to manipulate the piezoelectricity in ferroelectric membranes, highlighting their great potential for nano actuators, transducers, sensors and other NEMS device applications.

Prediction of the hardest BiFeO3 from first-principles calculations

BiFeO₃ is the only material with ferroelectric Curie temperature and Néel temperature higher than room temperature, making it one of the most well-studied multiferroic materials. Based on an ab initio evolutionary algorithm, we predicted a new cubic C-type antiferromagnetic structure (Fd3̄m-BiFeO₃) at ambient pressure. It was found that Fd3̄m-BiFeO₃ is the hardest BiFeO₃ (Vickers hardness ∼ 9.12 GPa), about 78% harder than R3c-BiFeO₃ (the well-known multiferroic material), which contributes to extending the life of BiFeO₃ devices. In addition, Fd3̄m-BiFeO₃ has the largest shear modulus (83.74 GPa) and the largest Young's modulus (214.72 GPa). Besides, we found an interesting phenomenon that among the common multiferroic materials (BiFeO₃, BaTiO₃, PbTiO₃, SrRuO₃, KNbO₃, and BiMnO₃), Pnma-BiMnO₃ has the largest bulk modulus, and its bulk modulus is about 15% larger than that of Fd3̄m-BiFeO₃. However, its Vickers hardness (4.47 GPa) is much smaller than that of Fd3̄m-BiFeO₃. This is because the Vickers hardness is proportional to the shear modulus and the shear modulus of Fd3̄m-BiFeO₃ is larger than that of Pnma-BiMnO₃. This work provides a deeper and more comprehensive understanding of BiFeO₃.

Braiding Lateral Morphotropic Grain Boundaries in Homogenetic Oxides

Interfaces formed by correlated oxides offer a critical avenue for discovering emergent phenomena and quantum states. However, the fabrication of oxide interfaces with variable crystallographic orientations and strain states integrated along a film plane is extremely challenging by conventional layer-by-layer stacking or self-assembling. Here, the creation of morphotropic grain boundaries (GBs) in laterally interconnected cobaltite homostructures is reported. Single-crystalline substrates and suspended ultrathin freestanding membranes provide independent templates for coherent epitaxy and constraint on the growth orientation, resulting in seamless and atomically sharp GBs. Electronic states and magnetic behavior in hybrid structures are laterally modulated and isolated by GBs, enabling artificially engineered functionalities in the planar matrix. This work offers a simple and scalable method for fabricating unprecedented innovative interfaces through controlled synthesis routes as well as providing a platform for exploring potential applications in neuromorphics, solid-state batteries, and catalysis.

Brief Theoretical Overview of Bi-Fe-O Based Thin Films

This paper will provide a brief overview of the unique multiferroic material Bismuth ferrite (BFO). Considering that Bismuth ferrite is a unique material which possesses both ferroelectric and magnetic properties at room temperature, the uniqueness of Bismuth ferrite material will be discussed. Fundamental properties of the material including electrical and ferromagnetic properties also will be mentioned in this paper. Electrical properties include characterization of basic parameters considering the electrical resistivity and leakage current. Ferromagnetic properties involve the description of magnetic hysteresis characterization. Bismuth ferrite can be fabricated in a different form. The common forms will be mentioned and include powder, thin films and nanostructures. The most popular method of producing thin films based on BFO materials will be described and compared. Finally, the perspectives and potential applications of the material will be highlighted.

Induced Ferromagnetism in Epitaxial Uranium Dioxide Thin Films

Actinide materials have various applications that range from nuclear energy to quantum computing. Most current efforts have focused on bulk actinide materials. Tuning functional properties by using strain engineering in epitaxial thin films is largely lacking. Using uranium dioxide (UO₂ ) as a model system, in this work, the authors explore strain engineering in actinide epitaxial thin films and investigate the origin of induced ferromagnetism in an antiferromagnet UO₂ . It is found that UO_{2+ x} thin films are hypostoichiometric (x<0) with in-plane tensile strain, while they are hyperstoichiometric (x>0) with in-plane compressive strain. Different from strain engineering in non-actinide oxide thin films, the epitaxial strain in UO₂ is accommodated by point defects such as vacancies and interstitials due to the low formation energy. Both epitaxial strain and strain relaxation induced point defects such as oxygen/uranium vacancies and oxygen/uranium interstitials can distort magnetic structure and result in magnetic moments. This work reveals the correlation among strain, point defects and ferromagnetism in strain engineered UO_{2+ x} thin films and the results offer new opportunities to understand the influence of coupled order parameters on the emergent properties of many other actinide thin films.

Why it is Unfortunate that Linear Machine Learning "Works" so well in Electromechanical Switching of Ferroelectric Thin Films

Machine learning (ML) is relied on for materials spectroscopy. It is challenging to make ML models fail because statistical correlations can mimic the physics without causality. Here, using a benchmark band-excitation piezoresponse force microscopy polarization spectroscopy (BEPS) dataset the pitfalls of the so-called "better", "faster", and "less-biased" ML of electromechanical switching are demonstrated and overcome. Using a toy and real experimental dataset, it is demonstrated how linear nontemporal ML methods result in physically reasonable embedding (eigenvalues) while producing nonsensical eigenvectors and generated spectra, promoting misleading interpretations. A new method of unsupervised multimodal hyperspectral analysis of BEPS is demonstrated using long-short-term memory (LSTM) β-variational autoencoders (β-VAEs) . By including LSTM neurons, the ordinal nature of ferroelectric switching is considered. To improve the interpretability of the latent space, a variational Kullback-Leibler-divergency regularization is imposed . Finally, regularization scheduling of β as a disentanglement metric is leveraged to reduce user bias. Combining these experiment-inspired modifications enables the automated detection of ferroelectric switching mechanisms, including a complex two-step, three-state one. Ultimately, this work provides a robust ML method for the rapid discovery of electromechanical switching mechanisms in ferroelectrics and is applicable to other multimodal hyperspectral materials spectroscopies.

Microstructural Origin of the High-Energy Storage Performance in Epitaxial Lead-Free Ba(Zr0.2Ti0.8)O3 Thick Films

In our previous work, epitaxial Ba(Zr_0.2Ti_0.8)O₃ thick films (~1-2 μm) showed an excellent energy storage performance with a large recyclable energy density (~58 J/cc) and a high energy efficiency (~92%), which was attributed to a nanoscale entangled heterophase polydomain structure. Here, we propose a detailed analysis of the structure-property relationship in these film materials, using an annealing process to illustrate the effect of nanodomain entanglement on the energy storage performance. It is revealed that an annealing-induced stress relaxation led to the segregation of the nanodomains (via detailed XRD analyses), and a degraded energy storage performance (via polarization-electric field analysis). These results confirm that a nanophase entanglement is an origin of the high-energy storage performance in the Ba(Zr_0.2Ti_0.8)O₃ thick films.

Freestanding complex-oxide membranes

Complex oxides show a vast range of functional responses, unparalleled within the inorganic solids realm, making them promising materials for applications as varied as next-generation field-effect transistors, spintronic devices, electro-optic modulators, pyroelectric detectors, or oxygen reduction catalysts. Their stability in ambient conditions, chemical versatility, and large susceptibility to minute structural and electronic modifications make them ideal subjects of study to discover emergent phenomena and to generate novel functionalities for next-generation devices. Recent advances in the synthesis of single-crystal, freestanding complex oxide membranes provide an unprecedented opportunity to study these materials in a nearly-ideal system (e.g. free of mechanical/thermal interaction with substrates) as well as expanding the range of tools for tweaking their order parameters (i.e. (anti-)ferromagnetic, (anti-)ferroelectric, ferroelastic), and increasing the possibility of achieving novel heterointegration approaches (including interfacing dissimilar materials) by avoiding the chemical, structural, or thermal constraints in synthesis processes. Here, we review the recent developments in the fabrication and characterization of complex-oxide membranes and discuss their potential for unraveling novel physicochemical phenomena at the nanoscale and for further exploiting their functionalities in technologically relevant devices.

Next-generation 2D optical strain mapping with strain-sensing smart skin compared to digital image correlation

This study reports next generation optical strain measurement with "strain-sensing smart skin" (S⁴) and a comparison of its performance against the established digital image correlation (DIC) method. S⁴ measures strain-induced shifts in the emission wavelengths of single-wall carbon nanotubes embedded in a thin film on the specimen. The new S⁴ film improves spectral uniformity of the nanotube sensors, avoids the need for annealing at elevated temperatures, and allows for parallel DIC measurements. Noncontact strain maps measured with the S⁴ films and point-wise scanning were directly compared to those from DIC on acrylic, concrete, and aluminum test specimens, including one with subsurface damage. Strain features were more clearly revealed with S⁴ than with DIC. Finite element method simulations also showed closer agreement with S⁴ than with DIC results. These findings highlight the potential of S⁴ strain measurement technology as a promising alternative or complement to existing technologies, especially when accumulated strains must be detected in structures that are not under constant observation.

Thin-Film Ferroelectrics

Over the last 30 years, the study of ferroelectric oxides has been revolutionized by the implementation of epitaxial-thin-film-based studies, which have driven many advances in the understanding of ferroelectric physics and the realization of novel polar structures and functionalities. New questions have motivated the development of advanced synthesis, characterization, and simulations of epitaxial thin films and, in turn, have provided new insights and applications across the micro-, meso-, and macroscopic length scales. This review traces the evolution of ferroelectric thin-film research through the early days developing understanding of the roles of size and strain on ferroelectrics to the present day, where such understanding is used to create complex hierarchical domain structures, novel polar topologies, and controlled chemical and defect profiles. The extension of epitaxial techniques, coupled with advances in high-throughput simulations, now stands to accelerate the discovery and study of new ferroelectric materials. Coming hand-in-hand with these new materials is new understanding and control of ferroelectric functionalities. Today, researchers are actively working to apply these lessons in a number of applications, including novel memory and logic architectures, as well as a host of energy conversion devices.

Deciphering the phase transition-induced ultrahigh piezoresponse in (K,Na)NbO3-based piezoceramics

Here, we introduce phase change mechanisms in lead-free piezoceramics as a strategy to utilize attendant volume change for harvesting large electrostrain. In the newly developed (K,Na)NbO₃ solid-solution at the polymorphic phase boundary we combine atomic mapping of the local polar vector with in situ synchrotron X-ray diffraction and density functional theory to uncover the phase change and interpret its underlying nature. We demonstrate that an electric field-induced phase transition between orthorhombic and tetragonal phases triggers a dramatic volume change and contributes to a huge effective piezoelectric coefficient of 1250 pm V⁻¹ along specific crystallographic directions. The existence of the phase transition is validated by a significant volume change evidenced by the simultaneous recording of macroscopic longitudinal and transverse strain. The principle of using phase transition to promote electrostrain provides broader design flexibility in the development of high-performance piezoelectric materials and opens the door for the discovery of high-performance future functional oxides.

Functional oxides with coexisting states of comparable energy typically exhibit extraordinary responses to external stimuli. Here, the authors demonstrate that coexisting phase structures provide large electric field-triggered volume change.

Multilevel polarization switching in ferroelectric thin films

Ferroic order is characterized by hystereses with two remanent states and therefore inherently binary. The increasing interest in materials showing non-discrete responses, however, calls for a paradigm shift towards continuously tunable remanent ferroic states. Device integration for oxide nanoelectronics furthermore requires this tunability at the nanoscale. Here we demonstrate that we can arbitrarily set the remanent ferroelectric polarization at nanometric dimensions. We accomplish this in ultrathin epitaxial PbZr_0.52Ti_0.48O₃ films featuring a dense pattern of decoupled nanometric 180° domains with a broad coercive-field distribution. This multilevel switching is achieved by driving the system towards the instability at the morphotropic phase boundary. The phase competition near this boundary in combination with epitaxial strain increases the responsiveness to external stimuli and unlocks new degrees of freedom to nano-control the polarization. We highlight the technological benefits of non-binary switching by demonstrating a quasi-continuous tunability of the non-linear optical response and of tunnel electroresistance.

Setting any polarization value in ferroelectric thin films is a key step for their implementation in neuromorphic devices. Here, the authors demonstrate continuous modulation of the remanent polarization at the nanoscale in PbZr_0.52Ti_0.48O₃ films.

Evolution from Lead-Based to Lead-Free Piezoelectrics: Engineering of Lattices, Domains, Boundaries, and Defects Leading to Giant Response

Piezoelectric materials are known to mankind for more than a century, with numerous advancements made in both scientific understandings and practical applications. In the last two decades, in particular, the research on piezoelectrics has largely been driven by the constantly changing technological demand, and the drive toward a sustainable society. Hence, environmental-friendly "lead-free piezoelectrics" have emerged in the anticipation of replacing lead-based counterparts with at least comparable performance. However, there are still obstacles to be overcome for realizing this objective, while the efforts in this direction already seem to culminate. Therefore, novel structural strategies need to be designed to address these issues and for further breakthrough in this field. Here, various strategies to enhance piezoelectric properties in lead-free systems with fundamental and historical context, and from atomic to macroscopic scale, are explored. The main challenges currently faced in the transition from lead-based to lead-free piezoelectrics are identified and key milestones for future research in this field are suggested. These include: i) decoding the fundamental mechanisms; ii) large temperature-stable piezoresponse; and iii) fabrication-friendly and tailorable composition. Strategic insights and general guidelines for the synergistic design of new piezoelectric materials for obtaining a large piezoelectric response are also provided.

Twisted oxide lateral homostructures with conjunction tunability

Epitaxial growth is of significant importance over the past decades, given it has been the key process of modern technology for delivering high-quality thin films. For conventional heteroepitaxy, the selection of proper single crystal substrates not only facilitates the integration of different materials but also fulfills interface and strain engineering upon a wide spectrum of functionalities. Nevertheless, the lattice structure, regularity and crystalline orientation are determined once a specific substrate is chosen. Here, we reveal the growth of twisted oxide lateral homostructure with controllable in-plane conjunctions. The twisted lateral homostructures with atomically sharp interfaces can be composed of epitaxial “blocks” with different crystalline orientations, ferroic orders and phases. We further demonstrate that this approach is universal for fabricating various complex systems, in which the unconventional physical properties can be artificially manipulated. Our results establish an efficient pathway towards twisted lateral homostructures, adding additional degrees of freedom to design epitaxial films.

It is challenging to construct lateral homostructures with controllable geometry and repeated alternating configurations. Here the authors develop a generic approach for fabricating twisted lateral homostructures with tunable crystal orientation, epitaxial constrain, and phase stability.

Hypothesis Learning in Automated Experiment: Application to Combinatorial Materials Libraries

Machine learning is rapidly becoming an integral part of experimental physical discovery via automated and high-throughput synthesis, and active experiments in scattering and electron/probe microscopy. This, in turn, necessitates the development of active learning methods capable of exploring relevant parameter spaces with the smallest number of steps. Here, an active learning approach based on conavigation of the hypothesis and experimental spaces is introduced. This is realized by combining the structured Gaussian processes containing probabilistic models of the possible system's behaviors (hypotheses) with reinforcement learning policy refinement (discovery). This approach closely resembles classical human-driven physical discovery, when several alternative hypotheses realized via models with adjustable parameters are tested during an experiment. This approach is demonstrated for exploring concentration-induced phase transitions in combinatorial libraries of Sm-doped BiFeO₃ using piezoresponse force microscopy, but it is straightforward to extend it to higher-dimensional parameter spaces and more complex physical problems once the experimental workflow and hypothesis generation are available.

Short Photoluminescence Lifetimes Linked to Crystallite Dimensions, Connectivity, and Perovskite Crystal Phases

Time-correlated single photon counting has been conducted to gain further insights into the short photoluminescence lifetimes (nanosecond) of lead iodide perovskite (MAPbI₃) thin films (∼100 nm). We analyze three different morphologies, compact layer, isolated island, and connected large grain films, from 14 to 300 K using a laser excitation power of 370 nJ/cm². Lifetime fittings from the Generalized Berberan-Santos decay model range from 0.5 to 6.5 ns, pointing to quasi-direct bandgap emission despite the three different sample strains. The high energy band emission for the isolated-island morphology shows fast recombination rate centers up to 4.8 ns^-1, compared to the less than 2 ns^-1 for the other two morphologies, similar to that expected in a good quality single crystal of MAPbI₃. Low-temperature measurements on samples reflect a huge oscillator strength in this material where the free exciton recombination dominates, explaining the fast lifetimes, the low thermal excitation, and the thermal escape obtained.

Morphotropic Relaxor Boundary Construction Highly Boosts the Piezoelectric Properties of Bi-Based Lead-Free Thin Films

To achieve large electrostrain and low hysteresis, we further optimized a morphotropic phase boundary (MPB) by modulating its local polar symmetries. The construction of a morphotropic relaxor boundary (MRB) in thin films can be achieved by suitable introduction of Bi(Fe_0.95Mn_0.03Ti_0.02)O₃ into (Bi_0.5Na_0.5)TiO₃-SrTiO₃ to form a solid solution. The designed thin film achieves surprising piezoelectric properties with an inverse piezoelectric coefficient of 179.7 pm V^-1 and negligible hysteresis. The composition of two relaxors with different local polar symmetries (tetragonal nanoregions and rhombohedral nanoregions), namely, an MRB, and the coexistence of multiscale domain structures can greatly weaken the anisotropy of polarization, degrade the energy barrier, attenuate the discontinuity of polarization, and achieve a large electrostrain and low hysteresis. The domain dynamics of the PNRs under the action of an external excitation field are analyzed to clarify the enhancement mechanism. This construction of MRBs is feasible for producing lead-free piezoelectric films with high-voltage electrical properties and low hysteresis, and various experimental design and theoretical references are provided.

Strain and orientation engineering in ABO3perovskite oxide thin films

Perovskite oxides with chemical formula ABO₃are widely studied for their properties including ferroelectricity, magnetism, strongly correlated physics, optical effects, and superconductivity. A thriving research direction using such materials is through their integration as epitaxial thin films, allowing many novel and exotic effects to be discovered. The integration of the thin film on a single crystal substrate, however, can produce unique and powerful effects, and can even induce phases in the thin film that are not stable in bulk. The substrate imposed mechanical boundary conditions such as strain, crystallographic orientation, octahedral rotation patterns, and symmetry can also affect the functional properties of perovskite films. Here, the author reviews the current state of the art in epitaxial strain and orientation engineering in perovskite oxide thin films. The paper begins by introducing the effect of uniform conventional biaxial strain, and then moves to describe how the substrate crystallographic orientation can induce symmetry changes in the film materials. Various material case studies, including ferroelectrics, magnetically ordered materials, and nonlinear optical oxides are covered. The connectivity of the oxygen octahedra between film and substrate depending on the strain level as well as the crystallographic orientation is then discussed. The review concludes with open questions and suggestions worthy of the community's focus in the future.

Liberating a hidden antiferroelectric phase with interfacial electrostatic engineering

Antiferroelectric materials have seen a resurgence of interest because of proposed applications in a number of energy-efficient technologies. Unfortunately, relatively few families of antiferroelectric materials have been identified, precluding many proposed applications. Here, we propose a design strategy for the construction of antiferroelectric materials using interfacial electrostatic engineering. We begin with a ferroelectric material with one of the highest known bulk polarizations, BiFeO₃. By confining thin layers of BiFeO₃ in a dielectric matrix, we show that a metastable antiferroelectric structure can be induced. Application of an electric field reversibly switches between this new phase and a ferroelectric state. The use of electrostatic confinement provides an untapped pathway for the design of engineered antiferroelectric materials with large and potentially coupled responses.

Exploring Causal Physical Mechanisms via Non-Gaussian Linear Models and Deep Kernel Learning: Applications for Ferroelectric Domain Structures

Rapid emergence of multimodal imaging in scanning probe, electron, and optical microscopies has brought forth the challenge of understanding the information contained in these complex data sets, targeting the intrinsic correlations between different channels, and further exploring the underpinning causal physical mechanisms. Here, we develop such an analysis framework for Piezoresponse Force Microscopy. We argue that under certain conditions, we can bootstrap experimental observations with the prior knowledge of materials structure to get information on certain nonobserved properties, and demonstrate linear causal analysis for PFM observables. We further demonstrate that the strength of individual causal links between complex descriptors can be ascertained using the deep kernel learning (DKL) model. In this DKL analysis, we use the prior information on domain structure within the image to predict the physical properties. This analysis demonstrates the correlative relationships between morphology, piezoresponse, elastic property, etc., at nanoscale. The prediction of morphology and other physical parameters illustrates a mutual interaction between surface condition and physical properties in ferroelectric materials. This analysis is universal and can be extended to explore the correlative relationships of other multichannel data sets, and allow for high-fidelity reconstruction of underpinning functionalities and physical mechanisms.

Materials for a Sustainable Microelectronics Future: Electric Field Control of Magnetism with Multiferroics

This article is written on behalf of many colleagues, collaborators, and researchers in the field of complex oxides as well as current and former students and postdocs who continue to enable and undertake cutting-edge research in the field of multiferroics, magnetoelectrics, and the pursuit of electric-field control of magnetism. What I present is something that is extremely exciting from both a fundamental science and applications perspective and has the potential to revolutionize our world, particularly from a sustainability perspective. To realize this potential will require numerous new innovations, both in the fundamental science arena as well as translating these scientific discoveries into real applications. Thus, this article will attempt to bridge the gap between fundamental materials physics and the actual manifestations of the physical concepts into real-life applications. I hope this article will help spur more translational research within the broad materials community.

Seeing Structural Mechanisms of Optimized Piezoelectric and Thermoelectric Bulk Materials through Structural Defect Engineering

Aberration-corrected scanning transmission electron microscopy (AC-STEM) has evolved into the most powerful characterization and manufacturing platform for all materials, especially functional materials with complex structural characteristics that respond dynamically to external fields. It has become possible to directly observe and tune all kinds of defects, including those at the crucial atomic scale. In-depth understanding and technically tailoring structural defects will be of great significance for revealing the structure-performance relation of existing high-property materials, as well as for foreseeing paths to the design of high-performance materials. Insights would be gained from piezoelectrics and thermoelectrics, two representative functional materials. A general strategy is highlighted for optimizing these functional materials’ properties, namely defect engineering at the atomic scale.

Interplay of piezoresponse and magnetic behavior in Bi0.9A0.1FeO2.95 (A = Ba, Ca) and Bi0.9Ba0.05Ca0.05FeO2.95 co-doped ceramics

In the pristine as well as the doped BiFeO3 samples, ferroelectric domains show switching behavior. The regions marked by yellow color loops show either 71° or 109°-domains, whereas those marked by white loops are 180°-domains.

Oxygen Vacancy Injection as a Pathway to Enhancing Electromechanical Response in Ferroelectrics

Since their discovery in late 1940s, perovskite ferroelectric materials have become one of the central objects of condensed matter physics and materials science due to the broad spectrum of functional behaviors they exhibit, including electro-optical phenomena and strong electromechanical coupling. In such disordered materials, the static properties of defects such as oxygen vacancies are well explored but the dynamic effects are less understood. In this work, the first observation of enhanced electromechanical response in BaTiO₃ thin films is reported driven via dynamic local oxygen vacancy control in piezoresponse force microscopy (PFM). A persistence in peizoelectricity past the bulk Curie temperature and an enhanced electromechanical response due to a created internal electric field that further enhances the intrinsic electrostriction are explicitly demonstrated. The findings are supported by a series of temperature dependent band excitation PFM in ultrahigh vacuum and a combination of modeling techniques including finite element modeling, reactive force field, and density functional theory. This study shows the pivotal role that dynamics of vacancies in complex oxides can play in determining functional properties and thus provides a new route toward- achieving enhanced ferroic response with higher functional temperature windows in ferroelectrics and other ferroic materials.

Interplay between Spin-Orbital Coupling and Electron-Correlation: Induction of Phase Transitions and Giant Magnetic Anisotropy in Strained LaSr_{1−x}Ca_xNiReO_6

In recent decades, 3d-5d based double perovskite oxides (DPO) have received considerable attention due to the existence of the Mott-insulating (MI) state, which is owing to the spin-orbit coupling (SOC)...

Anisotropic epitaxial stabilization of a low-symmetry ferroelectric with enhanced electromechanical response

Piezoelectrics interconvert mechanical energy and electric charge and are widely used in actuators and sensors. The best performing materials are ferroelectrics at a morphotropic phase boundary, where several phases coexist. Switching between these phases by electric field produces a large electromechanical response. In ferroelectric BiFeO₃, strain can create a morphotropic-phase-boundary-like phase mixture and thus generate large electric-field-dependent strains. However, this enhanced response occurs at localized, randomly positioned regions of the film. Here, we use epitaxial strain and orientation engineering in tandem-anisotropic epitaxy-to craft a low-symmetry phase of BiFeO₃ that acts as a structural bridge between the rhombohedral-like and tetragonal-like polymorphs. Interferometric displacement sensor measurements reveal that this phase has an enhanced piezoelectric coefficient of ×2.4 compared with typical rhombohedral-like BiFeO₃. Band-excitation frequency response measurements and first-principles calculations provide evidence that this phase undergoes a transition to the tetragonal-like polymorph under electric field, generating an enhanced piezoelectric response throughout the film and associated field-induced reversible strains. These results offer a route to engineer thin-film piezoelectrics with improved functionalities, with broader perspectives for other functional oxides.

In Situ Cryogenic HAADF-STEM Observation of Spontaneous Transition of Ferroelectric Polarization Domain Structures at Low Temperatures

Precise determination of atomic structures in ferroelectric thin films and their evolution with temperature is crucial for fundamental study and design of functional materials. However, this has been impeded by the lack of techniques applicable to a thin-film geometry. Here we use cryogenic scanning transmission electron microscopy (STEM) to observe the atomic structure of a BaTiO₃ film on a (111)-SrTiO₃ substrate under varying temperatures. Our study explicitly proves a structure transition from a complex polymorphic nanodomain configuration at room temperature transitioning to a homogeneous ground-state rhombohedral structure of BaTiO₃ below ∼250 K, which was predicted by phase-field simulation. More importantly, another unexpected transition is revealed, a transition to complex nanodomains below ∼105 K caused by an altered mechanical boundary condition due to the antiferrodistortive phase transition of the SrTiO₃ substrate. This study demonstrates the power of cryogenic STEM in elucidating structure-property relationships in numerous functional materials at low temperatures.

Probing Metastable Domain Dynamics via Automated Experimentation in Piezoresponse Force Microscopy

The dynamics of complex topological defects in ferroelectric materials is explored using automated experimentation in piezoresponse force microscopy. Specifically, a complex trigger system (i.e., "FerroBot") is employed to study metastable domain-wall dynamics in Pb_0.6Sr_0.4TiO₃ thin films. Several regimes of superdomain wall dynamics have been identified, including smooth domain-wall motion and significant reconfiguration of the domain structures. We have further demonstrated that microscopic mechanisms of the domain-wall dynamics can be identified; i.e., domain-wall bending can be separated from irreversible domain reconfiguration regimes. In conjunction, phase-field modeling was used to corroborate the observed mechanisms. As such, the observed superdomain dynamics can provide a model system for classical ferroelectric dynamics, much like how colloidal crystals provide a model system for atomic and molecular systems.

Oxidic 2D Materials

The possibility of producing stable thin films, only a few atomic layers thick, from a variety of materials beyond graphene has led to two-dimensional (2D) materials being studied intensively in recent years. By reducing the layer thickness and approaching the crystallographic monolayer limit, a variety of unexpected and technologically relevant property phenomena were observed, which also depend on the subsequent arrangement and possible combination of individual layers to form heterostructures. These properties can be specifically used for the development of multifunctional devices, meeting the requirements of the advancing miniaturization of modern manufacturing technologies and the associated need to stabilize physical states even below critical layer thicknesses of conventional materials in the fields of electronics, magnetism and energy conversion. Differences in the structure of potential two-dimensional materials result in decisive influences on possible growth methods and possibilities for subsequent transfer of the thin films. In this review, we focus on recent advances in the rapidly growing field of two-dimensional materials, highlighting those with oxidic crystal structure like perovskites, garnets and spinels. In addition to a selection of well-established growth techniques and approaches for thin film transfer, we evaluate in detail their application potential as free-standing monolayers, bilayers and multilayers in a wide range of advanced technological applications. Finally, we provide suggestions for future developments of this promising research field in consideration of current challenges regarding scalability and structural stability of ultra-thin films.

Controlling Strain Relaxation by Interface Design in Highly Lattice-Mismatched Heterostructure

Strain engineering plays an important role in tuning the microstructure and properties of heterostructures. The key to implement the strain modulation to heterostructures is controlling the strain relaxation, which is generally realized by varying the thickness of thin films or changing substrates. Here, we show that interface polarity can tailor the behavior of strain relaxation in a hexagonal manganite film, whose strain state can be tuned to different extents. Using scanning transmission electron microscopy, a reconstructed atomic layer with elongated interlayer spacing and minor in-plane rotation is observed at the interface, suggesting that the bond hierarchy at interface transits from three-dimension to two-dimension, which accounts for the strain-free heteroepitaxy. Utilizing interface polarity to control the strain relaxation highlights a conceptually opt route to optimize the strain engineering and the realization of strain-free heteroepitaxy in such highly lattice-mismatched heterostructure also provides possibility to transform more bulklike functional oxides to low dimensionality.

Periodic Polarization Waves in a Strained, Highly Polar Ultrathin SrTiO3

SrTiO₃ is generally paraelectric with centrosymmetric structure exhibiting unique quantum fluctuation related ferroelectricity. Here we reveal highly polar and periodic polarization waves in SrTiO₃ at room temperature, which is stabilized by periodic tensile strains in a sandwiched PbTiO₃/SrTiO₃/PbTiO₃ structure. Scanning transmission electron microscopy reveals that periodic a/c domain structures in PbTiO₃ layers exert unique periodic tensile strains in the ultrathin SrTiO₃ layer and consequently make the highly polar and periodic states of SrTiO₃. The as-received polar SrTiO₃ layer features peak polar ion displacement of ∼0.01 nm and peak tetragonality of ∼1.07. These peak values are larger than previous results, which are comparable to that of bulk ferroelectric PbTiO₃. Our results suggest that it is possible to integrate large and periodic strain state in oxide films with exotic properties, which in turn could be useful in optical applications and information addressing when used as memory unit.

Strain-Engineered Nano-Ferroelectrics for High-Efficiency Piezocatalytic Overall Water Splitting

Developing nano-ferroelectric materials with excellent piezoelectric performance for piezocatalysts used in water splitting is highly desired but also challenging, especially with respect to reaching large piezo-potentials that fully align with required redox levels. Herein, heteroepitaxial strain in BaTiO₃ nanoparticles with a designed porous structure is successfully induced by engineering their surface reconstruction to dramatically enhance their piezoelectricity. The strain coherence can be maintained throughout the nanoparticle bulk, resulting in a significant increase of the BaTiO₃ tetragonality and thus its piezoelectricity. Benefiting from high piezoelectricity, the as-synthesized blue-colored BaTiO₃ nanoparticles possess a superb overall water-splitting activity, with H₂ production rates of 159 μmol g^-1  h^-1 , which is almost 130 times higher than that of the pristine BaTiO₃ nanoparticles. Thus, this work provides a generic approach for designing highly efficient piezoelectric nanomaterials by strain engineering that can be further extended to various other perovskite oxides, including SrTiO₃ , thereby enhancing their potential for piezoelectric catalysis.

Identification and correction of temporal and spatial distortions in scanning transmission electron microscopy

Scanning transmission electron microscopy (STEM) has become the technique of choice for quantitative characterization of atomic structure of materials, where the minute displacements of atomic columns from high-symmetry positions can be used to map strain, polarization, octahedra tilts, and other physical and chemical order parameter fields. The latter can be used as inputs into mesoscopic and atomistic models, providing insight into the correlative relationships and generative physics of materials on the atomic level. However, these quantitative applications of STEM necessitate understanding the microscope induced image distortions and developing the pathways to compensate them both as part of a rapid calibration procedure for in situ imaging, and the post-experimental data analysis stage. Here, we explore the spatiotemporal structure of the microscopic distortions in STEM using multivariate analysis of the atomic trajectories in the image stacks. Based on the behavior of principal component analysis (PCA), we develop the Gaussian process (GP)-based regression method for quantification of the distortion function. The limitations of such an approach and possible strategies for implementation as a part of in-line data acquisition in STEM are discussed. The analysis workflow is summarized in a Jupyter notebook that can be used to retrace the analysis and analyze the reader's data.