Enhanced Piezoelectric Response at Nanoscale Vortex Structures in Ferroelectrics.

The piezoelectric response is a measure of the sensitivity of a material's polarization to stress or its strain to an applied field. Using in operando X-ray Bragg coherent diffraction imaging, we observe that topological vortices are the source of a 5-fold enhancement of the piezoelectric response near the vortex core. The vortices form where several low-symmetry ferroelectric phases and phase boundaries coalesce. Unlike bulk ferroelectric solid solutions in which a large piezoelectric response is associated with coexisting phases in the proximity of the triple point, the largest responses for pure BaTiO3 at the nanoscale are in spatial regions of extremely small spontaneous polarization at vortex cores. The response decays inversely with polarization away from the vortex, analogous to the behavior in bulk ceramics as the cation compositions are varied away from the triple point. We use first-principles-based molecular dynamics to augment our observations, and our results suggest that nanoscale piezoelectric materials with a large piezoelectric response can be designed within a parameter space governed by vortex cores. Our findings have implications for the development of next-generation nanoscale piezoelectric materials.

What can data science tell us about finding new superconductors?

Can data science guide researchers toward understanding superconductivity or discover new superconductors? We examine this question in light of a study in this issue of Patterns by Liu et al., who find that the superconducting transition temperature and certain computed energy intervals of the valence band are correlated.

Rapid Discovery of Efficient Long-Wavelength Emission Garnet:Cr NIR Phosphors via Multi-Objective Optimization.

High-efficiency long-wavelength emission near-infrared (NIR) phosphors are the key to next-generation LED light sources. However, high-efficiency phosphors usually exhibit narrow-band emission at shorter wavelengths due to the crystal field intensity. In this paper, we utilize multi-objective optimization to discover the NIR phosphor Gd3Mg0.5Al1.5Ga2.5Ge0.5O12:0.04Cr3+. It exhibits a broadband NIR emission from 650 to 1100 nm peaking at 763 nm, with a full width at half maximum (FWHM) of 150 nm, an internal quantum efficiency (IQE)/external quantum efficiency (EQE) of 90%/53.1%, and good thermal stability (85.3% @ 150 °C). The packaging results show that ∼53.2 mW of output power is achieved at 915 mW input power, which suggests promising applications for NIR pc-LED. Our approach is based on the data of emission wavelength (WL) and IQE for garnet:Cr NIR phosphors to construct machine learning models. An active learning strategy is used to make tradeoffs between WL and IQE, and we are able to find the targeted phosphor after only four iterations of synthesis and characterization.

Influence of Phase Transitions on Electrostrictive and Piezoelectric Characteristics in PMN-30PT Single Crystals.

The ultrahigh electrostrain and piezoelectric constant (d33) in relaxor piezoelectric PMN-30PT single crystals are closely related to the coexistence and transition of multiple phases at the morphotropic phase boundary (MPB). However, the key mechanisms underlying the stability of the phases and their transitions are yet to be fully understood. In this work, we undertake a systematic study of the influences of phase transitions on the electrostrictive and piezoelectric behaviors in ⟨001⟩-, ⟨011⟩-, and ⟨111⟩-oriented PMN-30PT single crystals. We first classify the various phase transitions within the quasi-MPB in electric field-temperature phase diagrams as either dominated by the electric field or by temperature. We find that the electrostrain reaches a maximum at each phase transition, especially in the electric-field-dominated transitions, whereas d33 only peaks at specific phase transitions. In particular, the electrostrain in the ⟨001⟩ crystal reaches a maximum of S = 0.52% at 55 °C under an external electric field with E = 15 kV/cm, primarily due to a joint contribution of the electric field-dominated rhombohedral-monoclinic and monoclinic-tetragonal phase transitions at the quasi-MPB. An ultrahigh d33 (∼2460 pC/N) only occurs at the rhombohedral-monoclinic phase transition in the ⟨001⟩ crystal and at the rhombohedral-orthorhombic transition in the ⟨011⟩ crystal (d33 ∼ 1500 pC/N) due to the lower energy barriers. The temperature-dominated phase transitions also contribute toward minor peaks in electrostrain and/or d33. This work provides a deeper and quantitative understanding of the microscopic mechanisms underlying electrostrictive and piezoelectric behaviors relevant for the design of high-performance materials.

Alkali-deficiency driven charged out-of-phase boundaries for giant electromechanical response.

Traditional strategies for improving piezoelectric properties have focused on phase boundary engineering through complex chemical alloying and phase control. Although they have been successfully employed in bulk materials, they have not been effective in thin films due to the severe deterioration in epitaxy, which is critical to film properties. Contending with the opposing effects of alloying and epitaxy in thin films has been a long-standing issue. Herein we demonstrate a new strategy in alkali niobate epitaxial films, utilizing alkali vacancies without alloying to form nanopillars enclosed with out-of-phase boundaries that can give rise to a giant electromechanical response. Both atomically resolved polarization mapping and phase field simulations show that the boundaries are strained and charged, manifesting as head-head and tail-tail polarization bound charges. Such charged boundaries produce a giant local depolarization field, which facilitates a steady polarization rotation between the matrix and nanopillars. The local elastic strain and charge manipulation at out-of-phase boundaries, demonstrated here, can be used as an effective pathway to obtain large electromechanical response with good temperature stability in similar perovskite oxides.

Knowledge-Based Descriptor for the Compositional Dependence of the Phase Transition in BaTiO3-Based Ferroelectrics.

Descriptors play a central role in constructing composition-structure-property relationships to guide materials design. We propose a material descriptor, δτ, for the composition dependence of the Curie temperature (Tc) on single doping elements in BaTiO3 ferroelectrics, which is then generalized to a linear combination of multiple dopants in the solid solutions. The descriptor δτ depends linearly on the Curie temperature and also serves to separate the ferroelectric phase from the relaxor phase. We compare δτ to other commonly used descriptors such as the tolerance factor, electronegativity, and ionic displacement. By using regression analysis on our assembled experimental data, we show how it outperforms other descriptors. We use the trained machine-learned models to predict compositions in our search space with the largest ferroelectric, dielectric, and piezoelectric properties, namely, d33, electrostrain, and recoverable energy storage density. We experimentally verify our predictions for Tc and classification into ferroelectrics and relaxors by synthesizing and characterizing six solid solutions in BaTiO3 ferroelectrics. Our definition of δτ can shed light on the design of knowledge-based descriptors in other systems such as Pb-based and Bi-based solid solutions.

Determining Multi-Component Phase Diagrams with Desired Characteristics Using Active Learning.

Herein, we demonstrate how to predict and experimentally validate phase diagrams for multi-component systems from a high-dimensional virtual space of all possible phase diagrams involving several elements based on small existing experimental data. The experimental data for bulk phases for known systems represents a sampling from this space, and screening the space allows multi-component phase diagrams with given design criteria to be built. This approach uses machine learning methods to predict phase diagrams and Bayesian experimental design to minimize experiments for refinement and validation, all within an active learning loop. The approach is proven by predicting and synthesizing the ferroelectric ceramic system (1-ω)(Ba0.61Ca0.28Sr0.11TiO3)-ω(BaTi0.888Zr0.0616Sn0.0028Hf0.0476O3) with a relatively high transition temperature and triple point, as well as the NiTi-based pseudo-binary phase diagram (1-ω)(Ti0.309Ni0.485Hf0.20Zr0.006)-ω(Ti0.309Ni0.485Hf0.07Zr0.068Nb0.068) designed for high transition temperature (ω ⩽ 1). Each phase diagram is validated and optimized through only three new experiments. The complexity of these compounds is beyond the reach of today's computational methods.

Accelerated Search for BaTiO3-Based Ceramics with Large Energy Storage at Low Fields Using Machine Learning and Experimental Design.

The problem that is considered is that of maximizing the energy storage density of Pb-free BaTiO3-based dielectrics at low electric fields. It is demonstrated that how varying the size of the combinatorial search space influences the efficiency of material discovery by comparing the performance of two machine learning based approaches where different levels of physical insights are involved. It is started with physics intuition to provide guiding principles to find better performers lying in the crossover region in the composition-temperature phase diagram between the ferroelectric phase and relaxor ferroelectric phase. Such an approach is limiting for multidopant solid solutions and motivates the use of two data-driven machine learning and design strategies with a feedback loop to experiments. Strategy I considers learning and property prediction on all the compounds, and strategy II learns to preselect compounds in the crossover region on which prediction is carried out. By performing only two active learning loops via strategy II, the compound (Ba0.86Ca0.14)(Ti0.79Zr0.11Hf0.10)O3 is synthesized with the largest energy storage density ≈73 mJ cm-3 at a field of 20 kV cm-1, and an insight into the relative performance of the strategies using varying levels of knowledge is provided.

Machine-Learning-Based Predictive Modeling of Glass Transition Temperatures: A Case of Polyhydroxyalkanoate Homopolymers and Copolymers.

Polyhydroxyalkanoate-based polymers-being ecofriendly, biosynthesizable, and economically viable and possessing a broad range of tunable properties-are currently being actively pursued as promising alternatives for petroleum-based plastics. The vast chemical complexity accessible within this class of polymers gives rise to challenges in the rational discovery of novel polymer chemistries for specific applications. The burgeoning field of polymer informatics addresses this challenge via providing tools and strategies for accelerated property prediction and materials design via surrogate machine-learning models built on reliable past data. In this contribution, we use glass transition temperature Tg as an example target property to demonstrate promise of the data-enabled route to accelerated learning of accurate structure-property mappings in PHA-based polymers. Our analysis uses a data set of experimentally measured Tg values, polymer molecular weights, and a polydispersity index for PHA-based homo- and copolymers that was carefully assembled from the literature. A fingerprinting scheme that captures key properties based on topology, shape, and charge/polarity of specific chemical units or motifs forming the polymer backbone was devised to numerically represent the polymers. A validated statistical learning model is then developed to allow for a mapping of the polymer fingerprints onto the property space in a physically meaningful and reliable manner. Once developed, the model can not only rapidly predict the property of new PHA polymers but also provide uncertainties underlying the predictions. The model is further combined with an evolutionary-algorithm-based search strategy to efficiently identify multicomponent polymer compositions with a prespecified Tg. While the present contribution is focused specifically on Tg, the surrogate model development approach put forward here is general and can, in principle, be extended to a range of other properties.

Competing Interface and Bulk Effect-Driven Magnetoelectric Coupling in Vertically Aligned Nanocomposites.

Room-temperature magnetoelectric (ME) coupling is developed in artificial multilayers and nanocomposites composed of magnetostrictive and electrostrictive materials. While the coupling mechanisms and strengths in multilayers are widely studied, they are largely unexplored in vertically aligned nanocomposites (VANs), even though theory has predicted that VANs exhibit much larger ME coupling coefficients than multilayer structures. Here, strong transverse and longitudinal ME coupling in epitaxial BaTiO3:CoFe2O4 VANs measured by both optical second harmonic generation and piezoresponse force microscopy under magnetic fields is reported. Phase field simulations have shown that the ME coupling strength strongly depends on the vertical interfacial area which is ultimately controlled by pillar size. The ME coupling in VANs is determined by the competition between the vertical interface coupling effect and the bulk volume conservation effect. The revealed mechanisms shed light on the physical insights of vertical interface coupling in VANs in general, which can be applied to a variety of nanocomposites with different functionalities beyond the studied ME coupling effect.

Enhanced magnetism in lightly doped manganite heterostructures: strain or stoichiometry?

Lattice mismatch induced epitaxial strain has been widely used to tune functional properties in complex oxide heterostructures. Apart from the epitaxial strain, a large lattice mismatch also produces other effects including modulations in microstructure and stoichiometry. However, it is challenging to distinguish the impact of these effects from the strain contribution to thin film properties. Here, we use La0.9Sr0.1MnO3 (LSMO), a lightly doped manganite close to the vertical phase boundary, as a model system to demonstrate that both epitaxial strain and cation stoichiometry induced by strain relaxation contribute to functionality tuning. The thinner LSMO films are metallic with a greatly enhanced TC which is 97 K higher than the bulk value. Such anomalies in TC and transport cannot be fully explained by the epitaxial strain alone. Detailed microstructure analysis indicates La deficiency in thinner films and twin domain formation in thicker films. Our results have revealed that both epitaxial strain and strain relaxation induced stoichiometry/microstructure modulations contribute to the modified functional properties in lightly doped manganite perovskite thin films.

Critical diffusivity in the reversibility-irreversibility transition of amorphous solids under oscillatory shear.

Recently it was shown that under oscillatory shear at zero temperature an amorphous solid transitions from asymptotically periodic to asymptotically diffusive steady-state at a critical maximal strain amplitude. Current understanding of the physics behind this transition is lacking. Here we show, using computer simulations, evidence that the diffusivity of the vector of coordinates of the particles comprising an amorphous solid, when subject to oscillatory shear, undergoes a second order phase transition at the reversibility-irreversibility transition point. We explain how such a transition is consistent with dissipative forced dynamics on a complex energy landscape, such as is known to exist in amorphous solids. We demonstrate that as the forcing increases, more and more state-space volume becomes accessible to the system, making it less probable for the state-space trajectory of the system to self-intersect and form a limit-cycle, which explains the slowing-down observed at the transition.

The Search for BaTiO3-Based Piezoelectrics With Large Piezoelectric Coefficient Using Machine Learning.

We employ a data-driven approach to search for BaTiO3-based piezoelectrics with large piezoelectric coefficient d33. Our approach uses a surrogate model to make predictions of d33 with uncertainties, followed by a design step that selects the next optimal compound to synthesize. We compare several combinations of choices of the model and design selection strategies on the training data assembled from many experiments that we have previously performed, and we choose the best two performers for guiding new experiments. This adaptive design strategy is iterated five times and in each iteration, four new compounds are synthesized based on the two different design selection criteria. The best new compound found in this work is (Ba0.85Ca0.15)(Ti0.91Zr0.09)O3 with a d33 of 362 pC/N, compared to the best compound BCT-0.5BZT in the training data with a d33 of ~610 pC/N. Our conclusion from this study is that although our model describes well most of the available d33 data, the especially large value for BCT-0.5BZT is difficult to fit with any surrogate model and emphasizes the need to combine a physics-based approach with a pure data-driven approach used in this study.

Mechanical relaxation and freezing in the room temperature strain glass alloy Ti50(Pd40Cr10).

The alloy Ti50(Pd40Cr10) undergoes a strain glass transition around room temperature evidenced by frequency dispersion of dynamic mechanical properties and lack of average structure change from that of the high symmetry austenite phase. However, since the strain glass transition is not a thermodynamic phase transition but a dynamic freezing process governed by the kinetics, a quantitative characterization of the slowing down of dynamics during the strain glass transition is still lacking. In the present study, the probability distribution function (PDF) of the relaxation time of the strain glass alloy is investigated spanning the whole transition temperature range (253 K-313 K). The slowing down of dynamics of the strain glass is indicated by the rapid increase of the characteristic relaxation time ([Formula: see text]) upon cooling. The [Formula: see text], as a function of temperature, shows a transition from Vogel-Fulcher relationship to an Arrhenius relationship. Such a change suggests two fundamentally different states: unfrozen strain glass state and frozen strain glass state. Furthermore, the spread of the PDF is connected to the fraction of quasi-static nanodomains, which helps the understanding of the dynamic freezing process in the strain glass.

Experimental search for high-temperature ferroelectric perovskites guided by two-step machine learning.

Experimental search for high-temperature ferroelectric perovskites is a challenging task due to the vast chemical space and lack of predictive guidelines. Here, we demonstrate a two-step machine learning approach to guide experiments in search of xBi[Formula: see text]O3-(1 - x)PbTiO3-based perovskites with high ferroelectric Curie temperature. These involve classification learning to screen for compositions in the perovskite structures, and regression coupled to active learning to identify promising perovskites for synthesis and feedback. The problem is challenging because the search space is vast, spanning ~61,500 compositions and only 167 are experimentally studied. Furthermore, not every composition can be synthesized in the perovskite phase. In this work, we predict x, y, Me', and Me″ such that the resulting compositions have both high Curie temperature and form in the perovskite structure. Outcomes from both successful and failed experiments then iteratively refine the machine learning models via an active learning loop. Our approach finds six perovskites out of ten compositions synthesized, including three previously unexplored {Me'Me″} pairs, with 0.2Bi(Fe0.12Co0.88)O3-0.8PbTiO3 showing the highest measured Curie temperature of 898 K among them.

Multi-objective Optimization for Materials Discovery via Adaptive Design.

Guiding experiments to find materials with targeted properties is a crucial aspect of materials discovery and design, and typically multiple properties, which often compete, are involved. In the case of two properties, new compounds are sought that will provide improvement to existing data points lying on the Pareto front (PF) in as few experiments or calculations as possible. Here we address this problem by using the concept and methods of optimal learning to determine their suitability and performance on three materials data sets; an experimental data set of over 100 shape memory alloys, a data set of 223 M2AX phases obtained from density functional theory calculations, and a computational data set of 704 piezoelectric compounds. We show that the Maximin and Centroid design strategies, based on value of information criteria, are more efficient in determining points on the PF from the data than random selection, pure exploitation of the surrogate model prediction or pure exploration by maximum uncertainty from the learning model. Although the datasets varied in size and source, the Maximin algorithm showed superior performance across all the data sets, particularly when the accuracy of the machine learning model fits were not high, emphasizing that the design appears to be quite forgiving of relatively poor surrogate models.

Accelerated Discovery of Large Electrostrains in BaTiO3 -Based Piezoelectrics Using Active Learning.

A key challenge in guiding experiments toward materials with desired properties is to effectively navigate the vast search space comprising the chemistry and structure of allowed compounds. Here, it is shown how the use of machine learning coupled to optimization methods can accelerate the discovery of new Pb-free BaTiO3 (BTO-) based piezoelectrics with large electrostrains. By experimentally comparing several design strategies, it is shown that the approach balancing the trade-off between exploration (using uncertainties) and exploitation (using only model predictions) gives the optimal criterion leading to the synthesis of the piezoelectric (Ba0.84 Ca0.16 )(Ti0.90 Zr0.07 Sn0.03 )O3 with the largest electrostrain of 0.23% in the BTO family. Using Landau theory and insights from density functional theory, it is uncovered that the observed large electrostrain is due to the presence of Sn, which allows for the ease of switching of tetragonal domains under an electric field.

Predicting displacements of octahedral cations in ferroelectric perovskites using machine learning.

In ferroelectric perovskites, displacements of cations from the high-symmetry lattice positions in the paraelectric phase break the spatial inversion symmetry. Furthermore, the relative magnitude of ionic displacements correlate strongly with ferroelectric properties such as the Curie temperature. As a result, there is interest in predicting the relative displacements of cations prior to experiments. Here, machine learning is used to predict the average displacement of octahedral cations from its high-symmetry position in ferroelectric perovskites. Published octahedral cation displacements data from density functional theory (DFT) calculations are used to train machine learning models, where each cation is represented by features such as Pauling electronegativity, Martynov-Batsanov electronegativity and the ratio of valence electron number to nominal charge. Average displacements for ten new octahedral cations for which DFT data do not exist are predicted. Predictions are validated by comparing them with new DFT calculations and existing experimental data. The outcome of this work has implications in the design and discovery of novel ferroelectric perovskites.

Statistics of twinning in strained ferroelastics.

In this review, we show that the evolution of the microstructure and kinetics of ferroelastic crystals under external shear can be explored by computer simulations of 2D model materials. We find that the nucleation and propagation of twin boundaries in ferroelastics depend sensitively on temperature. In the plastic regime, the evolution of the ferroelastic microstructure under strain deformation maintains a stick-and-slip mechanism in all temperature regimes, whereas the dynamic behavior changes dramatically from power-law statistics at low temperature to a Kohlrausch law at intermediate temperature, and then to a Vogel-Fulcher law at high temperature. In the yield regime, the distribution of jerk energies follows power-law statistics in all temperature regimes for a large range of strain rates. The non-spanning avalanches in the yield regime follow a parabolic temporal profile. The changes of twin pattern and twin boundaries density represent an important step towards domain boundary engineering.

Learning from data to design functional materials without inversion symmetry.

Accelerating the search for functional materials is a challenging problem. Here we develop an informatics-guided ab initio approach to accelerate the design and discovery of noncentrosymmetric materials. The workflow integrates group theory, informatics and density-functional theory to uncover design guidelines for predicting noncentrosymmetric compounds, which we apply to layered Ruddlesden-Popper oxides. Group theory identifies how configurations of oxygen octahedral rotation patterns, ordered cation arrangements and their interplay break inversion symmetry, while informatics tools learn from available data to select candidate compositions that fulfil the group-theoretical postulates. Our key outcome is the identification of 242 compositions after screening ∼3,200 that show potential for noncentrosymmetric structures, a 25-fold increase in the projected number of known noncentrosymmetric Ruddlesden-Popper oxides. We validate our predictions for 19 compounds using phonon calculations, among which 17 have noncentrosymmetric ground states including two potential multiferroics. Our approach enables rational design of materials with targeted crystal symmetries and functionalities.