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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Linking constituent phase properties to ductility and edge stretchability of two DP 980 steels

Two DP 980 steels were characterized with multiple methods to determine its microstructure characteristics, tensile properties and edge stretchability. The first (DP980-B) is a commercial grade DP980 steel produced by AK Steel, while the second (DP980-T) is a modification of the first one by a tempering process. Both contain two individual phases: ferrite and martensite with body centered cubic (BCC) and tetragonal (BCT) crystal structure respectively. ASTM standard tensile tests were performed for both materials, revealing that DP980-B has higher work hardening and larger total elongation than DP980-T. Standard hole piercing and subsequent hole expansion and extrusion tests were also performed. The critical hole expansion ratio (HER) of hole pierced sheet at different nominal clearances, on the other hand, show an opposite trend: the HER of DP980-T almost doubles that of DP980-B. This indicates the tensile ductility and edge stretchability are determined by different mechanisms due to different deformation modes. The ductility of sheet metal during uniaxial tension is determined by deformation instability, i.e. necking, due to less constraint at the region of deformation and fracture will occur quickly after necking. The contribution of post-necking deformation to the total elongation is insignificant for the high strength grades such as DP980 steels. The ductility during hole-expansion, however, is mainly determined by material fracture behavior that is dependent on phase property disparity and material intrinsic fracture parameters. With the individual phase properties for both DP steels determined by in situ tensile tests under high energy X-ray diffraction, the results show that DP980-T steel has lower property disparities between the two phases than DP980-B steel, due to the tempering process. This explains why the DP980-T steel has higher HER than DP980-B steel: lower phase disparity will lead to less local deformation during loading. The higher work hardening rate for DP980-B steel contributes to its higher uniform elongation compared with DP980-T steel based on the maximum load condition of deformation instability. An integrated finite element simulation framework for studying hole expansion is also presented here, based on the calculated individual phase properties from the combined high energy x-ray diffraction (HEXRD) and elastic plastic self-consistent modeling. The simulation results correlate well with the experimental results on the HER difference between the two materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Studies on the compositional dependent structural and electrical properties of CaTiO3-modified K0.5Na0.5NbO3 piezoelectric system

Lead-free piezoelectric ceramics of (1 − x)K0.5Na0.5NbO3-xCaTiO3 were fabricated, and their crystal structure, microstructure, and electrical properties were systematically studied. Rietveld refinement of the x-ray diffraction data and Raman spectroscopic analyses revealed a composition-dependent structural phase transition: three phase transitions, namely, from a pure orthorhombic phase for x ≤ 0.02 to a mixed phase of orthorhombic and tetragonal phases (0.03 ≤ x ≤ 0.08) and finally another mixed phase of tetragonal + cubic for x = 0.10 and 0.15 at room temperature (RT). The morphological study reveals a decrease in grain size along with a more uniform distribution of grains as the concentration of CaTiO3 (CT) increases; notably, a homogeneous distribution of grains is observed for x = 0.05. The temperature-dependent dielectric properties show two phase transitions, from orthorhombic to tetragonal (TO-T) and tetragonal to cubic (TC), for unmodified K0.5Na0.5NbO3 (KNN). However, both the phase transition temperatures (TO-T and TC) decrease, and the transition peaks broaden with an increase in CT substitution, and for x > 0.06, the TO-T shifted below RT. The broadening of the transition peak at TO-T may be due to the relaxation behavior. Among the prepared samples, the 5 mol. % CT-modified KNN shows the optimum electrical properties (d33 = 114 pC/N, ɛr = 412, and 2Pr = 15.25 μC/cm2) at RT. The enhanced electrical properties for x = 0.05 are due to the coexistence of orthorhombic and tetragonal phases, facilitating easy polarization rotation and flattening of the free energy profile. A phase diagram has been constructed based on the information gathered from the temperature-dependent dielectric measurements, RT x-ray diffraction, and Raman spectroscopy data and is discussed in detail.

Physics↗
DOE OSTI2025

A deep learning and finite element approach for exploration of inverse structure–property designs of lightweight hybrid composites

Hybrid composites have important applications, such as high-performance and lightweight materials in aerospace and automotive industries. Hybrid composites utilize the synergy of diverse fillers to achieve desired material properties, but usually have more complicated microstructures. While topology optimization can optimize a particular property, designing hybrid composites for customized mechanical performances, e.g. full-range stress–strain curve, remains challenging. Here, a computational framework that integrated finite element analysis (FEA) and artificial intelligence (AI) methods of Conditional Generative Adversarial Networks (cGAN) deep learning and transfer learning was developed to establish inverse structure–property relationships and design tailor-made hybrid composites. Based on FEA-generated datasets of hybrid fiber-particle–matrix microstructures and their corresponding full-range stress–strain curves, a cGAN architecture was trained to generate tailored microstructures and establish structure–property relationships. Similarity in microstructural features and well-matched stress–strain curves based on the AI-generated composites were achieved. In conclusion, transfer learning was used to expand the pre-trained model for designing different materials systems.

Hybrid composites↗
DOE OSTI2025

Tensile Performance Sensitivity to Variations of Standard 17-4 PH Heat Treatments on LPBF-Produced Material

Standard heat treatments for metals of a particular composition are typically designed with the assumption of a conventional starting microstructure, such as that produced by casting or wrought processing. When applied to metals fabricated by Laser Powder Bed Fusion (LPBF) metal additive manufacturing (AM), these heat treatments can produce inconsistent performance due to the unique as-built microstructures. This study investigates how modifications to standard heat treatments for 17-4 PH steel influence the microstructure and mechanical properties of LPBF-fabricated material. Specimens were produced and subjected to varying solutionizing and homogenizing treatments followed by standard aging treatments. Microstructures were characterized using optical microscopy, Electron Backscatter Diffraction (EBSD), and X-ray diffraction (XRD), and mechanical properties were evaluated through uniaxial tensile testing. Based on these results, recommendations are provided for achieving improved wrought-like performance in LPBF 17-4 PH steel.

17-4 PH↗
DOE OSTI2025

Additive manufacturing of soft magnetic high entropy alloys: A review

Additive manufacturing (AM) offers unique advantages in fabricating soft magnetic high-entropy alloys (HEAs), enabling precise control over material properties and the development of advanced components for applications such as magnetic cores, electric motors, and transformers. These HEAs exhibit superior magnetic performance, mechanical strength, and thermal stability, making them highly suitable for modern electronics applications. Here, this review explores the advancements in AM-processed soft magnetic HEAs, including ongoing research on process optimization, tailored microstructures, and enhanced magnetic properties. It emphasizes the importance of understanding the correlations between AM process parameters, resulting microstructures, and the soft magnetic properties of HEAs. By summarizing the state of the field, we provide insights into current progress and highlight future research trends, focusing on the potential for industrial adoption and advancements in this emerging area.

36 MATERIALS SCIENCE↗
NASA NTRS2004

Third-Generation TiAl Alloy Tested: Exhibits Promising Properties for Rotating Components

The Revolutionary Turbine Accelerator/Turbine-Based Combined Cycle (RTA/TBCC) Program for the next-generation launch vehicle has targeted gamma titanium aluminide as a potential compressor and structural material. Because of the high compressor inlet and exit temperatures, the TBCC engine requires higher temperature materials than conventional Ti alloys, and because of its stringent thrust-to-weight requirements, the engine requires low-density material to be utilized wherever possible. Third-generation gamma alloys offer higher temperature capability along with low density and high stiffness. A high-temperature, high-strength *-TiAl alloy with a high Nb-content (Gamma MET PX1) was selected for evaluation. The microstructure and mechanical properties of Gamma Met PX (GMPX) in both the as-extruded and a lamellar heat-treated condition and the influence of the microstructure on the tensile, creep, and fatigue properties were investigated in-house.

Draper, Susan L.↗
NASA NTRS2002

Effects of Thermomechanical History on the Tensile Behavior of Nitinol Ribbon

Shape memory alloys (SMAs) have enormous potential for a wide variety of applications. A large body of work exists on the characterization of the microstructure and stress-strain behavior of these alloys, Nitinol (NiTi) in particular. However, many attributes of these materials are yet to be fully understood. Previous work at NASA Langley Research Center (LaRC) has included fabrication of hybrid composite specimens with embedded Nitinol actuators and modeling of their thermomechanical behavior. An intensive characterization effort has been undertaken to facilitate fundamental understanding of this alloy and to promote implementation of Nitinol in aerospace applications. Previous work revealed attributes of the Nitinol ribbon that were not easily rationalized with existing data in the literature. In particular, tensile behavior at ambient temperature showed significant dependence on the thermomechanical history prior to testing. The present work is focused on characterizing differences in the microstructure of Nitinol ribbons exposed to four different thermomechanical histories and correlation of the microstructure with tensile properties. Differential scanning calorimetry (DSC) and x-ray diffraction (XRD) analysis were employed to rationalize the microstructures present after exposure to various thermomechanical histories. Three of the Nitinol ribbon conditions were reversible upon heating (in the DSC) through the reverse transformation temperature (A(sub f) to transform the microstructure to austenite. However, the prior thermomechanical conditioning for the Nitinol ribbon that reflected the entire fabrication procedure (4% thermal cycle condition) was found to have an irreversible effect on the microstructure, as it remained unchanged after repeated complete thermal cycles. Tensile tests were conducted to determine the effect of prior thermomechancal conditioning on both the tensile behavior of the Nitinol ribbons and the stress state of the microstructure. The stress-strain behavior of the Nitinol actuators appears to be governed by the interplay between two major variables: namely, microstructural constituents such as the R-phase and the martensite; and the stress state of these constituents (whether twinned with low residual stresses, or detwinned with high residual stresses). The most significant difference in the stress-strain behavior of the four conditions, the critical stress required to achieve an initial stress plateau, was found to depend on both the amount and stress state (twinned or detwinned) of R-phase present in the initial microstructure. Thus, the effect of prior thermomechanical processing is critical to the resulting tensile behavior of the Nitinol actuator. For numerical modeling inputs one must take into account the entire fabrication process on the Nitinol actuator.

Lach, Cynthia L.↗
NASA NTRS1972

Factors affecting the strength of multipass low-alloy steel weld metal

The mechanical properties of multipass high-strength steel weld metals depend upon several factors, among the most important being: (1) The interaction between the alloy composition and weld metal cooling rate which determines the as-deposited microstructure; and (2) the thermal effects of subsequent passes on each underlying pass which alter the original microstructure. The bulk properties of a multipass weld are therefore governed by both the initial microstructure of each weld pass and its subsequent thermal history. Data obtained for a high strength low alloy steel weld metal confirmed that a simple correlation exists between mechanical properties and welding conditions if the latter are in turn correlated as weld cooling rate.

Krantz, B. M.↗
DOE OSTI2021

High Temperature Thermal Barrier Coating Evaluation of Yttrium Aluminum Garnet for Gas Turbine Applications

The Solution Precursor Spray Process (SPPS) process has been shown to overcome the durability and property challenges of applying yttrium aluminum garnet (YAG) coating for high temperature thermal barrier coating (TBC) applications (1200°C+) but only limited testing has been performed in representative application environments. In this study, YAG coatings were developed to optimize microstructure and tailor properties for combustion components in an industrial gas turbine. Thermal conductivity, erosion resistance and furnace cycling durability were used to validate YAG properties against the standard yttria-stabilized zirconia coating (YSZ). Graded and multi-layered microstructures were applied to enhance performance while maintaining durability. Further YAG process development was required to replicate coating properties and optimize deposition on more complex fuel injector nozzle and combustion liner components. Rig testing of both components was performed and compared against the baseline YSZ coating validating the high temperature capability and lower thermal conductivity of the SPPS YAG coating. The components in both tests were cycled for a minimum of ten cycles with the fuel injector test targeting a higher operating temperature while the combustor liner operated at standard conditions. A development engine test is planned to further validate performance in a gas turbine engine of this promising material.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Evolution of carbide precipitates in Haynes® 282 superalloy processed by wire arc additive manufacturing

Precipitation hardening regulated with heat treatments is a critical technique for tuning the mechanical properties of Ni-based superalloys fabricated with additive manufacturing, where mechanical deformation is no longer viable for microstructural refinement. As one of the key precipitates, carbides prevail in the additively manufactured alloys, whose precipitation kinetics remain largely vague. This work studies the influence of heat treatments on the evolution of MC- and M 23 C 6 -type carbides within a Haynes® 282 superalloy prepared by wire arc additive manufacturing (WAAM). SEM-EDS analysis was performed to identify the evolution pathways of the carbides, and TEM and XRD characterizations were carried out to track the crystallographic features. The MC-type carbides are originally present in the as-printed alloy, which distribute uniformly across the whole material and remain largely unchanged in size during the heat treatments. By contrast, the incipiently non-existent M 23 C 6 -type carbides precipitate during an aging treatment at 1010 °C, which majorly extend along the grain boundaries as kinetically feasible sites. Further experimental and computational analysis confirms the enhancing effect of the M 23 C 6 -type carbides on the Vickers hardness. For the first time, this work revealed the evolution pathways of carbides within a Haynes® 282 superalloy prepared by WAAM, providing critical information for tunning the microstructure and mechanical properties. Finally, the carbide evolution kinetics established in this work can be potentially extended to other alloys prepared with WAAM, providing critical information to prevent mechanical failures associated with carbide coarsening.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Toward Optimizing Electrospun Nanofiber Fuel Cell Catalyst Layers: Polymer–Particle Interactions and Spinnability

We investigate the effect of the poly(acrylic acid) (PAA) carrier polymer concentration on the microstructure and rheological properties of catalyst inks for electrospun polymer–electrolyte membrane fuel-cell catalyst layers. Characterization of an ink microstructure using oscillatory shear rheology showed that the catalyst particles (platinum on carbon) are significantly agglomerated in the absence of PAA or an ionomer. Both the ionomer and PAA promoted the stability of the particles against agglomeration via electrosteric stabilization by adsorbing onto the particle surface. Increasing the PAA concentration increased the stability of the particles (or reduced the agglomerated structure) due to increasing PAA coverage onto the free surface area of the particles. However, beyond a certain increase in concentration, PAA was found to predominantly remain as an excess free polymer in the ink due to an insufficient free/available surface area on the particles for further PAA coverage. Extensional rheology measurements demonstrated that PAA enhances the extensional viscosities of the inks. Consequently, increasing the PAA concentration in the ink promoted the evolution of uniform nanofibers. However, beyond a certain concentration, a significant increase in the shear viscosities of the inks led to defective fiber morphologies because of the onset of flow instabilities. Electrochemical performance comparisons between catalyst layers with different PAA concentrations showed maximum performance at the PAA concentration that led to the least agglomerated structure of the catalyst, most uniform fiber morphologies, and low concentrations of free (non-adsorbing) PAA in the electrode. These results provide a rationale for optimization of electrospun catalyst nanofibers for both spinnability and electrochemical performance.

25 ENERGY STORAGE↗
NASA NTRS1998

Thermomechanical Fatigue Durability of T650-35/PMR-15 Sheet Molding Compound

Although polyimide based composites have been used for many years in a wide variety of elevated temperature applications, very little work has been done to examine the durability and damage behavior under more prototypical thermomechanical fatigue (TMF) loadings. Synergistic effects resulting from simultaneous temperature and load cycling can potentially lead to enhanced, if not unique, damage modes and contribute to a number of nonlinear deformation responses. The goal of this research was to examine the effects of a TMF loading spectrum, representative of a gas turbine engine compressor application, on a polyimide sheet molding compound (SMC). High performance SMCs present alternatives to prepreg forms with great potential for low cost component production through less labor intensive, more easily automated manufacturing. To examine the issues involved with TMF, a detailed experimental investigation was conducted to characterize the durability of a T650-35/PMR-15 SMC subjected to TMF mission cycle loadings. Fatigue damage progression was tracked through macroscopic deformation and elastic stiffness. Additional properties, such as the glass transition temperature (T(sub g) and dynamic mechanical properties were examined. The fiber distribution orientation was also characterized through a detailed quantitative image analysis. Damage tolerance was quantified on the basis of residual static tensile properties after a prescribed number of TMF missions. Detailed microstructural examinations were conducted using optical and scanning electron microscopy to characterize the local damage. The imposed baseline TMF missions had only a modest impact on inducing fatigue damage with no statistically significant degradation occurring in the measured macroscopic properties. Microstructural damage was, however, observed subsequent to 100 h of TMF cycling which consisted primarily of fiber debonding and transverse cracking local to predominantly transverse fiber bundles. The TMF loadings did introduce creep related effects (strain accumulation) which led to rupture in some of the more aggressive stress scenarios examined. In some cases this creep behavior occurred at temperatures in excess of 150 C below commonly cited values for T(sub g). Thermomechanical exploratory creep tests revealed that the SMC was subject to time dependent deformation at stress/temperature thresholds of 150 MPa/230 C and 170 MPa/180 C.

Castelli, Michael G.↗
NASA NTRSDate not supplied

Fast Assessment of Metal Performance through Dislocation Physics and Machine Learning

The microstructure of metals is key to their mechanical properties. The types, density, composition and morphology of crystal defects all have pronounced impact on the properties. Changes to the microstructure occurring during processing and use can be very striking. The emerging technology additive manufacturing (AM) has the potential to improve performance by allowing optimized designs, but the process and environments can lead to unusual microscale features whose properties must be understood and characterized to enable higher technological readiness levels and application. Experimentally, an extensive evaluation of mechanical properties of 3D printed metals is a challenge, and anomalous effects related to the AM process add complexity. We present a new machine learning (ML) model predicting mechanical response based on dislocation mediated plasticity simulations. A large set of 3D discrete dislocation dynamics simulations with wide ranges of loading conditions is transformed to preprocessed data ready for training with the ML model. The trained model can predict the mechanical response of Mo30W for a given microstructure evolution, providing key information essential for optimization of AM processing.

Jaehyun Cho↗
NASA NTRSDate not supplied

Fast Assessment of Metal Performance through Dislocation Physics and Machine Learning

The microstructure of metals is key to their mechanical properties. The types, density, composition and morphology of crystal defects all have pronounced impact on the properties. Changes to the microstructure occurring during processing and use can be very striking. The emerging technology additive manufacturing (AM) has the potential to improve performance by allowing optimized designs, but the process and environments can lead to unusual microscale features whose properties must be understood and characterized to enable higher technological readiness levels and application. Experimentally, an extensive evaluation of mechanical properties of 3D printed metals is a challenge, and anomalous effects related to the AM process add complexity. We present a new machine learning (ML) model predicting mechanical response based on dislocation mediated plasticity simulations. A large set of 3D discrete dislocation dynamics simulations with wide ranges of loading conditions is transformed to preprocessed data ready for training with the ML model. The trained model can predict the mechanical response of Mo30W for a given microstructure evolution, providing key information essential for optimization of AM processing.

Jaehyun Cho↗
DOE OSTI2021

Hydrothermal corrosion of laser printed SiC fibers under extreme environment

We report SiC/SiC fiber composites are proposed cladding materials to improve the accident tolerance of commercial light water nuclear reactor fuel. To evaluate their viability, understanding the kinetics of corrosion under irradiation and high-temperature, high-pressure aqueous environment is critical. In the present work, the microstructure and mechanical properties of novel SiC fibers manufactured by Laser Chemical Vapor Deposition (LCVD) are introduced. The LCVD technology has control over microstructure and stoichiometry while allowing for high purity manufacturing, all key qualities needed in search of an optimum SiC fiber for nuclear energy applications. The isolated hydrothermal corrosion of commercially available carbon-rich Hi-Nicalon Type-S fibers is compared to the LCVD stoichiometric and LCVD silicon-rich fibers. Autoclave testing was carried out at 310°C and 14 MPa in the absence of irradiation. In a separate study, the effect of gamma irradiation on the fibers in the room-temperature environment was analyzed. It was observed from the experiments that the dissolution of the fibers was highly dependent on the stoichiometric ratio, fiber surface morphology and thermal pre-treatment of fibers. Contrary to previous findings, fiber dissolution was also visible under low-temperature gamma irradiation in aqueous environment with LCVD fibers showing lower dissolution.

36 MATERIALS SCIENCE↗
NASA NTRS2023

Investigating the Effects of Space Weathering in Ryugu Samples Using Coordinated Microanalyses

Airless planetary surfaces are characterized by a distinct lack of an atmosphere or magnetic field, leading to direct exposure to the effects of hypervelocity micrometeoroid impacts and solar wind ion irradiation [1]. These processes, cumulatively known as space weathering, gradually alter the microstructural and chemical properties of the grains on airless surfaces. Signatures of space weathering include vesiculated textures, amorphous grain rims (upper ~100 nm), solar flare tracks, and Fe-bearing nanoparticles (npFe) [2,3]. The accumulation of these microstructural space weathering characteristics, particularly the presence of npFe, alters the spectral properties of airless regoliths resulting in changes in spectral slope and reflectance of the surfaces, and the attenuation of characteristic absorption bands in the visible to near-infrared (Vis-NIR) wavelengths. These spectral changes complicate our ability to accurately interpret the mineralogy of airless bodies via remote sensing spectroscopy [1,4]. Studies of space weathering have primarily focused on anhydrous silicate minerals, reflecting the main components of the available returned samples from the Moon and S-type asteroid Itokawa [3,5,6]. However, our understanding of space weathering of primitive, organic-rich carbonaceous materials is still a work in progress. The Japan Aerospace Exploration Agency (JAXA)’s Hayabusa2 mission offered the first opportunity to directly investigate carbonaceous asteroids by returning samples from C-type asteroid (162173) Ryugu. Initial studies of Ryugu samples show mineralogical similarities to CI chondrites along with surface modifications consistent with space weathering. These surface modifications are primarily in the form of μm-thick silicate melts, amorphized phyllosilicates, glassy spherules, and burst vesicles [3,7]. Here, we report results from coordinated microanalytical techniques to further our understanding of the mineralogy and space weathering of carbonaceous materials.

L E Melendez↗
DOE OSTI2022

The influence of nitrogen and nitrides on the structure and properties of proton irradiated ferritic/martensitic steel

The 12Cr1MoWV (wt%) ferritic/martensitic steel HT9 is a candidate material for fuel cladding in advanced nuclear reactors, such as the Versatile Test Reactor currently under development. As such, understanding the relationship between microstructure and mechanical properties in the context of irradiation environments for these steels is critical. N content, and more specifically interstitial N, has been hypothesized to be detrimental to irradiated properties at lower temperatures (less than 0.3T m ) to a total of 6 dpa; however, in this work at a dose of 1 dpa the irradiated microstructure was improved with added N, leading to less irradiation hardening. Three variants of HT9 were irradiated with 1.5 MeV protons to a dose of 1 dpa at 300°C. The HT9 variants included Low (10 ppm), Mid (190 ppm), and High (440 ppm) N alloys that were otherwise nearly identical. Changing the N content had a variety of effects on the irradiated defect structures. As N content increased, the average dislocation loop diameter decreased, while the number density of loops increased. Additionally, extensive Ni clustering was observed on dislocations and interfaces. The Mid and High N specimens exhibited significantly less hardening (ΔHV≃100) relative to the Low N specimen (ΔHV≃160). The decrease in hardening is attributed to vanadium carbonitride acting as a sink for Ni clusters that would otherwise form on dislocations. Under the irradiation conditions used, these results suggest increasing the N content in HT9 may have a desirable effect on the irradiated structure and properties at the dose studied, as well as the swelling resistance at higher doses. In other words, N content appears to be a powerful tool for tailoring the self-interstitial atom cluster mobility in F/M steels for different temperature and dose applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Bayesian Conavigation: Dynamic Designing of the Material Digital Twins via Active Learning

Scientific advancement is universally based on the dynamic interplay between theoretical insights, modeling, and experimental discoveries. However, this feedback loop is often slow, including delayed community interactions and the gradual integration of experimental data into theoretical frameworks. This challenge is particularly exacerbated in domains dealing with high-dimensional object spaces, such as molecules and complex microstructures. Hence, the integration of theory within automated and autonomous experimental setups, or theory in the loop-automated experiment, is emerging as a crucial objective for accelerating scientific research. The critical aspect is to use not only theory but also on-the-fly theory updates during the experiment. Furthermore, we introduce a method for integrating theory into the loop through Bayesian conavigation of theoretical model space and experimentation. Our approach leverages the concurrent development of surrogate models for both simulation and experimental domains at the rates determined by latencies and costs of experiments and computation, alongside the adjustment of control parameters within theoretical models to minimize epistemic uncertainty over the experimental object spaces. This methodology facilitates the creation of digital twins of material structures, encompassing both the surrogate model of behavior that includes the correlative part and the theoretical model itself. While being demonstrated here within the context of functional responses in ferroelectric materials, our approach holds promise for broader applications, such as the exploration of optical properties in nanoclusters, microstructure-dependent properties in complex materials, and properties of molecular systems.

Microscopy↗