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At least 217 records · Page 12

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DOE OSTI2021

Microstructural changes and mass transport in cement-based materials: A modeling approach

Highlights: • Concept to relate microstructural changes, mass transport, and chemical reactions in cement-based materials is presented. • Multi-physics modeling approach utilizing an extended version of the PNP equation and the geochemical code IPHREEQC. • Case studies indicate significant changes in mass transport properties due to alterations in the microstructure. • Microstructural changes depend on exposure and interactions between chemical reactions, pore structure, and mass transport. A generic modeling framework is presented to relate microstructural changes, i.e. changes in the pore volume distribution and phase assemblage, and mass transport in cement-based materials. The modeling framework accounts for mass transport and chemical equilibrium between ions in the pore solution and solid hydrates by means of an extended version of the Poisson-Nernst-Planck equation, in which the chemical equilibrium is solved by the external geochemical code IPHREEQC. Results of numerical studies concerning carbonation and leaching of a cement-based material indicate significant changes in mass transport properties due to chemical reactions leading to alterations in the microstructure. The resulting highly non-linear (both spatial and temporal) microstructural changes are thereby depending on the exposure and indicate that interactions between chemical reactions, pore structure changes, and mass transport have to be accounted for as a whole.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Leveraging a Neural Network-Enhanced Reproducing Kernel Particle Method for Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation has been developed to analyze this system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. Here, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RKPM is additionally used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

degradation↗

DOE OSTI2022

Intergranular ductile failure of materials with plastically heterogeneous grains

In several precipitation hardened alloys that are susceptible to intergranular ductile failure, precipitation does not always occur uniformly throughout the microstructure, and regions close to grain boundaries may remain precipitate-free. These precipitate-free zones (PFZs) in the material microstructures result in plastically heterogeneous grains, since PFZs are expected to have lower yield strength but higher strain-hardenability compared to the precipitate containing grain interior. Experimentally, the presence of PFZs in precipitation-hardened alloys has been associated with both increase and decrease in materials’ ductility, with or without significant change in the strength. Thus, to understand and rationalize the experimental observations, we have carried out extensive microstructure-based finite element calculations of intergranular ductile failure in materials under tensile loading conditions. In the calculations, both the grain boundaries and PFZs are discretely modeled, and a wide range of the values of yield strength, strain-hardenability and width of PFZs in the material microstructures are analyzed. Our results show that the effects of PFZs on the overall mechanical response of the material strongly depend on the values of yield strength and strain-hardenability of PFZs. Here, there exists an optimum combination of the values of these two parameters that can result in the overall ductility and tensile strength of the material microstructures with PFZs being greater than the microstructures without PFZs.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Automated Grain Boundary (GB) Segmentation and Microstructural Analysis in 347H Stainless Steel Using Deep Learning and Multimodal Microscopy

Austenitic 347H stainless steel offers superior mechanical properties and corrosion resistance required for extreme operating conditions such as high temperature. The change in microstructure due to composition and process variations is expected to impact material properties. Identifying microstructural features such as grain boundaries thus becomes an important task in the process-microstructure-properties loop. Applying convolutional neural network (CNN)-based deep learning models is a powerful technique to detect features from material micrographs in an automated manner. In contrast to microstructural classification, supervised CNN models for segmentation tasks require pixel-wise annotation labels. However, manual labeling of the images for the segmentation task poses a major bottleneck for generating training data and labels in a reliable and reproducible way within a reasonable timeframe. Microstructural characterization especially needs to be expedited for faster material discovery by changing alloy compositions. Here, in this study, we attempt to overcome such limitations by utilizing multimodal microscopy to generate labels directly instead of manual labeling. We combine scanning electron microscopy images of 347H stainless steel as training data and electron backscatter diffraction micrographs as pixel-wise labels for grain boundary detection as a semantic segmentation task. The viability of our method is evaluated by considering a set of deep CNN architectures. We demonstrate that despite producing instrumentation drift during data collection between two modes of microscopy, this method performs comparably to similar segmentation tasks that used manual labeling. Additionally, we find that naïve pixel-wise segmentation results in small gaps and missing boundaries in the predicted grain boundary map. By incorporating topological information during model training, the connectivity of the grain boundary network and segmentation performance is improved. Finally, our approach is validated by accurate computation on downstream tasks of predicting the underlying grain morphology distributions which are the ultimate quantities of interest for microstructural characterization.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Interface microstructure effects on dynamic failure behavior of layered Cu/Ta microstructures

Abstract Structural metallic materials with interfaces of immiscible materials provide opportunities to design and tailor the microstructures for desired mechanical behavior. Metallic microstructures with plasticity contributors of the FCC and BCC phases show significant promise for damage-tolerant applications due to their enhanced strengths and thermal stability. A fundamental understanding of the dynamic failure behavior is needed to design and tailor these microstructures with desired mechanical responses under extreme environments. This study uses molecular dynamics (MD) simulations to characterize plasticity contributors for various interface microstructures and the damage evolution behavior of FCC/BCC laminate microstructures. This study uses six model Cu/Ta interface systems with different orientation relationships that are as- created, and pre-deformed to understand the modifications in the plasticity contributions and the void nucleation/evolution behavior. The results suggest that pre-existing misfit dislocations and loading orientations (perpendicular to and parallel to the interface) affect the activation of primary and secondary slip systems. The dynamic strengths are observed to correlate with the energy of the interfaces, with the strengths being highest for low-energy interfaces and lowest for high-energy interfaces. However, the presence of pre-deformation of these interface microstructures affects not only the dynamic strength of the microstructures but also the correlation with interface energy.

42 ENGINEERING↗

DOE OSTI2022

Additive friction stir deposition of SS316: Effect of process parameters on microstructure evolution

Solid state nature of additive friction stir deposition (AFSD) additive manufacturing process is very advantageous in terms of defect formation and microstructural refinement in the material. Current study presents the process optimization, microstructural evolution and kinetics of recrystallization for AFSD deposited low stacking fault energy material - SS316. As deposited microstructure shows equiaxed ultra fine grains with an average grain size of ~5.0 ± 0.5 μm. Shear deformation at high temperature during processing leads to the operation of restoration mechanisms. Observation of necklace type microstructure in the as deposited SS316 is attributed to discontinuous dynamic recrystallization during processing. Recrystallization kinetics of the AFSD SS316 is characterized using Johnson-Mehl-Avarami-Kolmogorov (JMAK) model. Deformation – thermal cycling during AFSD process resulted in inconsistent recrystallization kinetics. Variation in strain, strain rate and temperature during processing with processing parameters result in varying microstructure and tool wear. Further, high strength-ductility combination and sustained work hardening in as deposited SS316 appear to arise from transformation and twinning during deformation, leading to the formation of hierarchical twins and martensitic phase after deformation.

36 MATERIALS SCIENCE↗

DOE OSTI2020

In-Operando Study of Shape Retention and Microstructure Development in a Hydrolyzing Sol–Gel Ink during 3D-Printing

3D printing of amorphous and crystalline ceramics is of paramount importance for the fabrication of a wide range of devices with applications across different technology fields. Printed ceramics are remarkably enabled by the sol-gel synthesis method in conjunction with continuous filament direct ink writing. During printing, multiple processes contribute to the evolution of inks including shape retention, chemical conversion, solidification, and microstructure formation. Traditionally, depending on the ink composition and printing environment, several mechanisms have been associated with the shape retention and solidification of 3D printed structures: gelation, rapid solvent evaporation, energy-driven phase transformation, and chemical-driven phase transformation. Understanding the fundamental differences between these mechanisms becomes key since they strongly influence the spatiotemporal evolution of the materials, as the out-of-equilibrium processes inherent to the extrusion, relaxation, and solidification of printed materials have significant effects on the materials properties. Herein, we investigate the shape retention mechanism and the hydrolysis-induced material conversion and microstructure formation during the 3D printing of a water reactive sol-gel ink that transforms into titanium dioxide-based ceramic. This study aims at identifying characteristic mechanisms associated with the material transformation, establishing connections between the microstructure development and the timescales associated with solidification under operando 3D-printing conditions. The investigation of this material's out-of-equilibrium pathways under processing conditions is enabled by time-resolved coherent X-ray scattering, providing simultaneous access to temporospatially resolved microstructural and dynamics information. Furthermore, we explore X-ray speckle tracking as a tool to resolve deformations of the microstructure in a printed filament associated with the deposition of consecutive filaments. Through this work, we aim at providing a fundamental understanding of the relationships behind these transformative processes in 3D printing and their timescales as the basis for achieving unprecedented control over printed materials microstructure.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Preliminary results addressing material qualification using combined ion irradiation and modeling data

Additively-manufactured (AM) materials have attracted increasing attention in recent years as a new method to make novel and customized components. While AM and conventionally produced materials are compositionally similar, they do possess different microstructures, necessitating assessment of materials produced via AM for their behavior in reactor environments. Some microstructures unique to AM materials, such as compositional micro-inhomogeneity and dislocation cell structures, are of particular importance since they may lead to different radiation performance. The performance of AM materials for advanced nuclear reactor applications is of interest to the Advanced Materials and Manufacturing Technologies (AMMT) program under the Department of Energy Office of Nuclear Energy. The AMMT program aims to demonstrate its new accelerated development and qualification methods via laser powder bed fusion (LPBF) 316 stainless steel (SS). Focusing on material bearing both 316L and 316H specifications, we integrate ion irradiation and modeling. This year, we focus on answering foundational questions related to process variability, alloy chemistry variation, and microchemical segregation. Experimental results provide information and motivate questions to the modeling effort, which aims to develop the ability to model radiation-driven microstructural evolution in additively-manufactured 316 stainless steel under a variety of advanced reactor conditions, including different temperatures, neutron spectra, and fluxes, in a sort of "virtual experiment". We perform in-situ and ex-situ ion irradiations and microstructural characterizations to support the development of AM materials for reactor applications, develop a phase field model of radiation-induced segregation in additively manufactured material with high angle grain boundaries and dislocation cells, and investigate the effect of carbon and chromium content on point defect behavior.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Simulation toolkit for digital material characterization of large image-based microstructures

In this paper, an efficient image-based simulation toolkit for material characterization is presented, which is scalable to work from personal computers to workstations. The effective thermal conductivity, elasticity, and permeability are evaluated employing a computational homogenization framework based on the Finite Element Method (FEM). Two complementary open-source packages are presented: one developed in Python, which can convert digital images into voxel meshes (pyTomoviewer); the other developed in Julia, that can run numerical simulations to compute effective material properties (chpack). Also, a CUDA C version of chpack is provided (chfem_gpu). They were designed to deal with large multi-phase models, so strategies were devised to minimize their memory footprint, while avoiding a high toll on execution time. The voxel-based approach significantly simplifies the FEM meshes and allows efficient matrix-free implementations. In that sense, to handle large linear systems of equations, the element-by-element (EBE) technique is adopted, in conjunction with a low-memory implementation of the Preconditioned Conjugate Gradient (PCG) method. Finally, the code was thoroughly tested on an artificial geometry made of a square array of cylinders, for which analytical solutions exist, as well as on a real micro-tomographic reconstruction of FiberForm TM , a carbon preform commonly used in thermal protection systems.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Heterogeneous energetic material damage simulator (HEDS): A deep learning approach to simulate damage–sensitivity linkages

Damage in the microstructures of energetic materials (EMs), such as propellants and plastic bonded explosives (PBXs), can significantly alter their response to external loads. Both sensitization and desensitization can occur, causing concerns with safety and performance in the field; predictive models that connect damage and the sensitivity of EMs can enable design and provide confidence in their robustness and reliability. However, modeling of damage evolution is challenging for real microstructures of EMs; samples of damaged EMs are difficult to obtain, thereby hindering experiments and direct numerical simulations to determine the sensitivity of EMs at various stages of damage. Here, we develop an approach to generate synthetic, i.e., in silico produced, damaged microstructures for use in simulations to connect damage levels to sensitivity. The development of the present workflow to generate and impose varying levels of damage in microstructures, known as HEDS (Heterogeneous Energetic Material Damage Simulator), begins with a small set of images of damaged PBXs and combines a collection of deep neural network techniques to generate microstructures with varying levels of damage. By making the synthetic microstructures conform closely to those observed in available real, imaged microstructures, we develop an ensemble of damaged microstructures that can be used for in silico shock experiments. HEDS develops these microstructure ensembles as level set fields, which are directly employed in a sharp interface Eulerian hydrocode where shock simulations are performed to quantify the energy release rate from hotspot fields generated in the microstructure. These capabilities can be useful for the analysis and assessment of changes in the sensitivity of EMs and to design formulations that are less susceptible to damage-induced changes in sensitivity and performance.

Fang, Irene (ORCID:0009000844557122)↗

DOE OSTI2022

Computing diffraction patterns of microstructures from phase-field simulations

The diffraction pattern of a material contains information not only on the crystal structures of its constituting phases, but also on its mesoscale spatial distributions of phases, grains, and ferroelastic, ferroelectric, and ferromagnetic domains. While diffraction patterns from experiments such as X-ray diffraction are presented in the reciprocal or Fourier space, mesoscale microstructure models such as the phase-field method naturally produce real-space images of spatial distribution of chemical composition, structural, and ferroic domains. Although one could rather readily compute the Fourier amplitudes of chemical and structural domain distributions generated by mesoscale simulations, they only contain information about the length scale and alignment of the real-space chemical and structure domains. Therefore, a direct comparison between diffraction experiments and mesoscale microstructure simulations is not possible. Here, we develop a theoretical approach to directly compute the crystal diffraction patterns of microstructures predicted by phase-field simulations. In particular, we consider five representative examples of microstructure patterns involving purely compositional domains, a single pair of tetragonal twin structures, multiple twin variants in a hexagonal system, ferroelectric polar vortices, and polycrystalline grains. The results are compared with previous experimental observations as well as X-ray diffraction experiments performed in the present study. Furthermore, the theoretical framework allows one to directly connect material microstructures and diffraction patterns predicted from phase-field simulations and the corresponding diffraction patterns from experiments, and thus providing guidance to experimental diffraction characterization and interpretation of microstructures.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Microstructure-Dependent Rate Theory Model of Radiation-Induced Segregation in Binary Alloys

Conventional rate theory often uses the mean field concept to describe the effect of inhomogeneous microstructures on the evolution of radiation induced defect and solute/fission product segregation. However, the spatial and temporal evolution of defects and solutes determines the formation and spatial distribution of radiation-induced second phase such as precipitates and gas bubbles/voids, especially in materials with complicated microstructures and subject to high dose radiation. In this work, a microstructure-dependent model of radiation-induced segregation (RIS) has been developed to investigate the effect of inhomogeneous thermodynamic and kinetics properties of defects on diffusion and accumulations of solute A in AB binary alloys. Four independent concentrations: atom A, interstitial A, interstitial B, and vacancy on [A, B] sublattice are used as field variables to describe temporal and spatial distribution and evolution of defects and solute A. The independent concentrations of interstitial A and interstitial B allow to describe their different generation rates, thermodynamic and kinetic properties, and release the assumptions of interstitial generation and sink strength used in the conventional rate theory. Microstructure and concentration dependent chemical potentials of defects are used to calculate the driving forces of defect diffusions. With the model, the effects of defect chemical potentials and mobilities on the RIS in polycrystalline AB model alloys have been simulated. The results demonstrated the model capability in predicting defect evolution in materials with inhomogeneous thermodynamic and kinetic properties of defects. The model can be extended to materials with complicated microstructures such as a wide range of grain size distribution, coating structure and multiphases as well as radiation-induced precipitation subject to severe radiation damage.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Mesoscale modeling and semi-analytical approach for the microstructure-aware effective thermal conductivity of porous polygranular materials

Here we established a comprehensive modeling approach for investigating the microstructure-aware effective thermal conductivity ($κ_{eff}$) for porous microstructures containing solid particles and gaseous pores. Our approach combines the mesoscale computational modeling framework and the semi-analytical method, allowing for efficient prediction of $κ_{eff}$ for realistic porous microstructures, while considering complicated microstructural thermal conduction pathways effectively in the prediction. We used the diffuse-interface mesoscale computational model to generate extensive simulated $κ_{eff}$ data for realistic digital representations of microstructures with wide ranges of porosity ($f_p$), thermal conductivity of the gas phase ($κ_g$), and thermal conductivity of the solid phase ($κ_s$). From the simulated data, we identified two property variation regimes for $κ_{eff}$: (1) a slow $κ_{eff}$ increase for $κ_s ~ κ_g$; and (2) a faster $κ_{eff}$ increase for $κ_s \gg κ_g$. To capture the key features of the relationship between the microstructure and $κ_{eff}$, we derived a semi-analytical model by introducing structure and intensification factors. The two new factors incorporate the calibrated effective contribution of the solid volume with $κ_s$ and additional interfacial effects into the prediction of $κ_{eff}$, respectively, allowing for consideration of parallel, serial, and interfacial conduction mechanisms effectively. Using the selected simulation data, we quantified key model parameters within the semi-analytical model and verified that the parameterized model exhibits excellent agreement with simulated $κ_{eff}$ for the entire range of the parameter space.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Systems and methods for additively manufacturing caloric microstructures

A method for additively manufacturing a microstructure from a caloric material includes providing a geometry of the microstructure to a processor of an additive manufacturing device, the geometry defining a plurality of microfeatures of the microstructure. The method also includes generating, via the processor, a three-dimensional (3D) model representative of the geometry of the microstructure, wherein one or more of the plurality of microfeatures are represented in the 3D model by a non-arcuate profile. Further, the method includes printing, via the additive manufacturing device, the microstructure from the caloric material according to the 3D model. As such, the non-arcuate profile reduces a file size of the 3D model as compared to an arcuate profile.

Schroeder, Michael Goodman↗

DOE OSTI2021

Evolution of Microstructure and Surface Characteristics of FeCrAl alloys when Subjected to Flow Boiling Testing

FeCrAl alloys are candidate materials for manufacturing accident-tolerant fuel (ATF) cladding intended for light water reactors to increase fuel reliability and safety during design-basis and beyond-design-basis accident scenarios. The evolution of the materials' surface characteristics, microstructure, and mechanical properties when exposed to the Critical Heat Flux (CHF) in flow boiling testing is crucial for safety analysis while providing insights into their thermal-hydraulic performance in nuclear reactors. After CHF, the surface chemistry of two FeCrAl alloys, APMT and C26M, was studied to understand their evolution at the early stage of high-temperature excursions in short time periods. The results indicated a thin layer composed of oxides and hydroxides of Al, Cr, and Fe with varying proportions at different depths in the layer, as indicated by X-ray photoelectron spectroscopy (XPS) and depth profiling. The cross-sections prepared by focused ion beam (FIB) revealed the growth of an oxide layer, in the range of 90-180 nm thick, on the alloys' surfaces. The evolution of the materials' surface chemistry also led to a noticeable post CHF excursion increase in their wettability, with a slight increase in roughness. Further, the investigation of the materials' mechanical properties indicated a modest increase in hardness by 10-15% as well as an increase in their yield strength, as evidenced by the microindentation and ring compression tests conducted before and after CHF testing. Scanning electron Microscopy (SEM) and X-ray diffraction (XRD) were used to investigate microstructural features of the materials and their changes after CHF treatment.

36 MATERIALS SCIENCE↗

DOE OSTI2025

hashin_shtrikman_mp: a package for the optimal design and discovery of multi-phase composite materials

hashin_shtrikman_mp is a tool for composites designers who have desired composite properties in mind, but who do not yet have an underlying formulation. The library utilizes the tightest theoretical bounds on the effective properties of composite materials with unspecified microstructure – the Hashin-Shtrikman bounds – to identify candidate theoretical materials, find real materials that are close to the candidates, and determine the optimal volume fractions for each of the constituents in the resulting composite. Its features include (i) leveraging of materials in the Materials Project database, (ii) integration with the Materials Project API, (iii) use of genetic machine-learning, (iv) agnosticism to underlying microstructure, and (v) ultimate engineering application, make it a tool with much broader applications than its predecessors.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Dynamic structural and microstructural responses of a metal–organic framework type material to carbon dioxide under dual gas flow and supercritical conditions

The structural and microstructural responses of a model metal–organic framework material, Ni(3-methyl-4,4'-bipyridine)[Ni(CN) 4 ] (Ni-BpyMe or PICNIC-21), to CO 2 adsorption and desorption are reported for in situ small-angle X-ray scattering and X-ray diffraction measurements under different gas pressure conditions for two technologically important cases. These conditions are single or dual gas flow (CO 2 with N 2 , CH 4 or H 2 at sub-critical CO 2 partial pressures and ambient temperatures) and supercritical CO 2 (with static pressures and temperatures adjusted to explore the gas, liquid and supercritical fluid regimes on the CO 2 phase diagram). The experimental results are compared with density functional theory calculations that seek to predict where CO 2 and other gas molecules are accommodated within the sorbent structure as a function of gas pressure conditions, and hence the degree of swelling and contraction in the associated structure spacings and void spaces. Furthermore, these predictions illustrate the insights that can be gained concerning how such sorbents can be designed or modified to optimize the desired gas sorption properties relevant to enhanced gas recovery or to addressing carbon dioxide reduction through carbon mitigation, or even direct air capture of CO 2 .

36 MATERIALS SCIENCE↗

DOE OSTI2021

A correlation between grain boundary character and deformation twin nucleation mechanism in coarse-grained high-Mn austenitic steel

Abstract In polycrystalline materials, grain boundaries are known to be a critical microstructural component controlling material’s mechanical properties, and their characters such as misorientation and crystallographic boundary planes would also influence the dislocation dynamics. Nevertheless, many of generally used mechanistic models for deformation twin nucleation in fcc metal do not take considerable care of the role of grain boundary characters. Here, we experimentally reveal that deformation twin nucleation occurs at an annealing twin (Σ3{111}) boundary in a high-Mn austenitic steel when dislocation pile-up at Σ3{111} boundary produced a local stress exceeding the twining stress, while no obvious local stress concentration was required at relatively high-energy grain boundaries such as Σ21 or Σ31. A periodic contrast reversal associated with a sequential stacking faults emission from Σ3{111} boundary was observed by in-situ transmission electron microscopy (TEM) deformation experiments, proving the successive layer-by-layer stacking fault emission was the deformation twin nucleation mechanism, different from the previously reported observations in the high-Mn steels. Since this is also true for the observed high Σ-value boundaries in this study, our observation demonstrates the practical importance of taking grain boundary characters into account to understand the deformation twin nucleation mechanism besides well-known factors such as stacking fault energy and grain size.

36 MATERIALS SCIENCE↗