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At least 37 records · Page 2

Integral X-ray diffuse scattering for studying irradiation-induced dislocation loops in single crystals

Numerical diffuse scattering cross-section calculations are used to establish a rigorous basis for determining the concentration and size distribution of dis­location loops in irradiated single crystals from integral X-ray diffuse scattering (XRDS) measurements. Differential XRDS intensities for prismatic {111} type dislocation loops are numerically calculated as a function of loop radius R and wavevectors q relative to Bragg reflections in tungsten. The results show the well known 1/q 2 Huang scattering form at small q that transitions to a ∼1/q 4 dependence associated with the Stokes–Wilson approximation for q ≳ 1/R. More importantly, they show further that the 1/q 4 falloff is not the asymptotic large-q form of the diffuse scattering for small loops (R < 200 Å) as has often been assumed. Rather, for loop sizes as small as R ≃ 5 Å with strong curvature, the calculations show definitively that the scattering transitions to a robust 1/q 5 falloff at larger q that arises due to the local strains near the dislocation core defining the circumference of the dislocation loops. The presence of this 1/q 5 asymptotic form for both small and large loops is experimentally confirmed using an integral XRDS measurement around the 110 reflection on self-ion-irradiated tungsten combined with numerically calculated integral XRDS cross-sections. Accordingly, the historical two-region theoretical treatment of the cross-sections for integral XRDS is extended to a three-region model that has direct sensitivity to the (first-moment) dislocation line lengths of dislocation loops. In conclusion, these developments enable the use of both numerical and analytically modeled cross-sections to make accurate integral XRDS determinations of dislocation loop sizes and concentrations using modest-intensity laboratory X-ray sources.

42 ENGINEERING↗

Sweep-tracing algorithm: in silico slip crystallography and tension-compression asymmetry in BCC metals

Abstract Direct Molecular Dynamics (MD) simulations are being increasingly employed to model dislocation-mediated crystal plasticity with atomic resolution. Thanks to the dislocation extraction algorithm (DXA), dislocation lines can be now accurately detected and positioned in space and their Burgers vector unambiguously identified in silico, while the simulation is being performed. However, DXA extracts static snapshots of dislocation configurations that by themselves present no information on dislocation motion. Referred to as a sweep-tracing algorithm (STA), here we introduce a practical computational method to observe dislocation motion and to accurately quantify its important characteristics such as preferential slip planes (slip crystallography). STA reconnects pairs of successive snapshots extracted by DXA and computes elementary slip facets thus precisely tracing the motion of dislocation segments from one snapshot to the next. As a testbed for our new method, we apply STA to the analysis of dislocation motion in large-scale MD simulations of single crystal plasticity in BCC metals. We observe that, when the crystal is subjected to uniaxial deformation along its [001] axis, dislocation slip predominantly occurs on the {112} maximum resolved shear stress plane under tension, while in compression slip is non-crystallographic (pencil) resulting in asymmetric mechanical response. The marked contrast in the observed slip crystallography is attributed to the twinning/anti-twinning asymmetry of shears in the {112} planes relatively favoring dislocation motion in the twinning sense while hindering dislocations from moving in the anti-twinning directions.

36 MATERIALS SCIENCE↗

Analysis of dislocation configurations in SiC crystals through X-ray topography aided by ray tracing simulations

Silicon carbide as a wide bandgap semiconductor is of great research interest for its widespread deployment in a range of electronic and optoelectronic devices, particularly in power electronics. However, defects in silicon carbide crystals are still major concerns that is hampering the development of high-performance devices. X-ray topography, particularly using the synchrotron beam has been instrumental in characterizing and analyzing defect configurations in silicon carbide crystals to optimize crystal growth as well as understand the effect of defects on device performance. Here, in recent years, the use of ray-tracing simulation technique based on the orientation contrast mechanism to simulate contrast of defects observed on actual X-ray topographs has proven to be an effective approach to investigate the nature of crystallographic defects in various semiconductors. This review discusses the principle of ray-tracing simulation and its application and modifications to incorporate the effects of surface relaxation and photoelectric absorption to better simulate different dislocations observed in 4H–SiC as well as 6H–SiC crystals of various orientations. The adaptation to weak beam topography and plane wave topography is also discussed. The application of ray-tracing simulation in dislocation characterization of silicon carbide of different polytypes is systematically reviewed including different types of dislocations observed in both off-axis wafers and axial-sliced samples through synchrotron X-ray topography under various beam conditions, recording geometries and reflections. The result of ray-tracing simulation is further utilized in other studies including the investigation of effective penetration depth of all types of dislocations lying on the basal plane on grazing-incidence X-ray topography.

Engineering↗

A general kinetic framework for dislocation mobility derived from probabilistic cellular automaton simulations of the kink-pair mechanism

Dislocation mobility laws are essential components of dislocation-density-based crystal plasticity models. For dislocations governed by the kink-pair mechanism, however, existing formulations are typically limited to specific regimes due to the com plex interplay between stochastic kink-pair nucleation and lateral kink migration. In this work, we develop a general kinetic framework that expresses the average dislocation velocity as a function of mechanism-level variables: positive/negative kink pair nucleation rates, kink migration velocity, dislocation segment length, critical kink-pair width, and kink height. Probabilis tic cellular automaton simulations are used to capture the behavior of conceptual dislocation segments between the limiting conditions of migration outpacing nucleation on the one end and nucleation outpacing migration on the other. An elemen tary functional form that captures the system dynamics is suggested and fitted against the simulation results. This framework remains valid for arbitrary combinations of the six variables and is, therefore, compatible with any admissible constitutive re lations that describe their stress and temperature dependence. Comparisons with established approaches and experimental results confirm the robustness and physical consistency of the formulation, making it broadly applicable to material systems in which dislocation motion is governed by the kink-pair mechanism.

36 MATERIALS SCIENCE↗

Automatic Determination of the Weak-Beam Condition in Dark Field X-ray Microscopy

Mechanical properties in crystals are strongly correlated to the arrangement of 1D line defects, termed dislocations. Recently, Dark field X-ray Microscopy (DFXM) has emerged as a new tool to image and interpret dislocations within crystals using multidimensional scans. However, the methods required to reconstruct meaningful dislocation information from high-dimensional DFXM scans are still nascent and require significant manual oversight (i.e. supervision). In this work, we present a new relatively unsupervised method that extracts dislocation-specific information (features) from a 3D dataset (x, y, Φ) using Gram-Schmidt orthogonalization to represent the large dataset as an array of 3-component feature vectors for each position, corresponding to the weak-beam conditions and the strong-beam condition. Finally, this method offers key opportunities to significantly reduce dataset size while preserving only the crystallographic information that is important for data reconstruction.

36 MATERIALS SCIENCE↗

Learning to Predict Crystal Plasticity at the Nanoscale: Deep Residual Networks and Size Effects in Uniaxial Compression Discrete Dislocation Simulations

The density and configurational changes of crystal dislocations during plastic deformation influence the mechanical properties of materials. These influences have become clearest in nanoscale experiments, in terms of strength, hardness and work hardening size effects in small volumes. The mechanical characterization of a model crystal may be cast as an inverse problem of deducing the defect population characteristics (density, correlations) in small volumes from the mechanical behavior. In this work, we demonstrate how a deep residual network can be used to deduce the dislocation characteristics of a sample of interest using only its surface strain profiles at small deformations, and then statistically predict the mechanical response of size-affected samples at larger deformations. As a testbed of our approach, we utilize high-throughput discrete dislocation simulations for systems of widths that range from nano- to micro- meters. We show that the proposed deep learning model significantly outperforms a traditional machine learning model, as well as accurately produces statistical predictions of the size effects in samples of various widths. By visualizing the filters in convolutional layers and saliency maps, we find that the proposed model is able to learn the significant features of sample strain profiles.

36 MATERIALS SCIENCE↗

Correlating dislocation structures to basal and prismatic slip bands near grain boundaries in tensile-tested Mg–4Al using a multiscale electron microscopy approach

Dislocation structures where basal and prismatic slip bands meet grain boundaries in tensile-tested Mg with 4 wt% Al (Mg–4Al) were studied using a multiscale electron microscopy approach to explore the assumptions made for the dislocation pileup theory: a) slip bands consist of dislocation arrays piling up near grain boundaries, and b) stress concentration in the adjacent grain is solely caused by dislocation pileup. After post-testing electron backscatter diffraction (EBSD) scans, focused-ion-beam (FIB) lift-out specimens were prepared from regions of interest so that the specimen plane is parallel to the bulk sample surface to allow for direct correlation between mesoscale and microscale characterization. High dislocation density and the dislocation arrays in the slip bands corroborated with the first assumption. Evidence of plastic deformation in all grains, however, showed that the second assumption was false. Additionally, dislocation structures including crystal rotation boundaries and dislocations dissociating to the basal plane provide additional stress relief mechanisms near grain boundaries that are not accounted for in many crystal plasticity models, which requires auxiliary models to more accurately predict the stress and strain distribution in a microstructure.

36 MATERIALS SCIENCE↗

Active learning of a crystal plasticity flow rule from discrete dislocation dynamics simulations

Continuum-scale material deformation models, such as crystal plasticity (CP), can significantly enhance their predictive accuracy by incorporating input from lower-scale (i.e. mesoscale) models. The procedure to generate and extract the relevant information is however typically complex and ad hoc, involving decision and intervention by domain experts, leading to long development times. In this study, we develop a principled approach for calibration of continuum-scale models using lower scale information by representing a CP flow rule as a Gaussian process model. This representation allows for efficient parameter space exploration, guided by the uncertainty embedded in the model through a process known as Bayesian optimization (BO). We demonstrate a semi-autonomous BO loop which instantiates discrete dislocation dynamics simulations whose initial conditions are automatically chosen to optimize the uncertainty of a model CP flow rule. Our self-guided computational pipeline efficiently generated a dataset and corresponding model whose error, uncertainty, and physical feature sensitivities were validated with comparison to an independent dataset four times larger, demonstrating a valuable and efficient active learning implementation readily transferable to similar material systems.

36 MATERIALS SCIENCE↗

Simulation of dynamic crystal plasticity with a Lagrangian discontinuous Galerkin hydrodynamic method

Here we present a new Lagrangian modal discontinuous Galerkin (DG) hydrodynamic method that supports a dynamic dislocation based crystal plasticity model for simulating the mechanical behavior of crystallographic materials, both single crystal and polycrystalline, under dynamic conditions. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated by Taylor series polynomials of varying degree. These polynomials describe macro-scale hydrodynamic behavior while their evolution is determined by evaluating the dynamic crystal plasticity model at material points within the element. The dynamic crystal plasticity model is sensitive to the time increment size, with too large of time increments leading to instability in the model. To mitigate this, the temporal evolution of the dynamic crystal plasticity model is achieved with the combination of a sub-incrementing scheme with Heun’s third-order time integration scheme, which is also used to temporally evolve the governing equations. The implementation of the dynamic crystal plasticity model within the DG framework is tested using a 2D approximation of the Taylor impact test with a single crystal material, using quadratic elements that have faces that can bend. In addition to the standard continuous material modeling, we propose a new simulation method that would represent the heterogeneous behavior of polycrystalline microstructures within an element by varying the position and material properties of the material points within the element. This method is demonstrated using random orientation distributions on materials points that are arranged in both structured and random configurations.

42 ENGINEERING↗

Dislocation-induced large local polarization inhomogeneity of ferroelectric materials

Dislocations in ferroelectrics play important roles in ferroelectricity, piezoelectricity, and dielectricity. However, the intrinsic charge-lattice coupling mechanism in ferroelectric crystals containing dislocations is still not well understood. Here, we report a large local polarization inhomogeneity of ~100 μCcm –2 induced by a single a[001] dislocation in the PbZr 0.2 Ti 0.8 O 3 /SrTiO 3 film/substrate heterostructure, the tensile region (~120 μCcm –2 ) and the compressive strain region (~21 μCcm –2 ) around the dislocation forms a butterfly-like area. Furthermore, this study reveals the dramatic effects of dislocations on local polarization and provides a strategy to manipulate the polarization magnitude and orientation of local polarization by defect engineering.

36 MATERIALS SCIENCE↗

Exploring poly-crystallization in semiconductors through assumption-less growth simulations: CdTe/CdS case study

Crystal growth is a complex process with far-reaching implications for high-performance materials across various fields. Recent advancements in structural analysis methods such as polyhedral template matching, which allows semiconductor-specific analysis, coupled with simulation technology, have enabled the comprehensive study of crystallization dynamics in semiconductors. However, the exploration of polycrystalline semiconductors created with minimal external intervention of the crystallization processes is relatively uncharted in comparison with metals. In this study, we employ molecular dynamics to simulate the growth of polycrystalline CdTe/CdS with the assumptions of classical mechanics, a Stillinger–Weber potential, an amorphous substrate, and common vapor growth conditions to allow the polycrystalline structures to evolve naturally. Post-simulation, we identify and analyze impactful structures and events, comparing them to theory and experiment to gain insight into various modes of crystallization dynamics. Two research questions guided the study: (1) How realistic are assumption-less simulated polycrystalline semiconductor structures? (2) To what extent can the approach provide insight into crystallization? The simulations, performed with minimal external control, yield polycrystalline structures mirroring experimental findings. The analysis reveals key crystallization insights, such as the role of amorphous atoms in the transition from nucleation to grain growth and the transformative impact of single events, such as dislocations, on crystallization dynamics. The method paves the way for reproducing and analyzing realistic polycrystalline semiconductor structures with minimal simulation assumptions across various growth modes.

Abdullah, Sharmin↗

Properties of Accelerating Edge Dislocations in Arbitrary Slip Systems with Reflection Symmetry

We discuss the theoretical solution to the differential equations governing accelerating edge dislocations in anisotropic crystals. This is an important prerequisite to understanding high-speed dislocation motion, including an open question about the existence of transonic dislocation speeds, and subsequently high-rate plastic deformation in metals and other crystals.

36 MATERIALS SCIENCE↗

Polarization near dislocation cores in SrTiO 3 single crystals: The role of flexoelectricity

Spontaneous polarization as large as ~28 μC/cm 2 was recently observed around the dislocation cores in non-polar SrTiO 3 bulk crystals, and its origin was attributed to the flexoelectric effect, i.e., polarization induced by strain gradients. However, the roles of flexoelectricity, relative to other electromechanical contributions, and the nature of dislocations, i.e., edge vs screw dislocations in the induced polarization, are not well understood. In this work, we study the role of flexoelectricity in inducing polarization around three types of dislocation cores in SrTiO 3 : b= a(100) edge dislocation, b= a(110) edge dislocation, and b= a(010) screw dislocation, where b is the Burgers vector. For the edge dislocations, polarization can be induced by electrostriction alone, while flexoelectricity is essential for stabilizing the symmetric polarization pattern. The shear component of the flexoelectric tensor has a dominant effect on the magnitude and spatial distribution of the flexoelectric polarization. In contrast, no polarization is induced around the b= a(010) screw dislocation through either electrostriction or flexoelectricity. Finally, our findings provide an in-depth understanding of the role of flexoelectricity in inducing polarization around dislocation cores and offer insights into the defect engineering of dielectric/ferroelectric materials.

36 MATERIALS SCIENCE↗

Comparison of EBSD, DIC, AFM, and ECCI for active slip system identification in deformed Ti-7Al

The use of SEM-DIC, AFM, ECCI, and HR-EBSD to characterize slip-system activity was assessed on the same material volume of Ti-7Al. This study presents a robust comparison of the various methods for the first time, including an assessment of their advantages and disadvantages, and how they can be used effectively in a complementary fashion. The analysis of the different approaches was carried out in a blind, round-robin manner at three different universities. A Ti-7Al specimen was deformed in uniaxial tension to approximately 3% axial strain, and the active slip systems were independently identified using (i) trace analysis; (ii) in-SEM digital image correlation, (iii) observations of residual dislocations from ECCI, and (iv) long-range rotation gradients through HR-EBSD, with consistent trace identification in all cases. Displacement data from AFM was used to augment SEM-DIC displacement data by providing complementary out-of-plane displacement information. Furthermore, short-range dislocation gradients (measured by DIC) provided insight into the residual geometrically necessary dislocation (GND) content, and was consistent with the GND content extracted from EBSD data and ECCI images, confirming the presence of residual GNDs on the dominant slip systems resulting in visible slip bands. Furthermore, these approaches can be used in tandem to provide multi-modal information on slip band identification, strain and orientation gradients, out-of-plane displacements, and the presence of GNDs and SSDs, all of which can be used to inform and validate the development of dislocation-based crystal plasticity and strain gradient models.

36 MATERIALS SCIENCE↗