Edge Dislocation Core Research Articles

Solute strengthening of prism edge dislocations in Mg alloys

The poor ductility of hcp Mg is attributed to the low activity of non-basal slip systems and so activation of prismatic slip can aid ductility in rolled sheets by providing three additional <a> Burgers vector slip systems. Experimental studies show that dilute additions of alloying elements such as Zn and Al leads to softening of prismatic slip at low temperatures but strengthening at higher temperatures. Here, the role of solute strengthening of prismatic edge dislocations is investigated as a possible explanation for the higher-T strengthening. Mg–Zn is studied using first-principles inputs in a parameter-free solute strengthening theory. First-principles DFT is necessary to accurately assess the strong solute chemical interaction energies in the core of the compact edge dislocation. Such calculations are subtle due to motion of the dislocation in the presence of the solute, and methods to obtain reliable results with acceptable computational cost are discussed. While interaction energies of Zn in the prism edge core can be quite large ( ± 0.34 eV), the edge solute strengthening of prismatic slip in dilute Mg–Zn remains well below experiments at high temperatures. However, the large difference (0.68 eV) in Zn/dislocation interaction energies across the core of the edge dislocation suggests strengthening by dynamic strain aging as an explanation for the higher-T strengthening.

Dissociation of edge and screw pyramidal I and II dislocations in magnesium

Pyramidal dislocations in magnesium (Mg) and other hexagonal close-packed metals play an important role in accommodating plastic strains along the c-axis. Bulk single crystal Mg only presents very limited plasticity in c-axis compression, and this behavior was attributed to out-of-plane dissociation of pyramidal dislocations onto the basal plane and resulted in an immobile dislocation configuration. In contrast, other simulations and experiments reported in-plane dissociation of pyramidal dislocations on their slip planes. Thus, the core structure and mode of dissociation of pyramidal dislocations are still not well understood. To better understand the dissociation behavior of pyramidal dislocations in Mg at room temperature, in this work, atomistic simulations were conducted to investigate four types of pyramidal dislocations at 300 K: edge and screw Py-I on {101¯1}, edge and screw Py-II on {112¯2} by using a modified embedded atom method (MEAM) potential for Mg and anisotropic elasticity dislocation model. The results show that when energy minimization was performed before relaxation, in-plane dissociation of edge dislocations on respective pyramidal plane could be obtained at room temperature for all four types of dislocation. Without energy minimization, the edge dislocations dissociated out-of-plane onto the basal plane. Calculations of potential energy and hydrostatic stress of individual atoms at the edge dislocation core show that the extraordinarily high energy and atomic stresses in the as-constructed dislocation structures caused the out-of-plane dissociation onto the basal plane. The core structures of all four types of pyramidal dislocation after in-plane dissociation were analyzed by computing the distribution of the Burgers vector.

Mapping Nanoscale Electrostatic Field Fluctuations around Graphene Dislocation Cores Using Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM).

Defects in crystalline lattices cause modulation of the atomic density, and this leads to variations in the associated electrostatics at the nanoscale. Mapping these spatially varying charge fluctuations using transmission electron microscopy has typically been challenging due to complicated contrast transfer inherent to conventional phase contrast imaging. To overcome this, we used four-dimensional scanning transmission electron microscopy (4D-STEM) to measure electrostatic fields near point dislocations in a monolayer. The asymmetry of the atomic density in a (1,0) edge dislocation core in graphene yields a local enhancement of the electric field in part of the dislocation core. Through experiment and simulation, the increased electric field magnitude is shown to arise from "long-range" interactions from beyond the nearest atomic neighbor. These results provide insights into the use of 4D-STEM to quantify electrostatics in thin materials and map out the lateral potential variations that are important for molecular and atomic bonding through Coulombic interactions.

Vacancy Energetics and Diffusivities in the Equiatomic Multielement Nb-Mo-Ta-W Alloy.

In this work, we study vacancy energetics in the equiatomic Nb-Mo-Ta-W alloy, especially vacancy formation and migration energies, using molecular statics calculations based on a spectral neighbor analysis potential specifically developed for Nb-Mo-Ta-W. We consider vacancy properties in bulk environments as well as near edge dislocation cores, including the effect of short-range order (SRO) by preparing supercells through Metropolis Monte-Carlo relaxations and temperature on the calculation. The nudged elastic band (NEB) method is applied to study vacancy migration energies. Our results show that both vacancy formation energies and vacancy migration energies are statistically distributed with a wide spread, on the order of 1.0 eV in some cases, and display a noticeable dependence on SRO. We find that, in some cases, vacancies can form with very low energies at edge dislocation cores, from which we hypothesize the formation of stable ‘superjogs’ on edge dislocation lines. Moreover, the large spread in vacancy formation energies results in an asymmetric thermal sampling of the formation energy distribution towards lower values. This gives rise to effective vacancy formation energies that are noticeably lower than the distribution averages. We study the effect that this phenomenon has on the vacancy diffusivity in the alloy and discuss the implications of our findings on the structural features of Nb-Mo-Ta-W.

Elastically non-linear discrete model for core of edge dislocation

To facilitate the modeling of crystal defects on their core scales, the present paper introduces a discrete stress balance equation that admits non-linear elasticity of the defected crystal cell and its arbitrary boundary conditions. Thus, the cell may be free or embedded into continuum. In the latter case, when considering a sufficiently large domain tractable by the proposed method, boundary forces can be related to long-range stresses of the defect. For a case study, an edge dislocation in the primitive cubic lattice is simulated to assess influence of the crystal dimensions and elastic properties on the microscopic discrete core.

Thermal Super-Jogs Control High-Temperature Strength in Nb-Mo-Ta-W Alloys

Refractory multi-element alloys (RMEA) with body-centered cubic (bcc) structure have been the object of much research over the last decade due to their high potential as candidate materials for high-temperature applications. Most of these alloys display a remarkable strength at high temperatures, which cannot be explained by the standard model of bcc plasticity dominated by thermally-activated screw dislocation motion. Recent research on Nb-Mo-Ta-W alloys points to a heightened role of edge dislocations on deformation, which is generally attributed to atomic-level chemical fluctuations in the material and their interactions with dislocation cores during slip. However, while this model accounts for a strengthening effect due to the chemical complexity of the alloy, it is not sufficient to explain its strength across the entire thermal range. Here we propose a new mechanism that captures the existing theories about enhanced lattice strengthening and a thermally-activated component that emanates directly from the chemical complexity of the RMEA. This compositional complexity results in unique vacancy formation energy distributions with tails that extend into negative energies, leading to spontaneous, i.e., athermal, vacancy formation at edge dislocation cores. These vacancies relax into atomic-sized super-jogs on the dislocation line, acting as extra pinning points that increase the activation stress of the dislocation. At the same time, these super-jogs can displace diffusively along the glide direction, relieving with their motion some of the extra stress, thus countering the hardening effect due to jog-pinning. The interplay between these two processes as a function of temperature confers an extra strength to edge dislocation at intermediate-to-high temperatures, in remarkable agreement with experimental measurements in Nb-Mo-Ta-W and across a number of different RMEA.

Constructing Machine-learned Interatomic Potentials for SiC: MD Analyses of Dislocation

In Molecular Dynamics (MD), the motion of atoms is calculated based on the interatomic potential, which is a mathematical model of the interatomic interaction. Recently, some types of machine-learning interatomic potentials (ML-IAPs) are being proposed, which will reproduce adequately results of first-principles calculation without any empirical assumption or data. First-principles calculations should be avoided for large simulation models, such as edge dislocations, due to its high calculation costs. However, it is expected for ML-IAPs to analyze crystalline defects in large systems with the same accuracy as first-principles calculations. In this research, SNAP, which is one of ML-IAPs, was created for silicon carbide with cubic crystalline structure (3C-SiC), and it was examined on the reproducibility when it is applied to MD computation. It is confirmed that the SNAP we built from scratch has higher reproducibility than any empirical one in terms of lattice constant, elastic modulus, and bulk modulus. The edge dislocation cores properly moved along the predicted slip plane of 3C-SiC. In addition, the Peierls stress estimated by SNAP agrees well with that of covalent materials which is usually high.

Spontaneous symmetry breaking of dislocation core in SrTiO3

Dislocation endows intriguing properties in materials and attracted extensive interest, while its potential is far from being fully explored. Here, we use first-principles simulations to explore the property of an edge dislocation core in SrTiO3, an incipient ferroelectricity with a prototype perovskite structure. We discovered the spontaneous symmetry breaking in the dislocation, which is introduced by the atomic movement in the core and the Ti–O octahedron's distortion in the nearby unit cells. Next, we systematically investigate the coupling relationship between strain modes and ferroelectric atomic displacement modes based on group representation theory, and further proposed a model to quantificationally estimate the atomic configuration of SrTiO3 under complex strain conditions, which predicts the polarization near the dislocation decently.

Interaction between dislocation and vacancies in magnesium oxide: Insights from atomistic simulations and elasticity theory

We determine the interaction between an $1/2\ensuremath{\langle}110\ensuremath{\rangle}{\overline{1}10}$ edge dislocation and charged vacancies in MgO, using both molecular static simulations and the elasticity theory developed in the framework of the elastic dipole approach. In this study, the confrontation of these two methods highlights the specific role of the dislocation core structure on the interaction. We thus show that in MgO, the edge dislocation core, within a region across the glide planes that expands over several Burgers vector, is strongly attractive for vacancies, especially those of oxygen. However, the resulting pinning force on the dislocation remains weak and should not contribute to a significant hardening.

Role of dislocation elastic field on impurity segregation in Fe-based alloys

Dislocation engineering in crystalline materials is essential when designing materials for a large range of applications. Segregation of additional elements at dislocations is frequently used to modify the influence of dislocations on material properties. Thus, the influence of the dislocation elastic field on impurity segregation is of major interest, as its understanding should lead to engineering solutions that improve the material properties. We report the experimental study of the elastic field influence on atomic segregation in the core and in the area surrounding edge dislocations in Fe-based alloys. Each element is found either to segregate in the edge dislocation core or to form atmospheres. The elastic field has a strong effect on the segregation atmosphere, but no effect on the dislocation core segregation. The theory is in good agreement with experiments, and should support dislocation engineering.

Ab initio study of the stability of H-He clusters at lattice defects in tungsten

The interaction of a H-He pair embedded in various types of lattice defects in the bcc tungsten, such as vacancies, tilt grain boundaries, a core of screw and edge dislocations has been studied using ab initio calculations. It is shown that H-vacancy and He-vacancy clusters are weaker traps for He and H single atoms, respectively, as compared to a single vacancy. H or He atom, solely, is strongly attracted to the studied grain boundary interfaces, while the mutual H-He interaction is negligible (close to the interaction in vacuum) if both atoms are placed in the adjacent trapping sites located on the grain boundary. The H-He pair placed in the core of the screw or edge dislocation exhibits the binding energy of ~0.2–0.3 eV, which is close to the H-He attraction in the bulk W. The ground-state configurations for H-He dimers located in various lattice defects in W were rationalized on the basis of atomic structure visualizations, bond analysis and charge density distributions. The obtained data are discussed in the frame of the thermal desorption spectroscopy results offering a better understanding of the detrapping stages of He and H isotopes under mixed plasma exposure conditions.

Dynamics of edge dislocation in Cu–Ni solid solution alloys at atomic scale

The mobility of edge dislocation in Cu–Ni solid solution alloys within a wide range of temperatures 100–1100 K and Ni concentrations 0–30 at.% is studied by molecular dynamics simulation. Two different regimes of the influence of substitutional Ni atoms on the motion of edge dislocation are observed. In the first regime, in which the velocity of edge dislocation is much less than the shear sound speed, Ni atoms act as barriers and slow the dislocation down. In this regime, the dependence of the edge dislocation velocity on Ni concentration weakens with increasing temperature. In the second regime, in which the dislocation moves faster, with a speed closer to the shear sound speed, Ni atoms accelerate its motion. The latter result is a consequence of higher shear sound speed along the [110] direction of Cu–Ni solid solution alloy associated with higher Ni content. The distance between Shockley partial dislocations representing the core of edge dislocation is analyzed as a function of temperature and Ni concentration. The partial splitting increases with temperature and decreases with Ni concentration. The latter result might be important for predicting strain hardening mechanisms in Cu–Ni alloys.

Noise filtering in atomistic stress calculations for crystalline materials

Spatially-varying stress fields can be obtained from atomistic simulations as weighted averages over a phase function that depends on the positions and momenta of the atoms and the interatomic forces between them. However atomistic stress fields exhibit significant nonphysical noise on atomic length scales even under uniform loading conditions. This makes it difficult to obtain accurate stress estimates near atomic-scale defects such as nanocrack tips and dislocation cores. To address this issue, we develop an algorithm to filter noise in the atomistic stress for crystalline materials based on a rigorous stress-invariance condition, which leads to a new class of lattice-dependent weighting functions. Stress fields computed using these weighting functions are identically noise-free under uniform conditions, and have greatly reduced noise in general. The method is demonstrated for three example problems: (1) uniform loading of nickel aluminide, (2) a mode I crack in silicon, and (3) screw and edge dislocation cores in aluminum. The noise filtering algorithm is implemented in MDStressLab++, an open source C++ library for computing atomistic stress fields available online at http://mdstresslab.org.

Nucleation mechanism of intra-granular blisters in tungsten exposed to hydrogen plasma

Despite being a subject of long-term research on fusion-reactor structural materials, the behaviour of hydrogen in tungsten under plasma exposure remains unclear. Here, the explicit transmission electron microscopy observations for recrystallised W after hydrogen plasma exposure are successfully obtained. These are the first observations to show the intra-granular blisters are located on the {100} planes. Molecular dynamics simulations confirm the hydrogen blister initiating at <100> dislocation core behaved similarly to those in experiment. We propose that the widely reported intra-granular hydrogen blisters are nucleated at the <100> edge dislocation core and develop along the (100) plane in tungsten.

Temperature Effect on Stacking Fault Energy and Deformation Mechanisms in Titanium and Titanium-aluminium Alloy

Alloying elements have great influence on mechanical properties of metals. Combining dislocation characterization and in-situ transmission electron microscope straining at ambient and liquid-nitrogen temperature in high-purity titanium and Ti-5at%Al, we investigated the modulation of Al on dislocation behaviours as temperature changed. It reveals that segregation of Al at edge dislocation cores in Ti-5at%Al generates strong obstacles, promoting room temperature cross-slips. However, the effect of Al on reducing stacking-fault energy (SFE) as decreasing temperature is significant. Consequently, the lower SFE in Ti-5at%Al results in ordinary planar dislocation slip while massive dislocation cross-slips occurred in Ti at liquid-nitrogen temperature.

Atomistic simulations of helium, hydrogen, and self-interstitial diffusion inside dislocation cores in tungsten

Tritium retention and microstructural modifications due to helium accumulation are two of the main concerns regarding plasma-facing materials in fusion applications. Crystal defects in tungsten (W), such as grain boundaries and dislocations, can serve as traps or channels for diffusion of hydrogen (H) and helium (He), and, as such, can affect the transport of these species. In this work, we study the diffusion of hydrogen, helium and self-interstitial atoms (SIA) inside screw and edge dislocations in W using molecular dynamics simulations. Stable sites for interstitials in dislocations are identified using a free-volume analysis and energy barriers for diffusion are predicted using a combination of the nudged elastic band (NEB) method and finite temperature molecular dynamics simulations. Overall, the simulations predict higher energetic barriers for He and H diffusion in both screw and edge dislocations compared to the bulk. However, the diffusion mechanism in both dislocations are shown to differ: simulations predict that interstitials are constrained to move in short channels inside the edge dislocation core so that long-range diffusion along the dislocation line happens only with the motion of the dislocation. In contrast, 1D diffusion of the interstitial along the dislocation core, independent of dislocation motion, is observed for screw dislocations.

Vacancy-assisted core transformation and mobility modulation of a-type edge dislocations in wurtzite GaN

In this study, core structure dependent dislocation dynamics of a-type edge dislocation in three slip systems (basal, prismatic and pyramidal) of wurtzite GaN have been investigated using classical molecular dynamics simulations. All potential a-type edge dislocation cores in the shuffle and glide planes of the three slip systems have been identified, and the corresponding dislocation dynamics were examined. Our calculations reveal that for all of the three slip systems, all of the shuffle cores are planar glissile and mobile, while being non-planar sessile and immobile for all of the glide cores. We further show that vacancy can be used to activate the motion of glide cores via core transition from glide to shuffle, which is also valid for AlN and InN. The critical shear stresses for the motion of glide cores are also determined at various vacancy concentrations. Our study clarifies core structure dependent dislocation dynamics characteristics and provides ways in tuning dislocation motions in wurtzite crystals.

Interaction of carbon with microstructural defects in a W-Re matrix: An ab initio assessment

The interaction of carbon atoms with point defects and the core of edge and screw dislocations with Burgers vector a0/2⟨111⟩ in W and a W-Re matrix is studied by means of ab initio calculations. The structure and energetics of the ground-state atomic configurations are presented and rationalized. It is found that di-vacancies, which are thermally unstable in pure W according to the state-of-the-art ab initio calculations, can nucleate at C and Re-C complexes, which fill the gap in the explanation of the emergence of nanovoids observed experimentally under irradiation. Also, on the basis of the recent experimental evidence and our calculations, the temperature ranges for the manifestation of the yield drop phenomenon, which is related to the obstruction of dislocation motion due to their decoration by impurities such as carbon, are revealed.

Characteristics of atomic elastic stiffness at GSF energy surface, edge and screw dislocation cores in fcc, bcc and hcp metals

Basic characteristics of 6 × 6 matrix of atomic elastic stiffness (AES), Bija=Δσia/Δεj, or the deformation resistance at each atom point, are discussed first in static analyses of generalized stacking fault (GSF) energy surface for 8 fcc, 4 bcc and 4 hcp metals with Zhou’s EAM potential. For hcp metals, the stress–strain peak along the GSF path exactly coincides with the point where the AES loses the resistance showing negative 1st eigenvalue ηa(1), or the solution of BijaΔεj=ηaΔεi=Δσia; however, all fcc and 2 bcc (Mo and W) never have negative ηa(1) along the GSF path. Fe and Ta transiently show ηa(1) &amp;lt; 0 while they also have positive ηa(1) at the GSF energy peak. Then we performed MD simulations of edge and screw dislocation dipoles in a periodic slab cell of typical elements of fcc, bcc and hcp; and discussed the eigenvalue and the corresponding eigenvector {Δεxx, Δεyy, Δεzz, Δγyz, Δγzx, Δγxy} of the dislocation cores. As expected from the results of the GSF analyses, dislocation cores in fcc Ni have no ηa(1) &amp;lt; 0 atoms, even in their glide process under external shear loading. Bcc Fe and hcp Co definitely have ηa(1) &amp;lt; 0 atoms in the dislocation cores and their migration direction can be visualized by the maximum shear direction of the strain tensor of the corresponding eigenvector.

Atomistic Defect Makes a Phase Plate for the Generation and High-Angular Splitting of Electron Vortex Beams.

Topological defects in solid-state materials by breaking the translational symmetry offer emerging properties that are not present in their parental phases. For example, edge dislocations-the 2π phase-winding topological defects-in antiferromagnetic NiO crystals can exhibit ferromagnetic behaviors. Herein, we study how these defects could give rise to topological orders when they interact with a high-energy electron beam. To probe this interaction, we formed a coherent electron nanobeam in a scanning transmission electron microscope and recorded the far-field transmitted patterns as the beam steps through the edge dislocation core in [001] NiO. Surprisingly, we found the amplitude patterns of the ⟨020⟩ Bragg disks evolve in a similar manner to the evolution of an annular solar eclipse. Using the ptychographic technique, we recovered the missing phase information in the diffraction plane and revealed the topological phase vortices in the diffracted beams. Through atomic topological defects, the wave function of electrons can be converted from plane wave to electron vortex. Technologically, this approach provides a feasible route for the fabrication of phase plates that can generate electron vortex beams with an angular separation that is 3 orders of magnitude larger than what traditional nanofabrication technology can offer. This advance will enable the collection of magnetic circular dichroism spectra with high spatial resolution and high efficiency, boosting the understanding of the relationship between symmetry breaking and magnetic property of individual topological defect at the atomic scale.