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At least 181 records · Page 10

A non-singular theory of dislocations in anisotropic crystals

Here we develop a non-singular theory of three-dimensional dislocation loops in a particular version of Mindlin's anisotropic gradient elasticity with up to six length scale parameters. The theory is systematically developed as a generalization of the classical anisotropic theory in the framework of linearized incompatible elasticity. The non-singular version of all key equations of anisotropic dislocation theory are derived as line integrals, including the Burgers displacement equation with isolated solid angle, the Peach-Koehler stress equation, the Mura-Willis equation for the elastic distortion, and the Peach-Koehler force. The expression for the interaction energy between two dislocation loops as a double line integral is obtained directly, without the use of a stress function. It is shown that all the elastic fields are non-singular, and that they converge to their classical counterparts a few characteristic lengths away from the dislocation core. In practice, the non-singular fields can be obtained from the classical ones by replacing the classical (singular) anisotropic Green's tensor with the non-singular anisotropic Green's tensor derived by Lazar and Po (2015b). The elastic solution is valid for arbitrary anisotropic media. In addition to the classical anisotropic elastic constants, the non-singular Green's tensor depends on a second order symmetric tensor of length scale parameters modeling a weak non-locality, whose structure depends on the specific class of crystal symmetry. The anisotropic Helmholtz operator defined by such tensor admits a Green's function which is used as the spreading function for the Burgers vector density. As a consequence, the Burgers vector density spreads differently in different crystal structures. Two methods are proposed to determine the tensor of length scale parameters, based on independent atomistic calculations of classical and gradient elastic constants. The anisotropic non-singular theory is shown to be in good agreement with molecular statics without fitting parameters, and unlike its singular counterpart, the sign of stress components does not show reversal as the core is approached. Compared to the isotropic solution, the difference in the energy density per unit length between edge and screw dislocations is more pronounced.

42 ENGINEERING↗

Dislocation-position fluctuations in solid 4He as collective variables in a quantum crystal

Abstract Quantum behavior at mesoscopic length scales is of significant interest, both from a fundamental-physics standpoint, as well as in the context of technological advances. In this light, the description of collective variables comprising large numbers of atoms, but nevertheless displaying non-classical behavior, is a fundamental problem. Here, we show that an effective-Hamiltonian approach for such variables, as has been applied to describe the quantum behavior of coupled qubit/oscillator systems, can also be very useful in understanding intrinsic behavior of quantum materials. We consider lattice dislocations – naturally occurring mesoscopic line defects in crystals – in the prototypical bosonic quantum crystal, solid 4 He. For this purpose, we map fully atomistic quantum simulations onto effective one-dimensional Hamiltonians in which the collective dislocation-position variables are represented as interacting, massive quantum particles. The results provide quantitative understanding of several experimental observations in solid 4 He.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Comparison of dislocation characterization by electron channeling contrast imaging and cross-correlation electron backscattered diffraction

In this paper, the relative capabilities and limitations of electron channeling contrast imaging (ECCI) and cross-correlation electron backscattered diffraction (CC-EBSD) have been assessed by studying the dislocation distributions resulting from nanoindentation in body centered cubic Ta. Qualitative comparison reveals very similar dislocation distributions between the CC-EBSD mapped GNDs and the ECC imaged dislocations. Approximate dislocation densities determined from ECC images compare well to those determined by CC-EBSD. Nevertheless, close examination reveals subtle differences in the details of the distributions mapped by these two approaches. Finally, the details of the dislocation Burgers vectors and line directions determined by ECCI have been compared to those determined using CC-EBSD and reveal good agreement.

36 MATERIALS SCIENCE↗

Models of dislocation glide and strengthening mechanisms in bcc complex concentrated alloys

Abstract The mechanical response of complex concentrated alloys (CCAs) deviates from that of their pure and dilute counterparts due to the introduction of a combinatorially sized chemical concentration dimension. Compositional fluctuations constantly alter the energy landscape over which dislocations move, leading to line roughness and the appearance of defects such as kinks and jogs under stress and temperature conditions where they would ordinarily not exist in pure metals and dilute alloys. The presence of such chemical defects gives rise to atomic-level mechanisms that fundamentally change how CCAs deform plastically at meso- and macroscales. In this article, we provide a review of recent advances in modeling dislocation glide processes in CCAs, including atomistic simulations of dislocation glide using molecular dynamics, kinetic Monte Carlo simulations of edge and screw dislocation motion in refractory CCAs, and phase-field models of dislocation evolution over complex energy landscapes. We also discuss pathways to develop comprehensive simulation methodologies that connect an atomic-level description of the compositional complexity of CCAs with their mesoscopic dislocation-mediated plastic response with an eye toward improved design of CCA with superior mechanical response. Graphical abstract

36 MATERIALS SCIENCE↗

Structure-dependent clustering-to-declustering solute segregation transitions near disconnections

Grain-boundary disconnections, characterized by a step and a dislocation, are pervasive interfacial line defects that play a critical role in governing the properties and performance of nanocrystalline alloys. Although segregation of alloying elements is frequently observed at GB disconnections, the underlying mechanisms remain poorly understood, particularly at elevated temperatures and non-dilute conditions. In this study, we employ atomistic simulations to study the segregation behavior of Ag at various faulted disconnections in Cu as a model material system. Our results demonstrate a pronounced size and compactness effect on the segregation behavior: more compact faulted disconnection structures promote the formation of Ag segregation clusters due to a highly localized tensile field, whereas more spread faulted disconnection structures (i.e., with wider partial dislocation spacing) exhibit much weaker clustering tendencies. Furthermore, with increasing temperature, Ag clustering in small disconnections initially intensifies and then disappears, indicating a thermally driven transition from clustering to declustering segregation behavior.

Disconnections↗

Nucleation of Grain Boundary Phases

Here, we derive a theory that describes homogeneous nucleation of grain boundary (GB) phases. Our analysis takes account of the energy resulting from the GB phase junction, the line defect separating two different GB structures, which is necessarily a dislocation as well as an elastic line force due to the jump in GB stresses. The theory provides analytic forms for the elastic interactions and the core energy of the GB phase junction that, along with the change in GB energy, determines the nucleation barrier. We apply the resulting nucleation model to simulations of GB phase transformations in tungsten. Our theory explains why under certain conditions GBs cannot spontaneously change their structure even to a lower energy state.

36 MATERIALS SCIENCE↗

Local chemical ordering of a neutron-irradiated CrFeMnNi compositionally complex alloy

While ion-irradiation studies are a critical first step in studying compositionally complex alloys (CCAs) for nuclear applications, they do not capture all the microstructural changes occurring under the low irradiation dose rates and different particles’ scattering patterns experienced in a nuclear reactor setting. To explore these phenomena in reactor-relevant conditions for the first time in CCA, the single-phase solid-solution Cr 10 Fe 30 Mn 30 Ni 30 was neutron irradiated up to 6.61 displacements per atom at 395 and 579 °C. Irradiation-enhanced local chemical ordering (LCO) well beyond the range of short range ordering was observed, and is predicted to be the precursor to the precipitation of a coherent Ni-Mn L1 0 phase and a Cr-rich α’ phase, though TEM analysis did not indicate the presence of either in any irradiation condition. The line density of faulted dislocation loops decreased from 6.47 to 1.69 ∙ 10 15 m -2 from 3.43 to 6.61 dpa at 579 °C despite no appreciable faulted loop content in the unirradiated material. LCO is expected to increase the complexity of the energy landscape within this alloy, restricting interstitial point defect mobility and creating local regions of greater stacking fault energy. These contribute to the negative correlation between irradiation dose and faulted dislocation loop density in this study, as well as the lack of void swelling observed.

36 MATERIALS SCIENCE↗

A general solution for accelerating screw dislocations in arbitrary slip systems with reflection symmetry

Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line defects moving at constant velocity. Troubled by singularities at certain ‘critical’ velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences are usually attributed to neglecting the finite size of the core and to the restriction to constant velocity. In the isotropic limit, accelerating pure screw and edge dislocations were studied some time ago. A generalization to anisotropic crystals has been attempted for pure screw and edge dislocations only for some special cases. This work aims to fill the gap of deriving a general anisotropic solution for pure screw dislocations applicable to slip systems featuring a reflection symmetry, a prerequisite to studying pure screw dislocations without mixing with edge dislocations. Finally, further generalizations to arbitrary mixed dislocations as well as regularizations of the dislocation core are beyond the scope of this paper and are left for future work.

42 ENGINEERING↗

Origin of micrometer-scale dislocation motion during hydrogen desorption

Hydrogen, while being a potential energy solution, creates arguably the most important embrittlement problem in high-strength metals. However, the underlying hydrogen-defect interactions leading to embrittlement are challenging to unravel. Here, we investigate an intriguing hydrogen effect to shed more light on these interactions. By designing an in situ electron channeling contrast imaging experiment of samples under no external stresses, we show that dislocations (atomic-scale line defects) can move distances reaching 1.5 μm during hydrogen desorption. Combining molecular dynamics and grand canonical Monte Carlo simulations, we reveal that grain boundary hydrogen segregation can cause the required long-range resolved shear stresses, as well as short-range atomic stress fluctuations. Thus, such segregation effects should be considered widely in hydrogen research.

36 MATERIALS SCIENCE↗

X-Ray Diffraction and Imaging Study of Imperfections of Crystallized Lysozyme with Coherent X-Rays

Phase-sensitive x-ray diffraction imaging and high angular-resolution diffraction combined with phase contrast radiographic imaging are employed to characterize defects and perfection of a uniformly grown tetragonal lysozyme crystal in symmetric Laue case. The fill width at half-maximum (FWHM) of a 4 4 0 rocking curve measured from the original crystal is approximately 16.7 arcseconds, and defects, which include point defects, line defects, and microscopic domains, have been clearly observed in the diffraction images of the crystal. The observed line defects carry distinct dislocation features running approximately along the <110> growth front, and they have been found to originate mostly at a central growth area and occasionally at outer growth regions. Individual point defects trapped at a crystal nucleus are resolved in the images of high sensitivity to defects. Slow dehydration has led to the broadening of the 4 4 0 rocking curve by a factor of approximately 2.4. A significant change of the defect structure and configuration with drying has been revealed, which suggests the dehydration induced migration and evolution of dislocations and lattice rearrangements to reduce overall strain energy. The sufficient details of the observed defects shed light upon perfection, nucleation and growth, and properties of protein crystals.

Hu, Zheng-Wei↗

Diffraction and Imaging Study of Imperfections of Protein Crystals with Coherent X-rays

High angular-resolution x-ray diffraction and phase contrast x-ray imaging were combined to study defects and perfection of protein crystals. Imperfections including line defects, inclusions and other microdefects were observed in the diffraction images of a uniformly grown lysozyme crystal. The observed line defects carry distinct dislocation features running approximately along the <110> growth front and have been found to originate mostly in a central growth area and occasionally in outer growth regions. Slow dehydration led to the broadening of a fairly symmetric 4 4 0 rocking curve by a factor of approximately 2.6, which was primarily attributed to the dehydration-induced microscopic effects that are clearly shown in diffraction images. X-ray imaging and diffraction characterization of the quality of apoferritin crystals will also be discussed in the presentation.

Hu, Z. W.↗

Diffraction and imaging study of imperfections of crystallized lysozyme with coherent X-rays

Phase-contrast X-ray diffraction imaging and high-angular-resolution diffraction combined with phase-contrast radiographic imaging were employed to characterize defects and perfection of a uniformly grown tetragonal lysozyme crystal in the symmetric Laue case. The full-width at half-maximum (FWHM) of a 4 4 0 rocking curve measured from the original crystal was approximately 16.7 arcsec and imperfections including line defects, inclusions and other microdefects were observed in the diffraction images of the crystal. The observed line defects carry distinct dislocation features running approximately along the <1 1 0> growth front and have been found to originate mostly in a central growth area and occasionally in outer growth regions. Inclusions of impurities or formations of foreign particles in the central growth region are resolved in the images with high sensitivity to defects. Slow dehydration led to the broadening of a fairly symmetric 4 4 0 rocking curve by a factor of approximately 2.6, which was primarily attributed to the dehydration-induced microscopic effects that are clearly shown in X-ray diffraction images. The details of the observed defects and the significant change in the revealed microstructures with drying provide insight into the nature of imperfections, nucleation and growth, and the properties of protein crystals.

Muramidase/chemistry↗

The inhibiting effect of dislocation helices on the stress-induced orientation of S' precipitates in Al–Cu–Mg alloy

The phenomenon of restrained stress-induced preferential orientation of S′ precipitates is investigated using a single-crystal of Al–1.23Cu–0.43 Mg alloy. Al–1.23Cu–0.43 Mg single-crystal specimens are subjected to stress aging, and the microstructure is analyzed by transmission electron microscopy (TEM). It is found that the stress-induced preferential orientation of S′ precipitates is restrained owing to the dislocations produced by a higher stress. The effect of dislocations on the oriented precipitates depends on the total length of the intersection lines for precipitate habit planes and dislocation glide planes. This investigation not only provides important insight into solving the anisotropy problem attributed to precipitation strengthening, but also offers a benchmark for choosing the appropriate stress range in manufacturing of Al–Cu–Mg alloys. - Highlights: • Single crystals of an Al–Cu–Mg alloy were prepared for the investigations. • A phenomenon of restrained stress-induced preferential orientation of S′ precipitates was found. • The influence of dislocation helices on precipitation during stress-aging was studied. • Difference of orientation degree of S′ precipitates and θ′ precipitates was explained. • A basis for choosing the appropriate stress range in manufacturing of Al–Cu–Mg alloys is provided.

36 MATERIALS SCIENCE↗

Quantifying irradiation defects in zirconium alloys: a comparison between transmission electron microscopy and whole-pattern diffraction line-profile analysis - 2016-0089

Irradiation-induced dislocations significantly affect the mechanical properties of zirconium alloys, altering slip and influencing creep and growth. Thus, the quantitative characterization of irradiation defects as a function of fluence, cold work, and/or thermal treatments is important for models that attempt to predict their impact on properties. Whole-pattern diffraction line-profile analysis (DLPA) is a well-established modern tool for microstructure characterization based on first-principle physical models for dislocation density measurements in plastically deformed materials. However, applying these DLPA methods directly to irradiated materials yields higher than expected dislocation density values compared with historical transmission electron microscopy (TEM) measurements and past line-broadening analysis studies calibrated to TEM observations. In an effort to understand these differences, a new microstructural model was developed for DLPA to specifically address dislocation structures consisting of elliptical - and -component loops. To compare the refined DLPA method with TEM measurements, high-resolution neutron diffraction patterns on nonirradiated and irradiated Zr-2.5Nb samples were collected with the Neutron Powder Diffractometer instrument at the Los Alamos Neutron Science Center and were evaluated. High-resolution TEM measurements were performed at the Reactor Materials Testing Laboratory, Queen's University, for comparison with the DLPA results. The capabilities and inherent uncertainties of both the refined DLPA and TEM methods are compared and discussed in detail. We show that the differences between the density values provided by DLPA and TEM are inherent to the methods and can be reconciled with the interpretation of the data. (authors)

36 MATERIALS SCIENCE↗

Automated extraction of interfacial dislocations and disconnections from atomistic data

Here we introduce Interfacial Line Defect Analysis (ILDA), a method for identifying and extracting interfacial dislocations and disconnections with little-to-no input from the user on the nature of the interface. By simply providing the orientations and coherency strains for the crystals in a coherent reference state of the interface, ILDA provides exact Burgers vectors. Alternatively, these orientations and strains can be estimated using local atomic deformation gradients, making ILDA fully automated and providing estimated Burgers vectors. ILDA also determines the step height associated with each defect line segment, in case the associated defect is a disconnection. The heart of the method is the identification of atoms residing at co-incidence sites between the two crystals and the construction of a surface mesh connecting these sites that is used to compose Burgers circuits and insert defect line segments. We demonstrate the performance of ILDA in two test cases: a twist grain boundary and a phase boundary.

36 MATERIALS SCIENCE↗

The revised elastic field of an edge dislocation

We modify the traditional linear-elastic field of an edge dislocation. The modifications stem from symmetry and energy requirements imposed in terms of embedded (deformed) coordinates. These requirements are satisfied if a line force is added to the dislocation field. The modification to the stress field is expressed by coefficients that are a function only of Poisson’s ratio. Qualitatively, the field of the dislocation is increased in the glide direction and decreased in the climb direction. There are small changes to the field of a screw dislocation that do not entail the addition of a line force. Effects of nonlinearity, anisotropic elasticity, and image forces are briefly considered.

Hirth, J. P.↗

Data-driven analysis of neutron diffraction line profiles: application to plastically deformed Ta

Abstract Non-destructive evaluation of plastically deformed metals, particularly diffraction line profile analysis (DLPA), is valuable both to estimate dislocation densities and arrangements and to validate microstructure-aware constitutive models. To date, the interpretation of whole line diffraction profiles relies on the use of semi-analytical models such as the extended convolutional multiple whole profile (eCMWP) method. This study introduces and validates two data-driven DLPA models to extract dislocation densities from experimentally gathered whole line diffraction profiles. Using two distinct virtual diffraction models accounting for both strain and instrument induced broadening, a database of virtual diffraction whole line profiles of Ta single crystals is generated using discrete dislocation dynamics. The databases are mined to create Gaussian process regression-based surrogate models, allowing dislocation densities to be extracted from experimental profiles. The method is validated against 11 experimentally gathered whole line diffraction profiles from plastically deformed Ta polycrystals. The newly proposed model predicts dislocation densities consistent with estimates from eCMWP. Advantageously, this data driven LPA model can distinguish broadening originating from the instrument and from the dislocation content even at low dislocation densities. Finally, the data-driven model is used to explore the effect of heterogeneous dislocation densities in microstructures containing grains, which may lead to more accurate data-driven predictions of dislocation density in plastically deformed polycrystals.

36 MATERIALS SCIENCE↗