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The dendron-shaped macromolecules AB n crystallize into well-ordered pyramid-like structures from mixed solvents, which is on the contrary to spherical motifs with curved structures in bulk.
Abstract Refractory high-entropy alloys (RHEAs) are designed for high elevated-temperature strength, with both edge and screw dislocations playing an important role for plastic deformation. However, they can also display a significant energetic driving force for chemical short-range ordering (SRO). Here, we investigate mechanisms underlying the mobilities of screw and edge dislocations in the body-centered cubic MoNbTaW RHEA over a wide temperature range using extensive molecular dynamics simulations based on a highly-accurate machine-learning interatomic potential. Further, we specifically evaluate how these mechanisms are affected by the presence of SRO. The mobility of edge dislocations is found to be enhanced by the presence of SRO, whereas the rate of double-kink nucleation in the motion of screw dislocations is reduced, although this influence of SRO appears to be attenuated at increasing temperature. Independent of the presence of SRO, a cross-slip locking mechanism is observed for the motion of screws, which provides for extra strengthening for refractory high-entropy alloy system.
The phase-field dislocation dynamics (PFDD) model is extended to simulate cross-slip in body-centered cubic materials. The model makes use of a non-orthogonal, body-centered cubic numerical grid such that all calculable points lie on dislocation glide planes. We demonstrate that the advanced PFDD model predicts a low-energy, non-planar core for screw dislocations and a planar core for edge dislocations. These core differences result in screw-edge character dependence in the critical stress to initiate glide and dislocation drag coefficients. Finally, we show that this model can be used to study the propensity of screw dislocations to cross-slip around or transmit through a coherent, crystallographic obstacle, depending on obstacle strength.
Here, the mass transport properties along dislocation cores in hcp 4 He are revisited by considering two types of edge dislocations as well as a screw dislocation, using a fully correlated quantum simulation approach. Specifically, we employ the zero-temperature path-integral ground state (PIGS) method together with ergodic sampling of the permutation space to investigate the fundamental dislocation core structures and their off-diagonal long-range order properties. It is found that the Bose-Einstein condensate fraction of such defective 4 He systems is practically null (≤ 10 –6 ), just as in the bulk defect-free crystal. These results provide compelling evidence for the absence of intrinsic superfluidity in dislocation cores in hcp 4 He and challenge the superfluid dislocation-network interpretation of the mass-flux-experiment observations, calling for further experimental investigation.
Dislocation, playing a crucial role in the plastic deformation of metals, can be significantly affected by introducing solute elements. Hydrogen (H) embrittlement is one such example, while the underlying mechanism for H affected dislocation structural stability and mobility remains unclear and the role of H has been controversial. Here, using first-principles calculations, we demonstrate that the effect of H on screw dislocation in bcc tungsten (W) is H concentration-dependent, signified by a H-induced transition of SD core structure. At low concentrations of H segregation, dislocation maintains the intrinsic easy-core structure, and H atoms are attached to the “periphery” of dislocation to enhance dislocation motion. In contrast, at high H concentrations, dislocation transforms into a hard-core, metal hydride-like structure, as H atoms become the “body” of dislocation to significantly reduce the dislocation mobility in W. Further, such local easy-to-hard transition can also be induced by the other solutes, including helium, carbon, nitrogen and oxygen. Our work sheds new light on the H-dislocation interactions in bcc W, having broad implications in the interstitial solute-related phenomena.
Refractory multiprincipal element alloys (MPEAs) are promising material candidates for high-temperature, high-strength applications. However, their deformation mechanisms, particularly at the dislocation scale, are unusual compared to those of conventional alloys, making it challenging to understand the origin of their high strength. Here, using an atomistically informed phase-field dislocation dynamics model, we study transitions in the morphology and critical stresses of long gliding screw dislocations over extended distances in a refractory MPEA. The model MPEA crystal accounts for the atomic-scale fluctuations in chemical composition across the glide planes via spatially correlated lattice energies and for the differences in glide resistances between screw and edge dislocations of unit length. Here, we show that the dislocation moves in a stop-start motion, alternating between wavy morphology in free flight and nearly recovered straight screw orientation in full arrest. The periods of wavy glide are due to variable kink-pair formation and migration rates along the length, where portions with higher rates glide more quickly. The critical stress to initiate motion corresponds to the stress required to form and migrate a kink pair at the weakest region along the length of the dislocation. Heterogeneity in lattice energy leads to variability in the local stress-strain response and to a strain hardening-like response, in which the critical stress to reactivate glide increases with glide distance. Statistical assessment of hundreds of realizations of dislocations indicates that the amount of hardening directly scales with the dispersion in underlying lattice energy.
To accurately predict the mechanical response of materials, especially at high strain rates, it is important to account for dislocation velocities in these regimes. Under these extreme conditions, it has been hypothesized that dislocations can move faster than the speed of sound. However, the presence of such dislocations remains elusive due to challenges associated with measuring these experimentally. In this work, molecular dynamics simulations were used to investigate the dislocation velocities for the basal edge, basal screw, prismatic edge, and prismatic screw dislocations in Mg in the sub-, trans-, and supersonic regimes. Also, our results show that only prismatic edge dislocations achieve supersonic velocities. Furthermore, this work demonstrates that the discrepancy between the theoretical limiting velocity and the MD results for Mg is due to its sensitivity to large hydrostatic stress around the dislocation core, which was not the case for fcc metals such as Cu.
A multi-scale study was carried out to quantify the effect of interstitial hydrogen concentration on plasticity in $α$-Fe. Here, in this work, the influence of hydrogen on the screw dislocation glide behavior was examined across several length-scales. The insights obtained were integrated to provide an accurate continuum description for the effect of hydrogen on the dislocation based plasticity in polycrystalline $α$-Fe. At the outset of this work, a new Fe—H interatomic potential was formulated that enhanced the atomistic estimation of the variation in dislocation glide behavior in presence of hydrogen. Next, the dislocation core reconstruction observed due to the addition of hydrogen using atomistic simulations was validated with the help of large-scale DFT calculations based on the DFT-FE framework. Several atomistic simulations were carried out to comprehensively quantify the effect of hydrogen on the non-Schmid behavior exhibited during the dislocation glide in $α$-Fe. Finally, crystal plasticity simulations were carried out to understand the effect of hydrogen on the meso-scale deformation behavior of polycrystalline $α$-Fe.
The microstructural evolution at and near preexisting grain boundaries (GBs) and dislocations in materials under high radiation doses is still poorly understood. In this work, we use the creation relaxation algorithm (CRA) developed for atomistic modeling of high-dose irradiation in bulk materials to probe the athermal limit of saturation of GB and dislocation core regions under irradiation in fcc Ni. We find that, upon continuously subjecting a single dislocation or GB to Frenkel pair creation in the athermal limit, a local steady-state disordered defect structure is reached with excess properties that fluctuate around constant values. Case studies are given for a straight screw dislocation which elongates into a helix under irradiation and several types of low- and high-angle GBs, which exhibit coupled responses such as absorption of extrinsic dislocations, roughening, and migration. A positive correlation is found between the initial GB energy and the local steady-state GB energy under irradiation across a wide variety of GB types. Metastable GB structures with similar density in the defect core region but different initial configurations are found to converge to the same limiting structure under CRA. The mechanical responses of pristine and irradiated dislocations and GB structures are compared under an applied shear stress. Irradiated screw and edge dislocations are found to exhibit a hardening response, migrating at larger flow stresses than their pristine counterparts. Mobile GBs are found to exhibit softening or hardening responses depending on GB character. Although some GBs recover their initial pristine structures upon migration outside of the radiation zone, many GBs sustain different flow stresses corresponding to altered mobile core structures.
The single-phase equiatomic CoCrFeMnNi alloy is a random solid solution of five elements on the face-centered cubic lattice, whose pure constituents crystallize in very different structures and exhibit diverse magnetic properties. Due to the randomness of the alloy, 80% of nearest neighbor bonds are between unlike elements and thus the details of bonding in pure structures are less important. The elastic moduli of this alloy give rise to small Cauchy pressure C 12 - C 44 , which suggests that the dominant part of bonding may be described by a simple pair potential. We test this hypothesis by developing a long-range Lennard-Jones potential in which the equilibrium crystal structures of pure constituents are taken as reference. The standard mixing rules for regular solutions are then adopted to obtain parameters for bonds between unlike elements in the quinary system. The transferability of this potential to quaternary CoCrFeNi, ternary CoCrNi, and binary FeNi alloys is investigated and the predictions compared with experiments and density functional theory calculations. By sampling over a large number of random configurations, we investigate the effect of compositional randomness on misfit volumes, energies of point defects and stacking faults, and the dislocation friction stresses experienced by moving edge and screw dislocations.
This project was awarded for an initial period of three years, followed by a no-cost extension for one year and a funded one-year renewal. During the first four years, the project focused on investigating the role of dislocation reactions and dislocation correlation in dislocation patterning in FCC metals. During the fifth year, the scope of research was expanded to investigate the effects of composition inhomogeneity on the mesoscale plastic response of Body-Centered Cubic (BCC) alloys. In addition to its impact on metal hardening during deformation, dislocation patterning provides the microstructure information required to understand phenomena like fracture and recrystallization in metals. The Continuum Dislocation Dynamics (CDD) framework was the methodology used during the first four years, followed by the use of Discrete Dislocation Dynamics (DDD) during the fifth year. CDD is a density-based formalism of dislocation dynamics in which the plastic deformation of crystals is predicted together with the mesoscale dislocation patterns by tracking the space-time evolution of dislocations as driven by the applied stress, short-range and long-range interactions of dislocations, and cross slip. CDD is a crystal mechanics approach in which the plastic constitutive part is replaced with the equations of dislocation dynamics, which is driven by the internal stress via a mobility laws, while the evolution of the density gives the eigenstrain required to update the internal stress itself. The governing equations are thus those of crystal mechanics cast as an eigenstrain problem and those of dislocation transport and reactions. Our investigations during the first four years were driven by the hypothesis that that dislocation patterning is triggered by spatiotemporal dislocation density and internal stress fluctuations, and that such fluctuations influence the collective dislocation dynamic through their effects on the short-range reaction rates and the collective dislocation mobility. This hypothesis was tested by modeling the influence of the dislocation reactions and dislocation correlations on collective dislocation dynamics. The main research components during the first four years were: 1) Reformulation of the CDD framework to integrate the dislocation correlations and dislocation reactions. 2) Simulation of the dislocation correlations and quantifying their contribution to the long-range stress of complex dislocation systems. 3) Computational implementation of the updated CDD model for FCC single crystals and development of an efficient CDD code. 4) Investigation of dislocation patterning in FCC crystals based on the updated CDD model. Some key findings from these investigations were: 1) The patterning of dislocations is initiated by cross slip and internal stress fluctuations, and the refinement of the pattern results from junction formation. 2) Patterning is more prominent under high stress. 3) The correlation stress was found to be a significant part of the mean field stress in continuum representations of dislocation dynamics. During the last year of the project, we have established a method for performing dislocation dynamics in inhomogeneous alloys and demonstrated the impact of composition inhomogeneity on the characteristics of initial yielding and dislocation character in BCC alloys. We also tested this method using an irradiated ferritic alloy in which the composition and dislocation loops effects are both present. In doing so, we have considered two aspects of the role of inhomogeneity, the creation of internal coherency stress due to the dependence of the lattice parameter on the local composition, and the dependence of the dislocation mobility on the local composition. These two aspects resulted in an unexpected behavior of the dislocation system, and, in turn, the yielding behavior of BCC alloys. Key findings include: 1) The composition inhomogeneity in BCC alloys alters the well-known role of screw dislocations by forcing a level of waviness on the average dislocation character, thus destroying the screw character dominance in the yielding observed in pure or homogeneous BCC metals. 2) In the case of irradiated alloys, while composition inhomogeneity by itself and dislocation loops by themselves result in some hardening, the superposition of the two mechanisms does not result in the sum of the two contributions via any known rule. The latter result contradicts the classical works related hardening via multiple mechanisms, which state that various hardening mechanisms can be added linearly or using some Pythagorean additive rule. We were able to rationalize this unexpected result by a closer loop at the origin of the hardening mechanisms themselves, which both involved long-range elastic interactions with dislocations. We reached the conclusion that the hardening resulting from the total stress associated with these two mechanisms (current work) differs from the sum of the effects of the individual stress fields (classical literature). We have also found a major flaw in the classical theory of spinodal hardening. The latter theory never considered the impact of composition undulation on the solute hardening. We have built a new general theory accounting for the effect of solute friction together with the composition undulations on the dislocation configuration at Critical Resolved Shear Stress (CRSS), which is yielding a new definition of the spinodal hardening and new different results. This work is the first to recognize the lack of the role of solute in spinodal hardening theory of 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
Figures in this slide show the drag coefficient from phonon wind for edge and screw dislocations in aluminum and copper as a function of velocity and temperature. Velocity βt is given in units of transverse sound speed at room T.
Over the past decade, a new class of unconventional alloys, where several constitutive elements are presented in close to equal concentrations, is considered as promising structural materials in many applications. Properties and behavior of many concentrated solid solution alloys (CSSAs) under different conditions, including mechanical loading, differs from that of conventional alloys and has been the subject of intensive studies by different techniques. A key feature of these materials is that there is no clear distinction between solute and solvent species of atoms, which is the conventional approach to considering dislocation motion in alloys. To understand this regime, we have recently reported on the glide of a screw dislocation glide in a simple equiatomic NiFe alloy and reported the two-mode character. At low applied stress, the dislocation motion is similar to a glide through a field of obstacles. In this work, we report the results of a detailed study on the nature of these internal obstacles. We demonstrate that these are not conventional localized “obstacles” but is the result of significantly different energies of instantaneous dislocation configurations over the alloy bulk. The strong pinning positions are associated with composition changes in the partial dislocation cores, while observing no significant composition changes along the stacking faults. Local energies can vary significantly, as demonstrated using simulations of short-periodicity dislocation lines. Therefore, the critical stress to move a dislocation under such conditions is not a constant Peierls stress but represents a wide spectrum of barriers between different non-straight valleys that the dislocation line accommodates in the bulk at particular stress/strain conditions.
Energy efficiency is motivating the search for new high-temperature (high-T) metals. Some new body-centered-cubic (BCC) random multicomponent “high-entropy alloys (HEAs)” based on refractory elements (Cr-Mo-Nb-Ta-V-W-Hf-Ti-Zr) possess exceptional strengths at high temperatures but the physical origins of this outstanding behavior are not known. Here we show, using integrated in-situ neutron-diffraction (ND), high-resolution transmission electron microscopy (HRTEM), and recent theory, that the high strength and strength retention of a NbTaTiV alloy and a high-strength/low-density CrMoNbV alloy are attributable to edge dislocations. This finding is surprising because plastic flows in BCC elemental metals and dilute alloys are generally controlled by screw dislocations. We use the insight and theory to perform a computationally-guided search over 10 7 BCC HEAs and identify over 10 6 possible ultra-strong high-T alloy compositions for future exploration.
Nonlinear ultrasonic parameters are highly sensitive to microstructural features that affect macroscale material behavior, providing a nondestructive means to characterize their evolution. Although dislocations are known to be a strong source of acoustic nonlinearity, establishing quantitative links between the acoustic nonlinearity parameter (β), measured via Second Harmonic Generation, and dislocation morphology—such as dislocation length and density—remains an open challenge. This work advances the numerical modeling of dislocation–β relationships using 3D dislocation dynamics (DD) simulations in two approaches: a “static” method computing strain and stress fields from dislocation configurations in the absence of external loading, and a “quasi-static” method to estimate β from the curvature of dislocation lines under applied load. First, the static method is combined with finite element analysis to investigate a recent assertion that heterogeneous initial strain fields can induce higher harmonic generation in a linear elastic medium; the present results do not corroborate this outcome. Then, the quasi-static method is applied to multiple-dislocation scenarios through parametric studies, revealing behaviors not predicted by analytical models, such as the competing interactions of edge and screw dislocations and the significant influence of applied stress on β. Finally, the simulations are used to model SHG experimental results and validate the hypothesis that β can decrease during plastic deformation, despite increasing dislocation density. As the DD code used here is open-source, it provides a practical platform for future investigation into microstructure–β relationships important to the interpretation of SHG results.
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.
Here, in this work, we investigate the dislocation-impurity interaction energies and their profiles for various 3d elements —V, Cr, Mn, Cu, Ni, and Co —in and around 1/2 $\langle111\rangle$ screw dislocations in α -Fe using ab initio methods. We consider the ferromagnetic and paramagnetic states, with the latter being modeled through both the disordered local moment model and a spin-wave approach. Our findings reveal that (1) magnetic effects are large compared to size misfit effects of substitutional impurities, and (2) dislocation-impurity interactions are dependent on the magnetic state of the matrix and thermal lattice expansion. In particular, Cu changes from core-attractive in the ferromagnetic state to repulsive in the paramagnetic state.