Dislocation Core Structure Research Articles

Solute segregation to near-coincidence site lattice grain boundaries in α-iron

Coincidence site lattice grain-boundaries (CSL-GBs) are commonly observed in steel alloys and play a major role in controlling their mechanical properties. In practice, CSL-GBs do experience deviations from their ideal configurations, where the deviation from the ideal symmetry plane can be modeled as sub-boundary network of misfit dislocations. In this study, segregation energy of hydrogen and carbon atoms to ∑3 (111), ∑3 (112), and ∑5 (310) CSL-GBs and their deviated configurations within Brandon’s criterion range in α-iron is studied using molecular statics simulations. Thereafter, through utilizing Rice–Wang model the change of the cohesive GB energy is computed and correlated to misfit dislocations structures. The results show significant correlation between the crystallographic aspects of the GBs and the hydrogen/carbon embrittlement/strengthening effect. While the ideal CSL-GBs consistently show the highest resistance to hydrogen enhanced decohesion effect, the deviations from the ideal configurations accompanied by misfit dislocation core structures along the boundaries show high solute carbon strengthening.

Atomic modeling of the segregation of vacancies on [formula omitted] dislocations in α-iron by diffusive molecular dynamics simulations

The interaction between dislocations and vacancies at finite temperature is crucial for many physical properties and phenomena in materials, such as vacancy segregation, strengthening effect, dislocation motion, and crystal plasticity. Conventional dislocation-vacancy interaction models use approximations based on elasticity theory and assumption that transition state energy can be deduced from the binding energy of the vacancies. The long-term vacancy diffusion near dislocation and the change of dislocation core induced by vacancy segregation are still difficult to capture. In this paper, we present the theoretical study on diffusion and segregation properties of vacancies near 111 edge or screw dislocation on slip planes of {110}, {112} and {123} in bcc iron. The calculations are performed with the distribution of vacancy concentration and dislocation-vacancy interaction energy as a function of distance from dislocation core using diffusive molecular dynamics (DMD). Meanwhile, the accompanying effects of the interaction on vacancy segregation, dislocation motion, and crystal plasticity are discussed. The vacancy diffusion near dislocation is a process highly anisotropic and inter-correlated towards equilibrium. The interaction of vacancies with the tensile stress field of edge dislocations is numerically stronger than that with the pure shear stress field of screw dislocations. The Peierls stress are calculated to reflect the effect of the vacancy segregation on dislocation motion. The slip planes of 111 dislocations have a significant influence on this interaction. With the slip planes changing from {110} to {123} to {112}, the absorption intensity of dislocation to vacancy and the ranges of the “effective interaction region” of both edge and screw dislocation decrease while the ranges of “absorption region” increases gradually. In addition, vacancy segregation produces a regulatory mechanism for the structure of dislocation core and promotes the transformation of dislocations on different slip planes to a more stable intermediate structure. This study visually presents the evolution of vacancies near dislocation, providing fundamental insights on the vacancy transport mechanisms which are essential for understanding dislocation-vacancy interaction, dislocation motion and plasticity of metallic materials.

Screw dislocation core structure in the paramagnetic state of bcc iron from first-principles calculations

Iron-based alloys are widely used as structural components in engineering applications. This calls for a fundamental understanding of their mechanical properties, including those of pure iron. Under operational temperatures the mechanical and magnetic properties will differ from those of ferromagnetic body-centered-cubic iron at 0 K. In this theoretical work we study the effect of disordered magnetism on the screw dislocation core structure and compare with results for the ordered ferromagnetic case. Dislocation cores control some local properties such as the choice of glide plane and the associated dislocation mobility. Changes in the magnetic state can lead to modifications in the structure of the core and affect dislocation mobility. In particular, we focus on the core properties of the $\frac{1}{2}\ensuremath{\langle}111\ensuremath{\rangle}$ screw dislocation in the paramagnetic state. Using the noncollinear disordered local moment approximation to address paramagnetism, we perform structural relaxations within density functional theory. We obtain the dislocation core structure for the easy and hard cores in the paramagnetic state, and compare them with their ferromagnetic counterparts. By averaging the energy of several disordered magnetic configurations, we obtain an energy difference between the easy- and hard-core configurations, with a lower, but statistically close, value than the one reported for the ferromagnetic case. The magnetic moment and atomic volume at the dislocation core differ between paramagnetic and ferromagnetic states, with possible consequences on the temperature dependence of defect-dislocation interactions.

Configurational thermodynamics of a 1/2〈111〉 screw dislocation core in Mo–W solid solutions using cluster expansion

In this work, we have developed a methodology to obtain an ab initio cluster expansion of a system containing a dislocation and studied the effect of configurational disorder on the 1/2〈111〉 screw dislocation core structure in disordered Mo1−xWx alloys. Dislocation cores control the selection of glide planes, cross slip, and dislocation nucleation. Configurational disorders in alloys can impact the dislocation core structure and affect dislocation mobility. For our calculations, we have used a quadrupolar periodic array of screw dislocation dipoles and obtained the relaxed structures and energies using density functional theory. We have obtained the dislocation core structure as a function of composition and the interaction energies of solutes with the dislocation as a function of position with respect to the core. With these energies, we performed mean-field calculations to assess segregation toward the core. Finally, with the calculated energies of 1848 alloy configurations with different compositions, we performed a first principle cluster expansion of the configurational energetics of Mo1−xWx solid solutions containing dislocations.

Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space

In this paper, we perform mathematical validation of the Peierls--Nabarro (PN) models, which are multiscale models of dislocations that incorporate the detailed dislocation core structure. We focus on the static and dynamic PN models of an edge dislocation. In a PN model, the total energy includes the elastic energy in the two half-space continua and a nonlinear potential energy across the slip plane, which is always infinite. We rigorously establish the relationship between the PN model in the full space and the reduced problem on the slip plane in terms of both governing equations and energy variations. The shear displacement jump is determined only by the reduced problem on the slip plane while the displacement fields in the two half spaces are determined by linear elasticity. We establish the existence and sharp regularities of classical solutions in Hilbert space. For both the reduced problem and the full PN model, we prove that a static solution is a global minimizer in perturbed sense. We also show that there is a unique classical, global in time solution of the dynamic PN model.

Neural network atomic potential to investigate the dislocation dynamics in bcc iron

To design the mechanical strength of body-centered-cubic (bcc) iron, clarifying the dislocation dynamics is very important. Using systematically constructed reference data based on density functional theory (DFT) calculations, we construct an atomic artificial neural network (ANN) potential to investigate the dislocation dynamics in bcc iron with the accuracy of DFT calculations. The bulk properties and defect formation energies predicted by the constructed ANN potential are in good agreement with the reference DFT calculations. The ${a}_{0}/2\ensuremath{\langle}111\ensuremath{\rangle}{110}$ screw dislocation core structure predicted by the ANN potential is compact and nondegenerate. The Peierls barrier predicted by the ANN potential is 35.3 meV per length of the Burgers vector. These results are consistent with the DFT results. Furthermore, not only the Peierls barrier, but also the two-dimensional energy profile of the screw dislocation core position predicted by the ANN potential are in excellent agreement with the DFT results. These results clearly demonstrate the reproducibility and transferability of the constructed ANN potential for investigating dislocation dynamics with the accuracy of the DFT. Combined with advanced atomistic techniques, the ANN potential will be highly useful for investigating the dislocation dynamics in bcc iron at finite temperatures.

Modification of the Peierls–Nabarro model for misfit dislocation**Project supported by the National Natural Science Foundation of China (Grant No. 11874093).

For a misfit dislocation, the balance equations satisfied by the displacement fields are modified, and an extra term proportional to the second-order derivative appears in the resulting misfit equation compared with the equation derived by Yao et al. This second-order derivative describes the lattice discreteness effect that arises from the surface effect. The core structure of a misfit dislocation and the change in interfacial spacing that it induces are investigated theoretically in the framework of an improved Peierls–Nabarro equation in which the effect of discreteness is fully taken into account. As an application, the structure of the misfit dislocation for a honeycomb structure in a two-dimensional heterostructure is presented.

Generalized Peierls–Nabarro model for studying misfit dislocation in a BN/AlN heterostructure

Based on the solution of the balance problem for a semi-infinite lattice, we propose a generalization of the Peierls–Nabarro equation that is applicable to an interfacial misfit dislocation array. We obtain a relationship between the mass center displacement and the relative displacement. Under the assumption that the change in the interfacial layer spacing is sufficiently small that it can be ignored, this relationship allows us to reveal the core structure of the misfit dislocation and determine the interfacial atomic coordinates. As an example, a boron nitride/aluminum nitride heterostructure with a large lattice mismatch is studied using the equation. We find a good match between the theoretically predicted interfacial atomic configuration and that obtained from a first-principles calculation. Furthermore, the adhesion energy of the heterostructure is also evaluated, and the theoretical result coincides with that obtained from first-principles simulations.

Computer simulations of hydrostatic pressure influence on screw <a> dislocation slip in Mg

Atomistic modeling of hydrostatic pressure influence on critical resolved shear stress was performed for glide of screw <a> dislocation in magnesium. It was found that application of pressure can change the resolved critical stress for basal and prismatic slip. The effect is dependent on dislocation core structure. It can be connected to the pressure dependence transient dilatation of the dislocation core.

An iterative scheme for the generalized Peierls–Nabarro model based on the inverse Hilbert transform

A new and efficient semi-analytical iterative scheme is proposed in this work for solving the generalized Peierls–Nabarro model. The numerical method developed here exploits certain basic properties of the Hilbert transform to achieve a reduction of the nonlocal and nonlinear equations characterizing the generalized Peierls–Nabarro model to a local model which is then solved using a fixed point iteration scheme. This is in sharp contrast to existing schemes for solving the generalized Peierls–Nabarro model like the semi-discrete variational Peierls–Nabarro model, or methods involving the fitting of the slip distribution to a linear combination of predefined elementary slip distributions, all of which involve the solution of nonlinear and nonlocal equations using gradient-based optimization tools. The key idea behind the proposed technique is to transform the nonlocal Peierls–Nabarro model into an equivalent local model, called the inverse Peierls–Nabarro model. From a computational viewpoint, the resulting local model is attractive since it can be solved without recourse to any gradient based algorithms; combined with appropriate acceleration schemes, the proposed algorithm provides a computationally expedient alternative to solving the generalized Peierls–Nabarro model. Further, the fixed point iterative scheme developed here easily lends itself to parallelization, unlike iterative methods for the fully nonlocal and nonlinear models currently in use. The proposed numerical scheme is validated both with simple examples involving the 1D Peierls–Nabarro model corresponding to a sinusoidal stacking fault energy, and with realistic examples involving calculations of the core structure of both edge and screw dislocations on the close-packed [Formula: see text] planes in Aluminum. An approximate technique to incorporate external stresses within the framework of the proposed iterative scheme is also discussed with applications to the equilibration of a dislocation dipole. Finally, the advantages, limitations and avenues for future extension of the proposed method are discussed.

Molecular dynamics simulations of extended defects and their evolution in 3C–SiC by different potentials

An important issue in the technology of cubic SiC (3C–SiC) material for electronic device applications is to understand the behavior of extended defects such as partial dislocation complexes and stacking faults (SFs). Atomistic simulations using molecular dynamics (MD) are an efficient tool to tackle this issue for large systems at comparatively low computation cost. At this, proper choice of MD potential is imperative to ensure the reliability of the simulation predictions. In this work, we compare the evolution of extended defects in 3C–SiC obtained by MD simulations with Tersoff, analytical bond order, and Vashishta potentials. Key aspects of this evolution are considered including the dissociation of 60° perfect dislocations in pairs of 30° and 90° partials as well as the dependence of the partial dislocation velocity on the Burgers vector and the atomic composition of core. Tersoff potential has been found to be less appropriate in describing the dislocation behavior in 3C–SiC as compared to two other potentials, which in their turn provide qualitatively equivalent predictions. The Vashishta potential predicts much faster defect dynamics than the analytical bond order potential (ABOP). It can be applied therefore to describe the large-scale evolution of the dislocation systems and SFs. On the other hand, ABOP is more precise in predicting local atom arrangements and reconstructions of the dislocation core structures. In this respect, synergetic use of ABOP and Vashishta potential is suggested for the MD simulation study of the properties and evolution of extended defects in the 3C–SiC.

Studying hydrogen effect on the core structure and mobility of dislocation in nickel by atomistically-informed generalized Peierls–Nabarro model

Hydrogen (H) atoms in the metallic crystalline lattice interact with the pre-existing dislocations and then remarkably affect the plastic deformation of metals. Thereby quantitatively characterizing the H-dislocation interaction is of great importance for understanding H-induced plasticity and failure. Most of the previous studies have focused on the long-range interaction between hydrogen and dislocation, but rarely considered the short-range interaction, especially the hydrogen effect on the dislocation core structure. Here, with the aid of the H-affected γ-surface calculated from atomistic modeling, an atomistically-informed generalized Peierls–Nabarro model is employed to study the hydrogen effect on the core structure of dislocation, the recombination energy of the extended screw dislocation, and the Peierls stress in nickel. Our results show that, on the one hand, hydrogen can decrease the stable stacking fault energy, leading to the increase of the stacking fault width for both extended edge and screw dislocations. Consequently, the recombination energy of extended screw dislocation is increased, indicating that hydrogen can suppress the cross-slip of screw dislocation and facilitate the slip planarity observed frequently in experiments. On the other hand, hydrogen can increase the unstable stacking fault energy, implying that hydrogen can inhibit the nucleation of partial dislocations. Moreover, hydrogen in the dislocation core increases the Peierls stress and thus increases dislocation slip resistance. Finally, quantitative relations between the Peierls stress and hydrogen concentration are given. These results are of great significance for understanding the H-affected dislocation plasticity mechanisms, and can be used for quantifying the hydrogen effect on dislocation dynamics.

Modeling dislocations with arbitrary character angle in face-centered cubic transition metals using the phase-field dislocation dynamics method with full anisotropic elasticity

In this study, we present a phase-field dislocation dynamics (PFDD) method that includes full anisotropic elasticity. We apply it to calculate the equilibrium core structures of dislocations with arbitrary character angle in eight face-centered cubic transition metals. The calculations investigate the effects of the gradient energy density in the total energy density and the choice of the averaging scheme to determine the isotropic equivalent elastic moduli (i.e., Voigt, Reuss, and Hill). We show that the addition of the gradient energy term increases the intrinsic stacking fault (ISF) widths for the edge and screw dislocations in most of the metals studied here, but decreases the ISF widths for the edge dislocations in four metals: Ir, Ni, Pd, and Rh. The analysis indicates that among the three isotropic averaging schemes, the Voigt isotropic equivalent modulus best predicts the ISF widths of the edge dislocations and the Reuss scheme for the ISF widths of the screw dislocations, compared to the full elastic anisotropy. Finally, a critical character angle ( ∼ 60∘) is revealed, at which the PFDD simulations with full elastic anisotropy and those with the isotropic Hill average predict the same ISF width. Our work advances the basic understanding of the elastic anisotropic effects on the equilibrium dislocation core structures and can help guide the choice of isotropic averaged moduli.

Synergetic effects of solute and strain in biocompatible Zn-based and Mg-based alloys

Zn-based and Mg-based alloys have been considered highly promising biodegradable materials for cardiovascular stent applications due to their excellent biocompatibility and moderate in vitro degradation rates. However, their strength is too poor for use in cardiovascular stents. The strength of these metals can be related to the sizes of the dislocation cores and the threshold stresses needed to activate slip, i.e., the Peierls stress. Using density functional theory (DFT) and an ab initio-informed semi-discrete Peierls–Nabarro model, we investigate the coupled effect of the solute element and mechanical straining on the stacking fault energy, basal dislocation core structures and Peierls stresses in both Zn-based and Mg-based alloys. We consider several biocompatible solute elements, Li, Al, Mn, Fe, Cu, Mg and Zn, in the same atomic concentrations. The combined analysis here suggests some elements, like Fe, can potentially enhance strength in both Zn-based and Mg-based alloys, while other elements, like Li, can lead to opposing effects in Zn and Mg. We show that the effect of solute strengthening and longitudinal straining on SFEs is much stronger for the Zn-based alloys than for the Mg-based alloys. DFT investigations on electronic structure and bond lengths reveal a coupled chemical-mechanical effect of solute and strain on electronic polarization, charge transfer, and bonding strength, which can explain the weak mechanical effect on Zn-based alloys and the variable strengthening effect among these solutes. These findings can provide critical information needed in solute selection in Zn-based and Mg-based alloy design for biomedical applications.

Atomistic simulations of hydrogen and carbon segregation in α-iron grain boundaries

During material deformation, the coincidence site lattice (CSL) grain boundaries (GBs) are exhibiting deviations from their ideal lattice structure. Hence, this will change the atomic structural integrity by generating full and partial dislocation joints on the ideal CSL boundaries. In this analysis, the ideal Σ5 (310) GB structures and its angular deviations in α-iron within the limit of Brandon criterion, in order to conserve the dislocation core structure, will be studied in depth using molecular statics simulations. Firstly, the hydrogen and carbon atoms energetics within the GBs core structure and their free surfaces are calculated. Then Rice-Wang cohesive structure model is applied to compute the embrittlement/strengthening effect of the solute atoms on the ideal and deviated GB structures. Hydrogen showed significant embrittlement and degradation in the mechanical properties of α-iron, while carbon showed a desirable atomic strengthening effect.

Ab initio-informed phase-field modeling of dislocation core structures in equal-molar CoNiRu multi-principal element alloys

In this work, selecting the equal-molar CoNiRu multi-principal element alloy (MPEA) as a model material, we study dislocation core structures starting from first principles. We begin by sifting through all possible configurations to find those corresponding to elastic stability and energetically favored face-centered cubic (fcc) phases and, then, for these configurations, employ a phase field-based model to predict the extent of dislocations lying within them. The main findings are that for the fcc phase, (i) large variations in atomic configuration for the same chemical composition can cause significant changes in the generalized stacking fault energy surface and (ii) the dispersion in defect fault energies are chiefly responsible for substantial variations in the intrinsic stacking fault (ISF) widths of screw and edge dislocations. For instance, positive the ISF energy can vary by 10 times, with the lower values correlated with entirely Ni and Ru atoms and higher values with only Co and Ru atoms across the slip plane. Variations in lattice parameter and stiffness tensor accompany local differences in atomic configuration are also taken into account but shown to play a lesser role. We find that the dislocation can experience profound variations (3–7-fold changes) in its associated ISF width along its line, with the screw dislocation experiencing a greater variation than the edge dislocation (6.02–43.22 Å for the screw dislocation, and 19.6–62.62 Å for the edge dislocation). We envision that the ab initio-informed phase-field modeling method developed here can be readily adapted to MPEAs with other chemical compositions.

AADIS: An atomistic analyzer for dislocation character and distribution

In atomistic simulations of crystal plasticity, the characterization and representation of the dislocation core structure play a significant role for the understanding of mechanical behavior for crystalline materials. For this purpose, we present an accurate and convenient command-line tool: Atomistic Analyzer for DISlocations character and distribution (AADIS) for the post-analysis of the defective structures observed in various atomistic simulations. The program has implemented the displacement vector analysis (DVA), the atomic strain tensor analysis (STA), the differential displacement analysis (DDA), the slip vector analysis (SVA), the interplanar disregistry analysis (IDA) and the Nye tensor analysis (NTA). Among these functionalities, a specific implementation of the program includes the extension of the NTA method and the characterization of misfit dislocations at bicrystal interfaces by various methods. The automatic feature provides a high throughput solution to the specific atomistic analysis on a batch of atomic configurations. Furthermore, several critical remarks on the advantages and shortcomings of each analysis method are revealed and discussed comprehensively, which provides guidance for their applications in atomistic simulations. Program summaryProgram title: AADISProgram files doi:http://dx.doi.org/10.17632/hgc34yd3m3.1Licensing provisions: GNU General Public License version 3Programming language: C++Nature of problem: To characterize and visualize the core structure of dislocations in atomic configurations for molecular dynamics (MD) simulations, including several vector and tensor analysis such as the Nye tensor [1].Solution method: Read a simulation dump file into the memory and then get it analyzed. Afterwards, the generated property will be printed into a new output dump file, which can be visualized by various free or commercial visualization software.

Determination of the dislocation-based mechanism(s) responsible for the anomalous ductility of a class of B2 intermetallic alloys

A class of stoichiometric, ordered MR alloys (where M denotes a metal and R either a rare earth or group IV refractory metal) with B2 (CsCl) crystal structure, were discovered to possess anomalous ductility by researchers at Ames Laboratory in the early 2000’s. Despite active research on the topic for over 15 years, a holistic explanation for the anomalous ductility of these metal alloys has not yet been accepted by the scientific community. The reason for this appears to be a failure to account for all relevant length scales. Researchers either focus on the atomistic length scale relevant to dislocation core structures, the microscopic length scale of dislocations and dislocation ensembles, the mesoscopic length scale of grains and their interactions, or the macroscopic scale of mechanical testing samples with millimetre dimensions or larger. Focused studies at each of these length scales have provided essential, but insufficient information to provide a complete answer to the question. The insight provided by in-situ diffraction studies, along with crystal plasticity modelling as an interpretive tool, and a novel grain-by-grain line profile analysis technique for assessing dislocation densities in polycrystals is highlighted. In addition to the primary <100> dislocations, which are most easily activated in all of these anomalous MR alloys, the results show that dislocations with large Burgers vectors (e.g., <110> and <111>) are present in large numbers beyond a transition in the strain hardening response. The motion of these large Burgers vector dislocations is experimentally observed to occur at stress levels consistent with atomistic modelling predictions of the Peierls resistance and simultaneously provides a satisfying explanation for the anomalous ductility and other experimental results.

A comparison of different continuum approaches in modeling mixed-type dislocations in Al

Mixed-type dislocations are prevalent in metals and play an important role in their plastic deformation. Key characteristics of mixed-type dislocations cannot simply be extrapolated from those of dislocations with pure edge or pure screw characters. However, mixed-type dislocations traditionally received disproportionately less attention in the modeling and simulation community. In this work, we explore core structures of mixed-type dislocations in Al using three continuum approaches, namely, the phase-field dislocation dynamics (PFDD) method, the atomistic phase-field microelasticity (APFM) method, and the concurrent atomistic-continuum (CAC) method. Results are benchmarked against molecular statics. We advance the PFDD and APFM methods in several aspects such that they can better describe the dislocation core structure. In particular, in these two approaches, the gradient energy coefficients for mixed-type dislocations are determined based on those for pure-type ones using a trigonometric interpolation scheme, which is shown to provide better prediction than a linear interpolation scheme. The dependence of the in-slip-plane spatial numerical resolution in PFDD and CAC is also quantified.

Dislocation core structures and Peierls stresses of the high-entropy alloy NiCoFeCrMn and its subsystems

High entropy alloys (HEAs) have emerged as promising next-generation structural materials. In order to understand the strengthening mechanism in these multicomponent alloys, a theoretical investigation is presented here in the framework of the Peierls-Nabarro (PN) model, which we consider would be appropriate for FCC HEAs due to their homogeneous feature, small lattice distortions and wide dislocation core structures. More importantly, there is no need to differentiate solutes and solvents in this model, which avoids the conceptual difficulties for such alloys. Using PN model, we calculate the dislocation core structures and Peierls stresses of the prototypical NiCoFeCrMn HEA and its six subsystems using the averaged gamma surfaces. The calculated stacking fault widths are in good agreement with available experimental data, and the obtained core structures are important for the future evaluation of the solute-dislocation interaction energies. The Peierls stresses in these multicomponent alloys are found to be much larger than pure FCC metals, and are generally in the same order of magnitude as the critical resolved shear stresses (CRSSs) extrapolated to zero temperature. The results indicate that in contrast to conventional FCC metals, the increased Peierls stresses in MEAs and HEAs could be responsible for their high yield stresses.