Dislocation Dipoles Research Articles

Dislocation mechanisms in the plastic deformation of monodisperse wet foams within an expansion-contraction microfluidic geometry.

Densely packed wet foam was subjected to gradual expansion and contraction in a wide (1400-1800 μm) microfluidic channel to study localized plastic deformation events within the monodisperse bubble matrix. Dislocation glide, reflection, nucleation, and dipole transformations from extensional and compressive stresses were observed across a range of fluid flow rates and bubble packing densities. Disparate, cyclic reflections occur in two independent regions of the flowing foam, and the mechanisms of dislocation reflection under tension are expanded. The use of an asymmetric channel created a dichotomy in the model crystalline system between straighter, aligned bubble rows and curved, misaligned rows due to the corresponding streamlines within the channel. The resulting gradient in crystalline alignment had numerous effects on dislocation mobility and plastic deformation. 7/7 dipoles were found to rearrange to a more stable configuration aligned with the foam flow before dissociating. Dislocations comprising 5/5 dipoles (resembling the inverse-Stone-Wales defect in carbon nanostructures) were discovered to pass through one another via intermediate ring structures, which most commonly consisted of three dislocation pairs around a triangular-shaped central bubble.

Temperature Effect on Stress-Strain Properties of Dispersion-Hardened Crystalline Materials with Incoherent Nanoparticles

In this paper, the mathematical simulation is used to study the effect from the size of incoherent nanoparticles on thermal strength of heterophase aluminum alloy in materials with the equal volume fraction of the strengthening phase. It is shown that during the deformation process, prismatic dislocation loops and dislocation dipoles contribute to the dislocation density. It is found that the behavior of the flow stress curves of materials with the equal volume fraction of strengthening particles depends on a combination of scale parameters of the strengthening phase at various deformation temperatures. The areas of strong and weak temperature dependence of the flow stress are identified.

Characterizing the interactions of edge dislocation dipole in hexagonal close packed Ti-Al alloys

The aim of the present work is to elucidate the interaction between dislocation dipoles decorated by trace addition of solute atoms in the model material of as-annealed coarse-grained Ti-3Al (weight percent, wt%) alloys. The morphology, activity, structure, strain field, and interaction of dislocation cores were systematically characterized. Theoretical predictions of equilibrium distribution of edge dislocation dipoles presenting an angle of 45° relative to each other were experimentally demonstrated. More importantly, we observed for the first time the 45°-rotating of strain fields around the dislocation core along a clockwise direction for stress equilibrium which is driven by the dislocation-dislocation interactions.

Separation of Elastic and Plastic Timescales in a Phase Field Crystal Model.

A consistent small-scale description of plasticity and dislocation motion in a crystalline solid is presented based on the phase field crystal description. By allowing for independent mass motion and lattice distortion, the crystal can maintain elastic equilibrium on the timescale of plastic motion. We show that the singular (incompatible) strains are determined by the phase field crystal density, while the smooth distortions are constrained to satisfy elastic equilibrium. A numerical implementation of the model is presented and used to study a benchmark problem: the motion of an edge dislocation dipole in a triangular lattice. The time dependence of the dipole separation agrees with continuum elasticity with no adjustable parameters.

A hybrid quasicontinuum method

SummaryQuasicontinuum (QC) is a partitioned‐domain multiscale method where the full‐atomistic description is retained in highly deformable subdomains while the energy in the remaining region is approximated using a continuum constitutive relation called the Cauchy‐Born (CB) rule. While the CB rule can capture the full nonlinearity of the strain energy, its computational cost is one or two orders of magnitude higher than the linear elasticity (LE) constitutive relation. In this paper, we propose an extension to the QC method, referred to as “hybrid QC,” where both the CB and LE relations are combined to increase the efficiency of the original QC method. This extension is summed up to a two‐step process. First, the continuum region is further divided into subregions with CB being restricted to subregions adjoining the atomistic region while LE is adopted in the remaining subregions. Second, a corrective scheme is applied to the LE subregion to recover the higher‐order accuracy. The hybrid QC method is validated through two examples: (i) a crystal containing a dipole of Lomer dislocations and (ii) a nanoindentation system. The simulation results show that the proposed hybrid QC method is numerically more efficient than the original QC method while maintaining virtually the same accuracy.

Depth sensitive imaging of graphene with an atomic resolution microscope

The three-dimensional information of atomic positions is required to determine the atomic structure of materials. However, images obtained using high-resolution transmission electron microscopes are generally two-dimensional projections of three-dimensional structures. The depth resolution of general microscopes is still on the order of nanometers, and a smaller depth of field is required to realize atomic depth-resolution imaging. Here, we propose highly depth-sensitive imaging using a low-voltage atomic-resolution transmission electron microscope equipped with a higher order geometrical aberration corrector and a monochromator. A long wavelength of low energy electrons and a large acceptance angle of the microscope allow for a shallow depth of field and atomic-level depth sensitivity. We demonstrate that the depth resolution and depth precision can allow for ångström and sub-ångström levels, respectively. Applying this highly depth-sensitive microscope, the depth deviation of monolayer graphene with dislocations is detected as the difference of defocus. The buckling structures of dislocation dipole and tripole are directly observed using a single image. Combining the proposed depth-sensitive microscope with through-focal imaging will allow for the analysis of various low-dimensional materials in three dimensions with atomic depth resolution.

Semicoherent heterophase interfaces with core-spreading dislocation structures in magneto-electro-elastic multilayers under external surface loads

Using the extended Stroh formalism combining with the Fourier-transform and dual variable and position techniques, semicoherent interfaces are introduced to simulate the appropriate structural interface conditions in three-dimensional magneto-electro-elastic (MEE) multilayered composites under external loads. The field solutions caused by both internal and external actions are expressed in terms of biperiodic Fourier series expansions in multilayered systems that are made of dissimilar, linear and anisotropic plates with planar lattice mismatches. For non-perfectly bonded internal interfaces, the semicoherent heterophase interfaces are atomistically described by infinitely-long, parallel, periodically-spaced, and core-spreading intrinsic dislocation structures in free-standing multilayers. On the other hand, subsequent solutions for general loads on the external surfaces with coherent interfacial conditions are consistently derived and superposed to the former dislocation-induced fields.Three application examples in bi-, tri-, and six-layered MEE systems are investigated. The first bilayered case illustrates the significant effects of the semicoherent interface with dislocation core-spreading widths on the elastic, electric, and magnetic fields in the CoFe2O4/BaTiO3 composite materials. The second example is a trilayered system made of A/B/A with two discrete sets of intrinsic dislocation dipoles on their semicoherent interfaces, analyzed by proposing a novel energy based criterion. Critical dislocation spacings and thicknesses of capped interlayers are quantified in nanoscale MEE heterostructures with different stacking sequences, providing possible guides for stable growth of layered nanostructures. Finally, the complex distribution of field solutions in a six-layered MEE system with a prescribed externally mechanical load shows the crucial role played by the topological defects in localizing the coupled electric and magnetic components at the semicoherent interfaces, which indicates the important interplay between the internal and external actions. These resulting features open up novel opportunities for designing atomic-scale heterostructures with unprecedented MEE properties by engineering the interfacial dislocation patterns when the multilayered structures are free or under external action.

Observing the dynamic rotation and annihilation process of an isolated nanograin at the atomic scale in Al

The atomic-scale dynamic evolution process of an isolated nanograin embedded within matrix under stress is recorded through in situ transmission electron microscopy tensile experiment on Al. the results reveal a 〈110〉 tilt grain boundary (GB) between the matrix and nanograin, with the misorientation angle increasing and GB shrinking during loading. A sudden annihilation of the nanograin occurs when the grain size reduces to ~4 nm. We then employ a dislocation dipole model to describe the GB structure in which the rotation, shrinkage and annihilation of nanograin can be interpreted as the approach and combination of opposite-sign dislocation pairs.

The Influence of Incoherent Nanoparticles on Thermal Stability of Aluminum Alloys

In this paper, the mathematical simulation is used to study the effect from the size of incoherent nanoparticles on thermal strength of heterophase aluminum alloy in materials with the similar volume fraction of the strengthening phase. It is shown that during the deformation process, the particle size affects the evolution of shear dislocations, prismatic dislocation loops and dislocation dipoles. It is found that if the volume fraction of incoherent particles is low, the behavior of the flow stress curves depends on the particle size. The paper identifies the variation range of scale parameters for thermal stability of dispersion-hardened materials.

Cluster on interface of LPSO phase and matrix in Mg-Gd-Y-Ni alloy: Atomic scale insight from HAADF-STEM

This paper reports on an atomic-scale investigation into the new rare earth element enriched clusters on the interface of long period stacking ordered (LPSO) structure and magnesium matrix in Mg-2Gd-1Y-1Ni alloy, using Cs-corrected high angle annular dark field-scanning transmission electron microscopy (HAADF-STEM). Corresponding strain mapping on the cluster was generated by GPA. Excess free volume on the interface and induced strain were applied to explain the existence of tilted arranged, periodic present clusters at the interface. The clusters, which were Gd and Ni enriched based on the EDS measurement, were periodically arranged based on the stacking sequence of LPSO structure. The strong strain field and the interaction of dislocation dipoles contributed to the tilted atomic arrangement within the cluster.

A displacement-based formulation for interaction problems between cracks and dislocation dipoles in couple-stress elasticity

Interaction problems of a finite-length crack with plane and antiplane dislocation dipoles in the context of couple-stress elasticity are presented in this study. The analysis is based on the distributed dislocation technique where infinitesimal dislocation dipoles are used as strain nuclei. The stress fields of these area defects are provided for the first time in the framework of couple-stress elasticity theory. In addition, a new rotational defect is introduced to satisfy the boundary conditions of the opening mode problem. This formulation leads to displacement-based hyper-singular integral equations that govern the crack problems, which are solved numerically. It is further shown that this method has several advantages over the slope formulation. Based on the obtained results, it is deduced that in all cases the cracked body behaves in a more rigid way when couple-stresses are considered. The effect of couple-stresses is highlighted in a small zone ahead of the crack-tip and around the dislocation dipole, where the stress level is significantly higher than the classical elasticity prediction. Further, the dependence of the energy release rate and the configurational force exerted on the defect on the characteristic material length and the distance between the defect and the crack-tip is discussed. In the plane problems, couple-stress theory predicts either strengthening or weakening effects while in the antiplane mode a strengthening effect is predicted.

Defect Annihilation Pathways in Directed Assembly of Lamellar Block Copolymer Thin Films.

Defects in highly ordered self-assembled block copolymers represent an important roadblock toward the adoption of these materials in a wide range of applications. This work examines the pathways for annihilation of defects in symmetric diblock copolymers in the context of directed assembly using patterned substrates. Past theoretical and computational studies of such systems have predicted minimum free energy pathways that are characteristic of an activated process. However, they have been limited to adjacent dislocations with opposite Burgers vectors. By relying on a combination of advanced sampling techniques and particle-based simulations, this work considers the long-range interaction between dislocation pairs, both on homogeneous and nanopatterned substrates. As illustrated here, these interactions are central to understanding the defect structures that are most commonly found in applications and in experimental studies of directed self-assembly. More specifically, it is shown that, for dislocation dipoles separated by several lamellae, multiple consecutive free energy barriers lead to effective kinetic barriers that are an order of magnitude larger than those originally reported in the literature for tightly bound dislocation pairs. It is also shown that annihilation pathways depend strongly on both the separation between dislocations and their relative position with respect to the substrate guiding stripes used to direct the assembly.

Interaction problems between cracks and crystal defects in constrained Cosserat elasticity

In this work, interaction problems between a finite-length crack with plane and antiplane crystal defects in the context of couple-stress elasticity are presented. Two alternative yet equivalent approaches for the formulation of crack problems are discussed based on the distributed dislocation technique. To this aim, the stress fields of climb and screw dislocation dipoles are derived within couple-stress theory and new ‘constrained’ rotational defects are introduced to satisfy the boundary conditions of the opening mode problem. Eventually, all interaction problems are described by single or systems of singular integral equations that are solved numerically using appropriate collocation techniques. The obtained results aim to highlight the deviation from classical elasticity solutions and underline the differences in interactions of cracks with single dislocations and dislocation dipoles. In general, it is concluded that the cracked body behaves in a more rigid way when couple-stresses are considered. Also, the stress level is significantly higher than the classical elasticity prediction. Moreover, the configurational forces acting on the defects are evaluated and their dependence on the characteristic material length of couple-stress theory and the distance between the defect and the crack-tip is discussed. This investigation reveals either a strengthening or a weakening effect in the opening mode problem while in the antiplane mode a strengthening effect is always obtained.

Acoustic Nonlinearity Parameters Due to Microstructural Defects

This study presents a general approach to derive the acoustic nonlinearity parameters induced by various types of dislocation configurations including dislocation strings (monopoles), dislocation dipoles, dislocation pileups and extended dislocations. It is found that expressions of the acoustic nonlinearity parameter induced by such a variety of dislocation configurations share a common mathematical form. They are all scaled with $$\left( {L_{\mathrm{ch}} /b} \right) ^{n}$$ , where $$L_{\mathrm{ch}} $$ is a characteristic length of the dislocation configuration, b is the magnitude of the Burgers vector, and n is either 3 or 4. Semiquantitative analysis is presented to compare the magnitudes of the acoustic nonlinearity parameters among different types of dislocation configurations.

The diffusive character of extension twin boundary migration in magnesium

A theoretical study of the coherent boundary migration of extension twin in magnesium is performed focusing on twinning transformations of host lattices and homogeneous nucleation of twinning dislocations. The twinning transformation of host lattice has a small activation volume which usually characterizes a civilian/diffusive mechanism. The critical width of a twinning dislocation dipole is less than fifteen nanometers. The corresponding per-atom energy to activate a dipole is lower than the thermal energy kBT at room temperature. A highly adaptive migration behavior of coherent twin boundary is expected and in accordance with previous experiment observations.

Dislocation mobility and Peierls stress of c-type screw dislocations in GaN from molecular dynamics

Motion of a single c-type screw dislocation, with [0001] Burgers vector, in single crystal GaN is explored using classical molecular dynamics (MD) simulations with both Tersoff and Stillinger-Weber (SW) interatomic potentials. Three different dislocation core structures (full, small void, and open) along two distinct glide planes ((11¯00) and (1¯1¯20)) are studied. The system is sheared by applying opposing forces to atoms near the surface, with interior atoms maintained at a temperature of 1300 K. This results in glide for screw dislocations with a full core structure, with velocities dependent on the choice of interatomic potential. Full core dislocation glide also results in the nucleation of void defects for both potentials. Small void dislocations glide cleanly with no debris using the SW potential, but glide is not observed for the Tersoff potential. The difference between the potentials is most fully demonstrated from the response of open core dislocations in the (1¯1¯20) slip system. For the Tersoff potential, full core screw dislocations are nucleated from the surface of the open core dislocations, while dislocation glide loops are nucleated for the SW potential. The discrepancy in results using the different potentials is discussed, and attributed to the short cut off distance of the Tersoff potential. Finally, a dislocation dipole system is used to calculate the Peierls stress of the {11¯00}〈0001〉 full core screw dislocation, and compared to experimental results.

Effects of material mismatch on interfacial cracking of ferroelectric film/substrate structures

This study investigates the effect of material mismatch on interfacial cracking in ferroelectric film/substrate structures, models the interfacial misfit strain using a Somigliana screw dislocation dipole, and solves the generalized stress functions, the stress intensity factor (SIF) and the electric displacement intensity factor (EDIF) in piezoelectric coupled field based on an equivalent model and the complex potential method. The results show that: (1) The lattice mismatch degree is the major factor influencing EDIF and SIF; (2) The effects of the elastic and dielectric constant ratios of substrate to film on EDIF depend on the mismatch effects resulting from the other two constant ratios of generalized stiffness, respectively, however the piezoelectric constant ratio can affect EDIF independently; (3) The increasing elastic constant ratio can lead to a monotonic and significant increase of SIF; and when the piezoelectric constant ratio is greater than 1, it can cause an obviously change in SIF; however dielectric constant ratio has little effect on SIF; and (4) The modest adjustment of the piezoelectric constant ratio within a specific range could be a potential route to decrease the failure risk of the ferroelectric film deposited on a piezoelectric substrate.

Defects and Polytype Instabilities

A model based on the generation and recombination of defect was developed to describe the stability of stacking faults and basal plane dislocation loops in crystals with layered polytype structures. The stability of the defects configuration was analysed for stacking faults surrounded by Shockley and Frank partial dislocation as well as Shockley dislocation dipoles with long range elastic fields. This approach allows the qualitative prediction of defect subsystems in polytype structure in external fields.

Dislocation dynamics and crystal plasticity in the phase-field crystal model

A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy and show that it obeys the stress strain relation of linear elasticity. Dislocations in a two dimensional hexagonal lattice are shown to be composite topological defects in the amplitude expansion of the phase field, with topological charges given by the Burgers vector. This allows us to introduce a formal relation between dislocation velocity and the evolution of the coarse grained envelopes of the phase field. Standard dissipative dynamics of the phase field crystal model is shown to determine the velocity of the dislocations. When the amplitude equation is valid, we derive the Peach-Koehler force on a dislocation, and compute the associated defect mobility. A numerical integration of the phase field crystal equations in two dimensions is used to compute the motion of a dislocation dipole, and good agreement is found with the theoretical predictions.

Cyclic softening in annealed Zircaloy-2: Role of edge dislocation dipoles and vacancies

The mechanism of cyclic softening in annealed Zircaloy-2 at low strain amplitudes under strain controlled fatigue at room temperature is rationalized. The unusual softening due to continuous decrease in the phenomenological friction stress is found to be associated with decrease in the resistance against movement of dislocations because of the formation and easy glide of pure edge dislocation dipoles and consequent decrease in friction stress from reduction in the shear modulus. Positron annihilation spectroscopy data strongly support the increase in edge dislocation density containing jogs, from increased positron trapping and increase in annihilation lifetime.