Dislocation Length Research Articles

The effect of void defect on the evolution mechanisms of dislocations and mechanical properties in nickel-based superalloys by molecular dynamics simulation of real γ/γ′ structures

It is acknowledged that voids are unavoidable manufacture defects influencing the microstructure evolution and mechanical properties of nickel-based superalloys. The present work investigates the influences of void on the dislocation evolution and mechanical properties of nickel-based superalloys under different thermal conditions and strain rates. The simulation uses an embedded cubic model with voids in which the γ′ phase with L12 structure is surrounded by γ phase with FCC structure to represent the real microstructure of single crystal superalloys. A model without voids is also studied. The existence of voids changes the misfit dislocation network by introducing cylindrical dislocation network around the voids which play a vital role on preventing the void coalescence at low strain. Dislocation extraction algorithm (DXA) analysis finds that new type of dislocation appears in the model with voids and the dislocation length is longer. The elastic modulus and yield strength are decreased by voids, as well as the ductility of the material. This paper demonstrates that the accumulation and reaction between dislocations are the most direct reason for declining the mechanical properties of nickel-based superalloys with void defects.

Uniaxial tension deformation study of copper/nickel laminated composites: Effects of lamella number and interlamellar spacing

The lamella number and interlamellar spacing are crucial structural parameters in determining mechanical properties of layered nanocomposites, while they are rarely discussed. Herein, we investigate effects of the two parameters on mechanical properties of copper/nickel (Cu/Ni) nano-laminated composites (NLCs) under uniaxial tension using molecular dynamic simulation. The Cu/Ni NLCs with one single Ni laminate exhibit the largest enhancement in Young’s modulus (E = 121 GPa) and yield strength (σz = 9.8 GPa), attributing to the stronger texture of Ni and interfacial blocking effect on the motion of dislocations. With different Ni layer spacing, the shockley dislocations form a crescent slip plane and enter the Cu matrices along the 45° direction with respect to the Ni laminate. According to the evolution of dislocation length, the flow stress shows a negative relationship with the mean dislocation length. The peak yield strength coincides with the stage of sudden increase of the total dislocation length, indicating decreased mechanical properties with increased dislocation length. These findings provide fundamental relationships between nanoscale laminated structure and macroscopic mechanical properties of Cu/Ni composites, shedding new lights on the rational design of NLCs with enhanced mechanical performances.

To the Explanation of the Magnetoplastic Effect in Diamagnetic and Paramagnetic Solids

This work is devoted to the theoretical study of the magnetoplastic effect that manifests itself in the motion of dislocations in solids in the presence of a magnetic field without mechanical loading. An expression is obtained for the effective magnetic charge per unit length of dislocation, which occurs due to the action of the magnetic field on the dislocation. The effects associated with the induced magnetic charges at dislocations are studied. It is shown that the effective magnetic charge occurs due to the interaction between the magnetic field and only the edge components of dislocations. An expression for the force that acts on a dislocation in the magnetic field is derived and it is shown that in experiments on studying the motion of dislocations in the presence of magnetic fields the projection of this force onto the dislocation glide plane must play a dominant role.

Dependence of tribological behavior of GaN crystal on loading direction: A molecular dynamics study

In order to investigate the tribological property of the gallium nitride (GaN) crystal at the nanoscale, a series of molecular dynamics nanoscratch simulations are carried out on the surfaces of c-GaN, a-GaN, and m-GaN. The key factors of scratch depth and scratch direction that greatly influence the deformation behavior are explored by analyzing the mechanical response, surface wear, and subsurface dislocation nucleation. The friction coefficient, wear rate, and total length of dislocations are all found to increase with the increase of scratch depth. A clear directional dependence could be recognized for c-GaN, where the friction coefficient along the [101¯0] direction is always lower than that along the [12¯10] direction, and the wear rate along the [101¯0] direction is higher than that along the [12¯10] direction, regardless of the scratch depth. On the contrary, the directional dependence of the wear rate and friction coefficient is unclear for a-GaN and m-GaN. For scratches at a specific depth, dislocations in c-GaN are smallest in length and occupy shallow positions close to the surface, while widely distributed dislocations could be observed in m-GaN.

Dependence of Dislocation Energy on Interatomic Distance

Dislocations span over distances that are much larger than the interatomic distance . Therefore, an asymptotic expansion of dislocation energy as is of interest. In this paper, such asymptotic expansion is constructed. It has a simple form of , where and are the functionals of the dislocation line (which do not depend on ) and is the dislocation length. Analytical formulas for and are obtained.

DFT modelling of the edge dislocation in 4H-SiC

We have presented ab initio study, based on density functional theory methods, of full-core edge dislocation impact on basic properties of 4H-SiC semiconductor. To enable calculations in periodic boundary conditions, we have proposed geometry with two dislocations with opposite Burgers vectors. For this geometry, which determines the distance between dislocations, we have estimated the creation energy per unit length of a single-edge dislocation. The radial distribution function has been used to assess the effect of the dislocations on the local crystal structure. The analysis of the electronic structure reveals mid-gap p states induced by broken atomic bonds in the dislocation core. The maps of charge distribution and electrostatic potential have been calculated, and the significant decrease in the electrostatic barriers in the vicinity of the dislocation cores has been quantified. The obtained results have been discussed in the light of previous findings and calculations based mainly on phenomenological models.

A new variational line tension model for accurate evaluation of the stress effect on cross-slip energy barrier in face-centered cubic metals

The present work developed a new variational line tension model (LTM) that accounts for contributions from the local line energy, long-range interaction among dislocation segments, and interplay between dissociated partials. This new LTM has been shown to accurately predict cross-slip energy barriers under different stress states, verified through atomistic simulations on the face-centered cubic (FCC) nickel model system. We demonstrated that the line tension in general is not a constant, but varies with the local dislocation length and the separation distance between dissociated dislocations, and thus the constant line tension assumption is inherently inadequate.

Effect of obstacle strength and spacing on the slope of Haasen plot

ABSTRACTThe rate sensitivity of multiple obstacle aluminium alloy system was measured using the stress relaxation method. A discrepancy was observed between the slope of the Haasen plot (rate sensitivity of dislocation–dislocation interaction) in pure metals and in alloys strengthened by multiple obstacles. Considering a simplifying assumption of the constant obstacle force–distance profile, it is suggested that slope of the Haasen plot is governed by glide dislocations’ length taking part in a thermally activated event. The relative strength and spacing of obstacles (forest dislocations, solutes and precipitates) is proposed to affect the thermally activated dislocation length, which in turn manifests as the difference in slope of the Haasen plot.

Dislocation Interaction and V-Shaped Growth of the Distorted Structure During Nanoindentation of Cu20Ni20Al20Co20Fe20 (high-entropy alloy)-Coated Copper: A Molecular Dynamics Simulation-Based Study

In this paper, the deformation behavior of Cu20Ni20Al20Co20Fe20 high-entropy alloy-coated single-crystal Cu substrate which undergoes nanoindentation has been investigated under molecular dynamic simulation with embedded-atom method potential. The dynamic structural evolutions under nanoindentation are presented using centrosymmetry parameter analysis, common neighbor analysis and radial distribution function plots. In the initial level of nanoindentation, the interface deformation is greatly confronted by the confined V-shaped growth of the distorted structure. But the sudden discrete dislocation burst account for avalanche break-down in the interface layer, which further get influenced by the evolution of multiple dislocation nodes that is significantly governed by core spreading, extended misfit dislocation generation and relative rotation. In the meanwhile, the subsequent generation of dislocation locks, complicated multiple dislocation loops, dislocation junctions and limited cross-slip in wide stacking faults (SFs) hasten the work hardening and in turn slows down the deformation progress. On the other hand, the intermediate appearance of narrow SFs and slip bands significantly reduces the work hardening rate that increases the optimum fracture strain value of the specimen. Moreover, the overall increase in dislocation density and dislocation length leads to a significant growth in dislocation sources which leads to forest hardening in the later stage.

Dislocation Motion in an Electric Field

An expression for the effective polarization electric charge per unit length of dislocation is obtained. It is shown that the polarization electric charge arises due to the interaction of an electric field only with the edge components of dislocations. An expression is obtained for the force that acts on a dislocation in the electric field and it is shown that the determining role in experiments would be played by the projection of this force onto the dislocation slip plane.

Unveiling the role of super-jogs and dislocation induced atomic-shuffling on controlling plasticity in magnesium

Magnesium (Mg) alloys are promising metals for many lightweight structural applications. However, the fundamental deformation mechanism in Mg that lead to poor ductility, formability and anomalous thermal-hardening response remain elusive. Here, atomistic simulations were utilized to unveil the mechanisms responsible for these undesirable properties. We show that pyramidal 〈c+a〉 screw dislocations glide in hexagonal-close packed crystals by a fundamentally new mechanism that involves atomic shuffling and kink pair formation on the trailing partial. Due to local fluctuations in the stresses in the dislocation core, stable super-jogs subsequently form due to inhomogeneities in the shuffling process along the dislocation length as well as due to kink pair collisions. The screw dislocation then moves while dragging these super-jogs, sometimes leaving debris behind (e.g. vacancies or interstitials) as well as long faulted loops on the basal plane that are aligned along the basal plane intersection with the pyramidal-II plane. These dragged out super-jogs dissociate athermally on the basal plane and exert a strong drag-effect on dislocation glide, resulting in dramatic work-hardening at small strains between 0 and 600K, which correlates with the experimentally observed low-ductility during c-axis compression of Mg. Furthermore, this new mechanism also accounts for the experimentally reported anomalous thermal-hardening as a result of the increase in the number of super-jogs per dislocation unit-length due to thermal activation.

Optimization of Graded Buffer Layers for Metamorphic Semiconductor Devices

Metamorphic semiconductor devices such as high electron mobility transistors (HEMTs), light-emitting diodes (LEDs), laser diodes, and solar cells are grown on mismatched substrates and typically exhibit a high degree of lattice relaxation. In order to minimize the incorporation of threading defects it is common to use a linearly-graded buffer layer to accommodate the mismatch between the substrate and device layers. However, some work has suggested that buffer layers with non-linear grading could offer superior performance in terms of limiting the surface density of threading defects. In this work, we have compared S-graded buffer layers with different orders and thicknesses. To do so we calculated the expected surface threading dislocation density for each buffer design assuming a GaAs (001) substrate. The threading dislocation densities were calculated using the LMD model, in which the coefficient for second-order annihilation and coalescence reactions between threading dislocations is considered to be equal to the length of misfit dislocations.

Interaction Length for Dislocations in Compositionally-Graded Heterostructures

Several simple models have been developed for the threading dislocation behavior in heteroepitaxial semiconductor materials. Tachikawa and Yamaguchi [Appl. Phys. Lett., 56, 484 (1990)] and Romanov et al. [Appl. Phys. Lett., 69, 3342 (1996)] described models for the annihilation and coalescence of threading dislocations in uniform-composition layers, and Kujofsa et al. [J. Electron. Mater., 41, 2993 (2013)] extended the annihilation and coalescence model to compositionally-graded and multilayered structures by including the misfit dislocation-threading dislocation interactions. However, an important limitation of these previous models is that they involve empirical parameters. The goal of this work is to develop a predictive model for annihilation and coalescence of threading dislocations which is based on the dislocation interaction length Lint. In the first case if only in-plane glide is considered the interaction length is equal to the length of misfit dislocation segments while in the second case glide and climb are considered and the interaction length is a function of the distance from the interface, the length of misfit dislocations, and the density of the misfit dislocations. In either case the interaction length may be calculated using a model for dislocation flow. Knowledge of the dislocation interaction length allows predictive calculations of the threading dislocation densities in metamorphic device structures and is of great practical importance. Here we demonstrate the latter model based on glide and climb. Future work should compare the two models to determine which is more relevant to typical device heterostructures.

Spall strength dependence on grain size and strain rate in tantalum

We examine the effect of grain size on the dynamic failure of tantalum during laser-shock compression and release and identify a significant effect of grain size on spall strength, which is opposite to the prediction of the Hall-Petch relationship because spall is primarily intergranular in both poly and nanocrystalline samples; thus, monocrystals have a higher spall strength than polycrystals, which, in turn, are stronger in tension than ultra-fine grain sized specimens. Post-shock characterization reveals ductile failure which evolves by void nucleation, growth, and coalescence. Whereas in the monocrystal the voids grow in the interior, nucleation is both intra - and intergranular in the poly and ultra-fine-grained crystals. The fact that spall is primarily intergranular in both poly and nanocrystalline samples is a strong evidence for higher growth rates of intergranular voids, which have a distinctly oblate spheroid shape in contrast with intragranular voids, which are more spherical. The length of geometrically-necessary dislocations required to form a grain-boundary (intergranular) void is lower than that of grain-interior (intragranular) void with the same maximum diameter; thus, the energy required is lower. Consistent with prior literature and theory we also identify an increase with spall strength with strain rate from 6 × 106 to 5 × 107 s−1. Molecular dynamics calculations agree with the experimental results and also predict grain-boundary separation in the spalling of polycrystals as well as an increase in spall strength with strain rate. An analytical model based on the kinetics of nucleation and growth of intra- and intergranular voids and extending the Curran-Seaman-Shockey theory is applied which shows the competition between the two processes for polycrystals.

Cross-slip of long dislocations in FCC solid solutions

Cross-slip of screw dislocations is a dislocation process involved in dislocation structuring, work hardening, and fatigue. Cross-slip nucleation in FCC solid solution alloys has recently been shown to be strongly influenced by local fluctuations in spatial arrangement of solutes, leading to a statistical distribution of cross-slip nucleation barriers. For cross-slip to be effective macroscopically, however, small cross-slip nuclei (∼40b) must expand across the entire length of typical dislocation segments (102−103b). Here, a model is developed to compute the relevant activation energy distribution for cross-slip in a random FCC alloy over arbitrary lengths and under non-zero Escaig and Schmid stresses. The model considers cross-slip as a random walk of successive flips of adjacent 1b segments, with each flip having an energy consisting of a deterministic contribution due to constriction formation and stress effects, plus a stochastic contribution. The corresponding distribution is computed analytically from solute-dislocation and solute-solute binding energies. At zero stress, the probability of high activation energies increases with dislocation length. However, at stresses of just a few MPa, these barriers are eliminated and lower barriers are dominant. For increasing segment length, the effective energy barrier decreases according to a weak-link scaling relationship and good analytic predictions can be made using only known material properties. Overall, these results show that the effective cross-slip barrier in a random alloy is significantly lower than estimates based on average elastic and stacking fault properties of the alloy.

Dislocation multiplication in stage II deformation of fcc multi-slip single crystals

Dislocation multiplication in plasticity research is often connected to the picture of a Frank-Read source. Although it is known that this picture is not applicable after easy glide deformation, plasticity theories often assume Frank-Read-type models for dislocation multiplication. By analyzing discrete dislocation dynamics simulations in a bulk like setting, a new view on dislocation multiplication is presented. It is observed that only two mechanisms provide a source for dislocations: cross-slip and glissile junctions. Both source mechanisms involve a change of glide system and transfer of dislocation density (line length) from the primary dislocation(s) slip system(s) to the one of the new dislocation. The motion of dislocations is found to be highly restricted by other dislocations and therefore the contribution to plastic deformation of each individual dislocation is small. Also a substantial fraction of the physical dislocation line length is annihilated by the collinear reaction, lowering dislocation storage during plastic deformation. Furthermore, multiplication events involve the loss of a substantial amount of dislocation length and curvature (sudden changes in line orientation) due to the topology changes in the dislocation network of the respective mechanisms. The findings are discussed in light of continuum dislocation theories, which currently barely account for dislocation density transfer to other systems and the limited contribution of plastic strain from individual dislocations.

Atomistic simulation analysis of the effects of void interaction on void growth and coalescence in a metallic system

Material deformation caused by the interaction between defects is a significant factor of material fracture failure. The present study employs molecular dynamics simulations of single-void and double-void crystalline Ni atomic systems to investigate inter-void interactions. Furthermore, simulations showing the evolution of dislocations for three different crystallographic orientations are conducted to study the void growth and coalescence. The simulations also consider the effect of the radius of the secondary void on dislocation evolution. The results show that double-void systems are more prone to yield than single-void systems. Further microstructural analysis indicates that the interaction between voids is realized by dislocation reactions. The simulation results of the dislocation evolution of the three orientations reveal that a relationship exists between the evolution of the dislocation density and the stress-strain curve. At the initial stage of dislocation, the dislocation grows slowly, and consists of Shockley partial dislocation. The dislocation growth rate then increases significantly in the sharply declining stage of the stress-strain curve, where most of dislocations are Shockley partial dislocation. Analysis of the dislocation length during the overall simulation indicates that the dislocation length of the [110] orientation is the longest, followed by that of the [111] orientation and the [100] orientation, which has the shortest dislocation length.

Threading Dislocations in InGaAs/GaAs (001) Buffer Layers for Metamorphic High Electron Mobility Transistors

In order to evaluate various buffer layers for metamorphic devices, threading dislocation densities have been calculated for uniform composition In x Ga1−xAs device layers deposited on GaAs (001) substrates with an intermediate graded buffer layer using the LMD model, where LMD is the average length of misfit dislocations. On this basis, we compare the relative effectiveness of buffer layers with linear, exponential, and S-graded compositional profiles. In the case of a 2 μm thick buffer layer linear grading results in higher threading dislocation densities in the device layer compared to either exponential or S-grading. When exponential grading is used, lower threading dislocation densities are obtained with a smaller length constant. In the S-graded case, lower threading dislocation densities result when a smaller standard deviation parameter is used. As the buffer layer thickness is decreased from 2 μm to 0.1 μm all of the above effects are diminished, and the absolute threading dislocation densities increase.

Model for threading dislocations in metamorphic tandem solar cells on GaAs (001) substrates

We present an approximate model for the threading dislocations in III–V heterostructures and have applied this model to study the defect behavior in metamorphic triple-junction solar cells. This model represents a new approach in which the coefficient for second-order threading dislocation annihilation and coalescence reactions is considered to be determined by the length of misfit dislocations, LMD, in the structure, and we therefore refer to it as the LMD model. On the basis of this model we have compared the average threading dislocation densities in the active layers of triple junction solar cells using linearly-graded buffers of varying thicknesses as well as S-graded (complementary error function) buffers with varying thicknesses and standard deviation parameters. We have shown that the threading dislocation densities in the active regions of metamorphic tandem solar cells depend not only on the thicknesses of the buffer layers but on their compositional grading profiles. The use of S-graded buffer layers instead of linear buffers resulted in lower threading dislocation densities. Moreover, the threading dislocation densities depended strongly on the standard deviation parameters used in the S-graded buffers, with smaller values providing lower threading dislocation densities.

Size of the Plastic Zone Produced by Nanoscratching

Nanoscratching of ductile materials creates plastic zones surrounding the scratch groove. We approximate the geometry of these zones by a semicylinder with its axis oriented along the scratch direction. The radius and the length of the cylinder, as well as the length of the dislocations in the network created quantify the plasticity generated. Using molecular dynamics simulations, we characterize the plastic zones in six metals with fcc, bcc, and hcp crystal structures. We find that the plastic zone sizes after scratch are comparable to those after indent. Due to dislocation reactions, the dislocation networks simplify, reducing the total length of dislocations. As a consequence, the average dislocation density in the plastic zone stays roughly constant. Individually, we find exceptions from this simple picture. Fcc metals show strong plastic activity, which even increases during scratch. The hcp metals on the other side show the least plastic activity. Here the plasticity may be strongly reduced during scratch and particularly during tip withdrawal.