The effect of edge-type dislocation wall strain field on the Hall mobility in n-type epitaxial GaN was theoretically investigated through deformation potential within the relaxation time approach. It was found that this channel of scattering can play a considerable role in the low-temperature transport at the certain set of the model parameters. The low temperature experimental data were fitted by including this mechanism of scattering along with ionized impurities and charge dislocation ones.
The strain field of a dislocation emerging at a free surface is partially relaxed to ensure stress free boundary conditions. We show that this relaxation strain at the outcrop of edge threading dislocations in GaN{0001} gives rise to a piezoelectric volume charge. The electric field produced by this charge distribution is strong enough to dissociate free excitons at distances over 100 nm from the dislocation line. We evaluate the impact of this effect on cathodoluminescence images of dislocations.
We analyze the lineshape of x-ray diffraction profiles of GaN epitaxial layers with large densities of randomly distributed threading dislocations. The peaks are Gaussian only in the central, most intense part of the peak, while the tails obey a power law. The $q^{-3}$ decay typical for random dislocations is observed in double-crystal rocking curves. The entire profile is well fitted by a restricted random dislocation distribution. The densities of both edge and screw threading dislocations and the ranges of dislocation correlations are obtained.
We theoretically analyze the contrast observed at the outcrop of a threading dislocation at the GaN(0001) surface in cathodoluminescence and electron-beam induced current maps. We consider exciton diffusion and recombination including finite recombination velocities both at the planar surface and at the dislocation. Formulating the reciprocity theorem for this general case enables us to provide a rigorous analytical solution of this diffusion-recombination problem. The results of the calculations are applied to an experimental example to determine both the exciton diffusion length and the reco…
Non-singular dislocation continuum theories are studied. A comparison between Peierls-Nabarro dislocations and straight dislocations in strain gradient elasticity is given. The non-singular displacement fields, non-singular stresses, plastic distortions and dislocation core shapes are analyzed and compared for the two models. The main conclusion of this study is that due to their characteristic properties, the non-singular displacement fields, non-singular stresses and dislocation core shape of screw and edge dislocations obtained in the framework of strain gradient elasticity are more realist…
We report on thermal transport properties of wurtzite GaN in the presence of dislocations, by using molecular dynamics simulations. A variety of isolated dislocations in a nanowire configuration were analyzed and found to reduce considerably the thermal conductivity while impacting its temperature dependence in a different manner. We demonstrate that isolated screw dislocations reduce the thermal conductivity by a factor of two, while the influence of edge dislocations is less pronounced. The relative reduction of thermal conductivity is correlated with the strain energy of each of the five st…
We investigate, both theoretically and experimentally, the drift, diffusion, and recombination of excitons in the strain field of an edge threading dislocation intersecting the GaN{0001} surface. We calculate and measure hyperspectral cathodoluminescence maps around the dislocation outcrop for temperatures between 10 to 200 K. Contrary to common belief, the cathodoluminescence intensity contrast is only weakly affected by exciton diffusion, but is caused primarily by exciton dissociation in the piezoelectric field at the dislocation outcrop. Hence, the extension of the dark spots around disloc…
Dislocation slip is a general deformation mode and governs the strength of metals. Via discrete dislocation dynamics and molecular dynamics simulations, we investigate the strain rate and dislocation density dependence of the strength of bulk copper single crystals using 192 simulations spanning over 10 orders of magnitude in strain rate and 9 orders of magnitude in dislocation density. Based on these large set of simulations and theoretical analysis, a new analytical relationship between material strength, dislocation density, strain rate and dislocation mobility is proposed, which is in exce…
The mechanism of recrystallization in epitaxial (1000) GaN film, introduced by indentation technique, is probed by lattice dynamic studies using Raman spectroscopy. The recrystallized region is identified by Micro-Raman area mapping. Pop-in bursts in loading lines indicate nucleation of dislocations and climb of dislocations. These processes set in plastic motion of lattice atoms under stress field at the center of indentation for the initiation of recrystallization process. A planar defect migration mechanism is evolved. A pivotal role of vacancy migration is pointed out, for the first time, …
Recent experiments suggest that Mg condensation at threading dislocations induce current leakage, leading to degradation of GaN-based power devices. To study this issue, we perform first-principles total-energy electronic-structure calculations for various Mg and dislocation complexes. We find that threading screw dislocations (TSDs) indeed attract Mg impurities, and that the electronic levels in the energy gap induced by the dislocations are elevated towards the conduction band as the Mg impurity approaches the dislocation line, indicating that the Mg-TSD complex is a donor. The formation of …
The current work extends the well established approach of Kocks and Mecking by a more realistic description of strain-hardening using an original dislocation density law with a revisited physical understanding of dynamic recovery, without new material parameters and keeping only one internal variable.
We study strain-controlled plastic deformation of crystalline solids via two-dimensional discrete dislocation dynamics simulations. To this end, we characterize the average stress-strain curves as well as the statistical properties of strain bursts and the related stress drops as a function of the imposed strain rate and the stiffness of the specimen-machine system. The dislocation system exhibits strain rate sensitivity such that a larger imposed strain rate results in a higher average stress at a given strain. In the limit of small strain rate and driving spring stiffness, the sizes and dura…
Strain relief in lattice mismatched heteroepitaxy is mediated by formation and/or propagation of dislocations. Due to their technological significance, the process of strain relief in materials with face-centred cubic (fcc) lattices has been analyzed by several researchers1,2 following the work by Matthews and co-workers in the late 1960s to early 1970s3-6. In the Matthews model, it is assumed that the strain relieved by any misfit dislocation is equal to the edge component of the dislocation burgers vector in the interface plane. This assumption has been used in all subsequent analyses of str…
Strain engineering is critical to the performance enhancement of electronic and thermoelectric devices because of its influence on the material thermal conductivity. However, current experiments cannot probe the detailed physics of the phonon-strain interaction due to the complex, inhomogeneous, and long-distance features of the strain field in real materials. Dislocations provide us with an excellent model to investigate these inhomogeneous strain fields. In this study, non-equilibrium molecular dynamics simulations were used to study the lattice thermal conductivity of PbTe under different s…
When metals are plastically deformed, the total density of dislocations increases with strain as the microstructure is continuously refined, leading to the strain hardening behavior. Here we report the fundamental role played by the junction formation process in the connection between dislocation microstructure evolution and the strain hardening rate in face-centered cubic (FCC) Cu, as revealed by discrete dislocation dynamics (DDD) simulations. The dislocation network formed during [001] loading consists of line segments whose lengths closely follow an exponential distribution. This exponenti…
We conduct dislocation dynamics (DD) simulations of Fe periodic single crystals under tensile load at several high strain rates and temperatures. The simulations are enabled by the recent development of temperature-dependent dislocation mobility relations obtained from atomistic calculations. The plastic evolution in the simulations is governed by rapid initial dislocation multiplication, followed by a saturation of the flow stress when the subpopulation of slow plastic carriers becomes stabilized by dislocation annihilation. Above 500 K, edge dislocations coexist with screw dislocations and c…
In the present study, molecular dynamics (MD) simulations have been performed to understand the effect of nanowire size, temperature and strain rate on the variations in dislocation density and deformation mechanisms in $<$100$>$ Cu nanowires. The nanowire size has been varied in the range 1.446-43.38 nm with a constant length of 21.69 nm. Different temperatures varying from 10 K to 700 K and strain rates in the range of $5 \times 10^7$ - $1 \times 10^9$ s$^{-1}$ have been considered. For all the conditions, the variations in dislocation density $(ρ)$ has been calculated as a function of strai…
Kinematical and dynamical contrast of dislocations in thick GaN substrates observed by synchrotron-radiation X-ray topography under six-beam diffraction conditions
Three-dimensional discrete dislocation dynamics simulations are used to study strain-controlled plastic deformation of face-centered cubic aluminium single crystals. After describing the rate and size dependence of the average stress-strain curves, we study the power-law distributed strain bursts and the average avalanche shapes, and find a universal power-law exponent $τ\approx 1.0$ for all imposed strain rates and system sizes, characterizing both the event sizes and their durations. We discuss the dependence of our results on loading rate and compare these with previous studies of strain-co…
A theory for conduction electron scattering by inhomogeneous crystal lattice strains is developed, based on the differential geometric treatment of deformations in solids. The resulting fully covariant Schrödinger equation shows that the electrons can be described as moving in a non-Euclidean background space in the continuum limit of the deformed lattice. Unlike previous work, the formalism is applicable to cases involving purely elastic strains as well as discrete and continuous distributions of dislocations --- in the latter two cases it clearly demarcates the effects of the dislocation str…
We develop a model for the gliding of dislocations and plasticity in solid He-4. This model takes into account the Peierls barrier, multiplication and interaction of dislocations, as well as classical thermally and mechanically activated processes leading to dislocation glide. We specifically examine the dc stress-strain curve and how it is affected by temperature, strain rate, and dislocation density. As a function of temperature and shear strain, we observe plastic deformation and discuss how this may be related to the experimental observation of elastic anomalies in solid hcp He-4 that have…
The full lattice strain tensor and lattice rotations induced by a dislocation in pure tungsten were mapped using high-resolution transmission Kikuchi diffraction (HR-TKD) in a SEM. The HR-TKD measurement agrees very well with a forward calculation using an elastically isotropic model of the dislocation and its Burgers vector. Our results demonstrate that the spatial and angular resolution of HR-TKD in SEM is sufficiently high to resolve the details of lattice distortions near individual dislocations. This capability opens a number of new interesting opportunities, for example determining the B…
We present a dislocation density-based strain hardening model for single crystal copper through a systematic coarse-graining analysis of more than 200 discrete dislocation dynamics (DDD) simulations of plastic deformation under uniaxial tension. The proposed constitutive model has two components: a generalized Taylor relation connecting resolved shear stresses to dislocation densities on individual slip systems, and a generalized Kocks-Mecking model for dislocation multiplication. The DDD data strongly suggests a logarithmic dependence of flow stress on the plastic shear strain rate on each sl…
A long-standing discrepancy exists between experiments and atomistic models concerning the critical strain needed for surface nucleation of dislocations in silicon-germanium systems. While dislocation nucleation is readily observed in hetero-epitaxial thin films with misfit strains less than 4%, existing atomistic models predict that a critical strain over 7.8% is needed to overcome the kinetic barrier for dislocation nucleation. Using zero-temperature energy barrier calculations and finite-temperature Molecular Dynamics simulations, we show that 3-dimensional surface features such as a sharpl…
In situ straining experiments were performed in a TEM on an equimolar CoCrFeMnNi (Cantor) high entropy alloy at room and cryogenic temperature. Perfect and partial dislocation activity were recorded in both cases. Twinning directly follows the development of partial dislocation shearing that has various origins (perfect dislocation splitting, anchoring). It is shown that, although twinning is more frequently observed at liquid nitrogen temperature, its prevalence depends mainly on crystal orientation. As a result, twinning and perfect dislocation plasticity are likely to occur jointly in rando…
High-throughput, Non-Destructive, Three-Dimensional Imaging of GaN Threading Dislocations with in-Plane Burgers Vector Component via Phase-Contrast Microscopy
Predicting the behaviour of complex systems is one of the main goals of science. An important example is plastic deformation of micron-scale crystals, a process mediated by collective dynamics of dislocations, manifested as broadly distributed strain bursts and significant sample-to-sample variations in the response to applied loading. Here, by combining large-scale discrete dislocation dynamics simulations and machine learning, we study the problem of predicting the fluctuating stress-strain curves of individual small single crystals subject to strain-controlled loading using features of the …
This paper develops the small strain continuum dislocation theory accounting for statistically stored dislocations and Taylor hardening for single crystals. As illustration, the problem of anti-plane constrained shear of single crystal deforming in single slip is solved within the proposed theory. The distribution of geometrically necessary dislocations in the final state of equilibrium as well as the stress-strain curve exhibiting the Bauschinger translational work hardening and the size effect are found. Comparison with the stress-strain curve obtained from the continuum dislocation theory w…
The aim of this paper is to study the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin's gradient elasticity. We consider simple but rigorous versions of Mindlin's first gradient elasticity with one material length (gradient coefficient). Using the stress function method, we find modified stress functions for all six types of Volterra defects (dislocations and disclinations) situated in an isotropic and infinitely extended medium. By means of these stress functions, we obtain exact analytical solutions for the stress and strain fields of dislocatio…
The strain incompatibility equations are discussed for nonlinear Kirchhoff-Love shells with sources of inhomogeneity arising due to a distribution of topological defects, such as dislocations and disclinations, and metric anomalies, such as point defects, thermal strains, and biological growth. The incompatibility equations are given for all topological surfaces, with or without boundary, which are isometrically embeddable in a 3-dimensional Euclidean space.
In classical elasticity theory the stress-field of a dislocation is characterized by a $1/r$-type singularity. When such a dislocation is considered together with an Allen-Cahn-type phase-field description for microstructure evolution this leads to singular driving forces for the order parameter, resulting in non-physical (and discretization-dependent) predictions for the interaction between dislocations and phase-, twin- or grain-boundaries. We introduce a framework based on first strain gradient elasticity to regularize the dislocation core. It is shown that the use of strain energy density …
The interaction of crystalline defects leads to strain hardening in bulk metals. Metals with high stacking fault energy (SFE), such as aluminum, tend to have low strain hardening rates due to an inability to form stacking faults and deformation twins. Here, we use in situ SEM mechanical compressions to find that colloidally synthesized defect-free 114 nm Al nanocubes combine a high linear strain hardening rate of 4.1 GPa with a high strength of 1.1 GPa. These nanocubes have a 3 nm self-passivating oxide layer that has a large influence on mechanical behavior and the accumulation of dislocation…
In this paper we discuss the effect of a non-constant dislocation drag coefficient on the very high strain rate regime within an analytic model describing mobile-immobile dislocation intersections applicable to polycrystals. Based on previous work on dislocation drag, we estimate its temperature and pressure dependence and its effects on stress-strain rate relations. In the high temperature regime, we show that drag can remain the dominating effect even down to intermediate strain rates. We also discuss the consequences of having a limiting dislocation velocity, a feature which is typically pr…
We investigate the impact of threading dislocations with an edge component (a or a+c-type) on carrier recombination and diffusion in GaN(0001) layers close to the surface as well as in the bulk. To this end, we utilize cathodoluminescence imaging of the top surface of a GaN(0001) layer with a deeply buried (In,Ga)N quantum well. Varying the acceleration voltage of the primary electrons and comparing the signal from the layer and the quantum well enables us to probe carrier recombination at depths ranging from the close vicinity of the surface to the position of the quantum well. Our experiment…
The statistical-thermodynamic dislocation theory developed in previous papers is used here in an analysis of high-temperature deformation of aluminum and steel. Using physics-based parameters that we expect theoretically to be independent of strain rate and temperature, we are able to fit experimental stress-strain curves for three different strain rates and three different temperatures for each of these two materials. Our theoretical curves include yielding transitions at zero strain in agreement with experiment. We find that thermal softening effects are important even at the lowest temperat…
Plastic relaxation of the misfit stress in core-shell semi-conducting nanowires can lead to structural defects, detrimental to applications. Core-shell Zn{0.7}Mg{0.3}O/ZnO quantum well heterostructures were deposited on ZnO nanowires. Strain along the a and c axes of the wurtzite structure is relaxed through the glide of dislocation half-loops from the free surfaces, within pyramidal and prismatic planes. Some half-loops are closed up in the barriers to accommodate the misfit at two consecutive interfaces of the quantum well stack. Dislocations are also observed within the nanowire core: contr…
Comprehensive determination of Burgers vectors of threading dislocations in GaN substrates by combining reflection and transmission synchrotron-radiation x-ray topography
Structural transitions are invariably affected by lattice distortions. If the body is to remain crack-free, the strain field cannot be arbitrary but has to satisfy the Saint-Venant compatibility constraint. Equivalently, an incompatibility constraint consistent with the actual dislocation network has to be satisfied in media with dislocations. This constraint can be incorporated into strain-based free energy functionals to study the influence of dislocations on phase stability. We provide a systematic analysis of this constraint in three dimensions and show how three incompatibility equations …
The trigonal/bcc orientation relationships (ORs) and their likelihood of occurrence are extensively studied using dispersed Y4Zr3O12nano-precipitates in bcc Fe matrix by means of transmission electron microscopy, image simulations, and a crystallographic model. Two orientation relationships related by a rotation:[1-20]||[111] with (21-2)||(-110) and [1-20]||[111] with (00-3)||(-110), are established and periodic arrays of misfit dislocation doublets are identified at the strained interface in (110) for both ORs. Further eighteen energetically feasible ORs in Y4Zr3O12/bcc system are deduced by …
The kinetics of dislocations is studied with computer simulation at loadings of different intensity. It is established that the dislocations have a few different structural states. The dislocations "with the micropore" play important role in the formation of large curved boundaries, and, as a consequence, in the formation of fine grains. Alternation of elastic and inelastic strain stages is established too. At shear loading, in view of special kinetics, the system would have to accumulate the whole set of dislocations leading to the formation of new boundaries and fine grains.
We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations bilinear in the elastic distortion tensor and dislocation density tensor for the force and pseudomoment stresses of an isotropic solid. The constitutive relations contain six material parameters. In this theory both the force and pseudomoment stresses are asymmetric. The theory possesses four characteristic lengths l1, l2, l3 and l4 which are given explicitely. We first derive the three-dimensional Green tensor of the master equation for the force stresses in …
The impact of decorated dislocations on the effective thermal conductivity of GaN is investigated by means of equilibrium molecular dynamics simulations via the Green-Kubo approach. The formation of "nanowires" by a few atoms of In in the core of dislocations in wurtzite GaN is found to affect the thermal properties of the material, as it leads to a significant decrease of the thermal conductivity, along with an enhancement of its anisotropic character. The thermal conductivity of In-decorated dislocations is compared to the ones of pristine GaN, InN, and random and ordered InxGa1-xN alloy, to…
An exactly solvable phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations resulting from a piecewise quadratic Peierls potential; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles and lattice friction, resulting in hardening, path depende…
Plastic deformation of microsamples is characterised by large intermittent strain bursts caused by dislocation avalanches. Here we investigate how ion irradiation affects this phenomenon during single slip single crystal plasticity. To this end, in situ compression of Zn micropillars oriented for basal slip was carried out in a SEM. The unique experimental setup also allowed the concurrent recording of the acoustic emission (AE) signals emitted from the sample during deformation. It was shown that irradiation introduced a homogeneous distribution of basal dislocation loops that lead to hardeni…
The common practice of ignoring the elastic strain gradient in measurements of geometrically necessary dislocation (GND) density is critically examined. It is concluded that the practice may result in substantial errors. Our analysis points to the importance of spatial variations of the elastic strain field in relation to its magnitude in inferring estimates of dislocation density from measurements.
The calculated effects of interstitial hydrogen on the elastic properties of alpha-iron from our earlier work are used to describe the H interactions with homogeneous strain fields using ab initio methods. In particular we calculate the H solublility in Fe subject to hydrostatic, uniaxial, and shear strain. For comparison, these interactions are parametrised successfully using a simple model with parameters entirely derived from ab initio methods. The results are used to predict the solubility of H in spatially-varying elastic strain fields, representative of realistic dislocations outside the…
Our experiments show that in $^4$He crystals, the binding of $^3$He impurities to dislocations does not necessarily imply their pinning. Indeed, in these crystals, there are two different regimes of the motion of dislocations when impurities bind to them. At lowdriving strain $ε$ and frequency $ω$, where the dislocation speed is less than a critical value (45 $μ$m/s), dislocations and impurities apparently move together. Impurities really pin the dislocations only at higher values of $ω$. The critical speed separating the two regimes is two orders of magnitude smaller than the average speed of…
Strain fields, dislocations and defects may be used to control electronic properties of graphene. By using advanced imaging techniques with high-resolution transmission electron microscopes, we have measured the strain and rotation fields about dislocations in monolayer graphene with single-atom sensitivity. These fields differ qualitatively from those given by conventional linear elasticity. However, atom positions calculated from two dimensional (2D) discrete elasticity and three dimensional discrete periodized Föppl-von Kármán equations (dpFvKEs) yield fields close to experiments when deter…
We study numerically the minimum energy path and energy barriers for dislocation nucleation in a two-dimensional atomistic model of strained epitaxial layers on a substrate with lattice misfit. Stress relaxation processes from coherent to incoherent states for different transition paths are determined using saddle point search based on a combination of repulsive potential minimization and the Nudged Elastic Band method. The minimum energy barrier leading to a final state with a single misfit dislocation nucleation is determined. A strong tensile-compressive asymmetry is observed. This asymmetr…
