Spatial Distribution Of Dislocations Research Articles

Delineating dislocation structures and residual stresses in additively manufactured alloys

Dislocation structures and residual stresses have tremendous impact over the properties of alloys produced by fusion-based additive manufacturing (AM) processes. Yet, their origin is still unclear. We quantify and map, for the first time, the spatial distribution of dislocations, including those classified as geometrically necessary dislocations (GND), lattice strains, and type-III residual stresses in body-centered cubic (BCC) Ti-42Nb alloy and face-centered cubic (FCC) stainless steel (SS) 316L using a combination of electron channeling contrast imaging and cross correlation-based electron backscatter diffraction. Our findings reveal distinct residual stresses, lattice strains, and dislocation arrangement along cell walls in both alloys. In particular, Ti-42Nb demonstrates no GND network in cell walls, while SS316L exhibits a high GND density. We show that the Ti-42Nb alloy primarily accommodates solidification strains and cooling stresses elastically while SS316L accommodates them by elasto-plastic deformation and builds GNDs. Our work establishes relationships between dislocations and residual stresses in BCC and FCC LPBF alloys and highlights that not all LPBF-manufactured materials contain a dense dislocation network in their microstructures. These findings can also be extended to other AM alloys, therefore enabling a better control over their properties and performance.

A predictive discrete-continuum multiscale model of plasticity with quantified uncertainty

Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of uncertainty in the computational predictions delivered by them. In this work, a sequential multiscale model has been developed, incorporating discrete dislocation dynamics (DDD) simulations and a strain gradient plasticity (SGP) model to predict the size effect in plastic deformations of metallic micro-pillars. The DDD simulations include uniaxial compression of micro-pillars with different sizes and over a wide range of initial dislocation densities and spatial distributions of dislocations. An SGP model is employed at the continuum level that accounts for the size-dependency of flow stress and hardening rate. Sequences of uncertainty analyses have been performed to assess the predictive capability of the multiscale model. The variance-based global sensitivity analysis determines the effect of parameter uncertainty on the SGP model prediction. The multiscale model is then constructed by calibrating the continuum model using the data furnished by the DDD simulations. A Bayesian calibration method is implemented to quantify the uncertainty due to microstructural randomness in discrete dislocation simulations (density and spatial distribution of dislocations) on the macroscopic continuum model prediction (size effect in plastic deformation). The outcomes of this study indicate that the discrete-continuum multiscale model can accurately simulate the plastic deformation of micro-pillars, despite the significant uncertainty in the DDD results. Additionally, depending on the macroscopic features represented by the DDD simulations, the SGP model can reliably predict the size effect in plasticity responses of the micropillars with below 10% of error.

High-Resolution Residual Stress Mapping of Magnesium AZ80 Friction Stir Welds for Three Processing Conditions

Low-angle synchrotron transmission diffraction has been used to create high-resolution 2D residual strain maps of friction stir welds made with three processing conditions. These spatial maps of residual strain reveal local concentrations not detectable by line scans, and confirm that the asymmetric material flow known to produce asymmetric temperature and texture distributions also results in asymmetric residual strain distributions. The experimental set-up permitted simultaneous measurement of both texture and strain, which provides strong evidence against the correlation of these features in magnesium friction stir welds. Mapping diffraction peak width across the weld provides insight into the spatial distribution of dislocations and microstrains, and indicates locations of interest for higher resolution research such as TEM. A diffraction method is presented to determine the solute content of a ternary system using the lower symmetry of a non-cubic system, which can be extended to detecting the onset of precipitation among other applications. Comparison of three friction stir-welding conditions shows how the residual strains at the interface can reverse from compressive to tensile with decrease in the heat input, explaining a significant disparity in the literature results. Lower residual stress values were found to be well-correlated with improved transverse tensile behavior.

Dislocation bending in GaN/step-graded (Al,Ga)N/AlN buffer layers on Si(111) investigated by STM and STEM

ABSTRACTThe distribution and bending of dislocations in GaN/step-graded (Al,Ga)N/AlN buffer layers grown on Si(111) are investigated by cross-sectional scanning tunnelling microscopy (STM) and scanning transmission electron microscopy (STEM). We observe dislocations with -type Burgers vector intersecting the m-plane cleavage surface and having line directions bent off the [0001] growth direction toward non-polar directions. The spatial distribution of dislocations intersecting the m-plane cleavage surface indicates consecutive bending of dislocations due to strain at interfaces between subsequent lattice mismatched buffer layers and at doping junctions, reducing the density of threading dislocations at the (0001) growth front. No interface misfit dislocations, v-shaped defects, or loss of crystalline quality are observed, demonstrating the high performance of the step-graded (Al,Ga)N/AlN buffer layers on Si for relaxing the lattice constant without creating large defect concentrations.

Resonances of the Spatial Distribution of Dislocations upon Interaction with the Structural Order Parameter

The interaction of a structural subsystem with dislocations under the superposition of an elastic torsion strain and an additional uniaxial spatially nonuniform time-constant pressure is studied. The analysis is carried out within of Landau’s phenomenological theory with refusal of the approximation of constant magnitudes of irreducible vectors. The rise of spatial resonances of the dislocation density in these conditions is shown.

Shape and quality of Si single bulk crystals grown inside Si melts using the noncontact crucible method

The noncontact crucible method enables production of Si bulk single crystals without crucible contact by intentionally establishing a distinct low-temperature region in the Si melt. In this contribution, we correlate crystal growth conditions to crystal material properties. The shape of the growing interface was generally convex in the growth direction. The quality of the Si ingots was determined by the spatial distributions of dislocations, resistivity, oxygen concentration, and minority-carrier lifetime. In an ingot with a convex bottom, swirl patterns with higher resistivity are present in the top, middle, and bottom of the ingot. The dislocation density decreased from the top (first to solidify) to the bottom of the ingot because dislocations in the ingot moved to the periphery from the center of the ingot during crystal growth owing to the convex growing interface. The oxygen concentration was concentrically distributed on the seed axis owing to the convex growing interface. The lifetime was as high as 1.8 ms after phosphorus diffusion gettering (PDG) and 205 µs before PDG at an injection level of 1 × 1015 cm−3. The lifetime was not strongly affected by the dislocation density, which was as low as 102–103 cm−2.

Numerical implementation of static Field Dislocation Mechanics theory for periodic media

This paper investigates the implementation of Field Dislocation Mechanics (FDM) theory for media with a periodic microstructure (i.e. the Nye dislocation tensor and the elastic moduli tensor are considered as spatially periodic continuous fields). In this context, the uniqueness of the stress and elastic distortion fields is established. This allows to propose an efficient numerical scheme based on Fourier transform to compute the internal stress field, for a given spatial distribution of dislocations and applied macroscopic stress. This numerical implementation is assessed by comparison with analytical solutions for homogeneous as well as heterogeneous elastic media. A particular insight is given to the critical case of stress-free dislocation microstructures which represent equilibrium solutions of the FDM theory.

Determination of the dislocation structure in paratellurite single crystals using the piezo-optic effect

It is shown theoretically and experimentally that dislocations in paratellurite single crystals can be revealed using the piezo-optic effect. The mechanical-stress distribution near dislocations is calculated. Dislocations in the samples are observed using the photoelastic method and chemical etching. Data on the spatial distribution of dislocations in Czochralski-grown paratellurite crystals are reported.

Spatial Distribution of Dislocations in Relation to a Substructure in High-Quality GaN Film

The dislocation distribution of high-quality single-crystal gallium nitride (GaN) films grown by the hybrid vapor phase epitaxy was analyzed. This study examined the domain structure of GaN from the dislocation distribution on the macroscale by optical microscopy. The surface structure of GaN consisted of domains with microcolumns as the substructure. The inner domains contained a lower density of dislocations but a large number of these dislocations were observed along the domain boundaries. The existence of a domain boundary structure doubly increased the total dislocation density.

Microscale Spatial Distribution of Dislocations and Long Range Internal Stresses in Cold Worked bcc Fe

Microscale Spatial Distribution of Dislocations and Long Range Internal Stresses in Cold Worked bcc Fe

Dislocation Formation in Trench-Based Dynamic Random Access Memory (DRAM) Chips

AbstractThis paper reports on our studies of dislocation formation in trench capacitor DRAM structures. Experimental results on process dependence and layout dependence of dislocation formation in cell layouts with minimum feature sizes from 0.5 μm to 0.25 μm are compared to two-dimensional stress simulations. It is shown that the nucleation and spatial distribution of dislocations can be explained by considering stress fields which are influenced by the overlay of deep trench and shallow trench isolation structures.

Influence of Dislocations on the I-V Characteristics of Silicon Solar Cells

AbstractThis paper presents a phenomenological approach for analysis of dislocations in a large-area device like a solar cell. A microscopic model of a dislocation is used to calculate the local effects of a dislocation on the dark and the illuminated characteristics of a p-n junction device. A statistical approach is then used to empirically arrive at the I-V characteristics of a small-area device with a uniform distribution of dislocations. Finally, these results are applied to develop a network model to determine the terminal characteristics of a large-area solar cell of a known spatial distribution of dislocations. We show that the performance of a solar cell is influenced not only by the density of dislocations but also by their spatial distribution; heavily dislocated regions exert a disproportionately large degradation effect on the device characteristics.

Applications of Scanning Defect Mapping System for Semiconductor Characterization

AbstractA laser scanning system has been developed by the National Renewable Energy Laboratory for the rapid characterization of crystal defects in single- and poly-crystalline semiconductors. The scanning defect mapping system has been commercialized by Labsphere, Inc. as the PVScan 5000. In the unprocessed material, the system produces digital color maps of the spatial distributions of dislocations and grain boundaries simultaneously. After device fabrication, the PVScan 5000 is used to produce photoresponsivity maps of the light beam induced current (LBIC) on a photovoltaic device such as a solar cell or a photodetector. An additional feature is that it also measures the spatial distributions of optical reflectance, both specular and diffuse, which can be applied to the LBIC maps to determine the internal responsivity of the device. The internal responsivity is proportional to the minority carrier diffusion length of silicon devices. It may be possible, therefore, to determine the diffusion length for certain devices.

Internal stresses and scaling laws

The internal stress associated with dislocation walls is calculated for the following cases: infinite periodic wall, disordered wall, incomplete walls or dihedral walls. The relation between the internal stress and the flow stress is discussed. Scaling laws connecting the latter with the spatial distribution of dislocations are derived.

Dislocation ensemble movement through random arrays of obstacles

Abstract The formation of gliding dislocation ensembles for different external stresses in a slip plane with randomly distributed obstacles of one and a few types has been investigated with the help of computer experiments. The spatial distribution of dislocations in such ensembles and the properties of single dislocations have been analysed.

Dislocations energy in deformed copper crystals

Measurements of the dislocation density and the energy released during recovery and recrystallization were used to calculate the specific dislocation energy in deformed copper crystals. The experimental data have been compared with the theoretical estimates on the energy stored by crystals with different spatial distributions of dislocations. The total energy of dislocations in deformed copper crystals has been shown to include the statistically averaged contributions from the short-range stresses due to the configurations similar to isolated dipoles or dispersed dislocations of opposite signs, as well as the long-range stresses from dislocation pile-ups or other dislocation groups. [Russian Text Ignored.]

An analysis of plastic deformation around stationary cleavage cracks

The spatial distribution of plastic deformation around cleavage cracks formed by the precipitation of hydrogen gas was observed as dislocation etch pits in iron-silicon single crystals. It was found that the spatial distribution of dislocations can be explained by the calculated angular variation of the force on dislocations near the crack tip. The variation of plastic deformation with temperature and silicon content is consistent with the temperature and composition dependence of the critical resolved shear stress.