Geometry Of Dislocations Research Articles

Atomic-scale models for hardening in fcc solid solutions

Atomic-scale simulations are associated with an elastic line model to analyze thoroughly the pinning strength experienced by an edge dislocation in some face-centered-cubic solid solutions, Al(Mg) and Ni(Al) with solute concentration comprise between 1 and $10\text{ }\text{at}\text{.}\text{ }\mathrm{%}$. The one-dimensional elastic line model is developed to sketch out the details of the atomic scale. The account of such details is shown to yield a proper description of the dislocation statistics for the different systems. The quantitative departure between hardening in Al(Mg) and Ni(Al) is then demonstrated to hinge on the difference in the short-range interaction between the partial dislocations and the isolated impurities. It is also shown that an accurate description of the solid-solution hardening requires the account for the dislocation geometry and the dislocation interaction with clusters of solute atoms. The elastic line model allows us to perform some computations at the microscopic scales meanwhile accounting for the most important atomic details. A comparison with experimental data is attempted.

Strain fields and line energies of dislocations in uranium dioxide

Computer simulations are used to investigate the stability of typical dislocations inuranium dioxide. We explain in detail the methods used to produce the dislocationconfigurations and calculate the line energy and Peierls barrier for pure edge and screwdislocations with the shortest Burgers vector . The easiest slip system is found to be the{100}⟨110⟩ system forstoichiometric UO2, in agreement with experimental observations. We also examine the differentstrain fields associated with these line defects and the close agreement betweenthe strain field predicted by atomic scale models and the application of elastictheory. Molecular dynamics simulations are used to investigate the processes of slipthat may occur for the three different edge dislocation geometries and nudgedelastic band calculations are used to establish a value for the Peierls barrier,showing the possible utility of the method in investigating both thermodynamicaverage behaviour and dynamic processes such as creep and plastic deformation.

Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction

The deformation around a 500-nm deep Berkovich indent in a large grained Fe sample has been studied using high resolution electron back scatter diffraction (EBSD). EBSD patterns were obtained in a two-dimensional map around the indent on the free surface. A cross-correlation-based analysis of small shifts in many sub-regions of the EBSD patterns was used to determine the variation of elastic strain and lattice rotations across the map at a sensitivity of ∼±10−4. Elastic strains were smaller than lattice rotations, with radial strains found to be compressive and hoop strains tensile as expected. Several analyses based on Nye's dislocation tensor were used to estimate the distribution of geometrically necessary dislocations (GNDs) around the indent. The results obtained using different assumed dislocation geometries, optimisation routines and different contributions from the measured lattice rotation and strain fields are compared. Our favoured approach is to seek a combination of GND types which support the six measurable (of a possible nine) gradients of the lattice rotations after correction for the 10 measurable elastic strain gradients, and minimise the total GND line energy using an L1 optimisation method. A lower bound estimate for the noise on the GND density determination is ∼±1012 m−2 for a 200-nm step size, and near the indent densities as high as 1015 m−2 were measured. For comparison, a Hough-based analysis of the EBSD patterns has a much higher noise level of ∼±1014m−2 for the GND density.

COMPARATIVE STUDY OF SINGLE CRYSTAL CONSTITUTIVE EQUATIONS FOR CRYSTAL PLASTICITY FINITE ELEMENT ANALYSIS

Two sets of single crystal constitutive equations used for the crystal plasticity finite element analysis are comparatively investigated by simulating simple deformation of oriented single crystals. The first of these consists of conventional constitutive equations, which have been adopted for the prediction of deformation texture and their parameters are generally obtained by back-fitting polycrystalline stress-strain response. The other set uses interactions between moving dislocations on the primary slip system and the corresponding forest dislocations. The idealized Orowan hardening mechanism is adopted for the calculation of the critical force, and constitutive parameters are determined by the geometry of dislocations, thus less fitting procedure is involved. The stress-strain curves of copper single crystal are used to demonstrate how the two models work for the orientation dependent stress-strain responses.

Threading dislocations in domain-matching epitaxial films of ZnO

The structures of high-quality ZnO epitaxial films grown by pulsed-laser deposition on sapphire (0001) without an oxygen gas flow were investigated by X-ray diffraction and transmission electron microscopy. The great disparity of X-ray diffraction line widths between the normal and in-plane reflections reveals the specific threading dislocation geometry of ZnO. Most threading dislocations are pure edge dislocations. From a combination of scattering and microscopic results, it is found that threading dislocations are not uniformly distributed in the ZnO films, but the films consist of columnar epitaxial cores surrounded by annular regions of edge threading dislocations in large density. The local surface morphology and capacitance signal obtained from atomic force and scanning capacitance microscopes indicate that the aggregation of threading dislocations leads to high interface traps at the annular regions.

Screw dislocations interacting with a partially debonded interface in cylindrically anisotropic composites

Interaction between screw dislocations and a partially debonded interface in cylindrically anisotropic composites subjected to uniform stress at infinity is investigated in this paper. Using Muskhelishvili’s complex variable method, the closed forms of complex potentials are obtained for a screw dislocation and a screw dislocation dipole located inside either matrix or inhomogeneity. Explicit expressions of stress intensity factors at the crack tips, image forces and image torques acting on dislocation or the center of dipole are provided. The results show that the crack and dislocation geometry combination plays an important role in the interaction between screw dislocations and interface crack. Furthermore, it is found that the anisotropy of solids may change the shielding and anti-shielding effects arising from screw dislocations and the equilibrium position of screw dislocations. The presented solutions are valid for anisotropic, orthotropic or isotropic composites and can be reduced to some novel or previously known results.

Interaction of a surface wave with a dislocation

The scattering of a surface wave by a pinned edge dislocation in a semi-infinite, homogeneous, isotropic, three-dimensional elastic solid is investigated analytically and numerically. An incident wave excites the dislocation that responds by oscillating as a string endowed with mass, line tension, and damping. The oscillations of the stringlike dislocation generate secondary (``scattered'') elastic waves that are the primary object of interest in this study. The back reaction of the re-emitted waves on the dislocation dynamics is neglected, but the wavelength of the radiation is allowed to be large, comparable, or small compared to the length of the dislocation. In view of recent experimental visualizations of these phenomena, we focus particularly on the field behavior at the free surface near the dislocation, and not just on the far field. For the same reason, it is the vertical component of displacement at the free surface that is studied in detail. An efficient numerical procedure for the computation of the appropriate components of the Green's function, using a Filon quadrature for the integration of rapidly oscillating functions, is developed. The numerics is validated with known analytical expressions. The secondary radiation generated by the response of the dislocation to the incident wave is also calculated numerically, and the results are also validated by comparing them with the analytical expressions that can be obtained when the radiation wavelength is very long compared to dislocation length. The interference pattern between incident wave and secondary wave that is generated at the free surface is studied in detail and found to depend strongly not only on wavelength and dislocation geometry (length and orientation) but also on dislocation depth, with the response of the dislocation being a particularly sensitive function of such depth. Results are compared with recent experiments of Shilo and Zolotoyabko [Phys. Rev. Lett. 91, 115506 (2003)] that report visualizations of the surface-wave--dislocation interaction using stroboscopic x-ray imaging. A satisfactory agreement is found. Dislocation velocities of a few percent of the speed of sound and viscosity coefficients of about ${10}^{\ensuremath{-}5}\phantom{\rule{0.3em}{0ex}}\mathrm{Pa}\phantom{\rule{0.2em}{0ex}}\mathrm{s}$ are inferred.

Association between dislocation, impingement, and articular geometry in retrieved acetabular polyethylene cups

We used a novel analysis technique and retrieved acetabular polyethylene liners to investigate relationships between impingement damage, dislocation history, and polyethylene liner geometry. Forty-eight polyethylene liners with neutral rim elevation were visually assessed for peripheral rim damage consistent with impingement between the liner rim and femoral component. Liner articular geometry was measured using a digital stylus, and the geometric relationships between the liner rim and center of the femoral head were characterized by lip height, head center inset, and head penetration into the polyethylene liner. Thirteen (27%) retrieved liners had rim impingement damage and 12 (25%) had a history of dislocation. The proportion of liners with impingement was not significantly different among dislocated and stable liners. Lip height, head center inset, and head penetration were not significantly different between liners with and without impingement damage. Dislocated liners had a significantly shorter head center inset, with significantly less head penetration because of shorter functional duration. Designing polyethylene liners with a sufficiently deep articular surface that exceeds 0.95 mm may prove beneficial for decreasing the prevalence of early dislocation, independent of impingement damage.

Geometry of dislocations in icosahedral quasicrystals

Quasicrystals are complex metallic alloys that are ductile at high temperatures close to their melting point. It has been early recognized that their plasticity is due to a flux of moving linear defects in all respects similar to dislocations in ordinary crystals. The present paper is an attempt to propose in a short didactic review a simple synthetic analysis of the basic underlying geometry of quasicrystalline dislocations exemplified with experimental and calculated images of electron microscopy in icosahedral phases.

Growth and characterization of semi-polar (11-22) GaN with in-situ SiNx interlayers

ABSTRACTSemi-polar (1122) GaN films were grown on (1100) m-plane sapphire substrates. Growth demonstrated surface striations aligned perpendicular to the in-plane GaN m-axis. SiNx interlayers were incorporated into the as-grown films with the purpose of decreasing the density of defects in the material. Inclusion of interlayers increased the characteristic length of surface striations and feature size. X-ray rocking curves widths are shown to be correlated to specific threading dislocation geometry. Skew-symmetric omega scan peak broadening suggests a decrease in the proportion of screw-type dislocations to edge-type dislocations with increasing number of interlayers.

Strain accumulation in the southern Alps (NE Italy) and deformation at the northeastern boundary of Adria observed by CGPS measurements

We use continuous GPS observations to investigate the rate of strain accumulation in the area affected by the 1976 Friuli earthquakes. Comparison between the motion predicted by the rigid‐rotation of Adria and the shortening observed across the study area suggests that the 2.0 ± 0.2 mm/yr motion of Adria is entirely absorbed in the southern Alps through thrusting and crustal thickening with very little or no motion transferred to the north. We use elastic dislocation modelling to investigate the rate of interseismic loading and the geometry of the shear zone at depth. The best‐fit solution indicates that a northward‐dipping creeping dislocation, whose edge is located within a 50 km wide area beneath the southern Alps, accomodates 2.1 ± 0.5 mm/yr of the Adria motion. Limited resolution on locking depth (acceptable values between 0 and 25 km) and trade‐off between dip and slip do not allow a precise reconstruction of the dislocation geometry. The range of acceptable model parameters is consistent with a 20°‐dipping dislocation, locked above 10 km depth and slipping at 2.4 mm/yr, whose geometry is suggested by seismological informations.

Interfacial reaction mechanisms and the structure of moving heterophase boundaries during pyrochlore- and spinel-forming solid state reactions

If bulk or thin-film ceramics consisting of more than one component are subjected to a high temperature during processing or use, interfacial solid – solid reactions occur between the components. To understand this type of reactions, the atomic structure of various reactive oxide/pyrochlore and oxide/spinel model interfaces is studied by high-resolution transmission electron microscopy. Kinetics of the pyrochlore- and spinel-forming reactions at these interfaces are shown to depend on the atomic structure of the interface, in particular on that of the interfacial dislocations. During the reaction, these dislocations have to move together with the advancing interface. Accordingly, reaction kinetics are determined by the mode of dislocation movement and, thus, by the Burgers vector geometry of the interfacial dislocations. The type of interfacial dislocations is, in turn, influenced by the stress conditions during the initial stage of the solid state reaction.

Nanopatterning of periodically strained surfaces: Predictive kinetic Monte Carlo simulation study

We present a method based on kinetic Monte Carlo simulations to atomically control the nanopatterning by using strain-assisted nucleation of adatom islands on periodically strained surfaces. It is presumed in the model that there is a capping layer of optional thickness terminated by an atomically flat surface above a dislocated interface. By varying the dislocation spacing and geometry as well as the capping layer material and thickness, the surface strain field can be modified. For the model system Co on Pt(111) the optimal growth condition is demonstrated for a surface strain field of period 9 nm for structures with an 8–10-ML-thick Pt capping layer. For these parameters strongly enhanced nucleation at maxima in the periodic strain field is achieved. We study also the effects on the self-organization of strain-relaxed adatom islands and the effects of modified potential energy barriers at step edges, i.e., the Ehrlich–Schwoebel (ES) barriers. Both strain relaxation and ES barriers are found to be of large importance for the nanopatterning. Finally, various nanostructures obtained for different strain fields including parallel, rhomboid, and hexagonal geometries are considered. The method described in this investigation is not restricted to the “Co on Pt(111)” and “Ag on Ag(111)” model systems. The simulation model is of general interest to predict strain-assisted growth of metals and also of semiconductors.

Slip geometry of dislocations related to cutting of the γ′ phase in a new generation single-crystal superalloy

The superdislocations in the γ′ phase of a fourth-generation single-crystal TMS-138 superalloy have been characterized after creep rupture at a stress of 137 MPa under different temperatures. The number of slip dislocations increases with the increase of creep temperatures from 1100 to 1150 °C. The dominant cutting mode of the γ′ phase is dislocation pairs coupled by an antiphase boundary (APB). The popular superdislocations in the γ′ phase show screw character with Burgers vectors <0 1 1> or <1 0 1>. Also, observed in the γ′ phase are 60° or screw superdislocations in either [1 1 0] or [ 1 1 ̄ 0 ] directions, and [0 0 1] edge superdislocations. Stacking faults are seen from the dissociation of superdislocations. These superdislocations are related to the damage of the rafted structure in the superalloy.

Misfit Accommodation by Screw Dislocations

Experiments in which a thin compliant layer, CS, is twist-bonded to a bulk substrate, BS, of the same material showed that heteroepitaxial deposits grown on the compliant layer were of a much higher quality (lower dislocation content) than those grown directly on the substrate. The explanation of this effect is that the compliant substrate, rather than the deposit, elastically deforms to accommodate the misfit and avoids the generation of misfit dislocations in the deposit with their accompanying threading segments. The elastic strain of the compliant substrate is facilitated by the presence of an array of interfacial screw dislocations that lower the energy barrier to sliding in the CS/BS interface. The additional role of the screw dislocations is to reorient their axes in the CS/BS interface to introduce an edge component that accommodates misfit. The geometry and energy of the interfacial dislocations is investigated and the energy changes to accommodate misfit are semi-quantitatively evaluated.

Free-Surface Effects in 3D Dislocation Dynamics: Formulation and Modeling

Recent advances in 3-D dislocation dynamics include the proper treatment of free surfaces in the simulations. Dislocation interaction and slip is treated as a boundary-value problem for which a zero-traction condition is enforced at the external surfaces of the simulation box. Here, a new rigorous method is presented to handle such a treatment. The method is semi-analytical/numerical in nature in which we enforce a zero traction condition at select collocation points on a surface. The accuracy can be improved by increasing the number of collocation points. In this method, the image stress-field of a subsurface dislocation segment near a free surface is obtained by an image segment and by a distribution of prismatic rectangular dislocation loops padding the surface. The loop centers are chosen to be the collocation points of the problem. The image segment, with proper selection of its Burgers vector components, annuls the undesired shear stresses on the surface. The distributed loops annul the undesired normal stress component at the collocation points, and in the process create no undesirable shear stresses. The method derives from crack theory and falls under “generalized image stress analysis” whereby a distribution of dislocation geometries or entities (in this case closed rectangular loops), and not just simple mirror images, are used to satisfy the problem’s boundary conditions (BCs). Such BCs can, in a very general treatment, concern either stress traction or displacements.

A coupled atomistic/continuum model of defects in solids

A method is introduced for reducing the degrees of freedom in simulations of mechanical behavior of materials without sacrificing important physics. The method essentially combines the quasicontinuum (QC) method with continuum defect models such as the discrete dislocation (DD) method. The QC formulation is used to couple a fully atomistic region to a defect-free elastic continuum. Defects existing in the elastic continuum region of the full problem of interest are treated by the DD-like methods with special boundary conditions. The full coupled problem is then solved by an Eshelby-like procedure involving superposition of the QC and DD problems, and is appropriate in both 2d and 3d. Special attention is given to dealing with dislocation defects. A procedure for the “passing” of dislocation defects from the atomistic to the continuum description in 2d problems is also presented. The overall 2d method with dislocation defects is validated by comparing the predictions of the coupled model to “exact” fully atomistic models for several equilibrium dislocation geometries and a nanoindentation problem in aluminum, and excellent agreement is obtained. The method proposed here should find application to a broad host of problems associated with the multiscale modeling of atomistic, nano- and micromechanical behavior of crystalline solids under mechanical loads.

Some Defect Types in Intermetallics and their Consequences

ABSTRACTThis short introductory overview focuses on point defects and their practical implications, on antiphase domains, and also on a feature that is not always perceived as a defect – imperfect long-range order. All these defect types have consequences for mechanical behavior of various kinds; imperfect LRO also affects the superconducting behavior of A15s. Other unfamiliar defects in intermetallics, to be outlined, include ‘rattling atoms’ in certain thermoelectric materials. Geometry and dynamics of dislocations in intermetallics are left to other contributors.

High quality two-dimensional photonic crystal slab cavities

We have fabricated and characterized donor-mode nanocavities formed by a single defect cavity defined within a two-dimensional photonic crystal slab. Quantum dots emitting in the 1.1–1.3 micron range were used as luminescence sources, and a design using fractional edge dislocations was used to demonstrate well-confined dipole modes with high quality factors. By applying the fractional dislocation geometry, the measured quality factor could be increased to values as high as 2800. This compares with typical quality factors of around 1500 measured from more conventional shallow donor mode cavities with larger mode volumes.

Dislocation geometry in the TGB(A) phase: linear theory.

We demonstrate that an arbitrary system of screw dislocations in a smectic-A liquid crystal may be consistently treated within harmonic elasticity theory, provided that the angles between dislocations are sufficiently small. Using this theory, we calculate the ground-state configuration of the TGB(A) phase. We obtain an estimate of the twist-grain-boundary spacing and screw dislocation spacing in a boundary in terms of the macroscopic parameters, in reasonable agreement with experimental results.