Magnetoresistivity of metals II. Application to point defects in copper

The general theory given previously is applied to copper single crystals containing various kinds of point defects. The matrix elements of the scattering potential with Wannier functions, which determine the transition probability, are chosen such as to satisfy the charge neutrality condition (Friedel's sum rule) and to give a prescribed electrical resistivity in zero magnetic field. Numerical calculations are carried out for the Fermi surface due toShoenberg andRoaf. The computed Kohler and rotation diagrams for magnetoresistivity, transverse-even effect, and Hall effect at low temperatures are in satisfactory agreement with measurements. The influence of different anisotropic scattering mechanisms and of the anisotropic Fermi surface is discussed in terms of the Kohler diagrams and rotation diagrams.     

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.     

Room temperature polarized photoreflectance and photoluminescence characterization of AlGaAs/InGaAs/GaAs high electron mobility transistor structures

We have characterized the properties of three AlGaAs/InGaAs/GaAs pseudomorphic high electron mobility transistor structures with two different well widths fabricated by molecular beam epitaxy on (0 0 1) GaAs substrates with different threading dislocation densities using room temperature photoreflectance (PR) and photoluminescence (PL). The samples were denoted as A, B and C with well widths of 140, 160 and 160 Å, respectively. Samples A and B were grown on substrates with lower threading dislocation densities. For samples B and C, the well width exceeds the pseudomorphic limit so that there is some strain relaxation and related misfit dislocations, as determined from X-ray measurements. In order to detect the anisotropic strain of the misfit dislocations related to strain relaxation, the PR measurements were performed for incident light polarized along [1 1 0] and directions. Evidence for the influence of the strain relaxation upon the relaxed channel was provided by the observed anisotropy of the polarized PR features and reduction of the intensity of PL signals in the InGaAs channel layer. The lowest lying intersubband transition has been confirmed by a comparison of the PR and PL spectra. Signals have been observed from every region of the sample making it possible to evaluate the In and Al compositions, channel width and two-dimensional electron gas density as well as the properties of the GaAs/AlGaAs multiple quantum well buffer layer.     

石墨烯/铝基复合材料在纳米压痕过程中位错与石墨烯相互作用机制的模拟研究

石墨烯因其优异的力学性能已成为增强金属基复合材料的理想增强体.然而,目前对石墨烯/金属基复合材料在纳米压痕过程中嵌入石墨烯与位错之间的相互作用仍不清晰.本文采用分子动力学模拟方法,对90°,45°和0°位向的石墨烯/铝基复合材料进行了纳米压痕模拟,研究了压痕加载和卸载过程中石墨烯/铝基复合材料的位错形核及演化,以获取不同位向的石墨烯与位错的相互作用机制,并分析其对塑性区的影响.研究发现,石墨烯可以有效阻碍位错运动,并且石墨烯会沿着位错滑移方向发生弹性变形.在纳米压痕过程中,位错与不同位向石墨烯之间的相互作用差异导致塑性区的变化趋势不同.研究结果表明,在石墨烯/铝基复合材料中,位向不同的石墨烯对位错阻碍强度和方式不同,且石墨烯位向为45°的复合材料的硬度高于其他模型.此外,石墨烯/铝基复合材料的位错线总长度的演化规律与石墨烯位向紧密相关.本文研究可为设计和制备高性能石墨烯/金属基复合材料提供一定的理论指导.     

Model of ideal relaxation of thermoelastic stresses in the course of growth of single crystals

A simple dislocation model is proposed for relaxation of thermoelastic stresses generated during the growth of single crystals from a melt. This model does not require a solution of the kinetic equations for dislocations involved in relaxation and makes it possible to obtain the lower estimate of the dislocation density in the bulk of a grown crystal.     

New mechanism of irradiation creep based on the radiation-induced vacancy emission from dislocations

A new mechanism of irradiation creep is proposed, which is based on the radiation and stress induced difference in emission (RSIDE) of vacancies from dislocations of different orientations with respect to the external stress. This phenomenon is due to the difference in vacancy formation energies, which is proportional to the external stress. The proposed model exhibits similarities with thermal creep models and it is distinct from stress-induced preferential absorption (SIPA) models based on the difference in the long-range interaction of point defects with dislocations. The RSIDE creep rate is essentially temperature independent and is proportional to the dislocation density, stress and irradiation flux. It is inversely proportional to the square of the vacancy formation energy, which is lower than the Frenkel pair formation energy. Experimental verification of the proposed model is discussed on the basis of the measurements of vacancy concentration and creep rate under sub-threshold electron irradiation.     

Quantifying the grain boundary resistance against slip transfer by experimental combination of geometric and stress approach using stage-I-fatigue cracks

In recent studies, many groups have investigated the interaction of dislocations and grain boundaries by bi-crystals and micro-specimen experiments. Partially, these experiments were combined with supplementary simulations by discrete dislocation dynamics, but quantitative data for the grain boundary resistance against slip transfer is still missing. In this feasibility study with first results, we use stage-I-fatigue cracks as highly localised sources for dislocations with well-known Burgers vectors to study the interaction between dislocations in the plastic zone in front of the crack tip and selected grain boundaries. The stress concentration at the grain boundary is calculated with the dislocation-free zone model of fracture using the dislocation density distribution in the plastic zone from slip trace height profile measurements by atomic force microscopy. The grain boundary resistance values calculated from common geometric models are compared to the local stress distribution at the grain boundaries. Hence, it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer to a self-contained concept. As a result, the prediction of the grain boundary resistance effect based on a critical stress concept is possible with knowledge of the geometric parameters of the grain boundary only, namely the orientations of both participating grains and the orientation of the grain boundary plane.     

Redistribution of dislocations in silicon near stress concentrators

The distribution of defects in dislocation tracks in silicon plates was studied for various indentation angles. The regularities of variations in the linear density and maximum path of dislocations in slip bands are established. A model is proposed to describe the distribution of dislocations in the dislocation tracks. By fitting the theory to the experimental data, the dependence of this distribution on the energy relaxation time is determined.     

Der Einfluß struktureller Fehlstellen in polykristallinem Kupfer auf den Magnetwiderstand

The longitudinal magnetoresistance of polycrystalline copper wires was observed at 4,6°K after various treatments. Deviations of the Kohler rule occur when the predominant scattering centers are changed from foreign atoms to self-interstitials and vacancies and to Frank dislocation loops. The experimental results show that the magnetoresistance depends on the configuration of scattering centers and can be used to investigate the scattering potentials for conduction electrons.     

Geometrically necessary dislocations in FCC polycrystalline metallic materials on the mesoscale

The dislocation structure of deformed copper alloys doped with Mn and Al was determined by selected area diffraction (SAD), performed using a transmission electron microscope. The scalar dislocation density, the density of geometrically necessary dislocations, and the density of statistically stored dislocations were measured. Special attention was given to the size of grains. The effect of size on the accumulation of geometrically necessary dislocations was studied.     

3D DDD modelling of dislocation–precipitate interaction in a nickel-based single crystal superalloy under cyclic deformation

Strain-controlled cyclic deformation of a nickel-based single crystal superalloy has been modelled using three-dimensional (3D) discrete dislocation dynamics (DDD) for both [0?0?1] and [1?1?1] orientations. The work focused on the interaction between dislocations and precipitates during cyclic plastic deformation at elevated temperature, which has not been well studied yet. A representative volume element with cubic γ′-precipitates was chosen to represent the material, with enforced periodical boundary conditions. In particular, cutting of superdislocations into precipitates was simulated by a back-force method. The global cyclic stress–strain responses were captured well by the DDD model when compared to experimental data, particularly the effects of crystallographic orientation. Dislocation evolution showed that considerably high density of dislocations was produced for [1?1?1] orientation when compared to [0?0?1] orientation. Cutting of dislocations into the precipitates had a significant effect on the plastic deformation, leading to material softening. Contour plots of in-plane shear strain proved the development of heterogeneous strain field, resulting in the formation of shear-band embryos.     

Selective excitation of two-wave structure depending on crystal orientation under shock compression

Single crystals subjected to shock compression exhibit responses with distinct two-wave structures for certain crystal orientations. However, little is known to date regarding how the shock response depends on crystal orientation, and especially why the two-wave structure depends on the crystal orientation. In this work, molecular dynamics simulations of shock compressions in copper single crystals are performed to investigate the orientation dependence of shock responses and the corresponding deformation mechanisms. Four copper single crystals with [001], [011], [012], and [123] crystal orientations along the depth direction are investigated. The [011], [012], and [123] crystal orientations of copper single crystals show distinct two-wave structures in their shock responses, while such a two-wave structure in the shock response is not seen for those orientations having a [001] crystal orientation. The potential causes are analyzed by considering the propagation velocities of both elastic and plastic waves. We develop a technique for identifying twin structures in face-centered cubic crystals and this technique can effectively identify the twin structure. The morphology of shock-induced defects(e.g., dislocations and twins) shows the significant dependence of crystal orientation and the mechanisms behind these are discussed in detail. Finally, the Johnson-Cook constitutive model describing dynamic deformations at high temperatures and high strain rates is used to analyze the relationships between the shock responses and microscopic defects. The predictions of the Johnson-Cook constitutive model are consistent with the results of the molecular dynamics simulations.     

An investigation of misfit dislocations in Al on (001) GaAs grown by chemical beam epitaxy

We report a transmission electron microscope study of the morphology and interfacial structure of Aluminium grown on (001) GaAs by chemical beam epitaxy (CBE). The Al grows in islands for all thicknesses deposited, and exhibits four distinct orientation relationships with respect to the substrate. One of these orientation relationships becomes dominant as growth progresses, with (011)_Al parallel to (001)_GaAs. Misfit dislocations can be seen in the interface between this orientation and the substrate with Burgers vector 1/4(110)_GaAs, and a crystallographic analysis shows that these dislocations are associated with interfacial steps of height 1/2[001]_GaAs. In (001)Al on (001)GaAs, the existence of these dislocations has in the past been regarded as evidence for the existence of a rigid-body shift of the Al in the interfacial plane. Using cross-sectional high-resolution TEM, it is shown that this shift is not present in the (011) orientation. The similarity in the microstructure and crystallography of the (001) and (011) orientations leads us to suggest that there is also no shift in (001) Al on (001)GaAs. This is in conflict with previous investigations of this system using a wide variety of techniques.     

Molecular dynamics investigations of the strengthening of Al-Cu alloys during thermal ageing

Classical molecular dynamics simulations of the interaction of edge dislocations with solid soluted copper atoms and Guinier-Preston zones (I and II) in aluminium are performed using embedded atom method potentials. Hereby, the strengthening mechanism and its modulus are identified for different stages of thermally aged Al-Cu alloys. Critical resolved shear stresses are calculated for different concentrations of solid soluted copper. In case of precipitate strengthening, the Guinier-Preston zone size, its orientation and offset from the dislocation plane are taken as simulation parameters. It is found that in case of solid soluted copper, the critical resolved shear stress is proportional to the copper concentration. In case of the two subsequent aging stages both the dislocation depinning mechanism as well as the depinning stress are highly dependent on the Guinier-Preston zone orientation and to a lesser degree to its size.     

Dislocation content of geometrically necessary boundaries aligned with slip planes in rolled aluminium

Previous studies have revealed that dislocation structures in metals with medium-to-high stacking fault energy, depend on the grain orientation and therefore on the slip systems. In the present work, the dislocations in eight slip-plane-aligned geometrically necessary boundaries (GNBs) in three grains of near 45° ND rotated cube orientation in lightly rolled pure aluminium are characterized in great detail using transmission electron microscopy. Dislocations with all six Burgers vectors of the ½?1?1?0? type expected for fcc crystals were observed but dislocations from the four slip systems expected active dominate. The dislocations predicted inactive are primarily attributed to dislocation reactions in the boundary. Two main types of dislocation networks in the boundaries were identified: (1) a hexagonal network of the three dislocations in the slip plane with which the boundary was aligned; two of these come from the active slip systems, the third is attributed to dislocation reactions (2) a network of three dislocations from both of the active slip planes; two of these react to form Lomer locks. The results indicate a systematic boundary formation process for the GNBs. Redundant dislocations are not observed in significant densities.     

Evolution of dislocation structures having various orientations in strained single crystals of the alloy Ni3Ge

The dislocation structure of strained single crystals of Ni₃Ge with various orientations is investigated by electron microscopy. The evolution of the dislocation structure parameters is studied as a function of the degree of strain, temperature, and orientation of the single crystals. Analysis of the experimental dependences of the yield stress on the density of dislocations leads to certain conclusions about how various mechanisms for dislocation drag make temperature-dependent contributions to the deforming stress, and about the nature of the thermal hardening of Ni₃Ge. Fiz. Tverd. Tela (St. Petersburg) 40, 672–680 (April 1998)     

Microstructural instabilities: dislocation substructures with pronounced mechanical effects

Microstructure evolution is largely dominated by the internal stress fields that appear upon the appearance of inhomogeneous structures in a material. The hardening behaviour of metals physically originates from such a complex microstructure evolution. As deformation proceeds, statistically homogeneous distributions of dislocations in grains become unstable, which constitutes the driving force for the development of a pronounced dislocation substructure. The dislocation structure already appears at early stages of deformation due to the statistical trapping of dislocations. Cell walls contain dislocation dipoles and multipoles with high dislocation densities and enclose cell-interior regions with a considerably smaller dislocation density. The presence and evolution of such a dislocation arrangement in the material influence the mechanical response of the material and is commonly associated with the transient hardening after strain path changes. This contribution introduces a micromechanical continuum model of the dislocation cell structure based on the physics of the dislocation interactions. The approximation of the internal stress field in such a microstructure and the impact on the macroscopic mechanical response are the main items investigated here.     

Continuum model for dislocation dynamics in a slip plane

In this paper, we present a continuum model for dislocation dynamics in a slip plane, which accurately incorporates both the long-range interaction and the local line tension effect of dislocations. Unlike the continuum models in the literature using dislocation densities, we use the disregistry across the slip plane to represent the continuous distribution of dislocations in the slip plane, which has the advantage of including the orientation dependence of dislocations in a very simple way. The continuum dislocation dynamics model is validated by linear instability analysis of a uniform dislocation array to small perturbations and comparisons of the results with those of the discrete dislocation dynamics model. Numerical examples for the evolution of distributions of dislocations and plastic slips in a slip plane are presented.     

Alternate dissociation of the screw dislocations in a (0 0 1) buried small-angle twist boundary in silicon

The square dislocation network of a (0 0 1) buried small-angle boundary in silicon was observed by dark-field transmission electron microscopy to examine the structures of more than 100 dissociated dislocation segments. Images were taken with g = (2 2 0), using a many-beam case along the reciprocal lattice row. Dissociation occurs on alternate close-packed planes without systematic rule, although a degree of ordering is taking place. Most of the dislocation segments have lengths equal to half of the square network period. Image simulation studies revealed that their experimental contrasts cannot be explained from the usual assumption of straight dislocations running in an infinite crystal. However, if these dislocations are supposed close and parallel to a nearby free surface, a reasonable agreement is found between the micrographs and the simulated images. A three-dimensional elastic model is proposed to explain the contrasts of the dislocation network.     

dHvA measurements of long range strain effects due to lattice dislocations in copper

Lattice dislocations have been shown to produce a factor of 10³ greater dHvA scattering temperature than an estimate from resistivity. The magnitude of this discrepancy is explained by a first principles phase smearing calculation, and is due to the sensitivity of the quantum oscillations to small angle scattering by the long range strain field. Breaking the cubic symmetry by introducing a forest of edge dislocations allows a test of the sensitivity of previously equivalent neck orbits to the relative orientation with respect to the dislocation lines. Both magnitudes and anisotropy agree with the theory. It is shown how to separate these effects from mosaic structure effects also present in these deformed crystals. In a separate experiment, neutron irradiation was used to produce dislocation loops. Here, the dHvA scattering is observed to be of the same order as resistivity scattering, due to the cancellation of the long range dislocation strain field in the loop geometry.