Stress assisted diffusion to dislocations—II: Higher order decay constants in an eigenfunction expansion description

Stress assisted diffusion to dislocations is considered in terms of an expansion in decaying exponentials. The dependence of higher order decay constants on dislocation density, Cottrell attraction parameter and temperature is determined by a numerical treatment of the boundary value problem. The results are discussed as they apply to sets of publsihed decay constants for stress relaxation in iron and for dislocation pinning in irradiated and/or cold worked NaCl, KCl and Pb.     

Stress assisted diffusion to dislocations: The first decay constant in an eigenfunction expansion description

Stress assisted diffusion to dislocations is considered in terms of an expansion in decaying exponentials. The dependence of the first decay constant in dislocation density, Cottrell attraction parameter, and temperature is determined by a numerical treatment of the boundary value problem. The results are discussed as they apply to strain aging in iron and to annealing of interstitial and vacancy defects to dislocations in cold worked and/or irradiated solids.     

Reprise: partial chemical strain dislocations and their role in pinning dislocations to their atmospheres

A correct solution for a dislocation atmosphere is provided using Hirth's Standard Model, confirming the errors in Hirth and Lothe. Contrary to what is given there, concentration changes in Cottrell atmospheres reduce an edge dislocation's stress and its elastic energy, thereby reducing the magnitude of the concentration changes. The chemical and elastic strain fields from Cottrell atmospheres are again shown to behave as partial dislocations with variable Burgers vectors that are not crystal translation vectors. The reality of partial dislocations provides a simpler explanation for pinning of dislocations by atmospheres. Much of the literature on dislocation properties in solid solutions should be re-examined.     

Dislocation dynamics in doped NaCl single crystals determined by pulsed NMR between RT and 300°C

The mean free path of mobile dislocations is measured by determination of the spin-lattice relaxation rate of deforming NaCl single crystals as a function of temperature and of the concentration of Ca⁺⁺ impurities. The latter may influence the magnitude of the mean free path but this depends to a large extent on the point defect configuration. The degree of association and the mobility of the point defects is studied by measuring the spin-lattice relaxation rate without deforming the samples. On the other hand the distribution of dislocations varies also with temperature and this affects the mobility of dislocations too. The work-hardening rate of the crystals is compared with the mean free path as a function of temperature and it is shown that both quantities have extremes under the influence of competitive mechanisms such as an enhanced thermal activation of dislocations at obstacles, an increasing mobility of point defects, and increasing number of intersections of mobile dislocations with dislocation dipoles.     

The interaction of a screw dislocation with point defects in bcc iron

In this study, we calculate the interaction energy of intrinsic point defects vacancies and interstitials) with screw dislocations in body-centered cubic iron. First (we calculate the dipole tensor of a defect in the bulk crystal using molecular statics. Using a formulation based on linear elasticity theory, we calculate the interaction energy of the defect and the dislocation using both isotropic and anisotropic strain fields. Second, we perform atomistic calculations using molecular statics methods to directly calculate the interaction energy. Results from these two methods are compared. We verify that continuum methods alone are unable to correctly predict the interactions of defects and dislocations near the core. Although anisotropic theory agrees qualitatively with atomistics far from the core, it cannot predict which dumbbell orientations are stable and any continuum calculations must be used with caution. Spontaneous absorption by the core of both vacancies and dumbbells is seen. This paper demonstrates and discusses the differences between continuum and atomistic calculations of interaction energy between a dislocation core and a point defect.     

On the isotropy of continuized dislocated crystals. I. The isotropic lattice distortion

The geometrical theory of continuous distributions of dislocations traditionally neglects the dependence of a distribution of dislocations on the existence of point defects created by this distribution (e.g., due to intersections of dislocation lines). In this paper the influence of such point defects on metric properties of the continuized dislocated Bravais crystalline structure is assumed to be isotropic. The influence of the point defects on the distribution of dislocations is then modeled by treating dislocations as those located in a conformally flat space. This approach leads (among others) to new results concerning the geometry of glide surfaces.     

Dislocations used to probe the defect state of an ionic crystal lattice excited by a pulsed magnetic field

This paper presents the results of an investigation into the effect of a pulsed magnetic field on the state of linear and point defects in ionic crystals. For different amplitudes (1–7 T) and pulse lengths (3×10⁻⁵ to 10² s) of the pulsed field the kinetics of the transformation of defects into a new state and their relaxation after the field is turned off are studied in the temperature range 77–400 K. It is found that the relaxation of the states of point defects is mainly through recombination, and the change of state of the dislocations and of the point defects contribute nonadditively to the change in the dislocation mobility. The exposure of the crystal to a magnetic field leads to an increase in the dislocation mobility when the sample is mechanically stressed and to a decrease in the dislocation displacement with a second field pulse. Fiz. Tverd. Tela (St. Petersburg) 39, 634–639 (April 1997)     

Intersection of screw dislocations in fcc crystals during torsional deformation

Dislocation reactions, including dislocation intersections during various processes in crystals, play an important and often crucial role. This is most pronounced during plastic deformation of crystalline solids, which attracts particular interest from researchers. Intersection of screw dislocations in fcc crystals during their deformation by uniaxial tension and compression was studied by A. Cottrell [1]. It was shown that the intersection of similar screw dislocations moving toward each other results in the formation of interstitial thresholds on them; in the case of intersection of opposite screw dislocations, vacancy thresholds are formed on them.     

Mechanisms of dislocation generation in Si structures with strained layers: Intrinsic point defects in dislocation nucleation

The peculiarities of dislocation production in silicon compositions with elastically strained layers fabricated by the molecular-beam epitaxy technique (SiGe/Si heterostructures) and by direct bonding of Si(110)/Si(100) wafers are studied with transmission electron microscopy. The role of intrinsic point defects during the process of nucleation of misfit dislocations is explained. The surplus concentration of these defects in heterostructures was produced via low-temperature epitaxial growth of buffer layers or with ion implantation of elastically strained heterostructures. The model of “optimal” and “inverse” intrinsic point defects providing an explanation for the relaxation of misfit strains in heterostructures is proposed.     

Equilibrium configurations and energetics of point defects in two-dimensional colloidal crystals

We demonstrate a novel method of introducing point defects (mono- and divacancies) in a confined monolayer colloidal crystal by manipulating individual particles with optical tweezers. Digital video microscopy is used to study defect dynamics in real space and time. We verify the numerical predictions that the stable configurations of the defects have reduced symmetry compared to the triangular lattice and discover that in addition they are characterized by distinct topological arrangements of the particles in the defect core. Surprisingly, point defects are thermally excited into separated dislocations, from which we extract the dislocation pair potential.     

Free energy change of a dislocation due to a Cottrell atmosphere

The free energy reduction of a dislocation due to a Cottrell atmosphere of solutes is computed using a continuum model. We show that the free energy change is composed of near-core and far-field components. The far-field component can be computed analytically using the linearized theory of solid solutions. Near the core the linearized theory is inaccurate, and the near-core component must be computed numerically. The influence of interactions between solutes in neighbouring lattice sites is also examined using the continuum model. We show that this model is able to reproduce atomistic calculations of the nickel–hydrogen system, predicting hydride formation on dislocations. The formation of these hydrides leads to dramatic reductions in the free energy. Finally, the influence of the free energy change on a dislocation’s line tension is examined by computing the equilibrium shape of a dislocation shear loop and the activation stress for a Frank–Read source using discrete dislocation dynamics.     

Dynamic interaction of edge dislocations with point defects and prismatic dislocation loops at high-strain-rate deformation of crystals

The motion of an ensemble of edge dislocations at high-strain-rate deformation of a crystal with a high concentration of prismatic dislocation loops and point defects has been analyzed. It has been shown that, under certain conditions, the drag of an edge dislocation by prismatic dislocation loops has the character of dry friction, and the magnitude of the drag force of the dislocation is determined by the relationship between the concentration of prismatic dislocation loops and the density of mobile dislocations. An increase in the density of mobile dislocations leads to an enhancement of their collective interaction, thus facilitating the overcoming of prismatic dislocation loops by edge dislocations. The total drag force of an edge dislocation is a nonmonotonic function of the concentration of point defects, which, under certain conditions, has a minimum.     

The effect of hydrogen disorder on dislocation movement and plastic deformation of ice

In the structure of ice at low pressures (ice I-h) the oxygen atoms are crystallographically arranged but the hydrogen atoms are believed to be randomly arranged consistent with the so-called Bernal-Fowler rules. The effect of this randomness is to make it impossible for a dislocation to move through the ice lattice without creating point defects (breaches of the Bernal-Fowler rules). A calculation of the energy of the defects that would have to be created gives a value so large that it would require a stress of about one tenth of the shear modulus of ice to push the dislocation through. It therefore seems likely that dislocations could not move through ice unless the hydrogen atoms are reoriented by thermally activated point defects ahead of the dislocation. This necessity will greatly slow down dislocations in ice and provides an explanation for the observed behaviour of ice single crystals in creep and constant strain-rate tests, and of the softening of ice at low temperatures produced by small concentrations of dissolved fluoride ions.     

Emission of Dislocation Loops from Nanovoids in an FCC Crystal Subjected to Shear Deformation under Post-Cascade Shock Waves

The method of molecular dynamics is applied to the study of the effect of post-cascade shock waves generated in a solid irradiated by high-energy particles on the heterogeneous formation of dislocation loops in a simulated gold crystal containing a spherical nanovoid, which is subjected to shear deformation. The interaction between atoms is described with the use of a potential calculated by the embedded atom method. Shock waves are created by assigning a velocity exceeding the speed of sound in the simulated material to the boundary atoms of the computational cell. It is shown that two regions of increased mechanical stress are formed under shear deformation near the surface of a nanovoid, which are the sources of emerging partial dislocations. The main mechanism for the formation of dislocations is the displacement of a group of atoms towards the inner surface of the void, which does not contradict modern ideas about the heterogeneous formation of dislocations. It is shown that, when the values of shear stress are insufficient for the formation of dislocations, loop emission can be initiated by a post-cascade shock wave generated in the computational cell. As temperature increases, the number of nucleated dislocation loops increases, and, in addition, the formation of Lomer–Cottrell dislocations is observed, which is attributed to the additional tangential stresses created by the unloading wave. In this case, the formation of a stable dislocation loop in which the linear tension is balanced by the Peach–Koehler force due to external stress requires that the shock wave front affect the regions of increased stress near the void surface while propagating through the simulated crystal.     

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.     

EPR studies of changes in the charge state of Cr over a cross section of dislocation pipes in ZnS crystals

Short-term high-temperature annealing of ZnS crystals in a zinc atmosphere is shown to cause rapid Zn diffusion through dislocation pipes along growth-dislocation lines. As a result, the impurity ions of divalent chromium localized in Cottrell atmospheres outside Read cylinders become singly ionized. Plastic deformation of such ZnS crystals or the passing of an electric current through them under a voltage higher than a certain threshold value leads to a decrease in the number of univalent chromium ions. This decrease can be explained by an increase in the radius of Read cylinders as growth dislocations leave Cottrell atmospheres and by an increase in the linear density of their electric charge.     

Collective overcoming of point defects by dislocations in the dynamic region

A mechanism of collective overcoming of point defects by dislocations during the over-barrier slip has been proposed. It has been shown that the interaction between dislocations promotes the overcoming of point defects at a high dislocation density.     

Dynamic dislocation–defect analysis

The dynamic internal variables which control plastic flow can only be assessed by dynamic materials testing at any given instance. The testing method championned by our studies has been precision strain rate sensitivity (PSRS) whereby the change in flow stress due to a set change in strain rate is taken to be an operational measure of the activation volume and its product with the flow stress gives rise to the operational activation work. Also, from the work hardening slope, a modelled parameter proportional to the mean slip distance (λ) is simultaneously determined. The deviation from the linear Cottrell–Stokes relation as determined with the Haasen plot indicates the evolution of secondary defects other than monopole dislocations. Hence PSRS can assess the theoretical predictions of the activation distance (d) and work as a function of temperature, resulting in quantitative values that are in accord with dislocation theory at temperatures below that where point defects become mobile. A method to calibrate λ using Stage II slope θ_II shows that λ/?, where ? is the mean forest dislocation spacing, is inversely proportional to θ, the work hardening coefficient. This analysis has led to a new plot of θ_II/θ versus b ²λ/ν where b is the Burgers vector and its slope is directly proportional to d. An example using an alumina-dispersed high conductivity copper shows that geometrically necessary punched out loops are continuously generated. The role of point defect mobility is dramatically illustrated by load drops in [001] aluminium crystals with the formation of slip clusters.     

Structure and dynamics of the Frenkel-Kontorova dislocations in electroconvection in liquid crystals

The Frenkel-Kontorova instability is studied in a 1D lattice of domains formed during electroconvection in nematic liquid crystals twisted by π/2. It is found that generation of defects by such instability can be observed in this model medium. Among other things, it is shown that several types of defects with singular and nonsingular cores, as well as with a extended core, are formed in the 1D domain structure above the electroconvective instability threshold. The extended cores of dislocations are dissociated into a line, and the entire structure is isomorphic to two partial dislocations spaced by a certain distance, which are not observed in free form. Defects with a nonsingular core (zero topological index) exist owing to spiral hydrodynamic flows in convective rolls and are not observed in layers with a homogeneous orientation of molecules. It is shown that the formation of both types of defects follows the scenario of decay of dislocations with extended cores via detachment of nonsingular defects (i.e., discretely); as a result, a dislocation with a singular core is left. “Breather” defects, which are the result of periodic creation and annihilation of dislocations with a topological index of ±1, are also observed. The effect of defects on the transition from the 1D to 2D structures is considered.     

Innere Reibung durch Mitschleppen von Punktfehlern

The dragging of mobile point defects effects a damping of dislocation motion. The frequency, concentration and amplitude dependence of internal friction caused by this relaxation mechanism is computed. For small oscillations it can be described by a simple relaxation process with concentration dependent relaxation strength and time. In the case of small concentrations that means no hysteresis damping the height of relaxation maximum decreases and shifts towards smaller frequencies with increasing amplitude.