Edge Dislocation Loops Research Articles

Competing processes in reactions between an edge dislocation and dislocation loops in a body-centred cubic metal

Molecular dynamics simulation was used to investigate reactions of a 1 2 〈 1 1 1 〉 { 1 1 0 } edge dislocation with interstitial dislocation loops of 1 2 〈 1 1 1 〉 and 〈1 0 0〉 type in a model of iron. Whether loops are strong or weak obstacles depends not only on loop size and type, but also on temperature and dislocation velocity. These parameters determine whether a loop is absorbed on the dislocation or left behind as it glides away. Absorption requires glide of a reaction segment over the loop surface and cross-slip of dipole dislocation arms attached to the ends of the segment: these mechanisms depend on temperature and strain rate, as discussed here.

Modeling nonlinear electromechanical behavior of shocked silicon carbide

A model is developed for anisotropic ceramic crystals undergoing potentially large deformations that can occur under significant pressures or high temperatures. The model is applied to describe silicon carbide (SiC), with a focus on α-SiC, specifically hexagonal polytype 6H. Incorporated in the description are nonlinear anisotropic thermoelasticity, electrostriction, and piezoelectricity. The response of single crystals of α-SiC of various orientations subjected to one-dimensional shock loading is modeled for open- and short-circuit boundary conditions. The influences of elastic and electromechanical nonlinearity and anisotropy on the response to impact are quantified. For elastic axial compressive strains less than 0.1, piezoelectricity, electrostriction, and thermal expansion have a negligible influence on the mechanical (stress) response, but the influences of nonlinear elasticity (third-order elastic constants) and anisotropy are not insignificant. The model is extended to incorporate inelastic deformation and lattice defects. Addressed are Shockley partial dislocations on the basal plane and edge dislocation loops on the prism plane, dilatation from point defects and elastic fields of dislocation lines, and cleavage fracture. The results suggest that electric current generated in shock-loaded α-SiC crystals of certain orientations could affect the dislocation mobility and hence the yield strength at high pressure.

The magnetic origin of anomalous high-temperature stability of dislocation loops in iron and iron-based alloys

The dominant occurrence of the b = a ( 0 0 1 ) prismatic edge dislocation loops in iron and iron-based alloys irradiated at temperatures approaching 500 °C is a striking anomaly distinguishing iron and its alloys from other bcc metals. It is surprising that the a ( 0 0 1 ) dislocation loops form at all, since there is an alternative b = a / 2 ( 1 1 1 ) dislocation loop configuration that, according to the conventional isotropic treatment of elasticity, has a lower self-energy. In this paper we highlight the magnetic aspect of the problem and note the fundamental link between the α – γ phase transition, the elastic anisotropy of iron, which is particularly significant at elevated temperatures, and thermal magnetic fluctuations.

Periodized discrete elasticity models for defects in graphene

The cores of edge dislocations, edge dislocation dipoles, and edge dislocation loops in planar graphene have been studied by means of periodized discrete elasticity models. To build these models, we have found a way to discretize linear elasticity on a planar hexagonal lattice using combinations of difference operators that do not symmetrically involve all the neighbors of an atom. At zero temperature, dynamically stable cores of edge dislocations may be heptagon-pentagon pairs (glide dislocations) or octagons (shuffle dislocations) depending on the choice of initial configuration. Possible cores of edge dislocation dipoles are vacancies, pentagon-octagon-pentagon divacancies, Stone-Wales defects, and 7--5-5--7 defects. While symmetric vacancies, divacancies, and 7--5-5--7 defects are dynamically stable, asymmetric vacancies and 5--7-7--5 Stone-Wales defects seem to be unstable.

Effect of theα−γPhase Transition on the Stability of Dislocation Loops in bcc Iron

Body-centered-cubic iron develops an elastic instability, driven by spin fluctuations, near the alpha-gamma phase transition temperature T(c) = 912 degrees C that is associated with the dramatic reduction of the shear stiffness constant c' (c(11)-c(12))/2 near T(c). This reduction of c' has a profound effect on the temperature dependence of the anisotropic elastic self-energies of dislocations in iron. It also affects the relative stability of the a[100] and a/2[111] prismatic edge dislocation loops formed during irradiation. The difference between the anisotropic elastic free energies provides the fundamental explanation for the observed dominant occurrence of the a[100], as opposed to the a/2[111], Burgers vector configurations of prismatic dislocation loops in iron and iron-based alloys at high temperatures.

Nanotunnels and pull-aparts: Defects of exsolution lamellae in alkali feldspars

We have studied defects associated with flat, lens-shaped perthitic albite lamellae in alkali feldspars using SEM and TEM. In orthoclase phenocrysts from the Shap granite, Cumbria, NW England, bulk composition Or 70.20 Ab 29.05 An 0.85 , no dislocations were found even in optically “fresh” parts of grains. Instead, dissolution inferred to be localized on edge-dislocation loops has created tiny “nanotunnels” typically T effect of the ~1% An in the feldspars is taken into account for commencement of coherent exsolution. The orientation of the Pericline twins was fixed shortly after coherent exsolution began. Previous work has indicated that edge dislocations would start to form during cooling at ≤400 °C, so that nanotunnels form at still lower T . Dry heating experiments were carried out to establish the stability of the defects and the homogenization behavior of the exsolution lamellae. Na ↔ K exchange is rapid on heating above the coherent solvus and chemical homogenization of lamellae is complete after 24 h at 700 °C. In contrast, nanotunnels persist for >148 h at 1000 °C and >5748 h at 700 °C. Below the coherent solvus, exsolution lamellae thin on heating, leaving nanotunnels stranded in the orthoclase matrix. Microtextures related to Si-Al ordering patterns in the framework, such as Albite twins, are not eliminated, forming ghost-like lamellar strain patterns in chemically homogeneous feldspar. The presence of nanotunnels in optically “fresh” alkali feldspars shows that not only granites but also granulite-facies rocks have been pervasively affected by fluids at low T . Both nanotunnels and pull-aparts have important implications for feldspar reactivity in the upper crust, for 18 O exchange, and for transport of 40 Ar both in nature and in laboratory step-heating.

Dynamics of drag of self-interstitial clusters by an edge dislocation in iron

Self-interstitial atom (SIA) clusters are created in metals under fast neutron irradiation and are believed to interact with dislocations and increase the flow stress. In this paper, atomic-scale computer simulations are used to investigate the dynamic interaction between an edge dislocation and small SIA loops that do not intersect the dislocation glide plane and whose Burgers vector is parallel to it. Such loops can be dragged by a moving dislocation and this effect is simulated as a function of temperature and loop size, spacing, stand-off distance and Burgers vector orientation. The results can be understood in terms of the one-dimensional mobility of SIA loops.

Interaction Analysis between Edge Dislocation and Self Interstitial Type Dislocation Loop in BCC Iron Using Molecular Dynamics

Self-interstitial atom (SIA) type dislocation loop is one of the possible candidates of the so-called matrix damage that causes hardening and embrittlement of blanket structural materials of fusion reactors and/or pressure vessel materials of light water reactors. We present in this paper molecular dynamics computer simulation results on the interactions between an edge dislocation and a SIA loop with Burgers vectors of b = a 0 /2 [111] and b = a 0 /2 [111], respectively, which are introduced in bcc-Fe crystal. Then shear stresses of several different magnitudes are applied so that the dislocation moves to meet the SIA loop. General observation is that the SIA loops with diameter of ∼2 nm can be obstacles to dislocation motion, and the strength as obstacles to dislocation motion depends on applied stress. The origin of the stress dependent strength can be explained athermally using the elastic theory of dislocation interaction. In most cases, the SIA loops are absorbed by the edge dislocations to form a large super-jog after the interactions. This suggests a possibility of localized deformation of irradiated bcc-Fe due to the formation of dislocation channeling.

Immobilization of interstitial loops by substitutional alloy and transmutation atoms in irradiated metals

Small platelike clusters of self-interstitial atoms (SIAs) in irradiated metals are extremely mobile. This mobility can be greatly reduced by foreign atoms. Where the plates are large enough to form edge dislocation loops, their immobilization is analysed as a solid solution hardening. The misfitting substitutional solute atoms can significantly reduce the mobility of small SIA loops when in the central cores of their edge dislocation lines. An activation energy is required to unpin a loop from such atoms and this – unlike in conventional solid solution hardening – remains finite even with no applied stress driving the dislocation. In dilute solutions break-away occurs by the thermally activated escape from single atom obstacles on the loops. Application to a proposed fusion power plant alloy (EUROFER 97) shows that the W alloy atoms provide the most severe immobilization, although Mn atoms produced by transmutation run a close second. The contribution of Cr is evaluated.

Dislocations around precipitates in AlGaN epilayers

Dislocations around precipitates in undoped AlGaN were investigated by transmission electron microscopy. The dislocation images were taken under different diffraction conditions. The dislocations are classified into two types, a pure edge dislocation loop and a close-;coiled helical dislocation. Both types of dislocations were found to depend on the shape and size of the precipitate sources. It is suggested that the pure edge dislocation loop results from homogeneous shear stress and the close-;coiled helical dislocation is caused by spherically symmetrical stress concentration at round ends of the precipitates and chemical force due to defect concentration change.

Meniscus and Dislocations in Free-Standing Films of Smectic-ALiquid Crystals

A flat, freely suspended film of smectic-A liquid crystal supports a pressure difference, Dp, across its two free surfaces. The size of its meniscus is about 10 mm, 2 orders of magnitude smaller than the capillary length, and its profile is predicted to be circular, in accordance with our measurement. The measurement of its radius of curvature gives Dp. We nucleate ex nihilo an elementary edge dislocation loop, and from its critical radius and growth dynamics (governed by Dp), we find the line tension ϳ8 3 10 27 dyn and the mobility of an elementary edge dislocation

Relations of the surface structure to the kinetics of metal electrodes

The electrochemical dissolution and deposition of metals proceeds by ion transfer at kinks in monoatomic steps according to experimental evidence from dislocation-free surfaces of silver and iron. The mean distance of kinks in steps on silver is comparable to the distance of neighbouring atoms. Due to the relatively large specific edge energy the mean equilibrium distances of kinks in steps on iron surfaces are very long. The surface concentration of kinks growing with overpotential and pH is due to a special mechanism of generating monoatomic steps and kinks. Specific edge energies are obtained by investigating twodimensional nucleation, and growth or dissolution at screw dislocations terminating at the surface. Edge dislocations and dislocation loops terminating at the surface are sites of preferential nucleation of etch pits as shown by experiments with iron single crystals.Lattice defects influencing the rate of ion transfer can be created by electrochemical processes. The dissolution of atomic hydrogen into iron produces mechanical stresses relaxing by formation of dislocation loops. During the dissolution of alloys the faster dissolving component may also dissolve from complete steps thereby creating pairs of kinks or injecting vacancies which facilitate interdiffusion.

On the shape of edge-dislocation loops in βNiAl

Abstract The shapes of edge dislocation loops in β-NiAl have been studied. These loops have {001} habit planes, 〈001〉 Burgers vectors and exhibit two distinct forms. One of these is roughly square with segments nearly parallel to 〈010〉; this corresponds to the equilibrium shape calculated on the basis of elastic anisotropy. The other form consists of segments aligned accurately parallel to 〈110〉, which should be elastically unstable. It is proposed that this second shape is stabilized by dissociation of the perfect dislocation into three partial dislocations on the intersecting {110} planes for example The consequences of such a dissociation for the plastic deformation of β-NiAl are discussed.

Defect model for melting of discotic liquid crystals.

We present a defect model for melting of discotic liquid crystals. It is explicitly shown that a discotic liquid crystal permeated by an equilibrium density of unbound screw and transversal edge dislocation loops behaves like a nematic liquid crystal in the so-called N+6 phase. We derive the dislocation part of the free energy and calculate the interaction energy between two parallel transversal edge dislocations. We then argue that dislocation-mediated melting of discotics into the N+6 phase implies strong anisotropic scaling with ${\ensuremath{\nu}}_{\ensuremath{\perp}}$=2${\ensuremath{\nu}}_{?}$. Some consequences follow about the critical behavior of Frank elastic constants previously derived.

Cross-slip on the first order pyramidal plane (10 $$\bar 1$$ 1) of a-type dislocations [1 $$\bar 2$$ 10] in the plastic deformation of ?-titanium single crystals

The nature of the cross-slip plane was determined by electron microscopy observations of α-titanium single crystal specimens, oriented for single prismatic slip (10\(\bar 1\)0) [1\(\bar 2\)10]. The occurrence of cross slip on the first order pyramidal plane (10\(\bar 1\)1) was proved for a-type dislocations [1\(\bar 2\)10]. Furthermore, two types of dislocation configuration due to the double cross-slip were observed: edge dislocation dipoles and loops elongated along the Burger's vector.

Stress-induced preferred absorption due to saddle-point anisotropy: The case of an infinitesimal dislocation loop

The effect of an external stress on point-defect migration into an edge dislocation loop in an Isotropic linear elastic medium is studied. The effects of the saddle-point anisotropy are considered. It is found that an external stress changes the bias of a dislocation loop in a way somewhat similar to the usual SIPA in having the same linear stress dependence and stress orientation dependence. Application of the theory to copper and iron shows that the magnitude of the change is much larger than that due to the usual SIPA.

A model for the evolution of a twist dislocation network

The transition from edge dislocation loops to a hexagonal grid of screw dislocations is followed for torsion of a single f.c.c. crystal with a (111) cross section and (112) faces, so that 〈 110〉 slip directions are parallel to the surface and in the plane of the cross section. Application of the results to stress-strain behavior, as well as computer modeling of the reactions, appears tractable.

The mechanisms of the formation and growth of water bubbles and associated dislocation loops in synthetic quartz

The development of water bubbles in synthetic quartz has been monitored by measurements of (i) the intensity of the light scattered and (ii) the increase in volume of the crystal, both as a function of temperature and time. These macroscopic measurements have been complemented by observations of the resulting microstructures, using transmission electron microscopy (TEM). A mechanism is proposed on the assumption that hydrogen is incorporated in the quartz structure by means of (4 H)Si defects. On heating, these defects diffuse and clusters develop. A cluster of n(4 H)Si produces a water bubble of (n−1)H2O, without any change of volume of the crystal. At any temperature T there is a critical bubble diameter above which the “steam” pressure P exceeds the pressure p for a spherical bubble in mechanical equilibrium. If P becomes greater than p, then the bubble increases in volume until P=p, the increase in volume being achieved by the pipe diffusion of Si and O away from the bubble site into a linked edge dislocation loop. This process produces the observed increase in volume of the crystal. The two diffusion processes take place virtually simultaneously and continue until all the (4 H)Si defects have been trapped in the bubbles. Values of the diffusion constant and the activation energy for the diffusion of the (4 H)Si defects are deduced. The relevance of these observations to the hydrolytic weakening of quartz is briefly discussed.

Intrinsic bias differential between vacancy loops and interstitial loops

Abstract Point-defect migration into an infinitesimal edge dislocation loop in an isotropic linear elastic medium has been studied. Particular care has been taken to include the effects of the saddle-point shape anisotropy of the point defect. The reaction radii and biases are derived and found to depend on the loop nature and the point-defect shape at the saddle point. Application of the theory to copper and iron shows that the bias differential between vacancy and interstitial loops can be very large.

Mechanical Properties of Polycrystalline TiC

The mechanical properties of fine-grained polycrystalline TiC were studied using both four-point bending and compression tests. The ductile-brittle transition (D-B) temperature in compression was determined to be =800°C and was found to depend on grain size. Yield-point behavior was observed for the first time in fine-grained TiC deformed in compression and was found to depend on grain size and test temperature. The yield stress as a function of grain size can be described by a Hall-Petch type of relation, i.e. yield stress α (grain size)-1/2. The dislocations resulting from deformation in compression at lower temperatures were predominately screw in character, with edge dipoles and dislocation loops being present. As the temperature of deformation was increased, the dipoles and loops were gradually annihilated by climb and the dislocations were observed in the form of hexagonal networks with a much-reduced dislocation density. A plot of log yield stress vs 1/T showed a change in slope, which suggests that two rate-controlling mechanisms are in operation during deformation at different test temperatures. Thermal activation analysis at T = 1050° to 1500°C suggested that the rate controlling mechanism during deformation in this temperature range is associated with cross slip.