Dislocation Line Tension Research Articles

Dislocation dynamics of elementary crystallographic shear

Dislocation dynamics of the crystallographic slip zone formation is investigated under the assumption that dislocation line tension is constant and the expanding closed dislocation loop keeps the form of a circle. The differential equations for expansion the ith dislocation loop produced by a dislocation source are considered.

Dislocation plasticity in persistent slip bands

Persistent slip bands dominate plastic flow under conditions of ‘saturation’, i.e. when a ductile material is cycled at constant plastic strain amplitude, the maximum stress in one cycle rises and then saturates. The saturation stress is identified as being to an excellent approximation equal to the endurance limit of the material, as measured by conventional stress cycling tests. When saturation is attained, plastic flow is confined to well-defined slip bands, which persist after electropolishing and resuming cyclic straining. These persistent slip bands have a well-defined dislocation structure, characterised by a length, which separates walls of dislocation dipoles. The persistent slip bands have a unique stress–strain curve, caused by the backward and forward motion of screw dislocations between the walls. Many authors have worked on these structures, and their main features are widely agreed. Persistent slip bands lead to the initiation of fatigue cracks, because where they intersect the external surface of the material, they cause stress concentrations and generate intrusions, which follow the interface between the persistent slip band and the matrix within which it is embedded. Many features of the cyclic plastic flow can be understood in terms of two basic concepts. Firstly, it is assumed that the bands are dissipative structures, shear structures, with a spacing determined by dynamic processes including the laying down of edge dislocation dipoles and the forces on groups of dipoles resulting from the motion of the screw dislocations producing them. Secondly, the mean free path of screw dislocations in the bands is determined by the probability of meeting and annihilating another screw dislocation of opposite sign. Very simple equations show that the saturation stress is equal to the plastic strain in the band multiplied by the elastic shear modulus divided by 4 π. This very simple result is borne out to within a few percent by recent data on copper single crystals. Other data relating the wall spacing to the saturation stress and the minimum distance apart of stable screw dislocations is accurately rationalised by the theory. Several aspects of the theory deserve comment. The theory indicates that the dislocation density does not matter. The strong temperature dependence of the wall spacing and the saturation stress receive natural explanation. And if the saturation stress is equal to the stress for the onset of stage III unidirectional work-hardening, one can rationalise one of the oldest rules in fatigue strength — the so-called ‘fatigue ratio’, whereby the endurance limit is proportional to the ultimate tensile strength. The picture of cyclic hardening implies that materials with steep initial hardening rates show low saturation stresses; cyclic hardening curves always cross. This is in agreement with observation. Objections raised by other authors are analysed briefly. The existence of internal stress in the structures, as deduced by Mughrabi in neutron irradiated copper, can be re-interpreted on the basis of the normally assumed variation of dislocation line tension with character. The picture of cross-slip which emerges, implies that cross-slip occurs at all stages in the stress–strain curve, but at the onset of stage III, every screw dislocation cross-slips to annihilation — no screw dipoles are possible. This seems consistent with observation.

Room temperature tensile properties of Fe-Al single crystals strengthened by excess vacancies

Effects of supersaturated excess vacancies on plastic deformation of Fe-Al were investigated by tensile testing at room temperature for three different single crystals (Fe-33, 41 and 44 mol% Al). Critical resolved shear stresses (CRSSs) of slowly-cooled specimens (as homogenized specimens) and well-annealed specimens (vacancy-eliminated specimens) were almost the same and did not show Al concentration dependence. On the other hand, the CRSS of vacancy-containing specimens (fast-cooled specimens) was significantly higher than that of the others, even for Fe-33 mol% Al, and showed strong Al concentration dependence. The fast-cooled specimens displayed serrated flow behavior during work-hardening at room temperature, and the serrated flow was more intensive at a higher Al composition. Deformation microstructures of Fe-44 mol% Al were examined by TEM, and it was found that dislocations in fast-cooled specimens were inhomogeneously distributed, suggesting jerky motion of slip dislocations. These dislocations were oriented along an unstable direction estimated from dislocation line tension. In addition, there were numerous dislocation loops. A dislocation mechanism of the excess vacancy strengthening is discussed on the basis of the experimental results.

Effect of temperature on elastic constants and dislocation properties of Fe [sbnd]30% Al single crystals

The elastic constants of Fe 30% Al single crystals were determined using a resonance technique over the temperature range, 293–1173 K, of the observed yield strength anomaly. While the elastic shear anisotropy, Zener's factor, is high, A = 4.6–6.8, the factor related to a shear with respect to the 〈111〉 direction is rather low, M = 1.2–1.3, over the temperature range. The elastic anisotropy factors for dislocation width calculated for the edge and screw orientations of the {110}〈111〉 slip give the ratio of K eS 66/K eS 44 = 2.4 at 773 K, suggesting that the mobility is significantly higher for edge than for screw character. In the absence of applied stress, a coplanar dissociation of two 〈111〉/4 screw partials with the APB partly lying on {110}, and partly on {112}, is not likely in Fe-30% Al. For a more detailed study of dislocation micromechanics to explain deformation behavior of Fe-30% Al, discussion is given on the anisotropy of APB energies, the relationship of non-Schmid effect with the anisotropic coupling coefficients, and possible glide resistance associated with the unstable orientation of dislocation line tension.

Line tension of screw dislocations on cross-slip planes

In this letter the line tension associated with screw dislocations is considered. First, it is shown that screw dislocations can be identified with negative line tensions on various cross-slip planes in cubic crystals; analytical or numerical conditions for negative line tension are given. Secondly, the relative magnitudes of the line tension on relevant cross-slip planes are calculated. The line tension on 100 and 111 screw dislocations is found to be fully independent of the crossslip plane, whereas that of 110 screw dislocations depends sensitively on the cross-slip plane and is at a maximum on the cube cross-slip plane for most materials. The implications of a negative line tension are discussed and a locking mechanism of elastically unstable screw dislocation is proposed.

Reorientation of Misfit Dislocations During Annealing in InGaAs/GaAs(001) Interfaces

ABSTRACTTransmission electron microscopy is applied to investigate the effect of post-annealing on misfit dislocations in an In0.2Ga0.8As/GaAs(001) heterostructure. An orthogonal array of 60º dislocations along [110] and [110] directions was observed in the interfaces of the samples grown by MBE at 520 ºC. When the as-grown samples were annealed at temperatures ranging from 600 to 800 ºC, the 60º dislocations were gradually reoriented by dislocation reactions occurring at the 90º intersections followed by nonconservative motion driven by dislocation line tension and the residual elastic misfit strain. The final result of this process was a dislocation array lying along [100] and [010] directions. The reoriented u=<100> dislocation has a Burgers vector , which is the same as that of 60º dislocation, but the edge component of its Burgers vector in the (001) interfacial plane is larger than that of 60º dislocation by a factor of , resulting in a greater contribution to elastic strain relaxation. This nonconservative reorientation of 60º dislocations to form the u=<100> dislocations represents a new strain relaxation mechanism in diamond or zinc blende semiconductor heterostructures.

High-velocity dislocations: Effective mass, effective line tension and multiplication

Abstract An expression is derived for the effective mass of an edge dislocation moving with uniform velocity v in an isotropic elastic medium. Ishioka's analysis of the effective line tension of stationary dislocations is extended to the uniformly moving dislocations. The effective line tension of the moving edge dislocation becomes negative for c ≥ v ≳ 0·81c, where c is the velocity of transverse sound waves, when Poisson's ratio v = 0·3. The limiting velocity v c of the edge dislocation is not c but about 0·81c. Because the edge dislocation becomes unstable for c ≥ v ≥ v c, multiplication of the dislocation is expected at v c.

Line tension of extended double kinks in thin films

We derive an expression for the dislocation line tension in thin-film structures for double-kink (dislocation dipole) extension of a threading dislocation. From these calculations, we conclude, that for a double kink that is a distance of more than three times the vertical dipole separation from the free surface, the effect of the free surface on the double-kink line tension is insignificant. We consider the specific case of a double-kink bounding a 60-nm-thick Si0.7Ge0.3 strained layer grown on a silicon substrate and buried under a silicon cap. For this specific configuration, line tension is seen to increase with cap thickness (which is equivalent to distance of the double kink from the surface) only up to a cap thickness of 100 nm.

The effect of frictional stress on the calculation of critical thickness in epitaxy

A critical-thickness model is proposed for lattice-mismatched epitaxial layers which incorporates for the first time both the equilibrium and kinetic components of misfit accommodation. The model is an attempt to provide a physical basis for the discrepancy between the observed and calculated critical thickness in zinc-blende semiconductors. The equilibrium components of the model use a force balance and a Volterra description of the dislocation line tension with frictional forces includiing Peierls barriers and dislocation atmospheres. The effect of the frictional forces is to shift the critical thickness to a larger value and to produce a residual elastic strain which persists for large thicknesses. The frictional barriers are low in face-centered-cubic metals and produce minor changes from the previous theories; however, for semiconductors the frictional forces may be high and produce a substantial increase in the predicted critical thickness. The kinetic component of misfit accommodation has been addressed through a dynamic frictional force. The explicit form of the kinetic component of misfit accommodation depends on the operative mechanism of misfit-dislocation generation. A simple criterion is proposed to estimate whether the generation of misfit dislocations will be controlled by equilibrium or kinetic factors.

In situ straining experiments in the Transmission Electron Microscope

Recently a number of in situ straining experiments have been carried out at temperatures between about 80 K and 1200 K. A new HVEM straining stage was constructed for temperatures above 1300 K. Its design features are: top entry double tilting stage, thermal expansion drive of high stiffness, heating by electron bombardment, and water cooling to quickly reach a steady state.The following deformation phenomena have successfully been treated by in situ experiments:Determination of the effective stress from the curvature of bowed-out dislocation segments: As shown by in situ experiments on MgO crystals, the line tension of dislocations may differ from its theoretical value. Nevertheless, the anomalous temperature dependence of the effective stress in ordered alloys as well as for prismatic slip in Be has been determined in accordance with macroscopic experiments. Measurement of velocities and kinematic behaviour of dislocations: In situ experiments allow the coordination of the motion of individual dislocation segments with their geometrical configuration.

Computer simulation of solid solution strengthening in Fcc alloys: Part II. At absolute zero temperature

Computer simulation techniques were used to explicate solid solution strengthening in fcc metals. With this approach, it was not necessary to make a number of the assumptions used in analytical investigations. A semicontinuum model, with a flexible dislocation line interacting with a random array of solute atoms, was employed. The dislocation line tension was assumed constant, and classical elastic size or modulus interactions were assumed between the solute atoms and the dislocation line segment. The size effect was again found to be dominant, and the yield stress was predicted as {\(\tau _y \)}=0.069 μe4/3 1/2. Although there were no adjustable parameters in this study, agreement with experimental data was quite good.

Plastic Flow in Si/Ge Quantum Well Structures

AbstractPlastic flow is driven by excess stress, which can be calculated from lattice strain and dislocation line tension. In order to better understand and model plastic flow, we have derived an expression for the dislocation line tension in thin film structures for double kink (dislocation dipole) extension of a threading dislocation. From these calculations, we conclude that the presence of a free surface (i.e. the vacuum/solid interface) significantly reduces the line tension for an extended double kink. For the specific case of a 50nm thick Si0.7 Ge0.3 layer capped with lum of silicon, we find that the line tension is approximately 30% less than the estimate of an analogous model that neglects the influence of a free surface. Therefore, in order to obtain an accurate estimate of the excess stress for a double kink, one must allow for the influence of a free surface.

A MODEL FOR LOW FREQUENCY INTERNAL FRICTION DUE TO EXTENDED DISLOCATIONS

We propose a model for internal friction at low frequency in fec alloys due to extended dislocations is proposed, in order to explain the internal friction peak around 210 K in heavily cold-worked concentrate Cu-Al and Cu-Zn alloys with measuring frequency of about 1 Hz.The motion of extended dislocations under the action of applied stress is divided into the relative motion (the relative displacement between two partial dislocations) and the overall motion (the displacement of the centre of extended dislocations). In addition to the restoring force due to the interaction between two partials and the restoring force due to the line tension of dislocations, the restoring force due to long range interaction among neighbouring dislocations is introduced. It is demonstrated that the last restoring force only influences the overall motion of extended dislocations, but does not influence their relative motion.The relative motion and the overall motion of extended dislocations each give rise to its internal friction peak respectively. The two peak temperatures are close to each other. The observed internal friction peak is a superposition of these two peaks. The predictions of the model in the present paper are in agreement with the experimental results.

Critical stresses for SixGe

We have measured the temperature-dependent onset of strain relief in metastable Si/sub x/Ge/sub 1-//sub x/ strained layers grown on Ge substrates. On the basis of these measurements, and physical arguments, we propose that strained-layer breakdown is most directly determined not by thickness and lattice mismatch, but rather by (1) an ''excess'' stress (the difference between that due to misfit strain and that due to dislocation line tension) and (2) temperature. With use of these parameters, observed regimes of stability and metastability are shown to be described within a simple, unified framework.

The line tension of dislocations in anisotropic media

Abstract The line tension of a dislocation determines its stability against small bow-outs from an equilibrium position. It is composed of a local term which includes a logarithmic singularity (avoided by some cut-off procedure), and a term which represents the interaction with the rest of the configuration. Whereas the prelogarithmic factor of the local term is known for elastic anisotropy, the interaction term has so far been determined only for isotropic media. In the present paper this interaction is calculated for arbitrary anisotropy for bow-outs of various shapes in straight dislocation lines, thereby establishing the final resolution of the elastic line-tension problem.

Capillary equilibria of surfaces intersected by dislocations

Abstract The equilibrium shape of the pit where a dislocation intersects a free surface is calculated in a variational formalism. The constant dislocation line tension approximation, made by previous workers, is shown to be clearly inadequate for all realistic cases. Employment of a variable dislocation line tension model for the case of finite dislocation density shows the existence of two regimes of behaviour. In the first, pits formed at dislocation-surface intersections have a well defined shape and are of finite depth. However, a second regime exists, in which the pit depth is infinite and the dislocation core size exceeds the bulk value. This may result in the formation of open-core dislocations, as discussed by Frank.

In situ observation of whiskers, pyramids and pits during the high-temperature oxidation of metals

A hot-stage, environmental scanning electron microscope has been used to observe the in situ development of oxide whiskers, pyramids, and pits in the oxidation of copper and nickel at elevated temperatures. The effects of oxidation temperature, metal deformation, and the presence of water vapor on these irregular oxidation features were studied. In each case, the feature results from the presence of a central screw dislocation which provides ledges for the extension of the oxide lattice, but the specific geometries are decided by factors such as surface diffusion along the dislocation core, the rate of the molecular dissociation step, and the balance of surface energy and dislocation line tension forces.

Elastic properties (the stiffness constants, the shear modulus and the dislocation line energy and tension) of [formula omitted]Al solid solutions and of the Nimonic alloy PE16

The stiffness constants C ik of the following nickel-base alloys were measured: NiAl solid solutions with aluminium contents up to 8 at.%, Nimonic alloy PE16 and an experimental alloy with the same composition as the matrix of fully precipitated PE16. The temperature range covered is 80–360 K. From the stiffness C ik a shear modulus and the dislocation line energy and tension are derived. Extrapolation formulae, which describe the temperature and concentration dependences of the elastic parameters, are given for the range 0–550 K.

DISLOCATION BENDS I N HIGH STRESS DEFORMED SILICON CRYSTALS

Different approximations for the line tension of dislocation bends in silicon are discussed and compared with experimental results obtained for low stress and high stress deformation.

Some new aspects concerning particle hardening mechanisms in γ' precipitating Ni-base alloys—I. Theoretical concept

Strengthening of Ni-base alloys by coherent, stress-free, ordered particles is critically discussed in the light of more recent theories. In part I. a theoretical concept is developed which rests on existing hardening models estimating the increase of the yield stress due to pairwise particle cutting and anti-phase domain boundary (APB) formation. The effect of the anisotropy on the dislocation line tension of two-phase material and on the Orowan stress is taken into account. It is shown that conventional hardening models which are derived in the framework of the Fleischer-Friedel theory are strictly limited to dilute alloys. For Ni-base alloys containing large volume fractions of γ'(Ni 3Al) precipitates the Labusch theory holds. Consequently, the new theory of Labusch and Schwarz is applied to the operating APB hardening. The yield stress of an anisotropic γ' hardening model system is calculated for large variations of particle parameters. Experimental results obtained with the commercial alloys Nimonic PE 16 and Nimonic 105 to check the theoretical estimates will be reported in a subsequent paper (part II).