Initial Dislocation Density Research Articles

Misfit dislocation dissociation and Lomer formation in low mismatch SiGe/Si heterostructures

Using transmission electron microscopy we observe the dissociation of 60° misfit dislocations at the interface of SiGe/Si multilayers, extending into the substrate for distances of 5.0–7.5 nm. Analysis using elasticity theory shows that this dissociationis the equilibrium configuration for individual 60° misfit dislocations, as it is for 60° mixed dislocations in bulk Si, and that the compressively strained multilayer film serves mainly to position the partial dislocations and stacking fault with respect to the free surface. We observe both undissociated 60° and Lomer edge dislocations after annealing, and conclude that these result from dislocation climb in the interface. Since the dislocations move off their slip plane during climb, they cannot remain dissociated. Significant climb and Lomer dislocation formation for these low misfit layers is observed at temperatures above 850 °C and for samples with a high initial dislocation density, such as found in thicker as-grown samples. The dislocation configuration formed during annealing is distinct from that reported to form during growth of higher mismatch films: the Lomer dislocations tend to be segmented, with the segments connected by perfect 60° dislocations.

Strain relaxation of GeSi/Si(001) heterostructures grown by low-temperature molecular-beam epitaxy

Plastic relaxation in GexSi1−x∕Si(001) heterostructures with x=0.18–0.62, grown at temperatures of 300–600 °C with the use of a low-temperature (350 °C) Si buffer layer, is considered. It is shown that the use of low-temperature Si and low temperature of growth of GeSi films decreases the density of threading dislocations to the value of 105–106cm−2 in heterostructures with a germanium content x<¯0.3, whereas the density of the threading dislocations in heterostructures with a higher content of Ge remains at the level of ∼108cm−2 and higher. By means of transmission electron microscopy, it is shown that the origination of dislocation half-loops from the surface in the case of a high content of germanium in the film is the main reason for the high density of threading dislocations. Growing of GeSi films with a two-step change in composition is considered. The fact that the density of the threading dislocations in the first step of the film is significantly higher than that in the substrate is noted. Because of their presence, the real thickness of insertion of misfit dislocations into the second step of the film is in ten times less than for the first layer. With an allowance for this effect, almost complete plastic relaxation of the second and further heterostructure steps can be reached at low temperatures and at a smaller thickness of GeSi films. It is concluded that the main factors of low-temperature epitaxy of GeSi, which reduce the density of the threading dislocations in heterostructures are (i) a decrease in the initial threading dislocation density and (ii) an increase in the rate of expansion of dislocation loops, which facilitates plastic relaxation with a smaller number of threading dislocations.

Change in flow stress and ductility of δ-phase Pu–Ga alloys due to self-irradiation damage

An internal state variable model for the mechanical behavior of aged Pu–Ga alloys is developed and used to predict the change of the material with accumulated self-irradiation damage or age. The material model incorporates microstructural data such as the primary irradiation-induced defect density from cascades, the density and average size of helium bubbles, the initial dislocation density, and the initial average segment length of the dislocation density as input parameters, and then evaluates the stress–strain response of a representative volume element of the material. Given this response at a single material point, the deformation behavior of tensile specimens is predicted, and it forecasts increased strength, decreased strain hardening, and more strain localization with aging. Although the material point behavior showed some slight strain softening, this strain softening is expected to be masked by statistical variations of different volume elements and by the strain rate sensitivity of the material. Hence, it is not expected to appear in the stress–strain response of macroscopic tensile specimens, and only the increase in flow stress will be measured.

Strengthening via the formation of strain-induced martensite in stainless steels

The strengthening that results from the low-temperature formation of strain-induced martensite in austenitic stainless steel was studied. Specifically, the work hardening behaviour was characterized, as well as the spatial distribution of the martensite as a function of prior strain. Neutron diffraction measurements revealed the degree of elastic strain partitioning between the austenite and martensite. It was found that a sufficiently high initial dislocation density leads to a localization of the martensite transformation in the form of a Luders front. The martensite acts as an elastic reinforcing phase as it supports a higher stress than the austenite tensile loading, even though the martensite co-deforms plastically with the austenite. A model was developed that predicts the volume fraction of martensite formed as a function of plastic strain. © 2004 Elsevier B.V. All rights reserved.

Effect of Dynamic Aging of Dislocations on the Deformation Behavior of Extrinsic Semiconductors

The Alexander-Haasen theory of deformation in semiconductor crystals with low dislocation density was generalized by taking into account the effect of dynamic aging of dislocation caused by the impurity drag. The generalized theory explains some qualitative distinctions of the elastic-plastic transition in Czochralski-grown Si crystals from that in crystals of higher purity. Particularly, this concerns the dependence of the height of the yield-point peak on the initial dislocation density and the weakening of the strain-rate sensitivity of the yield stress.

Swelling behavior of TIG-welded F82H IEA heat

Tungsten-inert-gas weld joints prepared from the IEA heat of F82H were irradiated with 10.5 MeV Fe ions and 1.05 MeV He ions at 450 °C. Transmission electron microscopy observation revealed a marked cavity growth up to 30 nm at 50 dpa in the over-tempered portion of the heat-affected zone (HAZ), while cavities in the quenched portion of HAZ remained smaller (up to 10 nm). Base metal results also showed that a specimen tempered at 780 °C contained larger cavities than those tempered at 750 °C. Cavities in cold-worked specimens were the smallest. Initial dislocation densities in F82H, which are affected by heat treatment and/or mechanical treatment, dominate the cavity growth.

The influence of grain size on the indentation hardness of high-purity copper and aluminium

Abstract Quasistatic microindentation hardness studies of specimens of high-purity polycrystals and single crystals of copper and aluminium have been made at room temperature using a Vickers diamond and a tungsten carbide-cobalt sphere of radius 200 μm. The polycrystalline specimens of copper were prepared by heavy deformation of as-received specimens followed by thermal annealing at different temperatures and for different times; the grain sizes produced were in the range 15-520 μm. The polycrystalline samples of the as-received aluminium had a grain size of 330 ± 40 μm. As-formed specimens of copper of different grain sizes were found to have different dislocation densities; the smaller the grain size, the higher was the dislocation density. The Vickers hardness for a given indenter load, determined using the projected contact areas of indentations, was found to increase with decreasing grain size. Similarly, the Meyer hardness increased with decreasing grain size. It is argued that the observed increase in hardness of the polycrystals with decreasing grain size is due to the initial dislocation densities in the grains and not due to the grain boundaries which, because of the lack of impurities at them, do not appear to act as dislocation barriers in these high-purity fcc metals. Moreover, as the indentation hardness values of single crystals of copper of different orientations are very similar, any differences in the orientations of contiguous grains will not affect the hardness values of polycrystals. Thus for large single crystals of copper (10 mm × 10 mm × 10 mm), having the same dislocation density as that of the polycrystalline specimens of copper of grain size 15 ± 7 μm, the indentation hardness values were quite similar. Experimental results from the indentation hardness tests, made using both Vickers and spherical indenters, on polycrystalline aluminium specimens and relatively large single crystals showed that there was insignificant influence of the grain size.

Microstructure and mechanical property of irradiated Zr−2.5Nb pressure tube in Wolsong unit-1

With the aim of assessing the degradation of Zr−2.5Nb pressure tubes operating in the Wolsong unit-1 nuclear power plant, characterization tests are being conducted on irradiated Zr−2.5Nb tubes removed after 10-year operation. The examined tube had been exposed to temperatures ranging from 264 to 306°C and a neutron fluence of 8.9×1021 n/cm2 (E>1 MeV) at the maximum. Tensile tests were carried out at temperatures ranging from RT to 300°C. The density of a-type and c-type dislocations was examined on the irradiated Zr-2.5Nb tube using a transmission electron microscope. Neutron irradiation up to 8.9×1021 n/cm2 (E>1 MeV) yielded an increase in a-type dislocation density of the Zr−2.5Nb pressure tube to 7.5×1014 m−2, which was highest at the inlet of the tube exposed to the low temperature of 275°C. In contranst, the c-component dislocation density did not change with irradiation, keeping an initial dislocation density of 0.8×1014 m−2 over the whole length of the tube. As expected, the neutron irradiation increased mechanical strength by about 17–26% in the transverse direction and by 34–39% in the longitudinal direction compared to that of the unirradiated tube at 300°C. The change in the mechanical properties with irradiation is discussed in association with the microstructural change as a function of temperature and neutron fluence.

Effect of dynamic aging of dislocations on the deformation behavior of extrinsic semiconductors

The Alexander-Haasen theory of deformation in semiconductor crystals with low dislocation density was generalized by taking into account the effect of dynamic aging of dislocation caused by the impurity drag. The generalized theory explains some qualitative distinctions of the elastic-plastic transition in Czochralski-grown Si crystals from that in crystals of higher purity. Particularly, this concerns the dependence of the height of the yield-point peak on the initial dislocation density and the weakening of the strain-rate sensitivity of the yield stress.

Analytical description of the yield drop in the Alexander-Haasen model

The analytical solution of the equations of the Alexander-Haasen model, which describes the shape of the deformation-curve peak (the so-called yield drop), has been obtained for the case of a low initial dislocation density. It is shown that the self-development of the dislocation structure results in the specific kinetic transition with a dramatic decrease of the elastic-deformation rate and an increase of the plastic-flow rate. It is natural to interpret this phenomenon as an elastoplastic transition, and to consider the corresponding stress as the yield stress despite the fact that, being considered in the traditional way, its value does not coincide with either the upper or lower yield stress. The conditions of the existence of the yield drop are studied, and the quantitative criterion of the corresponding change in the deformation-curve shape is proposed.

Synchrotron investigation of strain profiles in the implanted semiconductors

MOCVD grown AlxGa1−xAs epitaxial layers with x=0.45 and GaAs single crystals with an initial dislocation density less than 103/cm2 were implanted with different doses of 1.5MeV Se+ and 1.0MeV Si+ ions and 170keV protons at room (RT) and liquid nitrogen temperatures (LNT). In all cases the ion range was close to 1μm. The samples were studied with a number of complementary X-ray methods, most of them with synchrotron radiation. The synchrotron methods revealed many interference phenomena which were used for the strain profile analysis based on fitting the simulated rocking curves and Bragg-case section topographs. It was found that the amorphisation of Al0.45Ga0.55As took place only after implantation at LNT. Upon implantation at RT an increase of the lattice parameter was observed that eventually saturated with an increasing ion dose. Also the flattening of the strain profile close to the surface was observed. Most of the observed strain effects were attributed to the point defects in the matrix crystal. For the highest doses the second strain component corresponding to the distribution of introduced ions was revealed.

A Generalized Model of the Yield Drop for Impure Semiconductors

ABSTRACTThe Alexander-Haasen theory describing the deformation behavior of low-dislocated semiconductor crystals is generalized taking into account the dynamic ageing of dislocations due to the impurities dragging. The constitutive equations describing kinetics of the plastic deformation are modified for the case of a spectrum of age-dependent internal stresses. Besides the solution hardening, the theory developed explains a number of qualitative distinctions of the elastic-plastic transition in silicon crystals grown by the Czochralski and the float zone methods. Particularly, this concerns a dependence of the yield drop on the initial dislocation density, and a weakening of the strain rate sensitivity of the yield stress.

A Constitutive Model for the Mechanical Behavior of Single Crystal Silicon at Elevated Temperature

AbstractSilicon in single crystal form has been the material of choice for the first demonstration of the MIT microengine project. However, because it has a relatively low melting temperature, silicon is not an ideal material for the intended operational environment of high temperature and stress. In addition, preliminary work indicates that single crystal silicon has a tendency to undergo localized deformation by slip band formation. Thus it is critical to obtain a better understanding of the mechanical behavior of this material at elevated temperatures in order to properly exploit its capabilities as a structural material. Creep tests in simple compression with n-type single crystal silicon, with low initial dislocation density, were conducted over a temperature range of 900 K to 1200 K and a stress range of 10 MPa to 120 MPa. The compression specimens were machined such that the multi-slip <100> or <111> orientations were coincident with the compression axis. The creep tests reveal that response can be delineated into two broad regimes: (a) in the first regime rapid dislocation multiplication is responsible for accelerating creep rates, and (b) in the second regime an increasing resistance to dislocation motion is responsible for the decelerating creep rates, as is typically observed for creep in metals. An isotropic elasto-viscoplastic constitutive model that accounts for these two mechanisms has been developed in support of the design of the high temperature turbine structure of the MIT microengine.

Microstructural effects on shear instability and shear band spacing

A constitutive relation that accounts for the thermally activated dislocation motion and microstructure interaction is used to study the stability of a homogeneous solution of equations governing the simple shearing deformations of a thermoviscoplastic body. An instability criterion and an upper bound for the growth rate of the infinitesimal deformations superimposed on the homogeneous solution are derived. By adopting Wright and Ockendon's postulate, i.e., the wavelength of the dominant instability mode with the maximum growth rate determines the minimum spacing between shear bands, the shear band spacing is computed. The effect of the initial dislocation density, the nominal strain-rate, and parameters describing the initial thermal activation and the initial microstructure interaction on the shear band spacing are delineated.

Investigation of primary and secondary creep deformation mechanism of TiAl

Creep deformation behaviors in lamellar TiAl alloys have been investigated. As in the case with metals, the normal primary creep stage was observed. As creep strain increased within the primary regime, dislocation density decreased, and creep activation energy increased from 300 kJ/mol, the activation energy of the self-diffusion of Ti in TiAl, to about 380 kJ/mol, that of steady state creep deformation. During primary creep deformation of lamellar TiAl, as the initial dislocation density decreased, the α2 -phase was found to transform to a γ-phase, generating new dislocations which contributed to the creep deformation. In other words, this phase transformation is the source of the dislocation generation for continuous creep deformation. Therefore, we suggest that phase transformation is the rate controlling processes having an activation energy of about 400 kJ/mol, which is higher than that of self-diffusion. A small amount of prestrain was found to be responsible for the reduction of initial dislocation density. In addition, this prestrained specimen showed significantly reduced primary creep strain, and the creep activation energy in the primary stage was measured to be about 380 kJ/mol. These results clearly confirm the suggested creep deformation mechanism of lamellar TiAl alloys.

High strain-rate response of commercially pure vanadium

To understand the plastic flow behavior of commercially pure vanadium under high strain rates, uniaxial compression tests of cylindrical samples are performed using UCSD's enhanced Hopkinson technique. True strains exceeding 50% are achieved in these tests, over a range of temperature from 77 to 800 K at the strain rates of 2500 and 8000 s −1. The microstructure of the deformed and undeformed samples is observed by an optical microscope. The initial microstructure (the initial dislocation density, the grain size and its distribution) is found to have a strong effect on the yield stress and the initial stages of the flow stress. This effect becomes more significant with decreasing temperature. Deformation twins are observed. Their density is seen to increase with decreasing temperature. Adiabatic shearbands occur in vanadium at low temperatures. Finally, an experimentally based micromechanical model is developed for the dynamic response of this material. The model predictions are compared with the results of other high strain-rate tests which have not been used in the evaluation of the model parameters, and good agreement between the theoretical predictions and experimental results is obtained. In addition, the results of a series of low strain-rate tests are presented and briefly discussed.

Inverse critical strains for jerky flow in Al-Mg alloys

The influence of the initial precipitation microstructure, as produced by various treatments, has been investigated in the past years in several Al alloys. However, the results obtained so far have been inconclusive or contradictory. The working hypothesis to be tested in the present work is that the initial dislocation density governs the critical strain behavior. For this purpose, the influence of prestrains performed in different conditions is examined and discussed in simple terms.

Dislocation Multiplication in the Early Stage of Deformation in MO Single Crystals

AbstractInitial dislocation structure in annealed high-purity Mo single crystals and deformation substructure in a crystal subjected to 1% compression have been examined and studied using transmission electron microscopy (TEM) techniques in order to investigate dislocation multiplication mechanisms in the early stage of plastic deformation. The initial dislocation density is in a range of 106 σ 107 cm−2, and the dislocation structure is found to contain many grown-in superjogs along dislocation lines. The dislocation density increases to a range of 108 σ 109 cm−2, and the average jog height is also found to increase after compressing for a total strain of 1%. It is proposed that the preexisting jogged screw dislocations can act as (multiple) dislocation multiplication sources when deformed under quasi-static conditions. The jog height can increase by stress-induced jog coalescence, which takes place via the lateral migration (drift) of superjogs driven by unbalanced line-tension partials acting on link segments of unequal lengths. The coalescence of superjogs results in an increase of both link length and jog height. Applied shear stress begins to push each link segment to precede dislocation multiplication when link length and jog height are greater than critical lengths. This “dynamic” dislocation multiplication source is suggested to be crucial for the dislocation multiplication in the early stage of plastic deformation in Mo.

HARPER-DORN CREEP—PREDICTIONS OF THE DISLOCATION NETWORK THEORY OF HIGH TEMPERATURE DEFORMATION

Several experimental observations characteristic of the Harper-Dorn (H-D) creep of crystals are examined within the framework of the dislocation network theory of creep. It is demonstrated that the dislocation network theory provides an excellent quantitative prediction of the transition stress from H-D to power-law creep, provided the steady-state dislocation density, ρs, in the H-D regime is known. The dislocation network theory also explains the observation that σs in the H-D creep regime is independent of the applied stress. This is a consequence of the frustration of dislocation network coarsening, which arises because of the exhaustion of Burgers vectors that can satisfy Frank's rule at the nodes in the network. The dislocation network theory is also able to explain the dramatic reduction in the steady-state creep rate that obtains when the initial dislocation density is very large, such as those introduced by pre-deformation of specimens at low temperatures or recovery-resistant microstructures attendant to processing by cold or hot working. The theory also accounts quantitatively for the reduction in the dislocation density that occurs during primary creep in the H-D regime. None of the other theories of H-D creep are able to account for the totality of these experimental observations. © 1997 Acta Metallurgica Inc.

A time-dependent deformation mechanism in metallic f.c.c. crystals

In this article, we present a time-dependent deformation mechanism for f.c.c. metal single crystals in which the resulting deformation is produced by the cumulative effect of dislocation glide in each slip systems. This model presents a self-consistent micromechanical approach where both the time-dependent and independent deformations are linked together. The time-dependent mechanism considers that additional glide of a dislocation segment in a given slip system results by the net motion of forest obstacles at which the segment is detained. The net obstacle motion is then related to the dislocation climb rate. We consider that the obstacle velocity is a function of the rate at which jogs on the gliding plane and the forest plane meet. This approach requires the jog density evolution to be followed for all systems. Two main sources of jog production are considered in this article: cross-slip and dislocation intersection, both depending on the loading history of the material. The predictions of the theory are compared to creep tests. These tests are especially suited to studying the contribution of the time-dependent part since the time-dependent portion remains unaltered during testing. The proposed model captures the creep rate dependence with stress as well as several key micromechanical features such as the dislocation density evolution, the reduced creep rate for high initial dislocation density and the effect of stacking fault energy.