Dislocation Generation Mechanisms Research Articles

Dislocation-free zone model of fracture comparison with experiments

The dislocation-free zone (DFZ) model of fracture has been extended to study the relationship between the stress intensity factor, extent of plastic deformation, and crack tip geometry of an elastic-plastic crack as a function of applied stress. The results show that the stress intensity factor K decreases from the elastic value at first slowly, then goes rapidly to zero as the number of dislocations in the plastic zone increases. The crack with a zero stress intensity factor has its crack tip stress field completely relaxed by plastic deformation and hence is called a plastic crack. Between the elastic and plastic cracks, a wide range of elastic-plastic cracks having both a stress singularity and a plastic zone are possible. These elastic-plastic cracks with a DFZ are predicted if there is a critical stress intensity factor Kg required for the generation of dislocations at the crack tip. The expression for Kg is obtained from the crack tip dislocation nucleation model of Rice and Thomson. In most metals, the magnitude of Kg is less than the critical stress intensity factor for brittle fracture Kc. The values of K are determined from electron microscope fracture experiments for various metals and they are found to be in good agreement with the Kg predicted from the model. It is concluded that for most ductile and semibrittle metals, the mechanism of dislocation generation is more important than the fracture surface energy in determining the stress intensity factor at the crack tip.

Dislocation-free zone model of fracture

Recent observations by electron microscopy have shown that a dislocation-free zone (DFZ) is present between the crack tip and the linear pileup of dislocations in the plastic zone. A singular integral equation is formulated to describe the equilibrium configuration of the dislocations. The distribution function of the dislocations is obtained in terms of elliptic integrals. The condition of compatibility and the elastic stress intensity factor at the crack tip are also derived. At the crack tip the stress varies as 1/√r. It is found that the stress intensity factor K is approximately a function of the length of the DFZ, whereas the externally applied stress approximately determines the length of the plastic zone. Based on the mechanism of dislocation generation at the crack tip proposed by Rice and Thomson, it is shown that the formation of the DFZ is anticipated when the stress intensity factor K is less than a critical stress intensity factor Kg defined for a spontaneous generation of dislocations. The magnitude of Kg relative to the critical stress intensity factor for brittle fracture Kc determines the brittle-ductile nature of a material.

Generation Mechanism of Dislocations in Local Oxidation of Silicon

Local oxidation conditions and film thickness combinations of and are studied to investigate the generation mechanism of dislocations using (001) oriented silicon wafers. The nature of dislocations in Si is examined by Secco etching and transmission electron microscopy is used for the determination of Burgers vectors. Dislocations have been generated in the film combinations with more than 2000Å or with less than 78Å at 1000°C oxidation in wet . Edge and screw dislocations are found underneath and close to film, respectively. These dislocations are generated in the initial stage of oxidation.

Effects of the Crystal Diameter on the Dislocation Density in KCl Crystals Grown by the Czochralski Method

AbstractThe dependence of dislocation density on the crystal diameter of the Czochralski grown KCl crystals (both pure and Sr doped) was investigated by the method of the etch pit and X‐ray topograph. (1) The dislocation density drastically decreased with the decrease in diameter (D) for small D (D < 2 mm, Fig. 2). (2) The dislocation density in the Sr doped crystal was lower than that of pure component in the diameter examined. (3) Many helical dislocations and dislocation loops were observed in the thin crystals (D ∼ 0.5 mm) of the pure KCl and Sr doped one, respectively, by X‐ray projection topography. These results were discussed in connection with the dislocation generation mechanisms due to thermal stresses or supersaturated point defects.

A mechanism for dislocation generation in shock-wave deformation

Numerous articles describing the changes in structure and mechanical response of metals and alloys induced by shock waves have been published in the past twenty years (I-3). Increases in the concentration of point (4) and line defects (5), formation of twins (6), martensite (7) and precipitates (8) have been observed in the residual structures. Smith (9) proposed the f i rs t model accounting for dislocation generation in shock loading. According to this model, a two-dimensional array of dislocations separated the high-density shockedmaterial from the virgin material; the translation of this two-dimensional interface coincided with the shock-front propagation. Aware of the fact that the passage of such an interface would result in undeformed material, Smith (9) hypothesized the presence of sources and sinks of dislocations, moving with the velocity of the shock front. Hornbogen (lO), based on the fact that shock-loaded iron (between 7 and II GPa) presents a substructure characterized by straight screw dislocations, proposed a modification to Smith's (9) model. Shock loading would induce the formation of loops; the edge components would propagate with the front, basically forming a Smith interface. However, the screw components would stay behind and would therefore be the salient residual feature of the substructure. Cowan ( l l ) suggested that at shock pressures generating shear stresses above the theoretical shear stress of the material a difference in dislocation generation mechanism might be expected. Above this termed by him supercritical stress, the limitations imposed on dislocation velocity would no longer be valid, and a Smith (9) interface might become possible. No specific mechanism is however proposed by him.

Dislocations et croissance des cristaux d'aluminium par recristallisation secondaire

Dislocations of aluminium crystals grown under high vacuum ( P ⩽ 10 -8 torr) by secondary recrystallization at the expense of primary recrystallization cubic texture grains were investigated by X-ray Lang topography. We could see that quasi-linear dislocations, with Burgers vectors making an angle of 60° with dislocation lines arise from segmented helical-type dislocations present in these crystals. The origin of the latter type dislocations is ascribed to the climbing of screw dislocations under the small supersaturation of vacancies which form in the crystals during cooling. A generation mechanism of screw or quasi-screw dislocations associated with the boundary migration of secondary crystals (38° (22°) 〈111〉 Kronberg-Wilson boundary) is also described.

Generation of Dislocations and Stacking Faults at Surface Heterogeneities in Silicon

Dislocation and stacking fault generation around submicron-sized surface pits in shallow diffused bipolar transistors is examined. Under the combined action of the stress concentration effect of surface pits and phosphorus diffusion induced stresses, crystallographic defects are generated in the emitter area of shallow diffused transistors. Stacking faults are identified as sessile faults surrounding the micropits. Mechanisms of dislocation generation are examined and their applicability to the present results discussed. It is shown that the presence of nonplanar surfaces at discrete regions can introduce an additional diffusion front into the crystal and produce an increase in stress as well as an increase in the solute concentration leading to localized plastic flow. High-concentration phosphorus diffusions introduce extensive dislocation networks throughout the emitter area and cause stacking fault annihilation.

X-Ray Topographic Study of Tensile Deformation in Nearly Perfect Copper Crystals

Copper crystals of a cross section 0.5×0.1 cm and of an initial dislocation density N 50–5000 cm/cm3 were deformed in tension, and Borrmann x-ray topographs were taken after successive stress increments. All dislocations were observed and Burgers vectors determined. Stereo pairs were made. The grown-in dislocations were moved very little by the applied stresses. For crystals of lower initial N most of the dislocation generation could be related to localized stresses in the grip regions, while in the crystals with higher initial N the generation probably was related to grown-in dislocations. Slip bands were formed; neither the source nor the generation mechanism of dislocations in these bands was determined. Screw dislocations were left by edge segments running across the crystal. These screw dislocations cross slipped frequently at stresses of a few grams/mm2, and this process tended to fill the volume of crystal between the bands with dislocations. By counting all new dislocations the shear strain was computed and ``stress-strain'' curves were obtained.

Growth of Copper Crystals of Low Dislocation Density

A study was made of the perfection and the factors controlling perfection of copper crystals grown by a Bridgman technique. Crystals grown from 99.999+% and from (OFHC) copper were acid sawed and polished, and dislocation densities determined by etch pit techniques. The orientation of the growth direction of unseeded crystals of both purities was random. There was a correlation between perfection and growth direction for the 99.999+% copper crystals in that the more perfect crystals had growth direction far from the [111] zone. Dislocation densities as low as 103/cm2, with no subboundaries, were obtained in some of the purer as-grown crystals. The OFHC crystals were much less perfect and contained many subboundaries. After annealing slices of the purer crystals at 1075°C, dislocation densities as low as 102/cm2 were obtained. The vacancy condensation mechanism for dislocation generation apparently was not significant in accounting for the residual dislocation density in these crystals.

Microstraining in αCuAl single crystals

The early stage of plastic deformation in αCu-Al single crystals has been studied at room temperature using a strain sensitivity of 1 × 10 −6. The stress corresponding to this strain increases from 75 g/mm 2 in a 0.5 at.% Al alloy to 394 g/mm 2 in a 14 at.% Al crystal; the easy glide stresses for the same alloys are 415 and 1550 g/mm 2, respectively. During microstraining, the stress is generally proportional to the square root of the plastic strain. Assuming a dislocation generation mechanism, independent calculations with the microstrain work-hardening behavior and the 1 × 10 −6 “yield stress” give approximately the same value for the unpinned length of dislocation for each alloy. If the pinning is due to forest dislocations, the forest density increases with solute concentration. The barrier density is calculated to be about an order of magnitude smaller than the forest density and this observation is explained with a model given by Meakin and Wilsdorf (formation of Cottrell-Lomer dislocations). Sub-grain boundaries may also be acting as barriers. Slip lines were examined with a light microscope in a 14 at.% Al crystal during various stages of microstraining. The coarse primary and cross slip lines characteristic of easy glide deformation in this “α-brass type” crystal are observed at a stress of about 2 3 the easy glide stress.

Generation and Distribution of Dislocations by Solute Diffusion

The stress introduced by solute lattice contraction of boron and phosphorus in silicon is shown to be sufficient to generate dislocations in silicon wafers. Such dislocations were observed. Expressions for the density distribution and for the total number of dislocations generated are derived and a mechanism of dislocation generation and distribution during the diffusion process is postulated. The dislocation distribution is shown to be highly dependent upon the nature of the diffusion process, expressions being derived for the conditions of (1) constant surface concentration of solute and (2) diffusion from a finite source. An expression for and means to determine the residual stresses in diffused silicon wafers are given.