Dislocations loops

The back stress (or self-stress) ji acting on a pinned dislocation loop is given by... 

The response is extremely fast on the time scale of a shock-wave experiment. The dislocation loop adjusts very quickly to the applied stress t. 

Fig. 6. Radiation damage in graphite showing the induced crystal dimensional strains. Impinging fast neutrons displace carbon atoms from their equilibrium lattice positions, producing an interstitial and vacancy. The coalescence of vacancies causes contraction in the a-direction, whereas interstitials may coalesce to form dislocation loops (essentially new graphite planes) causing c-direction expansion.

As an indenter creates an indentation it causes at least three types of finite deformation. It punches material downwards creating approximately circular prismatic dislocation loops. At the surface of the material it pushes material sideways. It causes shear on the planes of maximum shear stress under itself. Therefore, the overall pattern of deformation is very complex, and is reflected... 

Figure 4.2 Quasi-hexagonal dislocation loop lying on the (111) glide plane of the diamond crystal structure. The <110> Burgers vector is indicated. A segment, displaced by one atomic plane, with a pair of kinks, is shown a the right-hand screw orientation of the loop. As the kinks move apart along the screw dislocation, more of it moves to the right.

High-resolution lattice images (e.g., Fig. 8(c)) reveal that the platelets are associated neither with dislocation loops nor with either intrinsic or extrinsic stacking faults. The platelets appear to be microcracks in which the separation between adjacent planes of Si atoms over a finite area is increased due to the slight displacement of these atoms from their substitutional lattice sites. From computer simulations, the lattice images are... 

A dislocation line characterizes a line of disruption in the crystal. This implies that the dislocation must either end on the surface of a crystal, on another dislocation, or else form a closed loop. Dislocation loops have been found to occur frequently in crystals. 

The Burgers vector of most dislocations is neither perpendicular nor parallel to the dislocation line. Such a dislocation has an intermediate character and is called a mixed dislocation. In this case the atom displacements in the region of the dislocation are a complicated combination of edge and screw components. The mixed edge and screw nature of a dislocation can be illustrated by the structure of a dislocation loop,... 

Figure 3.9 Part of a dislocation loop (a) pure edge, pure screw, and mixed dislocation character (b) glide is perpendicular to the Burgers vector, b, for the edge component, parallel to b for the screw component and at an angle to b for the mixed component and (c) continued glide results in removal of the dislocation from the crystal, leaving a step of height b on the surface.

Figure 3.13 Dislocation pinned at each end (a) can respond to stress by bowing out (b, c, d, and e) to form a dislocation loop and reform the pinned dislocation (/). The growth of the dislocation represented in (a)-(c) requires increasing local stress, whereas the steps in (d)-(f) are spontaneous once the point in (c) is passed.

INTERACTION OF DISLOCATIONS AND POINT DEFECTS 3.7.1 Dislocation Loops... 

The dislocation formation mechanism described in the previous section generates dislocation loops. A dislocation loop can also form by the aggregation of vacancies on a plane in a crystal. Vacancy populations are relatively large at high temperatures, and, if a metal, for example, is held at a temperature near to its melting point, considerable... 

Figure 3.14 Formation of dislocation loops (a) the aggregation of vacancies onto a single plane, (b) collapse of the plane to form a dislocation loop, and (c) aggregation of interstitials to form a dislocation loop.

An exactly similar situation can be envisaged if the crystal contains a high population of interstitial point defects. Should these aggregate onto a single plane, a dislocation loop will once again form (Fig. 3.14c). 

The aggregation of vacancies or interstitials into dislocation loops will depend critically upon the nature of the crystal structure. Thus, ionic crystals such as sodium chloride, NaCl, or moderately ionic crystals such as corundum, AI2O3, or rutile, TiC>2, will show different propensities to form dislocation loops, and the most favorable planes will depend upon chemical bonding considerations. 

Figure 3.15 Change of stacking across a dislocation loop in a face-centered cubic structure. The structure is that of a Frank sessile dislocation loop.

The edge dislocations bounding the dislocation loops just described cannot glide, but nevertheless the loop can grow by the continued collection of vacancies or interstitials. This method of movement of an edge dislocation, which allows edge... 

Figure 4.25 Growth of the planar defects (dislocation loops) as a function of annealing conditions. The total area covered by the defects saturates at about 1.8% of the total surface area studied by TEM.

Figure 22 Depth distribution of the number density of dislocation loops for austenitic stainless steels irradiated with 12-MeV Ni, 1-MeV He, and 350-keV H triple beams.

More generally, co is independent of the external gas pressure k is the Boltzmann constant (1.38 x 10 erg deg ) and T is the temperature in Kelvin. Furthermore, the equilibrium between co and a collapsed CS plane fault is maintained by exchange at dislocations bounding the CS planes. Clearly, this equilibrium cannot be maintained except by the nucleation of a dislocation loop and such a process requires a supersaturation of vacancies and CS planes eliminate supersaturation of anion vacancies (Gai 1981, Gai et al 1982). Thus we introduce the concept of supersaturation of oxygen point defects in the reacting catalytic oxides, which contributes to the driving force for the nucleation of CS planes. From thermodynamics. 

Under the action of a local shear stress, a, a straight dislocation line that is fixed at two points will bend out. The bending radius is inversely proportional to a. The dislocation becomes unstable if the bending radius is <1/2, where / is the distance between the anchor points (Fig. 3-3). Dislocation loops can be formed and macroscopic plastic deformation can continuously occur under stress if... 

Since a loss of coherency requires the formation of dislocation loops around the growing particle, and the formation of a loop may be rather difficult to achieve, rcril is sometimes larger than the value calculated from Eqn. (3.24). 

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