Dislocation surface intersections

The density of dislocations is usually stated in terms of the number of dislocation lines intersecting unit area in the crystal it ranges from 10 cm for good crystals to 10 cm" in cold-worked metals. Thus, dislocations are separated by 10 -10 A, or every crystal grain larger than about 100 A will have dislocations on its surface one surface atom in a thousand is apt to be near a dislocation. By elastic theory, the increased potential energy of the lattice near... 

The electrocrystallization on an identical metal substrate is the slowest process of this type. Faster processes which are also much more frequent, are connected with ubiquitous defects in the crystal lattice, in particular with the screw dislocations (Fig. 5.25). As a result of the helical structure of the defect, a monoatomic step originates from the point where the new dislocation line intersects the surface of the crystal face. It can be seen in Fig. 5.48 that the wedge-shaped step gradually fills up during electrocrystallization after completion it slowly moves across the crystal face and winds up into a spiral. The resultant progressive spiral cannot disappear from the crystal surface and thus provides a sufficient number of growth... 

Dislocation density is measured as the total length of dislocation lines in a unit volume of crystal, meters per meter cubed. However, experimentally it is often simpler to determine the number of dislocations that intersect a surface, so that a common measure of dislocation density is the number of dislocation lines threading a surface, that is, the number per meter squared. In a fairly typical material there will be on the order of 108 dislocation lines crossing every square centimeter of solid. However, it is known that if a solid is deformed, the dislocation density rises, perhaps by a factor of 103 or 104. Clearly, dislocations must be able to multiply under the conditions that lead to deformation. 

This method has the advantage of not requiring a knowledge of the foil thickness t, but it becomes very difficult to count surface intersections for dislocation densities higher than about 10 cm". Clearly, measurements of the number-density of small dislocation loops or small inclusions (such as bubbles or voids) requires a knowledge of thickness t. 

Frank [5.50] was the first to recognize the major role of screw dislocations in the process of the growth of real crystals. Due to the helicoidal structure of this crystal imperfection, a step originates from the point where the screw dislocation line intersects the surface of the crystal face (Fig. 5.26b). This step is constrained to terminate at the dislocation emergence point and winds up into a spiral during the growth process (Fig 5.27). 

Fig. 8-35 Lang topograph of a thin crystal of lithium fluoride. Dark lines are dislocations, some randomly arranged and some nearly parallel. The latter form the band running diagonally across the photograph these dislocations, which intersect the top and bottom surfaces of the crystal, constitute a small angle boundary between two subgrains. Mo KiXi radiation, 200 reflection. (Courtesy of A. R. Lang. [8.26.])...

Precise studies of the structural imperfections in copper single crystals were carried out by F. W. Young, Jr. after he received the Ph.D. degree and joined the Solid State Branch of ORNL. Young developed etchants that brought out the dislocations which intersected the surface. He was thus able to determine the number of imperfections that was present as a consequence of the single crystal growth process and to determine those that were introduced by various mechanical treatments. 

Fig. l.S(a) Grain boundary intersecting an etched metallographic surface and (b) etch pit at a dislocation interseaing an etched metallographic surface... 

By their nature, dislocations cannot end suddenly in the interior of a crystal a dislocation line can only end at a free surface or a grain boundary (or form a closed loop). Where a screw dislocation intersects a free surface there is inevitably a step or ledge in the surface, one atomic layer high, as shown in Fig. 20.30c. Furthermore, the step need not necessarily be straight and will, in fact, almost certainly contain kinks. 

Surface features can also be revealed by etching, which permits identification of points of intersection of line dislocations with the surface, and this is valuable in determining the role of these imperfections in chemical processes [45,214] and, in particular, nucleus formation. Smaller topographical details can be rendered visible by the evaporation of a thin (<0.5 nm) film of gold onto the surface [215,216]. Heights and depths of surface features can be determined by interferometry [203—205]. Microcinematography has also been used [217] to record the progress of solid phase reactions. 

Some limitations of optical microscopy were apparent in applying [247—249] the technique to supplement kinetic investigations of the low temperature decomposition of ammonium perchlorate (AP), a particularly extensively studied solid phase rate process [59]. The porous residue is opaque. Scanning electron microscopy showed that decomposition was initiated at active sites scattered across surfaces and reaction resulted in the formation of square holes on m-faces and rhombic holes on c-faces. These sites of nucleation were identified [211] as points of intersection of line dislocations with an external boundary face and the kinetic implications of the observed mode of nucleation and growth have been discussed [211]. 

Pit formation. If we consider a dissolution nucleus at a screw dislocation intersecting the surface which consists of a cylindrical hole of radius r, one atom layer deep (a), then the free energy of formation of this nucleus will be composed of a volume energy, surface energy, and elastic strain energy term, respectively, as follows ... 

Figure 3.16. Some simple defects found on a low-index crystal face 1, the perfect flat face, a terrace 2, an emerging screw dislocation 3, the intersection of an edge dislocation with the terrace 4, an impurity adsorbed atom 5, a monatomic step in the surface, a ledge 6, a vacancy in the ledge 7, a kink, a step in the ledge 8 an adatom of the same type as the bulk atoms 9, a vacancy in the terrace 10, an adatom on the terrace. (From Ref. 12, with permission from Oxford University Press.)...

A crystal growing from the vapor phase possesses a singular surface with two screw dislocations intersecting it. The dislocations are very close to one another (relative to the dimensions of the surface) and have opposite Burgers vectors. Describe the form of the step structure that is produced because of the presence of the two dislocations. 

Dislocation density is often determined by counting the number of dislocations per area intersecting a polished surface. If the dislocation density in cold-worked copper is found to be 2 x 1010/cm2, what is the total length of dislocation line per volume ... 

Fig. 1. Surface structure often found on low-index crystal faces. 1, A terrace perfectly flat crystal face. 2, An emerging screw dislocation. 3, The intersection of an edge dislocation with a terrace. 4, A ledge or monatomic step, 5. A kink a step in a ledge. 6, A vacancy in a ledge. 7, An adsorbed growth unit on a ledge.

Fig. 11. The formation of a spiral step pattern on a simple cubic 100 face. A single screw dislocation intersects the surface segment at the centre and at this point two steps originate. In equilibrium, the two steps are essentially straight but, when the driving force is applied, they advance and can eventually provide a dense array of edge sites over the crystal face. (Reproduced from ref. 25, 1980 by the American Association for the Advancement of Science.)...

In previous work (Chems and Jiao, 2001) dislocations with [0001]-line directions were aligned parallel to the electron beam, which is adequate to maximize the contribution of the line charge to the phase shift of the electron wave. However, the formation of pits at the intersection line of the dislocation with the surface due to ion etching of the sample is difficult to avoid and to detect. By analyzing embedded dislocations, thickness modifications, which also shift the phase with respect to the surrounding material according to Eq.(2), can be eliminated definitely. In addition, dynamical contributions to the phase shift are more difficult to exclude if... 

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