Intersection of dislocations

Dislocations are a particularly important type of obstacles for the movement of other dislocations. 

Dislocations oriented in parallel interact and exert forces on each other as we already learned in section 6.2.7. Repulsive forces hinder the approach of the dislocations, attractive forces hinder their separation. Both forces impede 

In earlier sections, the characteristics of single dislocations were discussed. It was indicated that a dislocation moves quite freely in certain glide planes under applied shear stress. However, even well-annealed crystals contain many dislocations at a level of 10 . Therefore, it is quite probable that moving dislocations will encounter others, known as forest dislocations , which will hinder their freedom to glide. Even the most favored planes will contain dislocations and, thus, moving dislocations will interact with those others present in the material. The term dislocation intersection refers to an interaction occurring between a moving dislocation and the others encountered while in motion. For the sake of simplicity, this section will describe the interactions between two dislocations. 

When dislocations intersect jogs, kinks may form. Kinks are steps occurring in dislocation lines within the same slip plane, while jogs are steps in another slip 

The intersection of two orthogonal dislocations with parallel Burgers vectors is illustrated in Fig. 3.50, before and after intersection. In this case, two kinks are formed with the Burgers vectors, namely bi and b2 for the AB and CD dislocations, respectively. Both these kinks have a screw orientation and an increase in energy occurs in each of their dislocation Unes. 

Other cases are the intersections between edge-screw and screw-screw dislocations, illustrated in Rgs. 3.51 and 3.52, respectively. Simply drawn, the intersecting planes in the figures below are orthogonal, but they do not have to be. 

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The relative number of vacancies which are formed at the intersection of dislocations Cin for face-centered crystals is given by [81]... 

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... 

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]. 

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. 

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.)...

The influence of plastic deformation on the reaction kinetics is twofold. 1) Plastic deformation occurs mainly through the formation and motion of dislocations. Since dislocations provide one dimensional paths (pipes) of enhanced mobility, they may alter the transport coefficients of the structure elements, with respect to both magnitude and direction. 2) They may thereby decisively affect the nucleation rate of supersaturated components and thus determine the sites of precipitation. However, there is a further influence which plastic deformations have on the kinetics of reactions. If moving dislocations intersect each other, they release point defects into the bulk crystal. The resulting increase in point defect concentration changes the atomic mobility of the components. Let us remember that supersaturated point defects may be annihilated by the climb of edge dislocations (see Section 3.4). By and large, one expects that plasticity will noticeably affect the reactivity of solids. 

It was at that time that Franck and Seitz proposed mechanisms for the multiplication and generation of vacancies by intersection of dislocations88 explaining the observed softness of crystals and providing models that were subsequently verified by the technique of decoration of dislocations.89... 

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.

A partial dislocation (called a stair rod dislocation) is formed at the intersection of two stacking faults on different planes with different fault vectors R and R2 and its Burgers vector is bp = Ri—R2. An extended summary of the contrast from partial dislocations in fee metals has been given by Edington (1975). 

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. 

Mackwell et al. (1985) found that when specimens that had been deformed under anhydrous conditions were subsequently further deformed under wet conditions, there was a significant change in microstructure. TEM observations revealed enhanced formation of dislocation walls, despite the reduced stress levels. This observation was interpreted as due to enhanced dislocation climb under wet conditions. However, the two walls illustrated by Mackwell et al. (1985) could be interpreted as healed or partly healed fractures. One wall consists of a very irregular network of dislocations with many bubbles, particularly at dislocation intersections. 

The etch pattern of dislocations is determined by the inclination of dislocations to the surface. For dislocations lying nearly parallel to the surface, dislocation lines are observed. For dislocations lying at a steep inclination to the surface, etch pits result. The basic unit of an etch pit is generally bounded by the (111) planes intersecting the surface. The shape of a dislocation etch pit, which can be viewed as a superposition of the basic units etched at different intervals along a dislocation, is uniquely determined by the orientation of wafer surfaces and dislocation lines. Figure 7.61 schematically illustrates the shapes of etch pits developed on the three major surfaces. 

The second key observation is that the intersections between a twin boundary and a crystal surface represent chemically activated sites (and mechanically soft areas) (Novak and Salje 1998a, 1998b). It appears safe to assume that similarly activated sites exist also at the intersection of APBs and dislocations with the surface (e.g. Lee et al. 1998, Hochella and Banfield 1995). Besides the obvious consequences for the leaching behaviour of minerals, these key observations lead to the hypothesis of confined chemical reactions inside mesoscopic patterns. The idea is as follows as the surface energy is changed near mesoscopic interfaces, dopant atoms and molecules can be anchored near such interfaces. Some particles will diffuse into the mineral and react with... 

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