Line Defects Dislocations

Only Orowan remained with the topic and contributed a number of seminal ideas to the theory of the interaction between moving dislocations and other dislocations 

After 1934, research on dislocations moved very slowly, and little had been done by the time the War came. After the War, again, research at first moved slowly. In my view, it was not coincidence that theoretical work on dislocations accelerated at about the same time that the first experimental demonstrations of the actual existence of dislocations were published and turned invention into discovery . In accord with my remarks in Section 3.1.3, it was a case of seeing is believing all the numerous experimental demonstrations involved the use of a microscope. The first demonstration was my own observation, first published in 1947, of the process of polygonization, stimulated and christened by Orowan (my thesis adviser). When a metal crystal is plastically bent, it is geometrically necessary that it contains an excess of positive over negative dislocations when the crystal is then heated, most of the dislocations of 

Mott played a major part, with his collaborator Frank Nabarro (b. 1917) and in consultation with Orowan, in working out the dynamics of dislocations in stressed crystals. A particularly important early paper was by Mott and Nabarro (1941), on the flow stress of a crystal hardened by solid solution or a coherent precipitate, followed by other key papers by Koehler (1941) and by Seitz and Read (1941). Nabarro has published a lively sequential account of their collaboration in the early days (Nabarro 1980). Nabarro originated many of the important concepts in dislocation theory, such as the idea that the contribution of grain boundaries to the flow stress is inversely proportional to the square root of the grain diameter, which was later experimentally confirmed by Norman Fetch and Eric Hall. 

The early understanding of the geometry and dynamics of dislocations, as well as a detailed discussion of the role of vacancies in diffusion, is to be found in one of the early classics on crystal defects, a hard-to-find book entitled Imperfections in Nearly Perfect Crystals, based on a symposium held in the USA in 1950 (Shockley et al. 1952). Since in 1950, experimental evidence of dislocations was as yet very sparse, more emphasis was placed on a close study of slip lines (W.T. Read, Jr., 

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In contrast to fluids, crystals have a greater number of control parameters crystal structure, strain and stress, grain boundaries, line defects (dislocations), and the size and shape of crystallites, etc. These are all relevant to kinetics. Treatments that go beyond transport and diffusion in this important field of physical chemistry are scarce. 

Line defects (dislocations) are produced by slippage or shear of the crystal lattice. If the slippage is perpendicular to a face of the crystal so that the lattice planes on either side of the dislocation are parallel but displaced with respect to one another, the defect is called an edge dislocation. If the slippage is angular, as if produced by rotation about the shear axis so that lattice planes on either side of the defect are not perpendicular, the defect is called a screw dislocation. 

Virtually all minerals contain defects. In addition to point defects (e.g., vacancies that exist in a thermodynamically determined equilibrium number, impurities etc ), macroscopic minerals contain line defects (dislocations), and planar defects such as stacking foults, antiphase boundaries and twins. Intergrown layers of different structure or composition, and polytypic disorder also may be present. 

Line defects dislocations, impurity atoms segregated to dislocations... 

As in crystals, defects in liquid crystals can be classified as point, line or wall defects. Dislocations are a feature of liquid crystal phases where tliere is translational order, since tliese are line defects in tliis lattice order. Unlike crystals, tliere is a type of line defect unique to liquid crystals tenned disclination [39]. A disclination is a discontinuity of orientation of tire director field. 

When plastic deformation occurs, crystallographic planes sHp past each other. SHp is fackitated by the unique atomic stmcture of metals, which consists of an electron cloud surrounding positive nuclei. This stmcture permits shifting of atomic position without separation of atomic planes and resultant fracture. The stress requked to sHp an atomic plane past an adjacent plane is extremely high if the entire plane moves at the same time. Therefore, the plane moves locally, which gives rise to line defects called dislocations. These dislocations explain strain hardening and many other phenomena. 

The other major defects in solids occupy much more volume in the lattice of a crystal and are refeiTed to as line defects. There are two types of line defects, the edge and screw defects which are also known as dislocations. These play an important part, primarily, in the plastic non-Hookeian extension of metals under a tensile stress. This process causes the translation of dislocations in the direction of the plastic extension. Dislocations become mobile in solids at elevated temperamres due to the diffusive place exchange of atoms with vacancies at the core, a process described as dislocation climb. The direction of climb is such that the vacancies move along any stress gradient, such as that around an inclusion of oxide in a metal, or when a metal is placed under compression. 

In a detailed study the dissolution kinetics of shock-modified rutile in hydrofluoric acid were carefully studied by Casey and co-workers [88C01], Based on the defect studies of the previous sections in which quantitative measures of point and line defects were obtained, dissolution rates were measured on the as-shocked as well as on shocked and subsequently annealed powders. At each of the annealing temperatures of 200, 245, 330, 475, 675, 850, and 1000 °C, the defects were characterized. It was observed that the dissolution rates varied by only a factor of 2 in the most extreme case. Such a small effect was surprising given the very large dislocation densities in the samples. It was concluded that the dissolution rates were not controlled by the dislocations as had been previously proposed. 

The simplest type of line defect is the edge dislocation, which consists of an extra half plane of atoms in the crystal, as illustrated schematically in Fig. 20.30a edge dislocations are often denoted by 1 if the extra half plane ab is above the plane sp, or by T if it is below. 

The second type of line defect is the screw dislocation, which is rather less easy to visualise. Consider, however, a block of material, half of which is sheared one interatomic distance with respect to the other half, as shown in Fig. 20.306. The line cdthen constitutes a screw dislocation the arrangement of atoms around a screw dislocation is shown in Fig. 20.30c. 

To a good approximation, only atoms within the dotted circles in Figs. 20.30a and b are displaced from their equilibrium position in a real, three-dimensional crystal the diameter d of these circles would be very much less than the length / of the dislocation, i.e. the length, perpendicular to the page, of the extra half plane of atoms ab in Fig. 20.30a, or of the line cd in Fig. 20.306. Dislocations strictly, therefore, are cylindrical defects of diameter d and length / however, since I d they are referred to as line defects. 

This type of volume defect in the crystal is known as a "screw dislocation", so-called because of its topography. Note that the spiral dislocation of the growing lattice deposits around the Une defect at right angles to the line defect. 

In the following diagram, given as 3.1.12. on the next page, amother representation is shown, detailing how the dislocation line (line defect) becomes a screw-dislocation. 

Dislocations Dislocations are stoichiometric line defects. A dislocation marks the boundary between the slipped and unslipped parts of crystal. The simplest type of dislocation is an edge dislocation, involving an extra layer of atoms in a crystal (Fig. 25.2). The atoms in the layers above and below the half-plane distort beyond its edge and are no longer planar. The direction of the edge of the half-plane into the crystal is know as the line of dislocation. Another form of dislocation, known as a screw dislocation, occurs when an extra step is formed at the surface of a crystal, causing a mismatch that extends spirally through the crystal. 

The usefulness of quadrupolar effects on the nuclear magnetic resonance c I 7 yi nuclei in the defect solid state arises from the fact that point defects, dislocations, etc., give rise to electric field gradients, which in cubic ciystals produce a large effect on the nuclear resonance line. In noncubic crystals defects of course produce an effect, but it may be masked by the already present quadrupole interaction. Considerable experimental data have been obtained by Reif (96,97) on the NMR of nuclei in doped, cubic, polycrystalline solids. The effect of defect-producing impurities is quite... 

Point defects have zero dimension line defects, also known as dislocations, are onedimensional and planar defects such as surface defects and grain boundary defects have two dimensions. These defects may occur individually or in combination. 

The second type of line defect, the screw dislocation, occurs when the Burger s vector is parallel to the dislocation line (OC in Figure 1.33). This type of defect is called a screw dislocation because the atomic structure that results is similar to a screw. The Burger s vector for a screw dislocation is constructed in the same fashion as with the edge dislocation. When a line defect has both an edge and screw dislocation... 

The lattice defects are classified as (i) point defects, such as vacancies, interstitial atoms, substitutional impurity atoms, and interstitial impurity atoms, (ii) line defects, such as edge, screw, and mixed dislocations, and (iii) planar defects, such as stacking faults, twin planes, and grain boundaries. 

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