Dislocations motion

Figure C2.11.6. The classic two-particle sintering model illustrating material transport and neck growtli at tire particle contacts resulting in coarsening (left) and densification (right) during sintering. Surface diffusion (a), evaporation-condensation (b), and volume diffusion (c) contribute to coarsening, while volume diffusion (d), grain boundary diffusion (e), solution-precipitation (f), and dislocation motion (g) contribute to densification.

An analogy to sHp dislocation is the movement of a caterpillar where a hump started at one end moves toward the other end until the entire caterpillar moves forward. Another analogy is the displacement of a mg by forming a hump at one end and moving it toward the other end. Strain hardening occurs because the dislocation density increases from about 10 dislocations/cm to as high as 10 /cm. This makes dislocation motion more difficult because dislocations interact with each other and become entangled. SHp tends to occur on more closely packed planes in close-packed directions. 

Dislocation motion in the clear region between obstacles is determined by the viscous drag coefficient B [2]. The relationship between the applied shear stress and dislocation velocity is... 

Figure 7.6. Mechanical threshold for long-range dislocation motion. Here G is the shear modulus in the compressed state.

This process of backward dislocation motion produces reverse plastic flow immediately upon reduction of longitudinal stress from the shocked state. A modification of the Orowan equation, (7.1), to the current situation is... 

P. Kumar and R.J. Clifton, Dislocation Motion and Generation in LiF Single Crystals Subjected to Plate Impact, J. Appl. Phys. 50, 4747-4762 (1979). 

Dislocation motion produces plastic strain. Figure 9.4 shows how the atoms rearrange as the dislocation moves through the crystal, and that, when one dislocation moves entirely through a crystal, the lower part is displaced under the upper by the distance b (called the Burgers vector). The same process is drawn, without the atoms, and using the symbol 1 for the position of the dislocation line, in Fig. 9.5. The way in... 

Fig. 17.1. (a) Dislocation motion is intrinsically easy in pure metals - though alloying to give solid solutions or precipitates con moke it more difficult. (b) Dislocation motion in covalent solids is intrinsically difficult because the interatomic bonds must be broken and reformed. ( ) Dislocation motion in ionic crystals is easy on some planes, but hard on others. The hard systems usually dominate. 

Analysis of stress distributions in epitaxial layers In-situ characterization of dislocation motion in semiconductors Depth-resolved studies of defects in ion-implanted samples and of interface states in heterojunctions. 

R. Mikulla, F. ICrul, P. Gumbsch, H.-R. Trebin. Numerical simulations of dislocation motion and crack propagation in quasicrystals. In A. Goldmann,... 

In most circumstances the kinetics of this reaction are controlled by the rate at which the hydrogen can diffuse into the underlying steel, and this reaction is essentially in equilibrium. Consequently it is difficult to study the kinetics of this reaction. A particular situation in which this may be very important relates to the conditions at crack tips, where the hydrogen may be transported into the bulk by dislocation motion, giving rise to very high rates of hydrogen entry. 

Other hand, when the dislocation density is high, the dislocations do interact and they become tangled up with each other dislocation motion is then difficult and the material is therefore strong. The interaction of dislocations with each other and with other structural features in metals is a very complex field it is also, however, extremely important, since it greatly affects the strength of metals. 

In covalently bonded crystals, the forces needed to shear atoms are localized and are large compared with metals. Therefore, dislocation motion is intrinsically constrained in them. 

The plastic deformation patterns can be revealed by etch-pit and/or X-ray scattering studies of indentations in crystals. These show that the deformation around indentations (in crystals) consists of heterogeneous rosettes which are qualitatively different from the homogeneous deformation fields expected from the deformation of a continuum (Chaudhri, 2004). This is, of course, because plastic deformation itself is (a) an atomically heterogeneous process mediated by the motion of dislocations and (b) mesoscopically heterogeneous because dislocation motion occurs in bands of plastic shear (Figure 2.2). In other words, plastic deformation is discontinuous at not one, but two, levels of the states of aggregation in solids. It is by no means continuous. And, it is by no means time independent it is a flow process. 

C44 measures the shear strengths of chemical bonds and the Chin-Gilman parameter indicates how directly they interact with dislocation motions which depends on how localized the bonding is. Thus it is relatively large for covalent bonding which is localized to pairs of atoms (electron pair bonding). 

The viscosity coefficients at dislocation cores can be measured either from direct observations of dislocation motion, or from ultrasonic measurements of internal friction. Some directly measured viscosities for pure metals are given in Table 4.1. Viscosities can also be measured indirectly from internal friction studies. There is consistency between the two types of measurement, and they are all quite small, being 1-10% of the viscosities of liquid metals at their melting points. It may be concluded that hardnesses (flow stresses) of pure... 

In impure metals, dislocation motion ocures in a stick-slip mode. Between impurities (or other point defects) slip occurs, that is, fast motion limited only by viscous drag. At impurities, which are usually bound internally and to the surrounding matrix by covalent bonds, dislocations get stuck. At low temperatures, they can only become freed by a quantum mechanical tunneling process driven by stress. Thus this part of the process is mechanically, not thermally, driven. The description of the tunneling rate has the form of Equation (4.3). Overall, the motion has two parts the viscous part and the tunneling part. 

In these crystals, dislocation motion is divided into two regimes, above and below their Debye temperatures. Above their Debye temperatures, dislocation motion is thermally activated. The activation energies are equal to twice the band energy gaps, consistent with breaking electron-pair bonds (Figure 4.3). 

A. V. Granato, Internal Friction Studies of Dislocation Motion, p. 117, in Dislocation Dynamics, Edited by A. R. Rosenfield, G. T. Hahn, A. L. Bement, and R. I. Jaffee, McGraw-Hill Book Company, New York (1968). 

A second major difficulty with the Peierls model is that it is elastic and therefore conservative (of energy). However, dislocation motion is nonconservative. As dislocations move they dissipate energy. It has been known for centuries that plastic deformation dissipates plastic work, and more recently observations of individual dislocations has shown that they move in a viscous (dissipative) fashion. 

Dislocation motion in covalent crystals is thermally activated at temperatures above the Einstein (Debye) temperature. The activation energies are well-defined, and the velocities are approximately proportional to the applied stresses (Sumino, 1989). These facts indicate that the rate determining process is localized to atomic dimensions. Dislocation lines do not move concertedly. Instead, sharp kinks form along their lengths, and as these kinks move so do the lines. The kinks are localized at individual chemical bonds that cross the glide plane (Figure 5.8). 

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