Crystals dislocation motion

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). 

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. 

In his early survey of computer experiments in materials science , Beeler (1970), in the book chapter already cited, divides such experiments into four categories. One is the Monte Carlo approach. The second is the dynamic approach (today usually named molecular dynamics), in which a finite system of N particles (usually atoms) is treated by setting up 3A equations of motion which are coupled through an assumed two-body potential, and the set of 3A differential equations is then solved numerically on a computer to give the space trajectories and velocities of all particles as function of successive time steps. The third is what Beeler called the variational approach, used to establish equilibrium configurations of atoms in (for instance) a crystal dislocation and also to establish what happens to the atoms when the defect moves each atom is moved in turn, one at a time, in a self-consistent iterative process, until the total energy of the system is minimised. The fourth category of computer experiment is what Beeler called a pattern development... 

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. 

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). 

Early in the history of crystal dislocations, the lack of resistance to motion in pure metal-like crystals was provided by the Bragg bubble model, although it was not taken seriously. By adjusting the size of the bubbles in a raft, it was found that the elastic behavior of the raft could be made comparable with that of a selected metal such as copper (Bragg and Lomer, 1949). In such a raft, it was further found that, as expected, the force needed to form a dislocation is large. However, the force needed to move a bubble is too small to measure. 

As early as 1938, internal friction in vibrating zinc crystals was observed at strain amplitudes as small as 10The friction was attributed (with good cause) to dislocation motion (Read, 1938). This strongly indicated that the Peierls model could not be accepted as being quantitative. 

Twins are commonly found or formed in all types of crystals. Their boundaries are of two general types coherent and incoherent. The coherent boundaries are usually also symmetric, so they offer little resistance to dislocation motion. However, the incoherent ones are not symmetric and may resist dislocation motion considerably. 

In order to treat hardness quantitatively, it is essential to identify the entities (energies) that resist dislocation motion as well as the virtual forces (work) that drive the motion. These are the ying and yang of hardness. They are very different in pure metals as compared with pure covalent solids, and still different in salts and molecular crystals. 

The disruption to the crystal introduced by a dislocation is characterized by the Burgers vector, b (see Supplementary Material SI for information on directions in crystals). During dislocation motion individual atoms move in a direction parallel to b, and the dislocation itself moves in a direction perpendicular to the dislocation line. As the energy of a dislocation is proportional to b2, dislocations with small Burgers vectors form more readily. 

The behavior of polycrystalline materials is often dominated by the boundaries between the crystallites, called grain boundaries. In metals, grain boundaries prevent dislocation motion and reduce the ductility, leading to hard and brittle mechanical properties. Grain boundaries are invariably weaker than the crystal matrix, and... 

Experiments have determined (8) that mechanical blocking of dislocation motion can be achieved quite directly by introducing tiny particles into a crystal. This process is responsible for the hardening of steel, for instance, where particles of iron carbide are precipitated into iron. 

Figure 5.11 Schematic illustration edge dislocation motion in response to an applied shear stress, where (a) the extra half-plane is labeled as A (cf. Figure 1.28), (b) the dislocation moves one atomic distance to the right, and (c) a step forms on the crystal surface as the extra half-plane exits the crystal. Reprinted, by permission, from W. Callister, Materials Science and Engineering An Introduction, 5th ed., p. 155. Copyright 2000 by John Wiley Sons, Inc.

The example in Fig. 13.4 is an extension of the model for the motion of a small-angle boundary by the glide and climb of interfacial dislocations (Fig. 13.3). Figure 13.4 presents an expanded view of the internal surfaces of the two crystals that face each other across a large-angle grain boundary. Crystal dislocations have... 

Although appealing from an engineering perspective, the analyses based on linear thermoelasticity do not address the action of defects and dislocations created by microscopic yield phenomena below the CRSS and of those that are incorporated in the crystal at the solidification front. In the previous works cited (104-108), the authors assume that no defects exist at the melt-crystal interface and that the stresses on this surface are zero. Constitutive equations incorporating models for plastic deformation in the crystal due to dislocation motion have been proposed by several authors (109-111) and have been used to describe dislocation motion in the initial stages of... 

K. S. Kim and R. J. Clifton, Dislocation Motion in MgO Crystals Under Plate Impact, Journal of Material Science, 19, 1428-1438 (1984). 

The mechanistic parallel of this equation to the well known equation in crystal plasticity involving dislocation motion has already been pointed out by Brown We now continue and examine in detail the nature of the three terms in Eq. (6). 

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