Dislocations

Another type of defect in a crystal is the dislocation. Dislocations are places where the crystal structure is discontinuous or offset in some way. The two basic types of dislocation, the edge dislocation and the

c-axis

Figure 4.2. (a) Stereographic view of the structure of ice Ih, viewed down the c-axis. Only half of the possible hydrogen sites, indicated by small circles, are occupied. (After Hamilton and Ibers, 1968.) (b) Structure of ice Ih viewed normal to the c-axis. Two of the hexagonal rings are shown. Short lines leading upward and downward from these rings are bonds to rings above and below. The oxygen shown with an open circle is the center of a tetrahedron, part of which is shown by the light dashed lines. (Modified from Hobbs, 1974, Figure 1.7.)

Figure 4.2. (a) Stereographic view of the structure of ice Ih, viewed down the c-axis. Only half of the possible hydrogen sites, indicated by small circles, are occupied. (After Hamilton and Ibers, 1968.) (b) Structure of ice Ih viewed normal to the c-axis. Two of the hexagonal rings are shown. Short lines leading upward and downward from these rings are bonds to rings above and below. The oxygen shown with an open circle is the center of a tetrahedron, part of which is shown by the light dashed lines. (Modified from Hobbs, 1974, Figure 1.7.)

screw dislocation, are illustrated in Figure 4.3. Virtually all crystalline materials contain dislocations.

Dislocations play a vital role in the deformation or creep of crystalline materials. If one tried to deform the perfect crystal in Figure 4.3a by shearing the top three layers of atoms over the bottom two, the stress

Figure 4.3. (a) A perfect crystal. (b) An edge dislocation. (c) A screw dislocation. (Modified from Hull, 1969, p. 17.)

Figure 4.3. (a) A perfect crystal. (b) An edge dislocation. (c) A screw dislocation. (Modified from Hull, 1969, p. 17.)

required would be enormous as every one of the bonds indicated by an "x" would have to be broken simultaneously. In contrast, the crystal in Figure 4.3b would deform much more easily because the bonds could be broken sequentially, one at a time. For instance, the bond between E and F could be broken and a new bond formed between D and F. Calculations show that, in the absence of dislocations, crystalline materials could not possibly deform under the stresses at which they are observed to deform. In fact, it was through such theoretical studies that the existence of dislocations was first inferred.

Upon application of a stress, the number of dislocations in a crystal increases. Some of these new dislocations are generated at Frank-Reed sources. A Frank-Reed source consists of a dislocation lying between two points at which the dislocation is fixed, called pinning points (Figure 4.4). Impurities or immobile tangles of dislocations may serve as pinning points. When a stress is applied, this dislocation is bowed

Figure 4.4. Generation of dislocations at a Frank-Reed source. Each line in (a) represents a successive position of a dislocation as it is bowed out between two pinning points. (b) shows the final stage with the new dislocation expanding outward and another dislocation between the pinning points.

Figure 4.4. Generation of dislocations at a Frank-Reed source. Each line in (a) represents a successive position of a dislocation as it is bowed out between two pinning points. (b) shows the final stage with the new dislocation expanding outward and another dislocation between the pinning points.

Dislocations

Figure 4.5. Generation of dislocations at a three-grain intersection due to grain-boundary slip.

Grain-boundary' slip out until it meets itself at "a". At this point, dislocations coming from opposite directions are of opposite sign, and the dislocation is locally annihilated, leaving a ring and a new dislocation between the pinning points (Figure 4.4b). This new dislocation can then repeat the process, so there is a continuous source of dislocations. The dislocation is of the edge type ahead of and behind the source, of the screw type at the sides, and of mixed type at intermediate positions. Some dislocations generated by a Frank-Reed source never complete a full cycle but rather multiply by spreading to neighboring planes, a process called multiple cross glide (Hull, 1969, pp. 165-7).

Dislocations also form at points of stress concentration on grain boundaries. For example, shear along a discrete atomic plane in one crystal can result in an offset of the crystal boundary. To accommodate this offset, the neighboring crystal must also yield, so dislocations are formed at the boundary and move into this crystal.

Slip along grain boundaries is believed to occur at temperatures above —10 °C. This, too, results in stress concentrations in neighboring crystals, and hence in generation of dislocations in these crystals (Figure 4.5).

Kinki>

Direction of movement of dislocation

Figure 4.6. Lateral movement of kinks causing forward movement of a dislocation. The symbol © represents situations in which a normal bond would form by passage of a kink. The symbol © represents situations in which a Bjerrum defect would be formed.

Dislocations move by formation of kink pairs (Figure 4.6), followed by lateral movement of the kinks. As long as the bond formed by movement of a kink is a normal bond, with only one hydrogen between two oxygens, the kink can move readily. However, if the movement would result in a Bjerrum defect the energy required for movement would be much higher. It is presumed that in such situations, movement of the kink is delayed until diffusion or rearrangement of the hydrogen atoms (proton rearrangement) results in a geometry such that the kink can migrate without formation of a Bjerrum defect. As shown in Figure 4.6, there may be a number of kinks along a dislocation line. Two kinks moving toward one another will annihilate each other when they meet, resulting in advance of the dislocation line.

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