Generation, multiplication and annihilation of dislocations

The line energy of dislocations is rather large. To create a dislocation by thermal activation (see appendix C.l) is therefore a highly improbable process (calculated in exercise 18), and the dislocation density in a metal in thermal equilibrium would be vanishingly small. Real metals usually show dislocation densities between 10 m and 10 m . Even in extremely pure single crystals, for instance made of 99.9999999% germanium, the dislocation density is about 10 m [98]. This discrepancy between realistic values of the dislocation density and those expected from thermal equilibrium is due to the fact that dislocations are created when the crystal solidifies from the melt. 

Because dislocations are one-dimensional, the dislocation density can be measured as length per volume or as the number of penetration points in a plane within the crystal. It unit is thus 1 /length.  

Another possibility to increase the dislocation density is a spiral dislocation, pinned at the centre. Similar to a dislocation loop, the spiral dislocation extends when shear stresses are acting on it. As its centre is pinned, the length of the spiral grows (figure 6.20). This process does not increase the number of dislocations, but their density. 

As mentioned above in the context of the Prank-Read source, dislocations can also be annihilated. A simple example are two opposite edge dislocations moving on the same slip plane. As explained in section 6.2.7, the superposition of their stress fields causes an attraction. If they approach, the additional upper and lower half planes can unite and form a complete plane, causing the dislocations to vanish. 

Generally, annihilation of dislocations can only happen if they meet exactly on the same slip plane. In addition, they have to be oriented so that the newly generated dislocation segments have the same Burgers vector and a continuous 

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