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The energy per unit length of a dislocation is ½ Gb^{2}. Dislocations dilate a close packed crystal structure very slightly, because at their cores the atoms are not close packed: the dilatation is ¼b^{2} per unit length of dislocation. It is found that the density of a bar of copper changes from 8.9323 Mg m^{–3} to 8.9321 Mg m^{–3} when it is very heavily deformed. Calculate:
a. the dislocation density introduced into the copper by the deformation.
b. the energy associated with that density. Compare these results with the latent heat of melting of copper (1833 MJ m^{–3}) (b for copper is 0.256 nm; G is 3/8 E).
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