Spins, Phonons, and Hardness
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Mat. Res. Soc. Symp. Proc. Vol. 410 ©1996 Materials Research Society
move concertedly; generally. In materials with discrete chemical bonds (covalently bonded crystals, "hard metals", and most transition metals. these lines move through the nucleation and movement of kinks along their lengths. The kinks tend to be localized to atomic dimensions. Although hard crystals show plastic yield-point drops at high temperatures as a result of dislocation multiplication, they do not show yield drops at low temperatures, even if they have been "seeded" with dislocations prior to being stressed. Therefore, it may be concluded that their hardness is not associated with a difficulty in nucleating, or multiplying dislocations. Instead, it is associated with difficulty in moving dislocations within them. This may be taken a step further to the deduction that their lack of mobility is not due to a difficulty in nucleating dislocations on dislocation lines, but is due to a difficulty in moving them. This deduction is based on the fact that, for some orientations of dislocation lines on their glide planes, they have high kink concentrations, but they still have low mobilities at low temperatures. All of these behavioral factors can be understood if kink motion is considered in terms of local (embedded) chemical reactions, as contrasted with mechanical processes [2]. A dislocation line marks the boundary between two areal regions of a glide plane. In one region sliding (translation) of the crystal on one side (say the top) of the plane has occurred relative to the part of the crystal that lies on the other side (say the bottom). In the other region, sliding has not occurred. In crystals, the amount of sliding is quantized in terms of the translation vectors of the structure, so the registry of the crystal is restored after the sliding. However, there remains a ribbon (or zone) of disregistry locally at the central position of the dislocation line (the core). The disturbed geometry at the core of a dislocation line (particularly the local change in the symmetry of the structure) causes a disturbance (or destruction) of the local chemical bonding. This is large for covalent bonding, for most ionic bonds, and for d-band bonds in transition metals. It is small for simple metallic bonding, and for special orientations of ionic bonding. A perfectly straight dislocation line cannot move concertedly through a crystal (too much force would be required). Instead, kinks form along the ribbon of disregistry (called a "stacking fault" in metals, but it might be more correctly called a "bonding fault" because it involves more than just geometry). The kinks can form heterogeneously as singlets at free surfaces, or other discontinuities, or they can form homogeneously in pairs along interior cores. Both their chemical and elastic effects tend to be localized to areas of the order of b2 , and volumes of the order of wb2, where b is the Burgers displacement and w is the kink width. If the average kink velocity is vk, and the average kink concentratio
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