19.dislocations

19.dislocations - T. Y. Tan 19. DISLOCATIONS As discussed...

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T. Y. Tan 1 19. DISLOCATIONS As discussed in section 14.4, the thermal equilibrium concentration of dislocations in a crystal is identical to zero. This is because it requires a rather high expenditure of Gibbs free energy to form a unit length of a dislocation line while the entropy of mixing thus introduced is so small that it does not provide a sufficiently large compensation for yielding a non-zero thermal equilibrium concentration of the defect. Nonetheless, dislocations literally exist in all crystalline materials, including the nominally dislocation-free single crystal semiconductors such as Si. These dislocations are introduced into the crystal during the growth and/or other treatment processes, due to the kinetic/energetic reason that formation of dislocations is the fastest process to release the excess Gibbs free energy of the system at the time. The released system excess Gibbs free energy due to dislocation formation is only a little smaller than the total excess Gibbs free energy the system possesses, and hence the driving force for producing the dislocations is very large. Once dislocations are generated, they are practically irremovable since the driving force will be so small that in practice it becomes kinetically improbable to be accomplished. Thus, the dislocations are often said to be frozen-in . The introduction of the dislocations into crystals represents the efforts of the crystal to minimize its Gibbs free energy via the kinetic processes that provided the maximum Gibbs free energy decrease rate the system can attain at the time. In polycrystals, the grain boundaries are consisting of arrays of dislocations that is lower in Gibbs free energy than a boundary which is more disordered. In single crystals, dislocations are generated either because of the need of the crystal to release its stain energy, called stress relaxation, or because of the need of the crystal to release its chemical energy, such as due to a high supersaturation of point defects or impurities. 19.1 Definitions and Dislocation Geometry 19.1.1 Edge and screw dislocations The most basic definition of a dislocation is a geometric one given by Voltera, which involves the Voltera-cut illustrated in Fig. 19.1. Take a cylindrical continuum material and cut it open about the plane defined by the axis and a radial vector of the cylinder, Fig. 19.1a. If the cut is glued back in the manner shown in Fig. 19.1b, which results from pushing one part of the cut material inward relative to the other part in the direction of the cylinder radius vector defining the cut plane, then an edge dislocation with a displacement vector of magnitude β is obtained, where β is the width of the external step so produced on the cylindrical surface of the cylinder.
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This note was uploaded on 07/13/2011 for the course ME 218 taught by Professor Dr.tan during the Fall '11 term at Duke.

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19.dislocations - T. Y. Tan 19. DISLOCATIONS As discussed...

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