Lecture note 23 (11-22-2011)

Lecture note 23 (11-22-2011) - MAE 581 Advanced Materials...

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1 MAE 581 Advanced Materials Science Lecture note 23 Planar defects (1) Grain boundaries Many planar defects occur in materials ranging from the large-angle grain boundary, which is an incoherent interface with a relatively high energy of 0.5 Jm 2 , to atomic planes in the crystal across which there is a mis-stacking of the atoms, i.e. twin interfaces and stacking faults that retain the coherency of the packing and have much lower energies ( 0 . 1 J / m 2 ). Generally, all these planar defects are associated with dislocations in an extended form. A small-angle tilt boundary can be described adequately by a vertical wall of dislocations. Rotation of one crystal relative to another, i.e. a twist boundary, can be produced by a crossed grid of two sets of screw dislocations, as shown in Figure 3.24. These boundaries are of a particularly simple kind, separating two crystals which have a small difference in orientation, whereas a general grain boundary usually separates crystals which differ in orientation by large angles. In this case, the boundary has five degrees of freedom, three of which arise from the fact that the adjoining crystals may be rotated with respect to each other about the three perpendicular axes, and the other two from the degree of freedom of the orientation of the boundary surface itself with respect to the crystals. Such a large-angle (30 – 40 ) grain boundary may simply be regarded as a narrow region, about two atoms thick, across which the atoms change from the lattice orientation of one grain to that of the other. Nevertheless, such a grain boundary may be described by an arrangement of dislocations, but their arrangement will be complex and the individual dislocations are not easily recognized or analyzed. The simplest extension of the dislocation model for low-angle boundaries to high-angle grain
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Lecture note 23 (11-22-2011) - MAE 581 Advanced Materials...

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