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The twin thickness saturated once a critical residual dislocations’ density reached the coherent twin-parent crystal boundary. [33] [49] Significant attention has been paid to the crystallography, [50] morphology [51] and macro mechanical effects [52] of deformation twinning.
A twin boundary is a defect that introduces a plane of mirror symmetry in the ordering of a crystal. For example, in cubic close-packed crystals, the stacking sequence of a twin boundary would be ABCABCBACBA. On planes of single crystals, steps between atomically flat terraces can also be regarded as planar defects.
Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion [1] and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep. [2]
As the partial dislocations repel, stacking fault is created in between. By nature of stacking fault being a defect, it has higher energy than that of a perfect crystal, so acts to attract the partial dislocations together again. When this attractive force balance the repulsive force described above, the defects are in equilibrium state. [4]
On either side of this domain, the lattice is still perfect, and the boundaries of the domain are referred to as antiphase boundaries. [1] Crucially, crystals on either side of an antiphase boundary are related by a translation, rather than a reflection (a crystal twin ) or an inversion (an inversion domain ).
Twinning is a phenomenon somewhere between a crystallographic defect and a grain boundary. Like a grain boundary, a twin boundary has different crystal orientations on its two sides. But unlike a grain boundary, the orientations are not random, but related in a specific, mirror-image way. Mosaicity is a spread of crystal plane orientations.
The stacking-fault energy (SFE) is a materials property on a very small scale. It is noted as γ SFE in units of energy per area.. A stacking fault is an interruption of the normal stacking sequence of atomic planes in a close-packed crystal structure.
The simplest case is that of two free boundaries, which Lord Rayleigh solved in 1916, obtaining Ra = 27 ⁄ 4 π 4 ≈ 657.51. [17] In the case of a rigid boundary at the bottom and a free boundary at the top (as in the case of a kettle without a lid), the critical Rayleigh number comes out as Ra = 1,100.65.