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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 ).
Figure 1: Hall–Petch strengthening is limited by the size of dislocations. Once the grain size reaches about 10 nanometres (3.9 × 10 −7 in), grain boundaries start to slide. In materials science, grain-boundary strengthening (or Hall–Petch strengthening) is a method of strengthening materials by changing their average crystallite (grain
In macroeconomics, the twin deficits hypothesis or the twin deficits phenomenon, [1] is the observation that, theoretically, there is a strong causal link between a nation's government budget balance and its current account balance.
The existence of a topological defect can be demonstrated whenever the boundary conditions entail the existence of homotopically distinct solutions. Typically, this occurs because the boundary on which the conditions are specified has a non-trivial homotopy group which is preserved in differential equations; the solutions to the differential equations are then topologically distinct, and are ...