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Twinning is crystallographically defined by its twin plane 𝑲 𝟏, the mirror plane in the twin and parent material, and 𝜼 𝟏, which is the twinning shear direction. Deformation twins in Zr are generally lenticular in shape, lengthening in the 𝜼 𝟏 direction and thickening along the 𝑲 𝟏 plane normal.
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.
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]
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). [1]
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.
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
The Swiss cheese model of accident causation is a model used in risk analysis and risk management. It likens human systems to multiple slices of Swiss cheese , which has randomly placed and sized holes in each slice, stacked side by side, in which the risk of a threat becoming a reality is mitigated by the differing layers and types of defenses ...
This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons , quarks , gauge bosons and the Higgs boson .