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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.
The relationship is defined by a symmetry operation called a twin operation. [1] [2] The twin operation is not one of the normal symmetry operations of the untwinned crystal structure. For example, the twin operation may be reflection across a plane that is not a symmetry plane of the single crystal. [1] [2]
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]
In mixed oxidation state materials like magnetite, antiphase domains and antiphase domain boundaries can occur as a result of charge-ordering even though there are no changes in atom locations. [4] For example, the reconstructed magnetite (100) surface contains alternating Fe II pairs and Fe III pairs in the first subsurface layer. [ 4 ]
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 terminology of a topological defect vs. a topological soliton, or even just a plain "soliton", varies according to the field of academic study. Thus, the hypothesized but unobserved magnetic monopole is a physical example of the abstract mathematical setting of a monopole ; much like the Skyrmion, it owes its stability to belonging to a non ...
In machine learning (ML), a margin classifier is a type of classification model which is able to give an associated distance from the decision boundary for each data sample. For instance, if a linear classifier is used, the distance (typically Euclidean , though others may be used) of a sample from the separating hyperplane is the margin of ...
This result implies the existence of an infinitely repeatable prime 2-tuple, [2] thus establishing a theorem akin to the twin prime conjecture. Zhang's paper was accepted by Annals of Mathematics in early May 2013, [6] his first publication since his last paper in 2001. [18] The proof was refereed by leading experts in analytic number theory. [7]