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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.
On the microscopic level, the twin boundary is characterized by a set of atomic positions in the crystal lattice that are shared between the two orientations. [ 1 ] [ 2 ] These shared lattice points give the junction between the crystal segments much greater strength than that between randomly oriented grains, so that the twinned crystals do ...
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 ]
This page focuses on finitary first order model theory of infinite structures.. The relative emphasis placed on the class of models of a theory as opposed to the class of definable sets within a model fluctuated in the history of the subject, and the two directions are summarised by the pithy characterisations from 1973 and 1997 respectively:
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 his famous paper on special relativity in 1905, Albert Einstein deduced that for two stationary and synchronous clocks that are placed at points A and B, if the clock at A is moved along the line AB and stops at B, the clock that moved from A would lag behind the clock at B. He stated that this result would also apply if the path from A to B ...
Peer review is widely used for helping the academic publisher (that is, the editor-in-chief, the editorial board or the program committee) decide whether the work should be accepted, considered acceptable with revisions, or rejected for official publication in an academic journal, a monograph or in the proceedings of an academic conference. If ...
The defect group of a block also has several characterizations in the more module-theoretic approach to block theory, building on the work of J. A. Green, which associates a p-subgroup known as the vertex to an indecomposable module, defined in terms of relative projectivity of the module. For example, the vertex of each indecomposable module ...