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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 ...
The classical Stefan problem aims to describe the evolution of the boundary between two phases of a material undergoing a phase change, for example the melting of a solid, such as ice to water. This is accomplished by solving heat equations in both regions, subject to given boundary and initial conditions. At the interface between the phases ...
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 ).
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 ...
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
Specifically, an SU(2) Chern–Simons theory describes the simplest non-abelian anyonic model of a TQC, the Yang–Lee–Fibonacci model. [2] [3] The dynamics of Chern–Simons theory on the 2-dimensional boundary of a 3-manifold is closely related to fusion rules and conformal blocks in conformal field theory, and in particular WZW theory. [1] [4]
Similarity theory is extensively used in boundary layer meteorology since relations in turbulent processes are not always resolvable from first principles. [ 2 ] An idealized vertical profile of the mean flow for a neutral boundary layer is the logarithmic wind profile derived from Prandtl 's mixing length theory , [ 3 ] which states that the ...