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An example is the Stone Wales defect in nanotubes, which consists of two adjacent 5-membered and two 7-membered atom rings. Schematic illustration of defects in a compound solid, using GaAs as an example. Amorphous solids may contain defects. These are naturally somewhat hard to define, but sometimes their nature can be quite easily understood.
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 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
A topological defect is perhaps the simplest way of understanding the general idea: it is a soliton that occurs in a crystalline lattice, typically studied in the context of solid state physics and materials science. The prototypical example is the screw dislocation; it is a dislocation of the lattice that spirals around. It can be moved from ...
The Kirkendall effect is the motion of the interface between two metals that occurs due to the difference in diffusion rates of the metal atoms. The effect can be observed, for example, by placing insoluble markers at the interface between a pure metal and an alloy containing that metal, and heating to a temperature where atomic diffusion is reasonable for the given timescale; the boundary ...
Singular perturbation theory is a rich and ongoing area of exploration for mathematicians, physicists, and other researchers. The methods used to tackle problems in this field are many. The more basic of these include the method of matched asymptotic expansions and WKB approximation for spatial problems, and in time, the Poincaré–Lindstedt ...