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The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions.
In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way. Such a shape is called an einstein, a word play on ein Stein, German for "one stone". [2]
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Nonmetallic material, or in nontechnical terms a nonmetal, refers to materials which are not metals. Depending upon context it is used in slightly different ways. In everyday life it would be a generic term for those materials such as plastics, wood or ceramics which are not typical metals such as the iron alloys used in bridges.
An example of such a tiling is shown in the adjacent diagram (see the image description for more information). A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. [3]
Amorphous materials will have some degree of short-range order at the atomic-length scale due to the nature of intermolecular chemical bonding. [ a ] Furthermore, in very small crystals , short-range order encompasses a large fraction of the atoms ; nevertheless, relaxation at the surface, along with interfacial effects, distorts the atomic ...
The term can also be used for non-periodic or aperiodic signals, like chirps and pulses. [3] In electronics, the term is usually applied to time-varying voltages, currents, or electromagnetic fields. In acoustics, it is usually applied to steady periodic sounds — variations of pressure in air or other media.
Origin of title phenomenon in crystallographic defects. Shown is a two-dimensional slice through a primitive cubic crystal system showing the regular square array of atoms on one face (open circles, o), and with these, places where atoms are missing from a regular site to create vacancies, displaced to an adjacent acceptable space to create a Frenkel pair, or substituted by a smaller or larger ...