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The vertices of all squares together with their centers form an upright square lattice. For each color the centers of the squares of that color form a diagonal square lattice which is in linear scale √2 times as large as the upright square lattice. In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space.
Latticework may be functional – for example, to allow airflow to or through an area; structural, as a truss in a lattice girder; [2] used to add privacy, as through a lattice screen; purely decorative; or some combination of these. Latticework in stone or wood from the classical period is also called Roman lattice or transenna (plural transenne).
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In mathematics, the n-dimensional integer lattice (or cubic lattice), denoted , is the lattice in the Euclidean space whose lattice points are n-tuples of integers. The two-dimensional integer lattice is also called the square lattice , or grid lattice.
In structural engineering, the term lattice tower is used for a freestanding structure, while a lattice mast is a guyed mast supported by guy lines. Lattices of triangular (three-sided) cross-section are most common, particularly in North America. Square (four-sided) lattices are also widely used and are most common in Eurasia.
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The difference is in the length and energy scales. Lattice constants of atomic crystals are of the order of 1Å while those of superlattices (a) are several hundreds or thousands larger as dictated by technological limits (e.g. electron-beam lithography used for the patterning of the heterostructure surface). Energies are correspondingly ...
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