In three dimensions, the face-centered cubic lattice offers the best " lattice " packing of spheres, and is believed to be the optimal of all packings.
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A typical crystal is the cubic lattice of table salt, in which atoms of sodium and chlorine alternate with each other in a kind of three-dimensional chess board.
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Each of the two atom types forms a separate primitive cubic lattice, with an atom of one type at the center of each cube of the other type.
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For a simple cubic lattice in this model, each atom is treated as a cube and bonding occurs at each face, giving a coordination number of 6 nearest neighbors.
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Fig . 3 : Examples of ( a ) miscut cubic lattice and ( b ) ordered surface roughness, and ( c, d ) the corresponding CTR profiles, respectively.
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For some systems, a cubic ( also called viscous isotropic ) phase may exist between the hexagonal and lamellar phases, wherein spheres are formed that create a dense cubic lattice.
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The challenge for Hales was to confirm that there is no combination of variables which leads to a packing efficiency that is higher than that of the face-centered cubic lattice.
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This example is readily extended to three dimensions, for example, to a body-centered cubic or face-centered cubic lattice by introducing the nearest neighbor vector locations in place of simply " n a ".
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In the case of a cubic lattice, for instance, & lang; 100 & rang; represents [ 100 ], [ 010 ] and [ 001 ] because each of these vectors is symmetrically equivalent.
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When scattered in open space or in the air, the repulsive forces between charged Minovsky particles cause them to spontaneously align into a regular cubic lattice structure called an I-field . " ".
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