In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occupied by spheres – that can be achieved by a regular lattice arrangement is
The same packing density can also be achieved by alternate stackings of the same close-packed planes of spheres, including structures that are aperiodic in the stacking direction. The Kepler conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular. This conjecture is now widely considered proven by T. C. Hales.
Many crystal structures are based on a close-packing of atoms, or of large ions with smaller ions filling the spaces between them. The cubic and hexagonal arrangements are very close to one another in energy, and it may be difficult to predict which form will be preferred from first principles.
Read more about Close-packing Of Equal Spheres: Fcc and Hcp Lattices, Lattice Generation, Miller Indices
Famous quotes containing the words equal and/or spheres:
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Are shadows, not substantial things;
There is no armour against fate;
Death lays his icy hand on kings:
Sceptre and crown
Must tumble down,
And in the dust be equal made
With the poor crooked scythe and spade.”
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—A. Holley, U.S. women’s magazine contributor. The Lily, p. 38 (May 1852)