Atomic Packing Factors and Examples
One important characteristic of a crystalline structure is its atomic packing factor. This is calculated by assuming that all the atoms are identical spheres, with a radius large enough that each sphere abuts the next. The atomic packing factor is the proportion of space filled by these spheres.
Assuming one atom per lattice point, in a primitive cubic lattice with cube side length a, the sphere radius would be a⁄2 and the atomic packing factor turns out to be about 0.524 (which is quite low). Similarly, in a bcc lattice, the atomic packing factor is 0.680, and in fcc it is 0.740. The fcc value is the highest theoretically possible value for any lattice, although there are other lattices which also achieve the same value, such as hexagonal close packed and one version of tetrahedral bcc.
As a rule, since atoms in a solid attract each other, the more tightly-packed arrangements of atoms tend to be more common. (Loosely packed arrangements do occur, though, for example if the orbital hybridization demands certain bond angles.) Accordingly, the primitive-cubic structure, with especially low atomic packing factor, is rare in nature, but is found in polonium. The bcc and fcc, with their higher densities, are both quite common in nature. Examples of bcc include iron, chromium, tungsten, and niobium. Examples of fcc include aluminium, copper, gold and silver.
Read more about this topic: Cubic Crystal System
Famous quotes containing the words atomic, packing, factors and/or examples:
“The pace of science forces the pace of technique. Theoretical physics forces atomic energy on us; the successful production of the fission bomb forces upon us the manufacture of the hydrogen bomb. We do not choose our problems, we do not choose our products; we are pushed, we are forced—by what? By a system which has no purpose and goal transcending it, and which makes man its appendix.”
—Erich Fromm (1900–1980)
“The good husband finds method as efficient in the packing of fire-wood in a shed, or in the harvesting of fruits in the cellar, as in Peninsular campaigns or the files of the Department of State.”
—Ralph Waldo Emerson (1803–1882)
“I always knew I wanted to be somebody. I think that’s where it begins. People decide, “I want to be somebody. I want to make a contribution. I want to leave my mark here.” Then different factors contribute to how you will do that.”
—Faith Ringgold (b. 1934)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)