3/16/11

Close Packing and Packing Fraction

I was interested in the various close-packing arrangements possible, in class we talked about hexagonal close packing (hcp), in which each layer is equivalent to (directly above) the layer 2 positions below it. One way to characterise the packing of atoms in a crystal structure is the 'Packing Fraction', which is the % of Volume of the unit cell taken up by atoms, i.e. Fraction = N*V_a/V_c, where N is the number of atoms in a unit cell (can be non-integer), V_a is the volume of an atom and V_c is the volume of the unit cell. The body-centred cubic bravais lattice has a packing fraction of 0.68, while the hcp has a fraction of 0.74.
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2 comments:

  1. Robert Lewis-SwanMarch 16, 2011 at 12:56 PM

    http://en.wikipedia.org/wiki/Close-packing_of_spheres

    You might be interested in that page. Apparently the maximum packing factor is just a little over 0.74, which would mean the face centered cubic and hexagonal close packed are the densest possible crystal lattices possible.

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  2. Ross H. McKenzieMarch 17, 2011 at 2:54 PM

    How about packing smarties or tetrahedra?

    see

    http://condensedconcepts.blogspot.com/2011/02/packing-it-in.html

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