Ask A Scientist Chemistry Archive

(Created prior to 1993)

Question: What is the closest packed crystal?  Simple cubic, Body-centered 
cubic, or Face-centered cubic?
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Face-centered cubic is more closely packed than simple cubic or 
body-centered cubic structures.  You can see why face centered cubic (fcc) is 
more closely packed than bcc or sc structures by noting that sc has 8 atoms at 
the corners of a cube, bc has these 8 atoms plus one at the cube's center, and 
fcc has the 8 corner atoms plus an atom on each of the cube's 6 faces.  So, in 
a each cube, sc has 8 atoms, bcc has 9, and fcc has 14 atoms.  More atoms per 
cube = more closely packed.
Topper
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Just to add on to Robert Topper's answer . . . it is correct but 
the numbers are off.  A simple cubic has 8 atoms but only the corners are 
contributing to the unit cell one-eighth each . . . there is only one atom in 
the unit cell.  For a body-centered cube, one whole atom is in the center and 
8 at the corners contributing one-eighth each again for a total of 2 in the 
unit cell.   The face-centered has 8 at the corners (1/8 each) and 6 at each 
face (contributing 1/2 each) for a total of 4 atoms in the unit cell.  Some 
baseballs and a small box may illustrate this better.
Joe Schultz
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Two additional points to the correct answers you have received.  
First:  there is another structure hexagonal close packed (hcPp) which has the 
same packing fraction as fcc.  They have different structures though.  Lay 
down a plane of tennis balls.  Put another plane in the whiles between them on 
top.  Adding the third layer gives you two choices.  If you put them over the 
first layer that s fcc.  If you put them in the holes, not over the first 
layer you get hcp.  Examples of fcc metals are gold, silver, copper and 
nickel.  Examples of hcp metals are zinc and titanium.  It was only last year 
(1992, I think) that a mathematician proved that fcc and hcp are the densest 
possible packing schemes.  Every one had always believed it but its nice to be 
sure!
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