Copper metal is known to crystallize in a face-centered cubic (fcc) unit cell. What is the coordination number of a copper atom?

Question

Copper metal is known to crystallize in a face-centered cubic (fcc) unit cell.  What is the coordination number of a copper atom?

BlackTom AI · Accepted Answer

Let's parse the question carefully: copper crystallizes in a face-centered cubic (fcc) unit cell, and we are asked for the coordination number (CN) of a copper atom in that structure.
Option 1: 'None of the others.' This is a catch-all incorrect choice unless none of the listed options were plausible; since fcc coordination is a well-known value, this is not a valid generic answer.
Option 2: '8' In a simple cubic array, each atom touches 6 neighbors, giving CN = 6. In a body-centered or simple cubic context you might see 8 in other lattice considerations, but not for fcc copper. Here 8 would misrepresent the actual neighbor count in fcc.
Option 3: 'It depends whether you are talking about a copper atom on a corner, or a copper atom on a face!' In an fcc lattice, all lattice sites are equivalent by symmetry; a corner atom and a face-centered atom share the same coordination number due to the periodic arrangement, so this conditional statement is incorrect for a pure fcc crystal.
Option 4: '6' A coordination number of 6 corresponds to a simple cubic or a hexagonal close-packed environment, not fcc. In fcc, each atom has more neighbors than in simple cubic, so 6 is too low for copper in fcc.
Option 5: '12' In an fcc structure, each atom is in contact with 12 nearest neighbors: 4 in the same layer (via the face-centered positions), 4 in the layer above, and 4 in the layer below when considering the packing arrangement. This results from the close-packed nature of fcc, where spheres touch along the 12 close-packed directions, giving CN = 12.
Putting these together, the statement in Option 5 aligns with the known geometry of fcc crystals, whereas the other options rely on incorrect counts or misunderstandings of equivalence of lattice sites.

Copper metal is known to crystallize in a face-centered cubic (fcc) unit cell. What is the coordination number of a copper atom?

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