Stacking of spheres

Compounds with non-directional bonding (such as ionic or metallic) can be modeled as solid spheres slotting together. There are different ways of doing this, and you can test it out in the real world by stacking oranges or other spherical objects.

For example, you could stack each orange directly on top of the previous orange, such as in the image below:

This method only uses up about 52% of the available volume. Its unit cell would be primitive cubic.

A more efficient use of space is to place them inside the dips created by other spheres. This creates a close-packed structure, which uses about 74% of the available space:

Since atoms attract eachother, metals and ions will prefer close-packed arrangements, if there is no directional covalent bonding interfering.

There are two types of close-packing, depending on how you place the third layer. If you place the third layer directly over the first, making an ABABABA pattern, it is called hexagonal close packing (hcp):

Hexagonal close-packing (hcp)

If you place the third layer over the holes instead, producing an ABCABCABC pattern, it is called face-centered cubic (fcp) or cubic close-packing:

The names refer to the types of unit cells they produce, hexagonal or face-centered cubic.