close packing
/ klohs PAK-ing /
Try to fill a box with as many identical marbles as you can. You quickly discover the trick: lay them in neat triangular layers and nestle each new layer into the hollows of the one below, never directly on top. That instinct — leaving no more empty space than geometry forces you to — is exactly what physicists mean by close packing.
Close packing is the densest way to arrange identical spheres so they fill the most space possible. It is achieved by stacking close-packed layers, each a triangular sheet of touching spheres, with every layer dropping into the dimples of the one below. In any such arrangement every sphere touches twelve others and the spheres occupy about 74 percent of the total volume, leaving the rest as gaps. There are infinitely many ways to choose the stacking order, but two stand out: ABCABC gives face-centered cubic, and ABAB gives hexagonal close-packed.
Close packing matters because nature loves it: most metals and many simple solids and even stacks of cells or foam bubbles settle into close-packed or nearly close-packed arrangements, because squeezing things together usually lowers their energy. The honest caveat, long suspected and finally proven, is that 74 percent really is the maximum for identical spheres — no clever irregular pile can beat it. But many crystals are not close-packed at all, because directional bonds or differently sized atoms force roomier structures, like the open diamond network.
Look at the pyramid of oranges at a fruit stand. Each orange rests in the pocket made by three below it — that is one close-packed layer sitting on another, the same geometry that copper and gold atoms adopt.
A stack of oranges is close packing you can see — the same as in metals.
The proof that 74 percent is unbeatable for identical spheres — Kepler's centuries-old conjecture — was only completed with computer assistance in the late 1990s. The intuition was always right, but proving it rigorously was surprisingly hard.