Chemistry · Chapter 10

Count the Atoms in a Unit Cell

A crystal is one small box repeated in every direction. Turn the box, share out the atoms that sit on its corners and faces, then use one measured edge length to predict the density of the metal.

Face-centered cubicdrag the sliders to turn it

corner atom, 1/8 inside face atom, 1/2 inside body atom, all inside

Share out the atoms8 × 1/8 + 6 × 1/2 = 4

Turn and resize

Turn left and right: 35°

Tip up and down: 22°

Sphere size: 55% of touching

This cellZ = 4

SiteCountEach ownsAtoms
Nearest neighbors12
Space filled74.0%
Radius from the edge–

Predict a density

Metal

Edge length a–
Molar mass M–
Density from the cell–
Measured density–

What you are seeing

Counting rule
Share every atom you see
A corner atom is shared by the eight cells that meet there, so this cell owns one eighth of it. A face atom is split between two cells. An atom inside belongs to this cell alone.