Crystals & Lattices

unit cell

/ YOO-nit sel /

Think about how a wallpaper pattern is made. There is one small motif — say a flower with a leaf — and the whole roll is just that motif printed again and again, side by side, with no gaps and no overlaps. If you cut out one rectangle containing the motif, you hold in your hand everything you need to recreate the entire wall. A crystal works the same way, and that one rectangle's three-dimensional cousin is the unit cell.

A unit cell is the smallest box that, stacked edge to edge in all three directions, reproduces the whole crystal. Its shape is set by three edge lengths and the angles between them, and inside it lives one full copy of the repeating contents — the atoms of the basis arranged just so. Translate the cell by its edge vectors and you tile all of space, perfectly filling the crystal with identical bricks. There can be more than one valid choice of cell; the conventional one is usually picked to make the crystal's symmetry easy to see.

Unit cells matter because they shrink an effectively infinite object down to a handful of numbers a person can actually work with: name the cell and its contents, and you have named the crystal. The caveat is that a unit cell is a human bookkeeping choice, not a real wall inside the material — atoms do not know where the box edges are, and the same crystal can be described by different but equivalent cells.

Table salt's conventional unit cell is a cube about 0.56 nanometres on a side, holding four sodium and four chloride ions. Stack billions of these cubes and you have a salt grain you can see with the naked eye.

One tiny cube, repeated billions of times, builds a grain of salt.

Do not confuse the conventional unit cell with the primitive cell. The conventional cell is chosen for clarity and may contain several lattice points; the primitive cell is the truly smallest one, holding exactly one.

Also called
repeating unit重复单元