primitive cell
/ PRIM-ih-tiv sel /
Imagine you are paying for floor tiles by the piece and want to cover a patterned floor as cheaply as possible. You would look for the absolutely smallest tile that still carries the full repeating design — no larger than it has to be, with not one scrap of the pattern wasted. That smallest possible repeating tile is the spirit of the primitive cell.
A primitive cell is the smallest possible unit cell of a lattice — the one that contains exactly one lattice point. (Points shared along edges and corners count as fractions, and those fractions add up to a single whole point.) Like any unit cell, copies of it stacked edge to edge fill all of space, but no smaller repeating box exists. Its volume is the smallest that can tile the crystal, and there are many equally valid shapes for it; one especially symmetric choice is the Wigner-Seitz cell, built from the region closer to one point than to any other.
Primitive cells matter because counting in them is honest: one cell, one lattice point, no double-counting. That makes them the natural unit for theoretical work like counting electrons or vibrational modes. The common confusion is that primitive does not mean the conventional cell people usually draw. The familiar face-centered cubic cube, for instance, holds four lattice points, so it is conventional but not primitive — its true primitive cell is a smaller, skewed box that is harder to picture but contains just one point.
The body-centered cubic cube you usually see has two lattice points (one corner-share plus the center), so it is not primitive. Its primitive cell is a squat, slanted box holding just one point — it tiles the same crystal with half the volume.
The familiar bcc cube holds two points; its primitive cell holds one.
A primitive cell always contains one lattice point, but it may still contain several atoms if the basis has more than one atom. One lattice point and one atom are not the same thing.