# How many atoms are in the primitive unit cell for diamond?

The primitive unit cell for diamond is pictured (the parallelepiped inside the cube). How many atoms are in the unit cell? My first guess is 3.5 and i know this must be wrong as the number of atoms in the primitive unit cell determines the number of phonon branches in the crystal and 3.5 does not make sense in that case. The way I came up with that number is by observing that the three face lattice vector atoms closest to the origin atom must be shared by parallel unit cells. Thus we have the origin atom and the inside atom and 1.5 from the faces. So what is the real number and how do I find them? Also what is the number of phonon branches in diamond?

• Diamond cubic has a two-atom basis. Thus, a true primitive cell should hold two atoms. Commented May 28, 2019 at 18:55
• So how are the atoms on the faces accounted for? Also, this means that diamond has one acoustic and one optical branch right? Commented May 28, 2019 at 18:56
• I usually find it easier to mentally translate the volume so no atoms are on corners, edges, or faces... Commented May 28, 2019 at 20:04
• Another option here would be to count the number in the conventional cell (8) and consider the ratio of volume of conventional:primitive cells. Commented May 28, 2019 at 20:19
• @JohnCuster 2 is the answer, so nut a comment. Commented May 28, 2019 at 23:34

## 1 Answer

Each of the eight atoms at the corners of the unit cell is shared with seven other unit cells. So in total these account only for one atom. Together with the atom in the middle you get two atoms per unit cell, as mentioned in the comments.