# Question #704b6

May 25, 2015

The formula unit for boron carbide is ${B}_{4} C$ because it better describes the crystal structure formed by the compound. As it turns out, ${B}_{4} C$ is an idealized view of what the structure actually looks like.

Boron carbide forms a very complex crystal structure that can best be described as having a rhombohedral lattice unit that consists of ${B}_{12}$ icosahedra and a three-atom chain that runs along the diagonal of each unit cell. Depending on what combination of boron and carbon atoms make up that three-atom chain, you can have different formula units for boron carbide. This three-atom chain is usually believed to consists of two carbon atoms that flank a boron atom.

As a consequesnce of this arrangement of atoms, the formula unit could be given as ${B}_{13} {C}_{2}$, which implies that the compound is carbon-deficient. If you get two boron atoms flanking a carbon atom in the three-atom chain, you'll see the formula unit given as ${B}_{14} C$, which implies that the compound is boron-rich.

A more conservative approach is to actually use ${B}_{12} {C}_{3}$ as a sort of "average" formula unit for boron carbide, which is equivalent to the more common ${B}_{4} C$ formula unit.

So, as a conclusion, the formula unit for boron carbide is usually given as ${B}_{4} C$ because it's an attempt at describing how the actual crystal structure looks like. ${B}_{4} {C}_{3}$ is not even close to matching experimental data on how boron carbide's lattice unit looks like.