Question

What is the value of z for a body-centred unit cell?

Answer 1

BCC Unit cell:

• A BCC Unit cell has an atom in the centre of the structure and atoms at each corner of the cube.
• An open structure is seen in the diagram below.
• The atom at the centre of the body, according to its structure, belongs entirely to the unit cell in which it is found.
• Every corner of the $\mathrm{BCC}\mathrm{unit}\mathrm{cell}$ has atoms.
• At the centre of the structure, there is only one atom.
• We have 1 atom in the centre of the body and $8\mathrm{atoms}$ in each of the $8\mathrm{corners}$ of the body in the BCC Cell.

The value of Z for a body-centred unit cell:

• The number of atoms in each corner is then calculated.

$=8\times \frac{1}{8}=1\mathrm{atom}$

• The atom at the centre of the body makes a complete contribution to the unit cell.
• Then $1\mathrm{atom}$ in the centre of the body equals $1\mathrm{atom}$.
• As a result, the total number of atoms per unit cell is $=1+1=2$.
• Therefore, the value of Z is 2 because the number of atoms in a body-centred cubic unit cell is 2.