Primitive Unit Cell of Face-Centred Orthorhombic Lattice
Beginning derivation with a unit cell which has all angles equal to \(90^{\circ}\) simplifies the process significantly, allowing simple working in a 2D representation. A 2D representation of the lattice is shown below.
The new unit cell vectors are as follows: $$\mathbf{a’} = \frac{1}{2} \mathbf{a} + \frac{1}{2} \mathbf{b}$$ $$\mathbf{b’} = \frac{1}{2} \mathbf{b} + \frac{1}{2} \mathbf{c}$$ $$\mathbf{c’} = \mathbf{c}$$