Primitive Unit Cell of the Base-Centred Monoclinic Lattice
Below is the primitive unit cell of the base-centred monoclinic lattice, shown in orange.
The primitive unit cell has equal a and b axes and angles \(\alpha\) and \(\beta\) are equal. As with all monoclinic unit cells, there are four lattice parameters free to vary. In the conventional unit cells this is the three axes and the angle \(\beta\). In the above unit cell the angles \(\alpha\) and \(\gamma\), and the a and c axes are free to vary.
In vector form, the primitive unit cell vectors in terms of the base-centred unit cell are:
$$\mathbf{a’} = \frac{1}{2}\mathbf{a} + \frac{1}{2}\mathbf{b}$$
$$\mathbf{b’} = \frac{1}{2}\mathbf{a} – \frac{1}{2}\mathbf{b}$$
$$\mathbf{c’} = \mathbf{c}$$