There are seven classifications of crystals, based on the degree of symmetry. These are triclinic, monoclinic, orthorhombic, tetragonal, cubic, rhombohedral (or trigonal), and hexagonal. These seven classes can be defined using the Miller system by quoting six parameters. Using one lattice point as a point of reference, or origin, the surrounding lattice points can be given coordinates on suitably orientated axes. This is represented in the figure below where the three reference axes are OX, OY and OZ. The nearest lattice points to the origin, O, on these axes are A, B and C at distances a, b and c respectively. The angles between the reference axes are α, β and γ.
Unable to display preview. Download preview PDF.