A three-dimensional Bravais lattice is obtained by replicating any of the five two-dimensional lattices and stacking the replicated lattices above one another. The space lattices formed have lattice points that are generated by a set of translation operations described by the three-dimensional position vector r = ua + vb + wc.
There are exactly fourteen types of three-dimensional Bravais lattices that are grouped into seven lattice systems:
Lattice system |
Primitive |
Base-centred |
Body-centred |
Face-centred |
Triclinic | ||||
Monoclinic | ||||
Orthorhombic | ||||
Tetragonal | ||||
Rhombohedral | ||||
Hexagonal | ||||
Cubic |
The unit cells of these lattices form the building blocks of all crystalline solids. We shall derive them in the following sections.