Cubic Space Groups
The three Bravais lattices which form cubic crystal systems are:
| Name | Primitive cubic | Body-centered cubic | Face-centered cubic |
|---|---|---|---|
| Pearson symbol | cP | cI | cF |
| Unit cell |
The primitive cubic system (cP) consists of one lattice point on each corner of the cube. Each atom at a lattice point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one atom (1⁄8 × 8).
The body-centered cubic system (cI) has one lattice point in the center of the unit cell in addition to the eight corner points. It has a net total of 2 lattice points per unit cell (1⁄8 × 8 + 1).
The face-centered cubic system (cF) has lattice points on the faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of 4 lattice points per unit cell (1⁄8 × 8 from the corners plus 1⁄2 × 6 from the faces).
The face-centered cubic system is closely related to the hexagonal close packed system, and the two systems differ only in the relative placements of their hexagonal layers. The plane of a face-centered cubic system is a hexagonal grid.
Attempting to create a C-centered cubic crystal system (i.e., putting an extra lattice point in the center of each horizontal face) would result in a simple tetragonal Bravais lattice.
Read more about this topic: Cubic Crystal System
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